7 Willard Nanocrystalline Soft Magnetic Alloys Two Decades of Progress

C H A P T E R
F O U R
Nanocrystalline Soft Magnetic Alloys
Two Decades of Progress
Matthew A. Willard1,2 and Maria Daniil3
Contents
1. Introduction
1.1. Historical perspective
1.2. Technical considerations
1.3. Applications
2. Alloy Processing
2.1. Rapid solidification
2.2. Annealing procedures
2.3. Core fabrication
2.4. Other processing methods
3. Alloy Design Considerations
3.1. Glass forming and primary crystallization
3.2. Microstructural and microstructure evolution considerations
3.3. Intrinsic property considerations
3.4. Domain structure considerations
4. Phase Transformations, Kinetics, and Thermodynamics
4.1. Thermal analysis techniques
4.2. Primary and secondary crystallization
4.3. Crystallization kinetics and phase stability
4.4. Order–disorder transformations
5. Structural and Microstructural Characterization
5.1. Crystal structure and phase identification
5.2. Microstructure and phase distribution
5.3. Magnetic domains and characteristic magnetic lengths
6. Magnetic Property Characterization
6.1. Magnetic moments and saturation magnetization
6.2. Temperature dependence of magnetization and Curie
temperatures
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1
U.S. Naval Research Laboratory, Magnetic Materials and Nanostructures Section, Washington, District of
Columbia, USA
The Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, Ohio,
USA
3
Department of Physics, George Washington University, Washington, District of Columbia, USA
2
Handbook of Magnetic Materials, Volume 21
ISSN 1567-2719, http://dx.doi.org/10.1016/B978-0-444-59593-5.00004-0
# 2013 Elsevier B.V.
All rights reserved.
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Matthew A. Willard and Maria Daniil
6.3. Magnetic anisotropy and magnetostriction
6.4. Exchange interactions and interphase coupling
6.5. Static hysteresis and AC core losses
6.6. Magnetocaloric effect
6.7. Giant magnetoimpedance
7. Other Physical Properties
7.1. Mechanical and magnetoelastic properties
7.2. Electrochemistry and oxidation
7.3. Resistivity and magnetoresistance
8. Conclusions
Acknowledgments
References
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Abbreviations
ac
ai
am
a
Å
Acr, Aam
A, Aex
Aeff
A1
A2
b
b
B
B2
BCC
w
C
Cn
dB
dm
dV/V
dimensionless pre-factor for coercivity calculation
direction cosines (where i ¼ 1, 2, 3)
dimensionless pre-factor for permeability calculation
lattice constant (Å)
ångstrom (1010 m)
exchange stiffnesses of crystalline and amorphous
phases (J/m)
exchange stiffness (J/m)
effective exchange stiffness (J/m)
Strukturbericht notation for face-centered cubic
(FCC)
Strukturbericht notation for body-centered cubic
(BCC)
critical exponent for magnetization approaching TC
shape factor
magnetic induction (T)
Strukturbericht notation for a BCC derivative phase
with prototype CsCl
body-centered cubic
susceptibility (various units)
Curie constant (1/K)
number of contact atoms for heterogeneous nucleation (atoms/m3)
Bloch wall width (m)
skin depth (m)
fractional change in volume of a magnetostrictive
material
Nanocrystalline Soft Magnetic Alloys
d‘=‘
DE
DG*
DGv
DSM
DT
d
e
D
D
DSC
DTA
D03
ddw
E
EA
EKu or EK
Es
ef
Emin
ETM
f
f, o
fA,B
fn
F
Fhkl
FCC
gs–l
gw
H
Happ
Hc
HCP
HDC
Hex
HK
HV
I
Jij
k
kB
175
fractional change in length of a magnetostrictive
material
change in elastic modulus with applied field (Pa)
nucleation activation energy barrier (J/mol)
driving force for nucleation (J/mol)
magnetic contribution to the entropy under an
applied magnetic field
temperature change (K)
Ribbon thickness (m)
diffusion coefficient (m2/s)
grain diameter (m)
differential scanning calorimetry
differential thermal analysis
Strukturbericht notation for a BCC derivative phase
with prototype BiF3
domain width (m)
elastic modulus (Pa)
activation energy (J/mol or eV/atom)
magnetocrystalline anisotropy energy density (J/m3)
shape anisotropy energy density (J/m3)
strain-at-fracture
lowest value of elastic modulus at a constant field (Pa)
early transition metals
heating rate (K/s)
switching frequency (Hz)
atomic scattering factor for atoms of type A or B
frequency factor for nucleation (1/s)
fundamental reflection
structure factor for the hkl Bragg reflection
face-centered cubic
solid–liquid interfacial energy (J/m2)
domain wall energy (J/m2)
magnetic field strength (A/m)
applied magnetic field (A/m)
coercivity (A/m)
hexagonal close packed
direct current bias field (A/m)
Heisenberg exchange Hamiltonian
anisotropy field (A/m)
Vickers hardness
current (A)
exchange energy (J)
reaction rate constant
Boltzmann’s constant (1.38 1023 J/K)
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km
k0
K1
Ks
hKi
Ku1,2
Ku or Kind
k
l
lw
lsam
lscr
leff
s
lsurf
s
L
Lex
L
L0
LTM
m
mA
m0
mr
ms, m t
M
Mr
Ms
MTM
n
N
Ñ
Na,b
Nv
Oi
j
j0
re
re0
Pcv
PTM
R
Matthew A. Willard and Maria Daniil
magnetomechanical coupling coefficient
reaction rate coefficient
first magnetocrystalline anisotropy constant (J/m3)
stress-induced anisotropy constant (J/m3)
effective magnetic anisotropy (J/m3)
first and second uniaxial magnetocrystalline anisotropy
constants (J/m3)
induced anisotropy constants (J/m3)
normalized anisotropy parameter
magnetostrictive coefficient (ppm)
Weiss mean field coefficient
magnetostrictive coefficient of the amorphous phase
magnetostrictive coefficient of the crystalline phase
effective magnetostrictive coefficient of the
nanocomposite material
interfacial contributions to magnetostrictive
coefficient
intergranular amorphous phase thickness (m)
magnetic exchange correlation length (m)
spatial wavelength number
natural exchange correlation length (m)
late transition metals
permeability (kg m/(A2 s2))
atomic moment (A m2 or J/T)
permeability of free space (4p 107 kg m/(A2 s2))
relative permeability (unit less)
permeability for mechanically fixed and freely vibrating samples
magnetization (A/m)
remanence or remanent magnetization (A/m)
saturation magnetization (A/m)
Magnetic transition metals
Avrami exponent
number of grains
nucleation rate (nuclei/m3 s)
demagnetization factors
number of moments per unit volume (1/m3)
volume of the ith phase (m3)
geometric/statistical parameter
spin rotation angle ( )
electrical resistivity (mO cm)
electrical resistivity with zero applied field (mO cm)
volume normalized core loss (W/m3)
metalloid or post-transition metal
ideal gas constant (8.3145 J/(K mol))
Nanocrystalline Soft Magnetic Alloys
Rm
s
sy
sc
S
S 1, S 2
y,c
t
t0
T
TTT
Tann
TC
TCam
TCx
Tg
Tmelt
Tp
Tx
Tx1
Tx2
Tx3
tR
tq
u
vi
Vex
X
Xm
z
Z
Zm
177
magnetoresistance (O)
stress (Pa)
yield stress (Pa)
Coble creep stress (Pa)
total spin angular momentum
superlattice reflections
angles (degrees)
time (s)
onset time (s)
temperature (K)
time–temperature transformation
annealing temperature (K)
Curie temperature (K)
Curie temperature of the amorphous phase (K)
Curie temperature of the crystalline phase (K)
glass transition temperature (K)
alloy melt temperature (K)
peak crystallization temperature
crystallization temperature (K)
primary crystallization temperature (K)
secondary crystallization temperature (K)
tertiary crystallization temperature (K)
relaxation time (s)
quench time (s)
frequency factor for constant heating rate kinetics
(1/Ks)
volume fraction of ith phase
exchange coupled volume (m3)
volume fraction transformed
magnetoreactance (O)
number of near neighbor moments
impedance (O)
magnetoimpedance (O)
1. Introduction
Revolutionary steps in materials development usually accompany the
discovery of new compounds, microstructures, or processing techniques
that provide improved properties. These types of advances allow a greater
flexibility in device design and sometimes enable completely new types of
devices to be produced. This has been specifically true for permanent
magnet materials, which show significant jumps in energy storage when
new, high-anisotropy compounds are discovered. Similarly, this has
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Matthew A. Willard and Maria Daniil
recently been the case in soft magnetic materials where new, nanocrystalline
microstructures have enabled smaller, lighter, and more efficient materials
for power generation, conversion, and conditioning applications.
This advancement in the field of soft magnetic materials has its beginnings
in the development of magnetic amorphous alloys. During the 1970s, amorphous magnets provided a new class of low loss materials with anisotropies
much lower than crystalline alloys due to their absence of long-range atomic
order. Crystallization of these materials resulted in large anisotropies that
degraded the magnetic properties as the newly formed grains rapidly grew
to micron-sized crystallites, leading to the notion that crystallization of
amorphous precursors should be avoided. It was for this reason that the
development of a partially devitrified material with exceptional magnetic
softness has created a significant stir in the soft magnetic materials community.
Since the first report of this class of nanocrystalline alloys in 1988 by Yoshizawa
et al. (1988a), the field has grown rapidly with authors reporting from around
the world, providing intuition-building knowledge and successful new alloys.
By definition, nanocrystalline materials consist of single or multiphase
polycrystals with grain diameters less than 50 nm. Materials of this type can
be synthesized by many techniques, including but not limited to: compacted
nanoparticles (e.g., chemically synthesized, plasma torch synthesized,
mechanically alloyed, etc.), thin film deposition techniques (e.g., sputtering,
pulsed laser deposited, etc.), and devitrified metallic glasses (e.g., splat quenching, melt spinning, etc.) (Wilde, 2006; Willard et al., 2004). This chapter
focuses on nanocrystalline alloys produced by a combination of rapid quench
synthesis and isothermal annealing. While there has been considerable activity
in the areas of nanocrystalline soft magnetic alloy wires (Barariu and Chiriac,
1999; Li et al., 2003, 2005; Neagu et al., 2001), thin films (Baraskar et al.,
2007; Gościa
nska et al., 1994, 2002; Joshi et al., 2006; Li et al., 2004;
Nakamura et al., 1994), and powders (Giri et al., 1996; Ji et al., 2001; Xu
et al., 2000), we will limit our discussion to rapidly solidified ribbons (please
see cited references for select studies on these topics). It is hoped that this
review compliments some previous reviews (Hernando et al., 2004; López
et al., 2005; McHenry and Laughlin, 2000) focused on specific alloys, update
some of the more comprehensive reviews of this field (De Graef and
McHenry, 2007; Herzer, 1997; McHenry et al., 1999) and act as a educational resource to compliment materials and physics textbooks (De Graef and
McHenry, 2007; OHandley, 2000).
1.1. Historical perspective
Throughout the 1980s, research efforts to improve the high-frequency
performance of Fe-based amorphous alloys were conducted in an effort to
replace Co-based amorphous alloys in saturable core reactors, choke coils,
and transformers (Kataoka et al., 1989). The Co-based alloys were better
performing than Fe-based alloys but suffered from lower saturation
Nanocrystalline Soft Magnetic Alloys
179
magnetizations and higher material costs. The lack of long-range periodic
order in both types of amorphous alloys reduced the magnetocrystalline
anisotropy (K1) and enhanced resistivity, giving them an advantage over
conventional soft magnetic materials (i.e., ferrites, Si-steels, permalloys,
etc.), which relied on large grains to provide the minimum coercivity.
And while Fe-based alloys solved the short-comings of Co-based alloys,
they suffered from large magnetostrictive coefficients (l) (Yoshizawa and
Yamauchi, 1990), which increased in value with the square of their magnetization, ultimately resulting in poor performance at high switching
frequencies. Annealing procedures were used to reduce the residual stress
in the alloys, and partial crystallization was found to increase the coercivity
substantially. For this reason, crystallization was largely avoided.
Nanocrystalline soft magnetic alloys were first demonstrated by Yoshizawa,
Oguma, and Yamauchi in 1988 (Yoshizawa et al., 1988a). The Fe–Si–B–Nb–
Cu alloy they described (which they named Finemet) was truly remarkable due
to its nanocomposite microstructure (i.e., Fe–Si crystallites within a residual
amorphous matrix) produced in a bulk ribbon form. The combination of large
magnetization and low magnetostrictive coefficient in a Fe-based alloy
provided an exciting advance for the field of soft magnetic alloys. And despite
the formation of crystallites in the alloy, the magnetocrystalline anisotropy
remained low as exemplified by the small coercivity. It was later discovered
that these improved properties were possible when the grains had reduced
dimensions (less than 15 nm diameter) and there was sufficient exchange
coupling between grains (described by the random anisotropy model). Balance
between positive and negative values for the amorphous and crystalline phases,
respectively, provides reduced magnetostrictive coefficients (Herzer, 1991).
The two-phase, nanoscale microstructure enabled these beneficial properties,
which were only possible due to new alloy design considerations. Since then, a
wide variety of compositions have been developed to achieve the same
nanocomposite microstructure, providing improved soft magnetic properties
for various working environments.
As a demonstration of the importance of these new nanocrystalline
materials and their relationship to other magnetic materials, a timeline for
the progress in magnetic materials over the past century is shown in Fig. 4.1.
The coercivity is a metric for the resistance of the magnetization to switching
in the material, having small values for so-called soft magnets and large values
for hard (or permanent) magnets. The distinction is important as soft and hard
magnetic materials are used in very different applications, largely due to the
differences in coercivity. Since the beginning of the twentieth century,
greater specialization of alloy compositions and processing methods have
improved the range of available materials to cover nearly 100 millionfold
differences between the softest and hardest magnetic materials available. Soft
magnetic materials are used in applications where switching occurs easily and
therefore a low value of coercivity (less than 5 Oe (400 A/m)) is desirable.
Hard magnetic materials rely on the resistance of their magnetizations to
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Matthew A. Willard and Maria Daniil
7
10
6
REPMs
10
Hexaferrites
FePt
5
10
Alnicos
4
Coercivity (A/m)
10
3
10
Steels
FeCo alloys
2
10
(Fe,Co)-b
ased
Spinel
ferrite
Fe-ba
sed
101
Si steels
Permalloys
(Fe
,Si)
0
10
-ba
sed
Nanocrystalline
alloys
Amorphous
alloys
Supermalloy
10
-1
1880
1900
1920
1940
1960
1980
2000
Year
2.5
FeCo alloys
Steels
Saturation magnetization (T)
2
1.5
45
Permalloy
FePt
REPMs
Nanocrystalline
alloys
Amorphous
alloys
Alnicos
1
78
Permalloy
Supermalloy
Hexaferrites
Spinel
ferrite
0.5
0
0.1
1
10
100
1000
104
105
106
Initial relative permeability (m 0)
Figure 4.1 (a) Timeline of progress in the improved performance for soft and hard
magnets as measured by the coercivity of different magnetic materials. (b) Diagram
showing the saturation magnetization and initial relative permeability for soft and hard
magnets.
181
Nanocrystalline Soft Magnetic Alloys
switching in an applied magnetic field, exemplified by large coercivities
(more than 125 Oe (10 kA/m)). Figure 4.1a illustrates the full range of
modern magnetic materials, showing excellent magnetic softness for amorphous and (Fe,Si)-based nanocrystalline alloys and superb magnetic hardness
for rare-earth transition metal compounds. Interestingly, the (Fe,Si)-based,
Fe-based (e.g., Nanoperm-type), and (Fe,Co)-based (e.g., HITPERM-type)
alloys all show reduced coercivity in nanocrystalline alloys (as shown in
Fig. 4.1a). While the coercivity has been optimized to specialize materials
for various applications, the saturation magnetization has been significantly
reduced (Fig. 4.1b). Saturation magnetization is an important figure of merit,
and while the nanocrystalline soft magnetic alloys do not have the highest
values, their low coercivities and moderate saturation magnetizations are
promising for many applications. Achieving the best combination of magnetic characteristics through alloy composition and microstructure evolution
has been areas of great scientific and technological efforts. A review of
progress in these areas is the topic of this chapter.
1.2. Technical considerations
Magnetic materials are characterized by their reaction to applied magnetic
fields. Characteristics that differentiate magnetic material performance can
be determined using the hysteresis loop. A schematic loop (as shown in
Fig. 4.2) reveals magnetic parameters that are microstructure independent
(i.e., intrinsic) and microstructure dependent (i.e., extrinsic properties).
Both types of properties affect the performance of the material and determine the suitability of the material for a given application. The M–H and
B–H loops are related to each other through a constitutive relationship:
B ¼ m0(M þ H) (in SI units), where B is the magnetic induction (in Tesla), M
is the magnetization (in A/m), H is the magnetic field strength (in A/m),
and m0 is the permeability of free space (4p 107 kg m/(A2 s2)).
Magnetization, M (A/m)
Remanent
magnetization, Mr (A/m)
Magnetic induction, B (T)
Saturation
magnetization, Ms (A/m)
Remanent induction, Br (T)
Susceptibility, X=M/H
Magnetic field strength, H (A/m)
Coercivity, Hc (A/m)
m 0= Permeability of free space
-7
2 2
(4p ⫻ 10 kg m/A s )
Permeability, m = B/H
Magnetic field strength, H (A/m)
Coercivity, Hc (A/m)
3
Core loss, Pcv (J/m )
(area within loop)
Figure 4.2 Schematic diagrams of hysteresis loops using (a) M–H and (b) B–H
coordinates.
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Matthew A. Willard and Maria Daniil
Intrinsic magnetic properties include the saturation magnetization (Ms),
magnetocrystalline anisotropy (K1), magnetostrictive coefficient (ls), and
Curie temperature (TC). The saturation magnetization can be determined
directly from the hysteresis loop at high fields. Large values of magnetization
are desirable for application since less material is required for a given
application as the magnetization is increased. The magnetocrystalline
anisotropy and magnetostrictive coefficients indirectly influence the hysteresis loop by their effect on the coercivity and core losses of the material.
Near isotropic switching behavior is observed when these quantities are
near zero, a factor that gives increased energy efficiency. Curie temperatures
are typically determined by measurement of the thermomagnetic response
of the material under a static field and not directly from the hysteresis loop.
While large values of Curie temperature are necessary for high-temperature
applications, in most cases, the Curie temperature should be large enough to
provide adequate exchange coupling at the operation temperature.
Extrinsic magnetic properties include permeability (m), susceptibility (w),
coercivity (Hc), remanence (Mr), and core losses (Pcv). These are influenced
not only by the microstructure but also by the geometry of the material
(through magnetostatic effects), the different forms of anisotropy found in
magnetic materials (e.g., magnetocrystalline, magnetoelastic, shape, induced,
etc.), and the effect of switching frequency of the applied fields. The core
losses are technologically one of the most important properties of the material
as they are a direct measure of the heat generated by the magnetic material in
application. The core loss is the area swept out by the hysteresis loop, which
should be minimized to provide good energy efficiency for the core. Contributions to the core loss include hysteretic sources from local and uniform
anisotropies and eddy currents at high frequencies. The permeability (and
related susceptibility) can be controlled by gapping the core or by field
annealing. For some applications, a large permeability is desirable (e.g.,
chokes) for others, a low, but constant value of permeability is important
(e.g., inductors). The hysteresis loop is influenced by the nanocomposite
microstructure in ways that are not commonly found in other classes of
magnetic materials. The unusual nature of the nanostructure shows a strong
microstructure dependence of the “effective” magnetocrystalline anisotropy
of the material (typically an intrinsic property). In order to appreciate the
importance of this effect, a brief description of the nanocomposites will be
given for context followed by details in later sections of this chapter.
In general, nanocomposite soft magnetic alloys include compositions rich
in ferromagnetic transition metals with small amounts of early transition metals
(ETMs), metalloids, and late transition metals (LTMs). The most studied type
of these alloys has nominal composition Fe73.5xSi13.5þxNb3B9Cu1,
although many other compositions have been investigated over the past
two decades (see Table 4.1). When optimally annealed this alloy possesses
a microstructure consisting of randomly oriented grains with diameters
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Nanocrystalline Soft Magnetic Alloys
Table 4.1 Nanocomposite alloy systems formed by rapid solidification processing
with subsequent annealing to form the identified primary crystalline phase
Alloy composition
Year Reference
Primary crystalline phase: a-(Fe,Si) or a1-Fe3Si
(70–80% Fe and m0Ms 1.2–1.4 T)
Fe–Si–M–B–Cu (M ¼ Nb, V)
1988 Yoshizawa (1988a)
Fe–Si–M–B–Au (M ¼ Nb, V, Hf, 1989 Kataoka (1989)
Ta, Mo, W, Cr)
Fe–Si–M–B–Cu (M ¼ Ta, Mo,
1991 Yoshizawa and Yamauchi (1991)
W, Cr)
Fe–Si–Al–Nb–B–Cu
1993 Lim (1993b)/Watanabe (1993)
Fe–Si–Ga–Nb–B
1994 Tomida (1994)
Fe–Si–U–B–Cu
1995 Konc (1995)
Fe–Si–Hf–B–Cu
1995 Mattern (1995)/Yamauchi
and Yoshizawa (1995)
Fe–Si–Al–Nb–Mo–B–Cu
1999 Frost (1999)
Fe–Si–Zr–B–Cu
2001 Kwapulinski (2001)
Fe–Si–Al–Ge–Zr–B–Cu
2002 Cremaschi (2002)
Fe–Si–Nb–P–B–Cu
2003 Chau (2003)
Primary crystalline phase: a-(Fe,M,Si) or a1-(Fe,M)3Si
(70–80% Fe/M and m0Ms 0.6–1.5 T)
Fe–Co–Si–Nb–B–Cu
1992 Yu (1992)
Fe–Ni–Si–Al–Zr–B
1993 Chou (1993)
Fe–Co–Si–Mo–B–Cu
1994 Kim (1994a)
Fe–Cr–Si–Mo–B–Cu
1994 Conde (1994)
Fe–Cr–Si–Nb–B–Cu
2001 Franco (2001b)
Fe–Mn–Si–Nb–B–Cu
2001 Tamoria (2001)/Hsiao (2001)
Fe–Ni–Si–Nb–B–Cu
2001 Atalay (2001)
Fe–Co–Si–Ge–Nb–B–Cu
2004 Cremaschi (2004b)
Fe–Co–Si–Zr–B–Cu
2004 Yoshizawa (2004)
Primary crystalline phase: a-Fe
(83–91% Fe and m0Ms 1.4–1.94 T)
Fe–M–B (M ¼ Hf, Zr)
1990 Suzuki (1990)
Fe–M–B–Cu (M ¼ Ti, Zr, Nb,
1991 Suzuki (1991c)
Hf, Ta)
Fe–Nb–B
1993 Suzuki (1993)
Fe–Zr–B–Si–Al
1996 Inoue (1996)
Fe–Zr–M–B–Cu (M ¼ Ti, V, Cr, 1999 Bitoh (1999)
Mn)
Fe–B–U–Cu
2000 Solyom (2000)
Fe–Nb–B–P
2001 Kojima (2001)
Fe–Zr–B–Ge–Cu
2002 Suzuki (2002b)
(Continued)
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Matthew A. Willard and Maria Daniil
Table 4.1 Nanocomposite alloy systems formed by rapid solidification processing
with subsequent annealing to form the identified primary crystalline phase—cont’d
Alloy composition
Year Reference
Fe–B–Si–Cu
2007 Ohta and Yoshizawa (2007)
Fe–Si–B–P–Cu
2009 Makino (2009)
(65-82% Fe and m0Ms 0.9–1.6 T)
Fe–P–C–Ge–Si–Cu
1991 Fujii (1991)
Fe–B–Nb–Cu
1995 Suzuki (1995)
Fe–B–M–Cu (M ¼ Zr, Hf, Nb) 1995 Kim (1995)
Fe–P–C–Mo–Si–Cu
1996 Tan (1996)
Fe–B–Zr–Cu
1998 Naohara (1998)
Fe–B–M–Cu (M ¼ Mo, Ti)
1999 Miglierini (1999)
Fe–P–B–Si–Al–Ga–Cu
2004 Pekala (2004)
Fe–Nb–B–P–Cu
2007 Makino (2007)
Primary crystalline phase: a-(Fe,Co) or a0 -FeCo*
(84–90% Fe/Co and m0Ms 1.5–1.9 T)
Fe–Co–Zr
1991 Guo (1991)
Fe–Co–Zr–B–Cu
1996 Muller (1996b)
Fe–Co–Zr–B–Cu*
1998 Willard (1998)
Fe–Co–Hf–B–Cu
1999 Iwanabe (1999)
Fe–Co–Zr–Nb–B–Cu
1999 He (1999)
Fe–Co–Zr–Hf–B–Cu
2002 Kulik (2002)
Fe–Co–Ge–Zr–B–Cu
2005 Blazquez (2005)
(62–80% Fe/Co and m0Ms 0.9–1.65 T)
Fe–Co–B–Al–Nb
1994 Cho (1994)
Fe–Co–Nb–B
1997 Kraus (1997)
Fe–Co–Nb–B–Cu
2001 Blazquez (2001)
Fe–Co–Ni–Zr–Nb–B–Cu
2001 Ausanio (2001)
Fe–Co–Zr–B–Si–Al–Cu
2004 Mitra (2004)
Fe–Co–Nb–Ta–Mo–B
2004 Um and McHenry (2004)
Fe–Co–Mo–B–C
2005 Yoshizawa and Fujii (2005)
Primary crystalline phase: g-(Fe,Co,Ni)
(80–90% Fe/Co/Ni and m0Ms 0.2–1.4 T)
Fe–Co–Ni–Zr–M–B (M ¼ Nb,
1997 Koshiba (1997)
Ta)
Fe–Ni–Co–Zr–B–Cu
2000 Muller (2000)
Fe–Ni–Zr–B–Cu
2001 Willard (2001b)
Co–Fe–Zr–B–Cu
2002 Willard (2002b)
Co–Ni–Zr–B–Cu
2012 Hornbuckle (2012)
less than 20 nm embedded in an amorphous matrix phase. Both the crystalline and the amorphous phases are ferromagnetically coupled when the best
magnetic properties are achieved. Alloys of this type have reduced magnetic
anisotropy (and therefore coercivity) as long as the grains are randomly
Nanocrystalline Soft Magnetic Alloys
185
oriented and their size remains small (as first discussed by Herzer in 1989)
(Herzer, 1989). To understand the origin of this “effective anisotropy”
exhibited by exchanged-coupled, fine-grained alloys, a few materials properties must be discussed first.
All magnetic materials possess magnetic anisotropy, which links the preferred direction of the material’s local moment with the local atomic arrangement (usually the crystalline lattice). This quantity is referred to as the
magnetocrystalline anisotropy (K1) in crystalline and amorphous materials
alike (although it is somewhat a misnomer in the latter). It is affected by
relatively short-ranged atomic arrangements (only a few atomic lengths) and
possesses the symmetry of its environment. For bulk soft magnetic materials,
the K1 is typically in the range of 103 to 105 J/m3 (OHandley, 2000). Another
important materials quantity is the magnetic exchange stiffness (A), which
determines how strongly magnetic moments prefer to remain in a common
direction. Most soft magnetic alloys have A near 1011 J/m (OHandley, 2000).
When the magnetization switches direction under the action of an applied
field, these two quantities oppose each other. Take the case of a crystalline
material with two magnetic domains separated by a 180 domain wall. The
magnetocrystalline anisotropy energy is lowest when the moments are aligned
with the preferred easy axis direction, so an abrupt change between domains
would be expected. The exchange energy is lowest when adjacent moments
are aligned with each other, so an infinitely wide wall would be expected.
Taking both of these factors into account, K1 acts to restrict the width of the
domain wall due to its propensity to keep the magnetic moments aligned with
the crystalline lattice and A acts to widen the wall keeping adjacent moments
aligned. For thep
specific
ffiffiffiffiffiffiffiffiffiffiffiffi case here, the width of the 180 domain wall is
proportional to A=K1 (Chen, 1986). This quantity, called the magnetic
exchange correlation length (Lex) or simply exchange length, is important to
our understanding of the soft magnetic behavior in nanocrystalline alloys,
showing the minimum length scale over which the magnetization can have a
noticeable change in direction.
When the structural correlation lengths are near the same size as the
magnetic correlation lengths (i.e., exchange length) then interesting magnetic
properties are produced. Considering an amorphous alloy, the structural correlation is limited to the arrangement of near-neighbor and next-near-neighbor
atoms. In this case, the magnetocrystalline anisotropy was found to be averaged
within the exchange length of the amorphous phase due to the local structure,
as described by Alben et al. in their formulation of a random anisotropy model
(Alben et al., 1978). The overall magnitude of the magnetic anisotropy is
lowered using the random anisotropy model, resulting in softer magnetic
behavior (a much reduced “effective anisotropy” is developed).
This formulation can be applied to nanocrystalline alloys as well. In
crystalline alloys, the structural correlation length is the grain diameter
(D). When the grain size is much smaller than the exchange length (Lex),
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Matthew A. Willard and Maria Daniil
the magnetocrystalline anisotropy is averaged over the volume encompassed
by Lex. The exchange energy, being longer range than the magnetocrystalline anisotropy, dominates and forces the magnetic moments to align
regardless of grain orientation. This results in an effective magnetic anisotropy, hKi, of K1(D/Lex)6 for a three-dimensional nanostructured material.
Since the coercivity (and ultimately the losses) of the soft magnetic material
is strongly dependent on the magnetic anisotropy, we can clearly see the
importance of this relation (as demonstrated in Fig. 4.3). As this equation
implies, the effective anisotropy can be decreased very effectively by reduction in the grain size of the alloy. For a 1-nm grain diameter, the hKi has
values ranging from 101 to 106 J/m3 (depending on the K1 of the crystallites). Using the measured magnetic correlation length from small-angle
neutron scattering (SANS) measurements, Loffler et al. determined that the
magnetization will only follow the anisotropy axes of individual grains
when the grain size exceeds a critical value, approximately the size of the
180 domain wall width (Löffler et al., 1999). When applied to (Fe,Si)based nanocrystalline materials (given K1 for a-(Fe,Si) is 8–10 kJ/m3), the
domain wall width is found to be 300 nm, marking the transition
between these two regimes. For grains larger than the domain wall width,
a 1/D dependence of coercivity is observed (see Fig.4.3).
When the losses are made small by reducing the magnetocrystalline
anisotropy through grain size reduction, other loss mechanisms become
dominant. One of these remaining and important loss mechanisms is the
10
4
Coercivity (A/m)
1000
D−1
100
D6
10
1
0.1
1
10
100
1000
4
10
5
10
6
10
Grain size (nm)
Figure 4.3 Diagram showing the variation of coercivity with grain size for soft
magnetic alloys without induced anisotropy. After Herzer (1990).
187
Nanocrystalline Soft Magnetic Alloys
magnetoelastic anisotropy, which is driven by internal or external stress
fields through the magnetostrictive coefficients of the material. The simultaneous reduction of both the magnetocrystalline and magnetoelastic energies is required to achieve the maximum permeabilities (and lowest losses)
in these alloys. This short description of the impact that nanocomposite
microstructure has on the hysteresis loop illustrates the importance of this
class of materials for a variety of applications.
1.3. Applications
A wide range of devices require soft magnetic materials for energy storage,
conversion, filtering, power generation, sensing, and many other uses
(Willard and Daniil, 2009). Before continuing to materials processing and
resultant properties, it is important to mention the potential impact of this
class of materials. The range of applications and corresponding materials
chosen for each are shown in Fig. 4.4 as a function of switching frequency
for the magnetic component. Nanocrystalline, amorphous, and polycrystalline alloys are limited to about 1 MHz switching frequency due to the
deleterious effects of eddy currents and their increased contribution to the
Materials
HIPERM
Nanocrystalline alloys — FinemetTM
NanopermTM
Co-based MetglasTM
Fe-based MetglasTM
NiZn-ferrites
Fe-Si; Fe-Ni alloys; Fe-Co Alloys
MnZn-ferrites
Applications
Saturable reactor cores
Inductors (Filters and converters)
Switch-mode power supplies
10 MHz
1 MHz
100 kHz
10 kHz
1 kHz
1000 GHz
Microwave
application
Distribution and power transformers
100 Hz
10 Hz
DC
Shielding
sensors
100 MHz
Stators and rotors
in motors and generators
Frequency
Figure 4.4 Soft magnetic materials and potential applications with varying frequency.
After Gutfleisch et al. (2011).
188
Matthew A. Willard and Maria Daniil
core loss and subsequent reduction of permeability with increasing frequency.
Above 1 MHz, oxide soft magnets with the spinel crystal structure (i.e.,
ferrites) are used, largely due to their high resistivity and limited eddy current
formation. However, the low saturation magnetization (less than 0.4 T) of
these oxide materials results in an opportunity for nanocrystalline soft magnetic alloys even at these frequencies if the eddy current components of the
core loss can be controlled (Marı́n and Hernando, 2000). In the design of new
materials, two characteristics are important for applications, namely, minimizing losses and maximizing saturation induction.
A leading advantage of the nanocrystalline alloys over other soft magnetic materials is their high saturation magnetization combined with their
core loss performance at frequencies up to 1 MHz. While there are many
soft magnetic thin film materials available with similar characteristics, their
thickness limits these materials to uses where lower power loads are
required. The ribbon-shaped nanocrystalline materials produced by rapid
solidification techniques allow more flexibility in design and production of
devices for higher power requirement applications. With the rising importance of distributed architectures for power conversion (Huljak et al., 2000),
the advantages of nanocrystalline soft magnetic alloys should provide an
option for smaller, lighter, and more efficient components. Reduction in
size makes energy-efficient devices based on nanocrystalline alloys more
affordable (Hasegawa, 2006).
Substantial federal and private investments have been made in an effort
improve performance by standardizing, modularizing, and miniaturizing
the packaging of power electronics components. Power electronics devices
are used to supply a specific voltage with a limited noise threshold. They
usually consist of semiconductor-based active devices designed for high
power loads and frequencies but also require inductors and capacitors for
power conditioning. Conversion of AC line frequencies to DC, followed
by DC/DC power conversion to match the different components the
power electronics support, requires high-performance soft magnetic materials. In the voltage regulation circuit for instance, the soft magnetic alloy
acts as a magnetic switch (sometimes referred to as a magnetic amplifier) that
requires low and high remanent states of the magnetization to be achieved
with small applied switching fields (Hasegawa, 2004). Ideally, the soft
magnetic material switches very sharply at the coercivity and the hysteresis
loop has good squareness (i.e., Mr/Ms > 0.9). The large squareness and low
coercivity allow good regulation behavior, reduced dead-time, and small
reset currents. While miniaturization and high-frequency performance of
active components have made significant progress, similar advances in
magnetic components have not been forthcoming. Efforts to provide miniature and modular integrated power electronics components remain a
leading motivation for efforts to improve soft magnetic alloys with larger
magnetization and lower core losses.
Nanocrystalline Soft Magnetic Alloys
189
Power converters also use choke coils to reduce high-frequency harmonics in the current source. In this case, the inductor coil will have a large
amount of current and the inductor should not be allowed to saturate under
this condition, requiring low remanence (i.e., Mr/Ms < 0.3) and high saturation magnetization. Large induced anisotropy and high electrical resistivity
are key parameters for extending converters to higher frequencies (Yoshizawa
et al., 2003). The recent use of Finemet-type alloys for a 1 MV DC power
supply illustrates the importance of nanocrystalline materials to power conditioning applications (Watanabe et al., 2006). Power conditioning refers to
reducing the harmonic distortion in the output signal caused by fast switching
during DC/DC conversion, for instance from a switched-mode power
supply. A common-mode choke is used in this case and requires a broadband
high permeability (Yoshizawa and Yamauchi, 1989).
In the field of power electronics, switched-mode power supplies have
been replacing conventional 50 Hz power supplies due to market demands
for higher efficiencies (Hilzinger, 1985). Higher frequency operation
(above 1 kHz) provides the added benefit of size reduction for these components, which limits the choices of materials to those with high resistivity.
The materials used for 50/60 Hz applications, including Si-steels, are not
suitable for these high-frequency applications due to the increased losses
caused by eddy currents. Nanocrystalline soft magnetic alloys provide
excellent performance in these applications due to their high magnetic
induction and low losses at frequencies up to 1 MHz (Hilzinger, 1990).
For transformer applications, low coercivity (less than a few A/m), high
saturation magnetization (greater than 1.5 T), and large remenance ratio
(more than 0.8) are desired characteristics (Hasegawa, 2006). Recent advances
in amorphous alloys have had an impact in this area; however, nanocrystalline
alloys continue to have great potential in this area, too. The improvement in
energy efficiency of the core material (by reducing core losses) indirectly
reduces greenhouse gas emissions by wasting less of the generated power as
Joule heating from core loss (Hasegawa, 2000), and the use of magnetic and
stress field annealing allows better control of the remenance ratio of the alloys,
providing improved performance of nanostructured materials.
Nanocrystalline ribbon materials have also been considered for lowfrequency ground fault circuit breakers due to their combination of low
remanent magnetization and permeability adjusted by magnetic field
annealing (Waeckerle et al., 2000). The low remanent magnetization is
necessary for this application to provide consistent working induction under
high dynamic variations and varying waveforms. The core losses must also
be relatively small to provide good sensitivity to low current surges.
Governmental regulations have been established to prevent the disruption
of medical devices and personal computers (susceptible to induced highfrequency noise from these devices) by the increasingly common portable
electronic devices (including cell phones and personal digital assistants) that
190
Matthew A. Willard and Maria Daniil
operate at frequencies above 1 MHz. Common-mode choke coils provide
protection of these devices by acting as a low impedance wire for the signal
(e.g., differential mode currents) and high impedance inductor for highfrequency noise (e.g., common-mode currents). Chokes of this type are used
in switched-mode power supplies, uninterruptible power supplies, inverters,
and frequency converters to limit electromagnetic interference (EMI). The
high permeability of (Fe,Si)-based ribbon materials is a favorable feature for
EMI reduction in the MHz to GHz frequency range (Nakamura et al., 2004).
The high saturation magnetization and low remanence of Finemet-type
and Nanoperm-type nanocrystalline alloys provide broadband voltage attenuation (100 kHz to 10 MHz), making these materials favorable for use in
common-mode choke coils. Reduction of the permeability in nanocrystalline
soft magnetic alloys allows them to store energy in the magnet. This is
especially important for choke coils used to prevent signal distortion in reactor
elements of phase modifying devices by smoothing out the higher harmonic
ripples in the rectified voltage waveform. Magnetic or stress field annealing
procedures may be used to lower the permeability as well as putting an air gap
in the core or using a powdered core of nanocrystalline alloy.
Core size reduction is a desired improvement, requiring simultaneous
increase in the saturation magnetization and lower core losses. The saturation
magnetization must be increased when the core is made smaller to maintain a
constant stored energy and the core loss must be reduced at the same time to
counteract the increased hysteresis loop area resulting from the increase
magnetization. A disadvantage of smaller cores is the reduced surface area
available for extracting the heat produced due to the core loss (Naitoh et al.,
1998). For this reason, thermal management is an important consideration
and reduction of core losses is emphasized as a means to produce less heat
from the start. Nanocrystalline soft magnetic alloys with induced anisotropy
are well suited for choke core applications for these reasons.
Induced anisotropy is preferred to powdered or gapped cores due to the
observed increases in core losses, resulting from these alternative means of
controlled reduction of permeability (Kim et al., 2003; Naitoh et al.,
1997b). Finemet-type alloys are restricted to 10% changes in permeability
during sustained use at temperatures as high as 100 C and limited use at
temperatures between 40 and 150 C. Due to their low values of magnetostriction, the acoustic noise emission is also limited. These features illustrate the importance of nanocrystalline materials over amorphous and ferrite
cores for use in switched-mode power supplies, frequency inverters, uninterruptible power supplies, adjustable speed drives, and other applications,
requiring robust noise suppression from rapid current changes.
Flux gate sensors have been used for ultra-sensitive magnetic field
detection (0.1 nT) using nanocrystalline soft magnets. The sensor is
made of two identical saturable cores with large permeability that are
oppositely wound (Nielsen et al., 1994). A small AC magnetic field is
Nanocrystalline Soft Magnetic Alloys
191
applied to each coil, and a differential voltage drop is measured when an
unvarying external field is applied. These sensors are used for magnetic
direction sensing applications. The near zero value of magnetostriction,
high permeability, and low Barkhausen noise makes nanocrystalline soft
magnetic alloys competitive for these applications. Finemet-type ribbons
annealed under a transverse magnetic field have shown 0.04 nT noise level
for a 16 nT peak-to-peak square applied waveform (Nielsen et al., 1994).
Recent studies by Ong et al. have shown that the higher harmonics
created in a soft magnetic amorphous ribbon can be used for accurate,
remote temperature measurement (Ong et al., 2002). The high permeability
and low coercivity found to be important for this sensor are similar to those
in nanocrystalline alloys, which might also be used in this capacity.
Nanocrystalline soft magnetic alloys have also been used for stress sensor
applications (with sensitivity up to 50 MPa) (Ahamada et al., 2002). The
tailored magnetostrictive coefficient of (Fe,Si)-based alloys along with the
induced anisotropy resulting from annealing under a stress field allowed
the development of a near linear change in magnetization with applied stress
(at an applied field of 400 A/m). The so-called giant magnetoimpedance
effect exhibited by some nanocrystalline soft magnetic alloys gives them
potential for use in magnetic field sensor applications (Naitoh et al., 1997a;
Yoshizawa et al., 1988b). The magnetoelastic resonance of ribbons with
transverse anisotropy has been used in article surveillance monitoring applications (Marı́n and Hernando, 2000).
Despite the significant benefits exhibited by this class of materials, many
challenges remain for alloy developers. Some of these include developing
new materials with improved processing in air, controllable permeability,
and reduction in embrittlement after crystallization. With progress in these
areas, even more widespread use of these materials is expected.
2. Alloy Processing
The optimal microstructure for soft magnetic nanocrystalline materials
consists of grains less than 10 nm in diameter surrounded by an amorphous
matrix phase less than a few nm in thickness. Both the small grain size and
the amorphous matrix phase help to provide the excellent magnetic properties found in these alloys. Substantial difficulties arise when conventional
alloy preparation techniques—such as solidified casting, forging, rolling,
sintering, extrusion, etc.—are employed for preparation of nanocrystalline
materials. These techniques process materials at high temperatures where
near-equilibrium conditions result in limited nucleation and uncontrolled
grain coarsening. These conditions are not conducive to the formation of
the nanocrystalline microstructure.
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Matthew A. Willard and Maria Daniil
Crystallization of a liquid occurs through a nucleation and growth
process, where the crystalline phase forms small transformed regions within
the liquid that subsequently grows as crystallization progresses. It is expected
that any processing technique capable of producing a large amount of
nucleation with a limited amount of grain growth would be a requirement
to achieve a nanocrystalline microstructure. For this reason, nonequilibrium
(metastable) processing methods are well suited for development of this
microstructure. Melting, evaporation, irradiation, applied pressure, and/or
mechanical deformation can be employed by nonequilibrium means to
create a fine-grain microstructure. Specific techniques that accomplish this
include rapid solidification, plasma processing, vapor deposition, mechanical alloying, and chemical synthesis. Many of these techniques provide a
precursor amorphous phase, which can be further processed to form the
nanocomposite microstructure.
The most commonly used method for producing nanocrystalline soft
magnetic alloys is the single-roller melt spinning technique either by planar
flow casting or by nozzle injection (a.k.a. jet casting). Both techniques
produce amorphous alloy ribbons with thicknesses less than 30 mm and
widths in the millimeter to centimeter range. Under the right processing
conditions, these ribbons can be many meters long. Isothermal annealing or
Joule heating is then used to produce the nanocrystalline microstructure
necessary for optimal magnetic performance. Annealing is typically carried
out in vacuum or in an inert-gas environment to prevent oxidation.
The following sections will describe progress in variations of the
processing parameters for rapid solidification (Section 2.1), annealing
(Section 2.2), and core fabrication (Section 2.3). While much of the work
on nanocrystalline soft magnetic alloys has been explored by melt spinning
followed by furnace annealing, important studies using novel techniques for
both nonequilibrium processing (e.g., wire, thin films, mechanical alloying,
etc.) and crystallization (e.g., irradiation, laser processing, Joule heating,
etc.) have also been studied (see Section 2.4).
2.1. Rapid solidification
Rapid solidification refers to processes where heat is extracted from a melt
at rates exceeding 105 K/s. Using this extreme cooling rate, alloys within
limited composition ranges can be kinetically arrested in a metastable,
amorphous, or glassy solid state. Metastable in this case refers to a state
where the alloy will transform to one or more crystalline phases, given
enough time (albeit extremely long times in this case). Should the cooling
rate be insufficient, a crystalline or partially crystalline alloy may be
produced instead of a fully amorphous alloy. It has been found that better
magnetic performance is possible when direct formation of crystallites
from the melt is avoided so rapid solidification techniques are employed
193
Nanocrystalline Soft Magnetic Alloys
to create an amorphous precursor with subsequent postprocessing for
crystallization.
Of the many “bulk” rapid solidification techniques (including planar
flow casting, roller quenching, melt extraction, atomization, etc.), the one
most commonly used for nanocrystalline soft magnetic alloy investigations
is the melt spinning technique. This technique produces ribbons or sheets
of alloy less than 30 mm thick by the expulsion of a melt onto a rapidly
rotating wheel. To ensure homogeneity, alloy ingots of the desired composition are formed from high purity elemental constituents using an arc
melting or induction melting technique prior to melt spinning. The
resulting alloy ingots are used as stock material for rapid solidification
processing. During the melt spinning process, the melt is typically
contained in a crucible with an orifice at the bottom and is heated by
induction coils (see Fig. 4.5). The surface tension of the molten alloy holds
the melt inside the crucible until the desired melt temperature is achieved.
The melt is then expelled onto the rotating wheel by a high-pressure gas
from the top of the melt. The resulting stream impinges on the quench
wheel, providing a large quench rate.
The melt spinning technique has many independently adjustable parameters, which can greatly affect the quality of the ribbon product. These
include the speed of the quench wheel, the temperature of the melt, the
orifice size and shape, the distance between the crucible and wheel, and
the ejection pressure. By controlling these parameters, the resulting ribbons
can have varied thicknesses, widths, quench rates, and degree of crystallinity. Ultimately, all of these factors affect the magnetic properties, stressing
the importance of understanding and controlling these parameters during
alloy processing.
Crucible
Molten
alloy
Induction
coils
Melt-spun
Ribbon
Quenching wheel
Figure 4.5
Schematic diagram of a single-wheel melt spinner.
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Matthew A. Willard and Maria Daniil
2.1.1. Melt temperature control
The melt temperature prior to alloy ejection onto the quench wheel has
been studied for alloys with composition Fe73.5Si13.5B9Nb3Cu1 (Chiriac
et al., 1999a; Lim et al., 1993a; Pi et al., 1993). These studies found trends in
the permeability and coercivity of alloys produced with different degrees of
excess heating above the equilibrium melting temperature of 1473 K. Care
was taken to maintain constant ribbon thickness by adjusting the orifice size
and wheel speed so that an accurate comparison between the resulting runs
could be made. A tripling in permeability (see Fig. 4.6) and a fourfold
increase in remanence ratio were observed when the melt temperature
was increased from 1513 to 1653 K (Lim et al., 1993a). Further increase
in melt temperature to 1723 K shows a precipitous drop in permeability.
Both effects can be explained by considering the relationship of the time
required for relaxation (tR) of the molten alloy into near-equilibrium
atomic clusters and the time required to quench the alloy (tq) from the
melt temperature (Tmelt) to the glass transition temperature (Tg).
An alloy with good glass-forming ability possesses a large tR, consistent
with the stability of the liquid over solid cluster formation (Pi et al., 1993).
The value of tq is directly increased as Tmelt increases. In order to produce
an amorphous alloy, the tq must be less than the tR or solid clustering will
occur during the quench. The alloy considered here, with composition
Fe73.5Si13.5B9Nb3Cu1, has a large fraction of glass-forming elements and
is considered a good glass-forming alloy. Increased Tmelt in this case
Chiriac (1999)
Relative permeability
35 000
Lim (1993)
30 000
25 000
20 000
15 000
1500
1550
1600
1650
1700
1750
Melt temperature (K)
Figure 4.6 Variation of permeability with melt temperature for Fe73.5Si13.5B9Nb3Cu1
alloys (Chiriac et al., 1999a; Lim et al., 1993a)
Nanocrystalline Soft Magnetic Alloys
195
(to 1650 K) is thought to increase the permeability due to its improved
homogeneity prior to quenching. However, this effect is limited to the
temperature range where tR > tq. As the Tmelt reaches 1723 K, the large
decrease in permeability can be attributed to tq exceeding tR, resulting in
cluster formation during the quench (due to the larger driving force for
crystallization imposed by the higher temperature) and degraded magnetic
performance (Chiriac et al., 1999a).
2.1.2. Wheel and crucible parameters
Four interrelated processing parameters control the ribbon cross section by
controlling the molten puddle on the quench wheel (both the puddle size and
the melt flow rate). These parameters are the wheel surface velocity, the
crucible orifice size, the melt ejection pressure, and the wheel-to-crucible
distance. While trends between these parameters and the ribbon thickness are
known for amorphous ribbons, (Liebermann and Graham, 1976) similar
tends have not been systematically studied for any of the nanocrystalline
alloys. However, most studies provide some of these parameters and they
are (not surprisingly) very similar to those used in amorphous alloy processing
(El Ghannami et al., 1994; GómezPolo et al., 1997; Mitra et al., 2001; Panda
et al., 2001; Tiberto et al., 1996b). Typical wheel surface velocity used in
these studies ranges from 20 to 50 m/s when a copper wheel is used for
quenching. The orifice size ranges from 0.75 to 2 mm in diameter and wheelto-crucible distances range from 0.5 to 5 mm. Ejection gases include helium
and argon with pressures between 25 and 50 kPa (about 0.25–0.5 psi).
Figure 4.7 illustrates the thickness variation with wheel surface velocity
and shows the influence of orifice diameter and wheel-to-crucible spacing.
Intuitively, the ribbon thickness is smaller for processing conditions that
make both the puddle size and the melt flow rate smaller. This includes
reducing the melt ejection pressure, reducing the orifice size, and increasing
the wheel surface velocity. The quench rate is improved under these
conditions, aiding in the formation of a fully amorphous ribbon. While by
changing these processing parameters the ribbon thicknesses can be varied,
the resulting material may not remain fully amorphous during the quench
for the same reasons described in Section 2.1.1 (i.e., tR must be greater than
tq). At some critical ribbon thickness (dependent on composition), the alloy
will begin to partially crystallize during the melt spinning process. The
grains formed by this process typically possess preferential orientation with
the expected growth texture for the crystalline phase formed (i.e., (1 0 0) for
BCC (body-centered cubic) or (1 1 1) for FCC (face-centered cubic)).
Direct crystallization from the melt of a Fe73.5Si13.5B9Nb3Cu1 alloy was
performed by El Ghannami et al. as a function of wheel speed (from 34.5
to 42.3 m/s) by quenching from very near the melting point of the
alloy (1438 K) (El Ghannami et al., 1994). The resulting alloys were
only 10% crystalline in the as-spun condition, consisting of grains about
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Matthew A. Willard and Maria Daniil
60
nozzle diameter (mm)
crucible—Wheel (mm)
eject pressure (kpa)
1.9
0.8
50
Ribbon thickness (μm)
50
40
1.0
0.5
50
30
1.4
0.5
50
1.4
0.5
50
20
1.2
5.0
50
10
0
15
?
0.6
25
Tiberto (1996)
Panda (2001)
Mitra (2001)
20
25
30
35
40
45
Wheel surface velocity (m/s)
Figure 4.7 Ribbon thickness variation with wheel surface velocity for Fe73.5Si13.5B9Nb3Cu1
alloys. Other important processing parameters are provided parenthetically (nozzle diameter,
crucible-to-wheel distance, and melt ejection pressure) (Mitra et al., 2001; Panda et al., 2001;
Tiberto et al., 1996b).
15 nm in diameter. Annealing resulted in the reduction of the coercivity
for all samples by a factor of 2, with the best results for the fastest wheel
speed (e.g., 0.8 A/m at 42.3 m/s). Similar alloys when quenched to a fully
amorphous phase typically have much lower coercivities ( 0.5 A/m) after
subsequent annealing (Yoshizawa et al., 1988a).
2.1.3. Atmospheric control
The effect of chamber gas during melt spinning has been examined by Todd
et al. (1999). In this study, comparisons of grain size, coercivity, and surface
roughness were made between samples prepared at pressures between vacuum and 1 atm. of argon, air, or helium gases. While the grain size remained
constant at about 10 nm, a significant change in coercivity was observed
when the chamber gas pressure exceeded about 1/3 atm. Samples prepared
in 1 atm. of argon or air had similar coercivities near 1 A/m, while samples
prepared under the same pressure of helium showed only 0.65 A/m. This
difference was attributed to a large surface roughness difference brought about
by gas entrapment between the melt puddle and wheel surface during melt
spinning. Good surface quality was reached at 0.2, 0.4, and 0.8 atm. for Ar,
air, and He gases, respectively. The variation in coercivity with ambient gas
pressure and type of gas is shown in Fig. 4.8 for Fe73.5Si13.5Nb3B9Cu1 alloys
with similar post-melt spinning anneals (Todd et al., 1999).
197
Nanocrystalline Soft Magnetic Alloys
Air
Ar
He
1.1
Coercivity (A/m)
1.0
0.9
0.8
0.7
0.6
0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Chamber pressure, Pamb (atm.)
Figure 4.8 Effect of ambient gas pressure and type on the coercivity of Finemet
annealed at 540 C for 3600 s (circle: Ar; triangle: air; square: He). Modified from
Todd et al. (1999).
2.2. Annealing procedures
Annealing the as-spun, amorphous alloy at temperatures near glass transition
but below the crystallization temperatures allows quenched-in stresses to
relax, which in some cases can improve the magnetic performance. The
structural relaxation effect is due to local rearrangement of atomic positions
to lower energy bonding conditions and a concomitant slight densification of
the alloy. While the stress relief may improve the magnetic remanence and
coercivity of many amorphous alloys, the intrinsic magnetic properties (e.g.,
magnetization, magnetostrictive coefficient, etc.) do not change much. By
annealing certain amorphous alloys, all of these properties can be improved
simultaneously due to the formation of a nanocomposite microstructure.
Crystallization of amorphous Finemet alloy ribbons (Fe73.5Si13.5B9Nb3Cu1)
occurs in three stages (see Fig. 4.9). During the early stages of annealing, copper
clusters form throughout the material, allowing the heterogeneous nucleation
of a massive number of a-(Fe,Si) nuclei necessary for the nanocrystalline
microstructure to develop. At primary crystallization, a-(Fe,Si) grains nucleate
and grow within an amorphous matrix phase. This phase has been identified
as disordered BCC and/or atomically ordered Fe3Si (D03 structure) (Kulik
et al., 1995). The primary crystallization process occurs near 510 C (783 K),
resulting in the formation of the a-(Fe,Si) phase surrounded by an amorphous
matrix phase (Herzer, 1989). During the crystallization process, the amorphous
matrix is enriched in Nb, helping to stabilize the fine-grained microstructure.
The grain size of the a-(Fe,Si) crystallites tends to arrest growth at about 10 nm
and increase Si content to about 20 at% regardless of annealing time for
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microstructure
Matthew A. Willard and Maria Daniil
Coarsening of a-(Fe,Si)
& Nb/B enrichment
of residual amorphous
Heterogeneous
nucleation of a-(Fe,Si)
Clustering of Cu
As spun
(uniform composition)
10 nm
550 °C 3600 s
550 °C 1800 s
550 °C 480 s
550 °C 120 s
Figure 4.9 Schematic diagram showing the crystallization of Fe73.5Si13.5Nb3B9Cu1
alloys with annealing time at 823 K. Modified from Ayers et al. (1998) with input from
Hono et al. (1999).
temperatures near primary crystallization (Varga et al., 1994b). At higher
temperatures, secondary crystallization occurs resulting in crystallization of
the remaining amorphous phase into Fe3B, Fe2Si, Fe2B, and other intermetallic
phases (Duhaj et al., 1991; Yamauchi and Yoshizawa, 1995; Zhu et al., 1991).
Both the primary and secondary crystallization transformations are thermally
activated.
Clearly, the crystallization conditions are an important factor in the
development of the optimal magnetic properties. In this section, the conditions for furnace annealing, Joule heating, and annealing under stress and
magnetic fields are discussed. The important parameters as well as advantages and disadvantages of each technique are presented.
2.2.1. Conventional furnace annealing
When amorphous alloys of an appropriate composition are annealed isothermally above the primary crystallization, but below the secondary crystallization
temperatures, the desired nanocrystalline microstructure can be achieved. For
example, in Fe73.5Si13.5B9Nb3Cu1 alloys, the annealing temperature should
remain between about 500 and 600 C. Under these conditions, a metastable
equilibrium of a-(Fe,Si) crystallites surrounded by a Nb-enriched remaining
amorphous phase is formed. Given sufficient time for grain growth (usually
near 1800–3600 s), the microstructure consists of nanocrystalline grains
embedded in a 20–25 vol% amorphous matrix. This microstructure is quite
resilient to further annealing in this temperature range.
Standard annealing procedure for most studies on nanocrystalline soft
magnetic alloys include annealing at temperatures near the primary crystallization temperature (Tx1) for at least 1800 s but usually 3600 s. The atmosphere is controlled by active vacuum or inert atmosphere (e.g., He, Ar, N2,
H2, etc.). This is accomplished either by encapsulation of ribbon samples in
an ampoule under vacuum or with inert gases or using a furnace with
flowing inert gas during annealing. In either case, the heating rate is limited
by the sample insertion speed or controlled by the heating rate of the
199
Nanocrystalline Soft Magnetic Alloys
furnace. Similar limits exist for cooling rates of the samples imposed by the
quench technique or cooling rate of the furnace; however, the cooling rates
are typically not as important.
The primary crystallization reaction is thermally activated and is therefore sensitive to both the annealing temperature and the annealing time.
Many isochronal annealing studies of Fe96zSixBzxNb3Cu1 alloys have
been performed to establish the relationship between these two parameters
and the resulting microstructure (see Fig. 4.10) (Maslov et al., 2001; Van
Bouwelen et al., 1993; Varga et al., 1994b). The first important feature to
notice is the extremely slow grain growth after about 1000 s of annealing
time near the primary crystallization temperature. This arrested grain
growth allows full microstructure development after the typical annealing
time of 3600 s. The second featurepofffiffiffiffiffinote
is illustrated by the plotted line in
ffi
e
the graph, corresponding to the Dt of Fe diffusing in a Fe–Si–B amore is the diffusivity and t is time at temperature (Horváth
phous alloy, where D
et al., 1988). The calculation indicates that significant diffusion would be
expected for Fe at times as small as 3600 s, resulting in an order of magnitude greater grain size than observed in these Fe–Si–B–Nb–Cu alloys. For
no Nb/Cu
100
Varga 773/798/823/848 K
van Bouwelen 776 K
776 K
823 K
10
848 K
Grain diameter (nm)
no Nb
Gupta 813 K
Ayers 823 K
√Dt for Fe–Si–B (am)
1
1
10
100
1000
104
105
106
Annealing time (s)
Figure 4.10 Variation of grain diameter with annealing time at various temperatures
above the primary crystallization temperature of Fe96zSixBzxNb3Cu1 alloys. All have
(x, z) ¼ (13.5, 22.5), except van Bouwelen (12.5, 20.5) and Gupta (16.5, 22.5). The
two Ayers alloys are Fe76.5Si13.5B9Cu1 (no Nb) and Fe77.5Si13.5B9 (no Nb/Cu). Annealing temperatures are indicated. Horvath’s diffusivity for Fe–Si–B (am) used to calculate
a diffusion distance expected at 823 K (Horváth et al., 1988; Maslov et al., 2001; Van
Bouwelen et al., 1993; Varga et al., 1994b).
200
Matthew A. Willard and Maria Daniil
studies with short annealing times, liquid metal baths (e.g., Ga, Sn, etc.)
were used with water or brine quenching.
In a study by Wang et al. (1997), improved magnetic performance and
refined grain size result from increased heating rate to an isothermal annealing temperature above primary crystallization. By varying the heating rate
from 8.3 103 to 4.3 K/s, the grain size was reduced from 14.6 to
10.6 nm and the resulting initial permeability was tripled from 26,000 to
92,000. This work and others on Fe73.5Si13.5B9Nb3Cu1 alloys emphasize
the importance of the early stages of crystallization on the nucleation and
growth processes, the topic of Section 4.3 (Ramin and Riehemann, 1999b;
Wang et al., 1997). Conventional annealing procedures under an applied pressure of 5 GPa resulted in the grain size reduction to about 5 nm for Fe73.5Si13.5B9Nb3Cu1 alloys (Zhang et al., 1997).
Vazquez et al. have examined the effect of annealing at temperatures
lower than the primary crystallization temperature on the permeability,
coercivity, and magnetostrictive coefficient (Vázquez et al., 1994). These
results show a slight magnetic softening of the Finemet alloy due to relaxation of the as-spun alloy (Tann 380 C), followed by magnetic hardening
just prior to crystallization of the alloy (400 C Tann 460 C). The
magnetic hardening was attributed to Cu-cluster formation in the alloy.
Conventional annealing can, however, provide an undesirable induced
anisotropy that can limit the magnetic softness of certain alloys, especially (a)
ones with low Curie temperature of the amorphous phase (e.g., Fe–Zr–B
alloys) and (b) those with significant pair-ordering potential (e.g., (Fe,Co)–
Zr–B). In the first case, at common annealing temperatures near primary
crystallization, the newly formed grains can remain far below their Curie
temperatures, yet above the Curie temperatures of amorphous phase from
which they crystallize. The magnetization from the newly formed grains
influences the crystallization behavior, adding a uniform anisotropy on a
relatively local scale to the sample, much the same as in a magnetic fieldannealed samples (but with much longer range in that case) (Ito and Suzuki,
2005). This can have deleterious effects due to the random orientation of
the crystallizing grains and therefore local random-induced anisotropies.
The induced anisotropy is somewhat small in these cases (<100 J/m3) but
can result in significant increases in the coercivity when the grain size has
been reduced to below about 15 nm in diameter (Suzuki et al., 2008a). In
the latter case, pair ordering can lead to significant induced anisotropies as
discussed in more detail in Section 2.2.3. One way of alleviating this effect is
to perform rotating field annealing (also to be discussed in Section 2.2.3).
2.2.2. Joule annealing
An alternative method for crystallizing amorphous ribbon samples is the
Joule annealing technique (also called current annealing) (Kulik et al.,
1992). The technique, originally developed for relaxation of amorphous
Nanocrystalline Soft Magnetic Alloys
201
alloys without crystallization (Allia et al., 1993b,c; Jagielinski, 1983), has
been successfully adapted for rapid crystallization rate using higher current
densities (Allia et al., 1993d). This technique passes an electrical current
through the ribbon with densities in the range of 10–50 MA/m2 to provide
the energy necessary for crystallization. The current may be pulsed (e.g.,
<10A for 1 ms), applied stepwise, or continuously for times up to a few
minutes at currents between 1 and 10 A.
An advantage of the Joule annealing technique is the much larger
heating rate compared to furnace annealing. In addition to potential
modifications of the nucleation and growth for nanocrystalline alloys,
this technique may provide a means to create otherwise inaccessible
metastable crystalline phases. Heating rates in the range 102–103 K/s have
been applied by this technique (Allia et al., 1993d). Performing Joule
annealing in a vacuum improves reproducibility by reducing temperature gradients from the ribbon surfaces. Mechanical properties, including
strain to fracture and hardness, are reported to have better performance by
Joule annealing than conventional annealing (Allia et al., 1993a, 1994; Moya
et al., 2001).
During the crystallization process, the resistivity of the sample measured
as a function of the time of applied current has two distinct features with
thermal origins (Mitrović et al., 2000). When a large enough current is
applied, the sample crystallizes generating heat from the exothermic crystallization reaction; this results in a peak in the resistivity due to the increased
temperature of the sample. After 10–20 s, the resistivity equilibrates as the
heat generation from the applied current and structural changes in the
sample are balanced with dissipation from the sample environment (radiation, convection, and conduction).
The temporal effect of current density on amorphous ribbons and
resulting phases formed in Fe73.5Si13.5Nb3B9Cu1 alloys is presented in
Fig. 4.11. Analogous to the time–temperature transformation diagram in
conventional annealing, a time–current density transformation diagram
shows the phase relations for crystallization. At low current densities and
short times, the ribbons consist of amorphous phase. At intermediate times
and current densities, the sample partially crystallizes into a-(Fe,Si) or a0 Fe3Si phases, indicated by þ and , respectively. At high current density
and long times, secondary crystalline phases are observed (indicated by
circles).
A drawback of this technique is the large temperature variations (30 K)
found as a function of position along the length of the ribbon (Allia et al.,
1993b). For the class of nanocomposite magnetic alloys, the optimal performance can vary with isothermal annealing temperature changes of 5 K, so
thermal control is critically important in these materials. Upscaling of this
technique to the toroid fabrication level is another factor that has not been
fully examined.
202
Matthew A. Willard and Maria Daniil
Current density (A/m2)
60 × 106
50
Fe2B/Fe3B
40
α-FeSi/α¢-Fe3Si
30
20
Amorphous
10 × 106
100
10
Time (s)
Figure 4.11 Time–current density transformation (TJT) diagram showing the crystallization transformation with varying exposure time to a given current density in
Fe73.5Si13.5Nb3B9Cu1 alloys (Allia et al., 1993a; Allia et al., 1993d; Baricco et al.,
1994; Gorrı́a et al., 1993; Murillo and González, 2000; Tiberto et al., 1996a). Dot
indicates amorphous phase; þ, a-(Fe,Si); , a0 -Fe3Si; and o, Fe2B/Fe3B.
2.2.3. Magnetic field annealing
When properly applied, induced anisotropies can be a transformative tool for
tuning hysteresis loop shapes. From early studies by Yoshizawa and Yamauchi,
the shape of the hysteresis loop was shown to be influenced greatly by annealing
samples in a magnetic field (Yoshizawa and Yamauchi, 1989). An applied
magnetic field during crystallization creates an induced uniaxial anisotropy
with easy axis along the applied field direction for (Fe,Si)-based alloys. The
magnitude of the induced anisotropy is in the order of 5–50 J/m3.
During the magnetic field annealing process, two typical orientations are
used to create an induced anisotropy (Ku) that dominates over other
anisotropies present in the material. Longitudinal field annealing creates a
square hysteresis loop in Fe–Si–Nb–B–Cu-type alloys, where switching is
dominated by 180 wall motion (Yoshizawa and Yamauchi, 1989). Transverse field annealing shears the hysteresis loop, providing a lower permeability that is directly related to Ku1. In this case, switching occurs largely by
rotation of the magnetization into the applied field direction. Alloy composition, annealing time and temperature, and magnetic field strength are all
factors that affect the anisotropy. Typically, the longitudinal field applied
during annealing is limited to 1 kA/m due to field/furnace geometry constraints. Transverse field annealing is performed in the 50–250 kA/m field
range. Examples of the differences in loops formed during the magnetic field
annealing process for Fe73.5Si13.5Nb3B9Cu1 alloys annealed at 813 K for
3600 s are shown in Fig. 4.12 (Herzer, 1996).
203
Nanocrystalline Soft Magnetic Alloys
Magnetic induction, B (T)
Fe73.5Si13.5B9Nb3Cu1
Z
1
R
F1
F2
0
−1
−10
0
10
Magnetic field, H (A/m)
Figure 4.12 DC hysteresis loops of nanocrystalline Fe73.5Si13.5Nb3B9Cu1 annealed at
540 C for 3600 s: (R) without applied magnetic field; (Z) with longitudinal applied
magnetic field; (F2) with transverse applied magnetic field; (F1) first crystallized
without magnetic field and then transverse field annealed at 350 C. Modified from
Herzer (1996).
In general, induced anisotropies shear the hysteresis loop in a way that
reduces the permeability and gives greater magnetic energy storage capacity
to the material. Assuming that the hysteresis is small and that the loop is
linear, the induced anisotropy (Kind) is related to the alloy’s saturation
magnetization (Ms) and anisotropy field (HK) through the equation:
Kind ¼ m0MsHK/2. A maximum permeability can be estimated through the
slope of the B–H hysteresis loop with the material saturating at the anisotropy field. By this consideration, the following equation can be used to
determine the permeability: mr ¼ m/m0 ¼ M2s /2Kind. Using this expression,
the permeability is 40,000, 600, and 75 for induced anisotropy values of
15, 1000, and 8000 J/m3, respectively (for m0Ms ¼ 1.23 T, a typical value for
(Fe,Si)-based nanocrystalline alloys).
Magnetic field annealing can be performed either during or after primary
crystallizations; however, the magnitude of Kind is greatly reduced when a twostep annealing process is used. Single-step annealing of a Fe73.5Si13.5B9Nb3Cu1
alloy at 530 C in a 192 kA/m transverse field gives an induced anisotropy of
30–50 J/m3 (Lovas et al., 1998). In contrast, an alloy of the same composition
annealed without a magnetic field at 530 C to create the nanocrystalline
microstructure and subsequently annealed in a 192 kA/m transverse field at
temperatures up to 450 C has an induced anisotropy limited to 7 J/m3. The
permeability and remanence ratio were controlled independently when a
Fe73.5Si15.5B7Nb3Cu1 alloy was annealed with a magnetic field for part of
the crystallization process immediately followed by a field free annealing period
(Waeckerle et al., 2000). A range of anisotropies induced using magnetic
204
Magnetic field-induced anisotropy (J/m3)
Matthew A. Willard and Maria Daniil
50
Fe73.5Si13.5B9Nb3Cu1
tann = 3600 s
Hann > 185 kA/m
40
30
20
813 K
10
803 K
843 K
0
500
550
600
650
700
750
800
850
Field-annealing temperature (K)
Figure 4.13 Magnetic field-induced anisotropy against magnetic field-annealing temperature for Fe73.5Si13.5Nb3B9Cu1 alloys annealed for 3600 s with applied magnetic
field exceeding 185 kA/m. Circles: Herzer (1994a); squares: Yoshizawa and Yamauchi
(1989) and Yoshizawa and Yamauchi (1990); triangle: Ferrara et al. (2000); downward
triangle: Lovas et al. (1998). Closed symbols: field crystallized (no preanneal); open
symbols: conventional anneal (no field, temperature specified) with subsequent field
annealing.
field annealing are shown in Fig. 4.13 for a Fe73.5Si13.5B9Nb3Cu1 alloy.
Samples were annealed at temperatures above primary crystallization for
3600 s with fields above 185 kA/m applied during annealing (closed symbols).
We follow the terminology of Ohodnicki et al. and call these field-crystallized
samples (Ohodnicki et al., 2008c). The open symbols indicate samples that
were crystallized without magnetic field (as indicated), followed by magnetic
field annealing after crystallization to provide induced anisotropy. The effect of
magnetic field annealing on induced anisotropy for samples without prior
crystallization was found to be somewhat larger for most samples.
Considerably larger anisotropies are induced by magnetic field annealing
in the (Fe,Co)-based alloys. Figure 4.14 demonstrates this effect on magnetic field-annealed and magnetic field-crystallized alloys. The magnetic
field-annealed samples were found to have a maximum in the induced
anisotropy for 50:50 ratio of Fe:Co, as might be expected for a pairordering model (see Chikazumi and Graham, 1997). On the other hand, a
sharp increase in induced anisotropy is observed at Co-rich compositions in
the field-crystallized (Fe,Co)78.8Nb2.6B9Si9Cu0.6 and (Fe,Co)88Zr7B4Cu1
alloys (Ohodnicki et al., 2008d; Yoshizawa et al., 2004). This has been
attributed to a strong dependence of the amorphous phase Curie temperature on the composition of the alloy (Ohodnicki et al., 2008d).
205
Nanocrystalline Soft Magnetic Alloys
Magnetic field-induced anisotropy (J/m3)
(a)
Field annealed
FA (Co,Fe)89Zr7B4/(Co,Fe)88Zr7B4Cu1
FA (Co,Fe)90Zr10
2500
2000
1500
1000
500
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.8
0.9
1.0
Co fraction
(b)
Magnetic field-induced anisotropy (J/m3)
2500
Field crystallized
FC (Co,Fe)89Zr7B4/(Co,Fe)88Zr7B4Cu1
FC (Fe,Co)81Nb7B12
FC (Fe,Co)90Zr7B3
FC (Fe,Co)78.8Nb2.6Si9B9Cu0.6
2000
1500
1000
500
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Co fraction
Figure 4.14 Induced magnetic anisotropy for (a) magnetic field-annealed samples
of (Fe,Co)89Zr7B4, (Fe,Co)88Zr7B4Cu1, and (Fe,Co)90Zr10 alloys (Fukunaga and
Narita, 1982; Ohodnicki et al., 2008d) and (b) magnetic field-crystallized samples
of (Fe,Co)89Zr7B4, (Fe,Co)90Zr7B3, (Fe,Co)88Zr7B4Cu1, (Fe,Co)81Nb7B12, and
(Fe, Co)78.8Nb2.6B9Si9Cu0.6 alloys (Ohodnicki et al., 2008d; Škorvánek et al., 2006;
Suzuki et al., 2006; Yoshizawa et al., 2003).
206
Matthew A. Willard and Maria Daniil
Annealing-induced anisotropies are controlled by application of a static
magnetic field during annealing, resulting in a coherent uniaxial anisotropy.
However, magnetic-induced anisotropies are not exclusively found in materials which have been magnetic field processed. Even in samples that have
been annealed without applied magnetic fields, induced anisotropies
have been identified in samples where the annealing temperature exceeds
the Curie temperature of the amorphous matrix. The effect results from the
local magnetic fields of the ferromagnetic grains as they form in the paramagnetic matrix, creating localized regions of induced anisotropy (not coherent
across the sample as in magnetic field annealing). This case is exemplified
in Fe84Nb7B9 alloys, where the coercivity was lowered using a rotating
applied field to remove annealing induced uniaxial magnetic anisotropies
(Ito and Suzuki, 2005). In this case, the induced anisotropy is randomly
distributed, but on a larger scale than the magnetic exchange length.
2.2.4. Stress annealing
Stress annealing is a technique for creating induced anisotropy in nanocrystalline ribbons by applying a stress to the material during stress relaxation, crystallization, or post-crystallization anneals. The anisotropy
induced in this way is proportional to the applied tensile stress and can
be used to create an easy axis that is parallel or perpendicular to the
applied stress direction (depending on the magnetoelastic effects of the
alloy which are composition dependent). The effects are not directly
related to the magnetostriction of the alloy, rather the local atomic
environment contributions to magnetostriction (anelastic polarization of
amorphous matrix) have been suggested to give rise to the induced
anisotropy due to stress annealing. A normalized anisotropy parameter
(k) can be used to describe the stress-induced anisotropy (Ks) in a similar
form to anisotropy from magnetostrictive sources, namely, Ks ¼ 2ks/3
(Herzer, 1994b). Comparison of the magnetostrictive coefficient and
normalized anisotropy parameter for a series of Fe96zSixBzxNb3Cu1
alloys annealed under different conditions is presented in Fig. 4.15. The
volume fraction transformed seems to be the correlating factor between k
and ls, leading to the conclusion that a magnetoelastic anisotropy is
responsible for the induced anisotropy, and it is mediated by
crystallization-induced stresses in the sample and an elastic polarization
of the amorphous matrix (Herzer, 1994b).
This anisotropy induced in samples by annealing in a stress field (sometimes referred to as creep-induced anisotropy) tends to have orders of
magnitude larger values than those samples annealed in a magnetic field.
A linear dependence of the stress-induced anisotropy on the applied stress
during crystallization has been observed in Fe73.5Si13.5B9Nb3Cu1 alloys
using standard annealing temperatures and times (see Fig. 4.16). The highest
values of induced anisotropy, near 8 kJ/m3, can reduce the permeability to a
207
Nanocrystalline Soft Magnetic Alloys
z = 18.5 ls
z = 20.5 ls
z = 22.5 ls
z = 23.5 ls
z = 18.5 k
z = 20.5 k
z = 22.5 k
z = 23.5 k
10
k and ls (ppm)
ls
5
k = -2/3 K/s
0
-5
0
2
4
6
8
10
12
14
16
18
20
Si content (at%)
Figure 4.15 Comparison of a creep-induced anisotropy parameter and magnetostrictive coefficient with variation of Si content in Fe96zSixBzxNb3Cu1 alloys. From
Herzer (1994b).
75
7000
6000
100
5000
150
4000
3000
2000
300
Herzer 813 K
Hofmann 813 K
Fukunaga 803 K
1000
0
0
200
400
600
800
600
1200
Approximate relative permeability, m r
Stress induced anisotropy (J/m3)
8000
1000
Stress (MPa)
Figure 4.16 Variation in stress-induced anisotropy with applied stress for Fe73.5Si13.5Nb3B9Cu1 alloys annealed for 3600 s (at 803 (Fukunaga et al., 2000) or 813 K (Herzer,
1994b; Hofmann and Kronm€
uller, 1996)).
great extent (Hofmann and Kronmüller, 1996). Such materials have advantages over the commonly used gapped ferrite cores as they produce a
tunable permeability (by stress applied during crystallization) over a wide
frequency range, with larger saturation magnetization and without the
detrimental leakage flux issues.
208
Matthew A. Willard and Maria Daniil
Stress-induced anisotropy(J/m3)
8000
7000
Fe73.5Si13.5B9Nb3Cu1
tann = 3600 s
845 MPa
718
630
600
6000
5000
4000
520
527
450
3000
213
353
2000
272
236
145
139
1000
151
90
82
0
760
780
800
820
840
860
880
900
920
Stress-induced anisotropy (J/m3)
Annealing temperature (K)
813 K/450 MPa
1000
808 K/139 MPa
100
788 K
139 MPa
778 K
139 MPa
103
768 K
139 MPa
104
105
Annealing time (s)
Figure 4.17 (a) Stress-induced anisotropy variation with annealing temperature for
uller
Fe73.5Si13.5Nb3B9Cu1 alloys annealed for 3600 s (circles: Hofmann and Kronm€
(1996); squares: Alves et al. (2000); triangle: Lachowicz et al. (1997); downward
triangle: Nielsen et al. (1994)) and with applied stress (MPa) marked for reference.
(b) Effect of annealing time on stress-induced anisotropy for Fe73.5Si13.5Nb3B9Cu1
alloys annealed at 768 (closed symbols), 778 (open symbols), 788 (right-filled symbols),
808 (left-filled symbols), and 813 K (diamonds) and with applied stress 82 (circles), 139
(squares), 145 (triangles), and 450 MPa (diamonds) (Alves et al., 2000; Hofmann and
Kronm€
uller, 1996).
When crystallization is not allowed to fully progress, the induced anisotropy has a commensurately lower value. In Fig. 4.17, the stress-induced
anisotropy variation with annealing time and temperature is shown for
Fe73.5Si13.5B9Nb3Cu1 alloys. When the annealing temperature is varied
for samples annealed for 3600 s, the induced anisotropy is found to increase
with applied stress at all temperatures, but the stress only gives its fullest
Nanocrystalline Soft Magnetic Alloys
209
effect when the temperature allows a large volume fraction of crystallites to
form (near the primary crystallization temperature, see Fig. 4.17a). This
effect can be more clearly seen in Fig. 4.17b, where the dependence of
stress-induced anisotropy on annealing time is shown. With reference to
Fig. 4.10, the stress-induced anisotropy begins to saturate at annealing times
that are consistent with the slowing of grain coarsening (indicating that the
microstructure is fully developed).
Typical domain structures for as-quenched ribbons consist of a “stress
pattern,” resulting from the quenched-in stresses from the rapid solidification process (Schäfer, 2000). Field-annealed specimens show wide stripe
domains with magnetization perpendicular to the applied stress direction
(and in the plane of the ribbon). A stripe domain width repeated with period
of 250 mm was observed by Kraus et al. for a sample with composition
Fe73.5Si13.5B9Nb3Cu1 and annealed at 540 C for 1 h and under a stress of
150 MPa (Kraus et al., 1992). Similar transverse domain formation has been
observed by others with stripe widths ranging from 25 to 150 mm, depending on the annealing conditions (Alves and Barrué, 2003; Fukunaga et al.,
2000; Hofmann and Kronmüller, 1996). Annealing at temperatures as low
as 330 C for 4 h is enough to destroy the stress-induced anisotropy.
Stress-induced anisotropy in Fe–Si-based alloys has been interpreted to
originate from magnetoelastic effects, atomic short-range pair ordering, and
anelastic polarization of the residual amorphous phase. While the interpretations vary, a few facts about the structural aspects of stress-annealed
samples have been reported in common. Stress-annealed samples do not
exhibit crystallographic texture or grain elongation (Hofmann and
Kronmüller, 1996; Kraus et al., 1992). The stress-induced anisotropy is
destroyed at temperatures where only short-range diffusion or relaxation
effects are possible (Herzer, 1994b; Hofmann and Kronmüller, 1996; Kraus
et al., 1992), and a stress-induced uniaxial anisotropy can be achieved in
previously crystallized ribbons, although the kinetics for creating the
induced anisotropy is slower (Herzer, 1994b; Hofmann and Kronmüller,
1996; Kraus et al., 1992).
Based on these observations, Kraus suggested the polarization of interatomic bonds due to anelastic strains formed in the intergranular amorphous
phase during annealing resulted in the stress-induced anisotropy (Kraus
et al., 1992). Similar reasoning was used to describe the induced anisotropy
from sputtered SiO2 coatings on Fe–Si-based nanocrystalline alloy ribbons
(Delreal et al., 1994). Herzer found a strong correlation between both the
magnetostriction of the nanocrystallites and the induced anisotropy as a
function of Si content in alloys composition Fe96zSixNb3BzxCu1
(Herzer, 1994b). From this observation, the induced anisotropy was attributed to the magnetoelastic effect from the crystalline phase caused by an
anelastic polarization of bonding in the amorphous matrix, which occurred
during stress annealing. Hofmann and Kronmuller suggested use of the Neel
210
Matthew A. Willard and Maria Daniil
pair order model to describe the effect (although they do not rule out either
of the preceding opinions) (Hofmann and Kronmüller, 1996).
The recent work of Ohnuma et al. has shown the anisotropy in an X-ray
diffracted beam from the (6 2 0) planes of the Fe3Si phase in stress-annealed
Fe73.5Si15.5Nb3B7Cu1 alloys, when the sample is rotated parallel and perpendicular to the applied stress direction (Ohnuma et al., 2003a, 2005). As the
applied stress during annealing was increased from 10 to 621 MPa, so too were
the deviations between the d-spacings in the parallel and perpendicular orientations (see Fig. 4.18). This study provides physical evidence for plastic flow of
the residual amorphous phase during the strain-annealing process, resulting in
an induced anisotropy with magnetoelastic origin (Ohnuma et al., 2005).
(a)
1.0
10 MPa
B (T)
0.5
103 MPa
0.0
334 MPa
-0.5
621 MPa
-1.0
-4000 -2000
0
2000
H (A/m)
4000
46.5
47.0
2q (degree)
47.5
(b)
Intensity (arb. units)
621 MPa
334 MPa
103 MPa
10 MPa
45.5
46.0
Figure 4.18 (a) Magnetization curves and (b) XRD profiles of Fe73.5Si15.5Nb3B7Cu1
ribbons annealed under different tensile stresses. All curves in sad were measured along
the RD (parallel to the tensile stress). In (b), the circles indicate a diffraction vector
parallel to the RD, while the lines mark a vector perpendicular to the RD. Reprinted with
permission from M. Ohnuma, et al. Applied Physics Letters 86, 152513, (2005). Copyright
2005, American Institute of Physics.
Nanocrystalline Soft Magnetic Alloys
211
Stress annealing has also been reported in conjunction with Joule
annealing. An induced anisotropy as high as 1000 J/m3 was reported for
an alloy with composition Fe73.5Si13.5Ta3B9Cu1 (González et al., 1994).
The maximum induced anisotropy was observed for short annealing times
(less than 30 s) at a large enough current density (30–35 A/mm2) to promote primary crystallization (Miguel et al., 2000). However, the hysteresis
loops do not exhibit the same constant permeability over a wide field range
as the conventionally stress-annealed samples. This may be an indication of a
switching mechanism different than the coherent rotation typically
observed in conventionally stress-annealed samples.
Alves et al. have used flash annealing under an applied stress to achieve
induced anisotropy in an alloy with composition Fe74.3Si15.5Nb2.7B6.5Cu1
(Alves and Barrué, 2003; Alves et al., 2000). Using the activation energy of
4.5 eV/atom, the temperature necessary to achieve the optimal microstructure was estimated in a short annealing time, in this case 660 C and 15 s.
The resulting anisotropy of 2340 J/m3 was obtained with an applied stress of
270 MPa (Alves and Barrué, 2003). A transverse stripe domain structure was
observed with domain widths of 150 mm, resulting in permeabilities as
low as 300.
Even though stress annealing has clear benefits for applications where the
permeability must be low, there are some difficulties to overcome for
commercial application. The common industrial technique used for stress
annealing of amorphous alloys involves applying a tensile stress to the alloy
as the ribbon is passed through a furnace. Using this process for nanocrystalline alloys results in alloy embrittlement as the amorphous precursor crystallizes, limiting this technique’s general use. Yanai et al. have used a
continuous stress-annealing furnace with tensile stresses limited to
150 MPa to demonstrate induced anisotropy in a rapid, consistent manner
over lengths of ribbon up to 50 cm (Yanai et al., 2005). While ribbon
brittleness was not discussed, cores with 3 mm ID were produced from the
straight, annealed ribbons.
Recent efforts to address this problem have shown some success by
wrapping a pair of ribbons with similar compositions into a toroidal shape
prior to devitrification (Günther, 2005). The ribbon pair is selected to have
crystallization temperatures separated by 20 K so that the density reduction
that accompanies crystallization (typically 1%) can be used to create the
necessary tensile stress on the sample. A resulting permeability of 8000 was
achieved by this technique. A drawback of this technique is the necessity of
one ribbon being magnetostrictive to get the induced stress effect, resulting in
higher losses than a magnetostriction-free alloy. Fukanaga et al. used a technique to constrain the ribbon samples at different toroid radii (between 1 and
3.2 cm ID) to control the stress within the sample and ultimately optimize the
stress state of the core simply by geometry (Fukunaga et al., 2002a). This
resulted in constant, relative permeabilities between 260 and 300 for frequencies up to 1 MHz. While this technique showed lower losses compared to a
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Matthew A. Willard and Maria Daniil
gapped ferrite core, the flexibility in controlling sample inductance is limited
by the fixed core geometry (Fukunaga et al., 2002a; Yanai et al., 2005).
2.3. Core fabrication
Most cores consist of ribbon windings around a mandrel to create a laminated
structure referred to as a tape-wound core. Due to ribbon embrittlement after
annealing, amorphous ribbons are typically wrapped prior to primary crystallization. When long, continuous ribbons are wound in this manner, the
resulting core has low losses and high permeability into the hundreds of of
kHz frequency range (Yoshizawa et al., 1988a). This fabrication technique
has limitations in the geometry and size of the resulting core.
Other methods have been investigated for core fabrication to allow
more flexibility in the geometry of the core shape and size. Powder cores
have been produced from melt spun ribbon materials with subsequent
milling, annealing, and consolidation. Various milling techniques have
been employed to achieve both ribbon flakes (e.g., 1–3 mm length) and
powders (e.g., 1–1000 mm). Two different types of annealing procedures
have been reported: crystallization annealing above primary crystallization
and stress relaxation annealing (usually at lower temperatures). Sometimes
both annealing steps are done simultaneously after core fabrication. Hot and
cold pressing have been used, typically with a binder to ensure isolation of
the particles and a high degree of densification.
Some general characteristics have been observed for nanocrystalline soft
magnetic alloy powder cores, which are described in the following paragraphs. First, regardless of the milling method, the coercivity of the cores tends
to increase as smaller sized particles are used to make the core (Kim et al., 2003;
Leger et al., 1999). As an example, cores made from 56- to 90-mm-sized
particles were found to have more than 3.5 times the coercivity of cores
made from 1- to 1.4-mm flake cores (Nuetzel et al., 1999). This effect is
likely due the larger amounts of deformation imposed on the ribbons to
create the smaller particles. Stress relaxation by annealing has been performed; however, the coercivity is never recovered to a level equal to
wound ribbon cores (Heczko and Ruuskanen, 1993; Müller et al., 1999;
Nuetzel et al., 1999).
Next, cold-pressed powder cores tend to have lower permeability than
hot-pressed powder cores; however, their switching frequency limit tends
to be higher for the cold-pressed than for hot-pressed cores. The reduced
value of permeability for cold-pressed cores is due to the high internal
demagnetization fields from the smaller isolated particles that make up the
core. Since the particles are well isolated, the eddy current effects remain
small until frequencies near 1 MHz (Kim et al., 2003; Leger et al., 1999).
Hot pressing improves the magnetic performance at lower frequencies by
providing higher density compacts and higher permeability; however, the
Nanocrystalline Soft Magnetic Alloys
213
particles do not remain isolated resulting in higher eddy current losses at
higher frequencies (Iqbal et al., 2002; Nuetzel et al., 1999). Iqbal et al.
report a high packing density and good uniformity for a puck milled powder
core annealed at 540 C and possessing an initial permeability of 1100 but
with a relaxation frequency of 10 kHz (Iqbal et al., 2002).
Finally, coatings have been used to aid in separation of individual
particles prior to consolidation. Jang et al. showed a factor of 2 improvement
in core loss at 10 kHz by applying a Zn-phosphate coating to powders with
size less than 45 mm over powders without the coating (Jang et al., 2006;
Kim et al., 2003).
While the hysteretic and core losses tend to be larger for powder cores,
the low, constant permeability is beneficial to some applications (e.g.,
reactors and choke coils). With the proper binder, powder cores may be
suitable for machining, allowing better flexibility in the fabrication of
complex core geometries.
2.4. Other processing methods
2.4.1. Thin film processing
Various nanocrystalline soft magnetic thin film materials have been produced by either devitrification of amorphous films or direct formation of
nanostructures via heated substrates. Early work in this area was accomplished by inhibiting grain growth in Fe–M–C alloys (M ¼ Zr, Hf, Ta, etc.)
by formation of an MC phase at the triple points during crystallization of
sputtered amorphous films (Hasegawa et al., 1993). Due to the reduced size
of the carbide phase (<3 nm diameter), the material maintained good
intergranular coupling and exhibited strong soft magnetic performance
with saturation induction of 1.6 T and 1 MHz permeability of 6000.
Thin film materials were found to exhibit coercivity proportional to the
grain size squared (Hc D2) for Fe–Si–B–M–Cu alloys (where M ¼ Nb, Ta,
W, Mo, Zr, V) (Yamauchi and Yoshizawa, 1995). This result differs from the
D6 dependence for coercivity observed in ribbon materials and is due to the
two-dimensional geometry of the thin film sample (compared to the threedimensional geometry of the ribbon). A similar correspondence between
grain size and coercivity was observed recently in nanocrystalline Fe66Ni11Co11Zr7B4Cu1 alloys with low ferromagnetic resonance line widths produced by a one-step physical laser deposition onto a heated substrate (Yoon
et al., 2008). The origin of the reduction in grain size dependence with
nanostructure dimensionality is discussed in more detail in Section 6.3.
2.4.2. Mechanical alloying and powder processing
High-energy ball milling can be used to mechanically alloy powders of
nanocrystalline soft magnetic alloys, where the repeated process of welding
and fracturing of the alloy imparts enough energy for significant grain
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Matthew A. Willard and Maria Daniil
refinement or vitrification. This is different from the milling of rapidly
solidified ribbons, where the starting materials are already amorphous.
The breakingup of ribbons by ball milling has been discussed in Section 2.3.
Several studies of Fe73.5Si13.5B9Nb3Cu1 alloys have investigated mechanical milling effects on magnetic properties. When elemental powders of the
desired composition are mechanically alloyed, the resulting powders tend to
have high coercivity which increases linearly with milling time up
to 3.6 106 s, to a maximum value between 7 and 25 kA/m (Chiriac
et al., 1999b; Kováč et al., 2002; Raja et al., 2000). Milling of amorphous
or partially crystalline ribbons of the same composition tends to have an
increased coercivity for milling up to 2.5 106 s and decreasing coercivity
for longer milling times (Fechová et al., 2004). The peak value of coercivity
was around 10 kA/m and was attributed to a change in the magnetization
switching mechanism to coherent rotation as the critical single domain
particle size was produced. Further milling was consistent with the formation
of superparamagnetic particles and a commensurate reduction in coercivity.
Mechanically milled nanocrystalline Fe66Ni11Co11Zr7B4Cu1 alloys
were prepared from melt spun ribbons with subsequent anneal for crystallization and then screen printed on Mylar to produce thick film cores
(Baraskar et al., 2008). The sample milled for 10 h was found to have a
saturation magnetization of 1.3 T and a coercivity of about 5.8 kA/m with
an average particle size of about 5 mm. The screen-printed samples showed
an ferromagnetic resonance (FMR) linewidth of about 80 kA/m.
Powder cores provide a sheared hysteresis loop that can be advantageous
for applications where low, constant permeability is required over a large
field range. Near net-shaped cores have been examined for DC–DC converter applications at frequencies around 100 kHz (Vincent and Sangha,
1996). Oxide-coated coarse flakes (0.5–2 mm diameter) were hot-pressed at
550 C to produce the desired permeability (above 1000). Insulation layers
were produced by a Mn-doped phosphoric acid solution, resulting in
improved high-frequency performance over uninsulated pressed cores. In
another study, samples of Fe73.5Si13.5B9Nb3Cu1 were shock-compacted to
form dense cores from powdered amorphous ribbons (Ruuskanen et al.,
1998). Annealing was required to provide the desired nanocrystalline
microstructure and reduce stress-induced anisotropies. The preparation of
cores made from powder inert-gas condensation, high-energy ball milled,
and cryogenic melted powders has been recently reviewed by Mazaleyrat
and Varga (2000).
2.4.3. Surface treatments and laser processing
As-spun ribbons have large-scale undulations, in the order of tens of
microns, on their wheel-side surfaces resulting from the rapid quenching
of the alloy. The free side of the as-spun ribbons tends to have a smoother
surface than the wheel side with much larger scale fluctuations observable
Nanocrystalline Soft Magnetic Alloys
215
without microscopes. This surface morphology has been observed by scanning tunneling microscopy (STM) and atomic force microscopy (AFM) to
be slightly changed by primary crystallization of Fe73.5Si13.5B9Nb3Cu1
ribbon samples (Gorrı́a et al., 2003; Nogues et al., 1994). However, AFM
and STM studies have shown that crystallization of Fe86Zr7B6Cu1 and
Fe44Co44Zr7B4Cu1 alloys results in an increased surface roughness, consisting of elliptically shaped bumps a few hundred nanometers in diameter
(Hawley et al., 1999; Nogues et al., 1994). This observation has been
attributed to the presence of stress effects from the crystallization process
which are more limited in the (Fe,Si)-based alloys due to the redistribution
of Si or the influence of higher diffusivity on the surface of the ribbon
during crystallization.
Kollar et al. have used a XeCl-excimer laser to melt pits into the ribbon
surface a few microns deep (Kollár et al., 1999). The pits were found to
increase the local surface coercivity by 300% compared to the regions
without laser treatment. The sample coercivity increased as the pits were
spaced more closely. As observed by Kerr microscopy, the transverse
component of the magnetization switched at the laser surface treated area
(although longitudinal components of magnetization did not see to be
affected) (Zeleňáková et al., 2001). Small core loss benefits were reported
for close line spacing of laser-treated samples at frequencies above 20 kHz
(Ramin and Riehemann, 1999a).
Laser processing has been used to crystallize amorphous ribbons in recent
studies. An advantage of this technique is the laser’s ability to achieve rapid
heating and cooling rates and uniformly crystallize the sample in a short
period of time. Lanotte and Iannotti used a CO2 laser irradiation technique
to crystallize amorphous Fe73.5Si13.5B9Nb3Cu1 ribbon samples by translating the laser beam over the sample at a rate of 3 cm/s and under incident
laser power between 20 and 50 W (Lanotte and Iannotti, 1995). While this
technique showed the capability of laser annealing to establish the nanocrystalline microstructure, the grain sizes were not as fine as those produced
by conventional furnace annealing. Due to the larger grain sizes, the resulting permeability was lower for the laser-processed ribbons than for the
conventionally annealed samples.
3. Alloy Design Considerations
A wide variety of nanocrystalline soft magnetic alloy compositions
have been explored, necessitating a short taxonomy to distinguish a few
important varieties. As a matter of classification, the alloys can be arranged
into groups that are distinguished by the phases formed during primary
crystallization, their compositions, and ultimately their properties. In
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Matthew A. Willard and Maria Daniil
Table 4.2 Elemental makeup of typical nanocomposite soft magnetic alloys with four
major components (grouped parenthetically): magnetic transition metals (MTM), early
transition metal (ETM), metalloid/post-transition metals (PTM), and late transition
metal (LTM)
Fe Cr
Co Mn
Ni
1 0
1
Ti V
B C
Cu
@ Zr Nb Mo A @ Al Si P A
Au 01
6691 Hf Ta W 28 Ga Ge
231
!
0
Atomic percentages of common ranges for each major component are shown in subscript. Specific alloy
designations are shown in Table 4.1.
general terms, a nanocrystalline soft magnetic alloy consists of elements from
at least two, but typically three or four of the following groups: magnetic
transition metal (MTM), ETM, metalloid or post-transition metals (PTM),
and LTM (Table 4.2).
Ferromagnetic transition metals are obviously a necessary component
of these alloys, with larger quantity increasing the magnetization of the
alloy. Cr and Mn are part of this designated group since they typically
combine substitutionally with the ferromagnetic elements in a nanocomposite alloy (although they are clearly not ferromagnetic elements) (Sobczak
et al., 2001; Tamoria et al., 2001). A less obvious, but equally essential,
component is the ETM (esp. Nb, Zr, Hf, Ta, Mo), which prevents
excessive grain growth during annealing due to its ability to decrease the
diffusivity of the MTM. Ti and V are less effective in preventing grain
growth in these materials. The ETM elements have been found to inhibit
the formation of borides and impede grain coarsening. While not all of
these alloys possess metalloids (e.g., B, Si, Ge, etc.) or post-transition metals
(e.g., Al, Ga, etc.), most alloys include at least one of these elements to aid in
glass formation and provide thermal stability for the amorphous phase.
Finally, in some alloys, the LTM elements (e.g., Cu, Au) have been found
to aid in the nucleation of the primary crystallites, but not all alloys benefit
from this alloying addition.
Specific classes of nanocrystalline soft magnetic alloys have been identified largely by the primary crystalline phase. The first class of alloys, with
trade names Finemet or Vitroperm, has either the solid solution a-(Fe,Si) or
atomically ordered Fe3Si phase as the primary crystallite and typically has a
composition of Fe–Si–Nb–B–Cu (Herzer, 1996; Yoshizawa et al., 1988a).
The Fe content in these alloys typically falls in the range of 67–79 at% with
at least 5 at% Si. Both Nb and Cu are essential for the microstructure
development in these alloys. These alloys are presently the only nanocrystalline soft magnetic alloys available commercially (via Hitachi Metals (Japan),
Vacuumschmelze (Germany), Imphy (France), etc.). The second class of
alloys, with trade name Nanoperm (via Alps Electric Co. (Japan)), is made
Nanocrystalline Soft Magnetic Alloys
217
up of a-Fe primary crystallites and typical composition Fe–Zr–B–Cu
(Makino et al., 1997; Suzuki et al., 1991a). These alloys typically have
80–90 at% Fe which provides a larger saturation magnetization compared
to the (Fe,Si)-based alloys. The third class, HITPERM alloys, has a0 -(Fe,
Co) or a-(Fe,Co) as the primary crystalline phase and typical compositions
of Fe–Co–Zr–B–(Cu) (Willard et al., 1998). Other alloys that do not fit
these categories include Co–(Fe)–Zr–B–(Cu) and Ni–(Fe,Co)–Zr–B–(Cu)
alloys where either the e-Co or g-(Fe,Co,Ni) phases form during primary
crystallization (Pascual et al., 1999; Willard et al., 2001a; Willard et al.,
2002a). The alloy composition in each class requires amorphous phase
formation using rapid quenching and a fine-grained, equiaxed microstructure within a residual amorphous matrix phase after an annealing process.
The following sections discuss the processing, structure, and property
considerations, which put limits on the potential compositions of nanocrystalline materials with exceptional magnetic performance. These critical
factors for good alloy design include (1) glass-forming ability of an amorphous precursor; (2) primary crystallization of a desirable magnetic phase;
(3) alloying additions to form and/or maintain an optimal microstructure;
(4) optimization of intrinsic magnetic properties; and (5) control of the
magnetic domain structure.
3.1. Glass forming and primary crystallization
The desired microstructure, with limited grain size and large nucleation
density, has been most easily achieved by first forming an alloy consisting of
a single, amorphous phase followed by an isothermal annealing step for
crystallization (as described in Section 2.2). The amorphous precursor to
the nanocrystalline alloy puts limitations on the amount of MTM in the
alloy due to the necessary introduction of alloying elements used to stabilize
the liquid. As the liquid is most stable for alloy compositions at the eutectic
point (i.e., liquid in equilibrium at the lowest temperature), the addition of
alloying elements having deep eutectics with MTMs is most desirable. The
deep eutectics ensure that the maximum amount of magnetic transition metal
can be incorporated into the alloy. In Fe–Si–Nb–B–Cu alloys, a wide range
of good glass-forming compositions are available due to the large amounts of
Si, Nb, and B, which have deep eutectics with Fe. In Fe–M–B and (Fe,Co)–
M–B alloys (where M ¼ Zr, Nb, Hf), the glass-forming region is smaller and
the best performance (with highest magnetization) is near the Fe/Co-rich
compositions. In both cases, increasing the glass-forming elements (e.g., B,
M, and/or Si) aids in the formation of the amorphous precursor phase—an
essential starting point for optimal microstructure development. However,
consideration of Curie temperature of the residual amorphous phase and the
saturation magnetization of the alloy requires as much MTM as possible,
requiring sensitivity to all issues in the alloy design process.
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Matthew A. Willard and Maria Daniil
Cr
V
Ti/Mo/W
Nb/Ta
Zr/Hf
5
ETM content (at%)
Amorphous
4
3
Crystalline (BCC)
2
1
Fe89 – x Mx Zr4B6Cu1
0
1.80
1.85
1.90
1.95
2.00
2.05
2.10
2.15
2.20
ETM atomic radius (Å)
Figure 4.19 Glass-forming limits for as-spun Fe89xZr4MxB6Cu1 alloys with varying
early transition metal radius (Suzuki et al., 1991c). Dots indicate amorphous phase and
open circles indicate BCC phase.
Most nanocrystalline soft magnetic alloys have boron as an alloying element. The reasons for this include its stabilizing effect on the amorphous phase
(and increase in Tx1); its near zero solubility in the nanocrystallites of a-Fe, a0 (Fe,Co), and a-(Fe,Si); and its strengthening of the intergranular coupling after
crystallization (via the increased Curie temperature of the residual amorphous
phase (Suzuki et al., 1996)). The addition of small amounts of Cu to Fe–Si–
Nb–B alloys has been shown to increase the number of nucleation sites during
primary crystallization (Noh et al., 1990). After annealing, Cu-rich precipitates
have been observed due to coarsening of these elements which are not soluble
in the MTM-rich matrix (Hono et al., 1992; Zhang et al., 1996b).
In Fe89xZr4B6Cu1Mx alloys, the ETM type and amount are very important for glass formability. As illustrated in Fig. 4.19, ETMs with large atomic
radii tend to have greater glass formability and larger content of these elements
aids in glass formation (Suzuki et al., 1991c). The use of Hf and Zr is most
common in these alloys due to their easy of vitrification with minimal B
content; however, the glass-forming ability can be improved with other
ETMs when concurrent substitutions with B are made (Suzuki et al., 1993).
3.2. Microstructural and microstructure evolution
considerations
The unusual microstructure, consisting of nanocrystalline grains surrounded
by an amorphous phase, facilitates the low core losses found in these
alloys. Control of the microstructure necessitates an understanding of
Nanocrystalline Soft Magnetic Alloys
219
compositional effects on the resulting microstructure and the processing
that allows the best grain refinement. Achievement of the desired microstructure necessitates a large nucleation density at the early stages of crystallization
combined with slow crystallite growth rate to maintain the fine-grain size.
Conventional amorphous alloys relied on metalloids to aid in glass formation while maintaining a large atomic fraction of MTMs. However,
the magnetic properties are found to degrade rapidly with prolonged
exposure at 300 C due to the dendritic a-Fe formation once nucleation
had occurred (Naohara, 1996a). Crystallization occurs more quickly in
Fe–Si–B alloys at higher temperatures, with smallest achievable grains
sizes limited to 40 nm (Tong et al., 1992). In nanocrystalline soft magnetic
alloys, the use of ETM alloying elements has been found to both aid in glass
formability of the amorphous precursor alloy (by raising Tx1) and retard grain
growth during the isothermal annealing step (Naohara, 1996b; Yoshizawa
and Yamauchi, 1990). Furthermore, the addition of an element without solid
solubility in Fe (e.g., Cu or Au) has been found to increase the nucleation
density (Kataoka et al., 1989; Yoshizawa and Yamauchi, 1990). The best
refinement of the microstructure by crystallization of an amorphous precursor
via annealing has been found to correlate with the smallest value of the free
energy barrier to nucleation (Shi et al., 1995).
A widely accepted model for the crystallization of (Fe,Si)–Nb–B–Cu
alloys is shown in Fig. 4.9. In 1990, Yoshizawa and Yamauchi discussed the
basis of this model in the most general terms, being largely refined with
specific details by Ayers et al. and Hono et al. (Ayers et al., 1994; Hono
et al., 1992; Yoshizawa and Yamauchi, 1990). The four-stage microstructure evolution process begins with the rapidly quenched alloy consisting of a
compositionally homogeneous amorphous phase (Ayers et al., 1997, 1998;
Hono et al., 1999). After the alloy has been rapidly solidified in the first stage
of microstructure evolution, the resulting amorphous alloy is isothermally
annealed. The development of a uniform nanocrystalline microstructure
throughout the full volume of the material is only possible if crystallization is
avoided during the rapid solidification process.
Due to the significant separation of primary and secondary crystallization
temperatures for Fe96zSixBzxNb3Cu1 alloys (with 18.5 < z < 23.5 and
15 < x < 16.5), a wide range of annealing temperatures will result in the
desired nanocrystalline microstructure. Typical annealing conditions consist
of isothermal temperatures (spanning the range from crystallization onset
to 100 C above onset) and times near 3600 s. The second stage is identified by the formation of fine-grained Cu-rich regions within the amorphous
matrix phase. The positive heats of mixing of Cu with Fe and Nb and
near zero value for Cu with B are thought to be largely responsible for
the Cu-clustering effect. This stage has been observed during short annealing
experiments by 3D atom probe field ion microscopy (APFIM) (Hono
et al., 1991, 1993) and extended X-ray absorption fine structure (EXAFS)
220
Matthew A. Willard and Maria Daniil
(Ayers et al., 1993, 1994; Kim et al., 1993). It is expected to also occur in the
early part (first hundreds of seconds) of the conventional annealing process,
although Cu clustering has been observed even below the primary crystallization temperature (Kim et al., 1993). These Cu clusters are limited in size
during the second stage to less than a few atomic planes in size making them
difficult to observe by electron microscopy (Ayers et al., 1993). The Cu
clusters have atomic coordination consistent with the FCC phase as determined by EXAFS (Ayers et al., 1993; Kim et al., 1993). A 3D APFIM study
showed the Cu-cluster density in the alloy was about 1024/m3, a value high
enough to be consistent with the number density of nanocrystalline grains in
the final microstructure and consistent with values from the electron microscopy studies (Hono et al., 1999; Tonejc et al., 1999a). When the Cu content
of the alloy was less than 1 at%, the resulting microstructure suffered from
inhomogeneous grain size with resulting deterioration of magnetic properties
(Yoshizawa and Yamauchi, 1990).
Heterogeneous nucleation of a-(Fe,Si) crystallites on the preexisting Cu
clusters occurs during the third stage of microstructural evolution (Ayers
et al., 1993). Samples annealed for 600 s at the optimal annealing temperature
show direct contact of the Cu-rich clusters with each a-(Fe,Si) nanocrystalline grain, as observed by APFIM (Hono et al., 1999). The Cu clusters remain
at the interphase interface as the crystallites grow and the remaining amorphous phase becomes enriched in Nb and B due to their low solubility in the
crystalline phase (Hono et al., 1999). During this early stage of crystallization,
the a-(Fe,Si) crystallites tend to have larger amounts of Si than the overall
composition, near 16 at%, by Mössbauer spectroscopy (Knobel et al., 1992).
The well-known Nishiyama–Wasserman or Kurdjumov–Sachs orientation
relationships between the FCC and BCC close-packed planes/directions may
provide the low-energy interface, enabling an easier nucleation by the introduction of Cu in these alloys. This may be a reason for the greater stability of
the a-(Fe,Si) phase over the intermetallic phases which tend to form when
slow cooling is used instead of rapid solidification.
The fourth stage is characterized by the coarsening of the (Fe,Si)-rich
crystallites and stabilization of a diffusion-inhibiting, residual amorphous
phase, enriched in Nb, B, and Cu. This stage ultimately results in the
optimum microstructure consisting of 70–80 vol% crystalline phase with
grain diameters near 10 nm. The remaining amorphous phase surrounds the
equiaxed crystallites forming a 1- to 2-nm-wide region between grains. The
crystallites formed by this process are enriched in Fe and Si compared to
the remaining amorphous phase, which has higher Nb and B contents
(Hono et al., 1991, 1993). The Si content of the crystalline phase was progressively increased from stage 2, reaching 18–20 at% in the optimally crystallized
sample (Herzer, 1990; Knobel et al., 1992). As crystallization progresses
during the fourth stage, atomic ordering in the crystalline phase having the
D03 structure and Fe3Si composition is found (as discussed in Section 4.4)
221
Nanocrystalline Soft Magnetic Alloys
(Ayers et al., 1998; Herzer and Warlimont, 1992). Annealing at temperatures above 600 C has shown increased crystallite Curie temperatures, an
indication of reduced Si content by this thermal treatment (Herzer, 1990).
The arresting of the grain growth for extended annealing times in these
Fe96zSixBzxNb3Cu1 alloys is due to the residual amorphous matrix phase,
which prevents both the contact of adjacent nanocrystallites and the resulting grain boundary diffusion. Since the grains do not share a boundary, the
surface area-driven coarsening of the grains does not occur. With sufficient
annealing time at the optimum annealing temperature, the Cu clusters
coarsen by Ostwald ripening and are commonly seen by XRD (Zhang
et al., 1996a). It is also important for good magnetic properties that intermetallic phases, such as Fe2B and Fe3B, are avoided at primary crystallization. Typically, these phases are observed if the annealing temperature
exceeds about 600 C, resulting in relatively large intermetallic boride phases
to form (50–100 nm diameters) at the expense of the intergranular amorphous
matrix.
The role of Nb and Cu on microstructure refinement in the
Fe96zSixBzxNb3Cu1 alloys is illustrated in Fig. 4.20, where a schematic
microstructure is shown for four (Fe,Si)-based materials. The combination
of both Nb and Cu in the Fe–Si–B base alloy is necessary to provide the
optimized microstructure (Noh et al., 1990; Yoshizawa and Yamauchi,
1990). Less than 3 at% Nb results in increased grain sizes (above 15 nm
diameter), which significantly reduced the magnetic performance of
the alloys (Ayers et al., 1994; Yoshizawa and Yamauchi, 1991). The addition
of a few at% of ETM elements improves the stability of the nanocrystalline
microstructure; however, too much of these elements result in a considerable
(a)
(b)
(c)
(d)
Fe73.5Si13.5B9Nb3Cu1
Fe74.5Si13.5B9Nb3
Fe76.5Si13.5B9Cu1
Fe77.5Si13.5B9
550 °C 1800 s
550 °C 1800 s
550 °C 1800 s
550 °C 1800 s
10 nm
Equiaxed grains of
a-(Fe,Si) with Nb/B-rich
residual amorphous matrix
(8–10 nm)
100 nm
no Cu
Equiaxed grains of
a-(Fe,Si) and Fe23B6
(30–50 nm)
100 nm
no Nb
Spheroidal
a-(Fe,Si) grains
(50–100 nm)
100 nm
no Nb/Cu
Large dendritic grains
(1–2 mm)
Figure 4.20 Schematic diagram of the evolved microstructures for amorphous alloys
annealed at 550 C for 1800 s: (a) Fe73.5Si13.5B9Nb3Cu1, (b) Fe74.5Si13.5B9Nb3,
(c) Fe76.5Si13.5B9Cu1, and (d) Fe77.5Si13.5B9.
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Matthew A. Willard and Maria Daniil
decrease in the Curie temperature of the amorphous phase and degraded
magnetic performance. The absence of Cu in the alloys showed a much
smaller nucleation rate and consequently larger grain sizes (Yoshizawa et al.,
1988a). Amounts of Cu as small as 1 at% provide a substantial increase in the
separation of primary and secondary crystallization temperatures, allowing the
microstructure to evolve without intermetallic borides (Noh et al., 1990).
Similar stages in microstructure evolution are found in Fe–Zr–B and
(Fe,Co)–Zr–B alloys; however, the fine-grained microstructure does not
always require Cu in these alloys (which removes stage 2 of the process). For
instance, in the (Fe0.5Co0.5)88Zr7B4Cu1 alloy, Cu was not found to cluster
during the early stages of annealing and was partitioned to the intergranular
amorphous phase as the nanocomposite microstructure evolved during
annealing (Ping et al., 2001). The lessened glass-forming ability of these
alloys and compositional fluctuations in the rapid solidification process may
be reasons for the large number of nucleation sites in the as-cast ribbons
without Cu (Goswami and Willard, 2008; Suzuki et al., 1994). Although
Cu is not necessary for producing the nanocomposite microstructure, in
some cases, it has been shown to improve the soft magnetic properties.
Replacement of the Cu as a nucleation aid has been investigated in several
studies. The substitution of the noble metals Pt and Pd for Cu in the
Fe73.5Si13.5B9Nb3Cu1 alloy resulted in a significant increase in the crystallization onset temperature; however, the primary crystallization products were
Fe3B and a-(Fe,Si), with 20 nm grain diameters (Conde et al., 1998). The
presence of the Fe3B phase and the larger than desired grain size indicate that
Pt and Pd do not share the same role in the crystallization process with Cu.
Substitution of Ag for Cu resulted in larger grain sizes (above 30 nm) and
commensurate higher coercivity (10 A/m) (Chau et al., 2005). On the
other hand, substitution of Au for Cu has been demonstrated to provide
similar microstructure evolution (Kataoka et al., 1989).
The microstructure evolution is critically dependent on the amount and
type of ETMs. Many studies have examined the role of ETMs in the
Fe73.5xSi13.5þxB9M3Cu1 alloys where Ti, V, Cr, Mn, Zr, Mo, Hf, Ta,
and W have replaced Nb. A summary of the grain size variation with
annealing temperature for different ETM substitutions is provided in
Fig. 4.21. A clear trend in the grain size can be observed, with smaller
ETM elements (e.g., Mn, V, Cr, Ti) acting as a less effective deterrent to
grain growth and large ETMs (esp. Mo, Hf, Ta, and Nb) are good diffusion
inhibitors (Mattern et al., 1995; Yamauchi and Yoshizawa, 1995;
Yoshizawa and Yamauchi, 1991). As long as the temperature remains
significantly below the secondary crystallization temperature, only slight
variations in the grain size are found for all samples that were annealed for
times between 1200 and 3600 s, regardless of ETM type. The effect of
exceeding the secondary crystallization temperatures for samples with Mo
and Nb can clearly be seen by the increased grain size with annealing
223
Nanocrystalline Soft Magnetic Alloys
100
Fe73.5Si13.5B9M3Cu1
Grain diameter (nm)
80
60
Mn
Cr
40
V
Ti
20
Mo
Ta
0
700
750
800
850
900
950
1000
Annealing temperature (K)
Figure 4.21 The effect of annealing temperature on the grain diameter for
Fe73.5xSi13.5þxB9M3Cu1 alloys annealed for 1200–3600 s (where M ¼ Ti (open circle),
V (open square), Cr (open triangle), Mn (open downward triangle), Zr (half-closed
circle), Mo (closed downward triangle), Hf (closed circles), Ta (closed square), W (closed
triangle), Nb (closed diamonds), and x 2) (Cziráki et al., 2002; Frost et al., 1999; Hakim
and Hoque, 2004; Hernando and Kulik, 1994; Kulik and Hernando, 1994; Liu et al.,
1997b; Mattern et al., 1995; Mazaleyrat and Varga, 2001; Noh et al., 1993; Yamauchi and
Yoshizawa, 1995; Yoshizawa and Yamauchi, 1991; Zhang et al., 1998a).
temperature. Taking average grain sizes for samples annealed at low temperatures (nearly constant values in Fig. 4.21), a correlation is found when
plotted against the ETM atomic radius (see Fig. 4.22) (Müller et al., 1996a).
ETMs with large atomic radii tend to provide the smaller grain sizes that
lead to desirable magnetic properties.
While the Nb and Cu have been found critically important to the development of the nanostructured microstructure, the grain size itself is strongly
dependent on the B content of the alloy and the type of ETM used in the alloy
(see Fig. 4.23). This is not only true for (Fe,Si)–Nb–B–Cu alloys (Herzer,
1997) but also for Fe–Zr–B–(Cu) alloys. This indicates that B may also be
involved in the grain growth inhibition; however, its effect is insufficient to
create the nanocrystalline microstructure unless it is assisted by Nb (or another
ETM). The ETMs tend to suppress the formation of boron-containing intermetallics, making the combined use of B and ETMs necessary.
The processing–composition relationship described above is extremely
important in the context of providing the essential microstructure that
drives the low coercivity observed in these materials. Limiting the grain
size to less than about 15 nm explains the ultra-low coercivities using the
random anisotropy model in Section 6.3. Establishing the desired primary
crystalline phase allows an increase in the magnetization, resulting in
224
Matthew A. Willard and Maria Daniil
Mn
Average grain diameter (nm)
50
Fe73.5Si13.5B9M3Cu1
Cr
Tann ~ 823 K
V
40
Ti
30
20
Mo
W
Ta
Nb
10
Zr
Hf
0
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
2.15
2.20
Atomic radius (Å)
Figure 4.22 Variation of grain diameter with early transition metal radius in optimally
annealed Fe73.5Si13.5B9M3Cu1 alloys (where M ¼ Mn, Cr, V, Ti, Mo, W, Ta, Zr, Hf)
(Cziráki et al., 2002; Frost et al., 1999; Hakim and Hoque, 2004; Hernando and Kulik,
1994; Kulik and Hernando, 1994; Liu et al., 1997b; Mattern et al., 1995; Mazaleyrat
and Varga, 2001; Noh et al., 1993; Yamauchi and Yoshizawa, 1995; Yoshizawa and
Yamauchi, 1991; Zhang et al., 1998a).
18
Grain diameter (nm)
16
Fe–Si–Nb–B–Cu
Fe–Zr–B–(Cu)
14
12
10
8
6
4
0
2
4
6
8
10
12
14
16
18
20
22
24
B content (at%)
Figure 4.23 Grain size dependence on the boron content of (Fe,Si)–Nb–B–Cu
(Herzer, 1997) and Fe–Zr–B–(Cu) alloys. Grain sizes for the Fe–Zr–B–(Cu) alloys
are plotted as an average from the following studies (Arcas et al., 2000; Garitaonandia
et al., 1998; Gómez-Polo et al., 1996; Kaptás et al., 1999; Kim et al., 1994b; Kopcewicz
et al., 1997; Ślawska-Waniewska et al., 1994; Suzuki et al., 1991b; Suzuki et al., 1996;
Zhou and He, 1996).
Nanocrystalline Soft Magnetic Alloys
225
improved miniaturization of components, further discussed in Section 6.1.
In addition, maintaining a residual amorphous phase provides a robust
resistivity, allowing increased operation frequencies for these materials, to
be discussed in Section 6.5.
3.3. Intrinsic property considerations
The success in reducing the losses in Fe–Si–Nb–B–Cu alloys has as much to
do with the microstructure as it does with the composition of the phases
formed during optimal annealing. The Si-rich crystallites approach the
composition where bulk Fe–Si has a low magnetocrystalline anisotropy
( 20 at%) (Herzer, 1995). The Nb/B-rich residual amorphous phase has
been found to possess a positive magnetostriction coefficient which balances
that of the Si-rich crystallites (which have a negative value), giving an
overall near zero value. Both of these circumstances aid the reduced losses
observed in these alloys. Based on these findings, it is not surprising that
varied amount and type of alloying have a strong effect on both the
magnetic properties, the crystallization behavior of the alloy, and the optimal annealing conditions.
For most soft magnetic applications, the saturation magnetization is a
figure of merit with larger values being more desirable. In Fe–Si–Nb–B–Cu
alloys, the saturation magnetization is somewhat low with m0Ms 1.25–
1.35 T. The saturation magnetization is larger for Fe–Zr–B with values
above 1.5 T; however, the coercivity is increased. Substitution of different
types of Co for Fe in Fe–Co–Zr–B alloys has been found to vary the
saturation magnetization in a way similar to the well-known Slater–Pauling
curve (Fig. 4.24) (Pauling, 1938; Slater, 1937). Using the average number of
combined 4s and 3d electrons per atom (e/atom) as a composition variable, the saturation magnetization shows a pronounced peak near 8.35 e/
atom for alloys with small amounts of Si added (<5 at%). When the Si
content is increased to 10 at% or more, the peak in saturation magnetization
is shifted to compositions consisting of a greater fraction of Fe (near 8.1–8.2
e/atom). As shown in Fig. 4.24a, the peak can be completely eliminated
when Si content is increased beyond about 13 at%. While MTMs can be
used to improve the saturation magnetization of the alloy, the coercivity
tends to increase by these same composition variations (see Fig. 4.24b).
Again, the balance of alloy design parameters requires a good understanding
of the application needs.
The addition of Cr as an alloying element has been studied widely due to
its extreme effect on the Curie temperature of the amorphous phase (especially after partial crystallization) (Chau et al., 2006; Conde et al., 1994;
Hajko et al., 1997; Marı́n et al., 2002). Replacing 4.5 at% Fe with Cr has
been found to reduce the Curie temperature of the amorphous phase by
110–470 K (Hajko et al., 1997). The Curie temperature of the amorphous
226
Matthew A. Willard and Maria Daniil
(a)
Saturation magnetization (T)
1.8
(Fe1 - xCox)86B6Zr7Cu1
1.6
1.4
1.2
1.0
(Fe1 - xCox)73.5Si15.5B7Nb3Cu1
0.8
0.6
0.4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Co content, x (Co/(Fe+Co))
(b)
Coercivity (A/m)
10,000
1000
100
(Fe1–xCox)86B6Zr7Cu1
10
(Fe1–xCox)73.5Si15.5B7Nb3Cu1
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Co content, x (Co/(Fe + Co))
Figure 4.24 Variation of (a) saturation magnetization and (b) coercivity with magnetic transition metal content in (Fe,Co)73.5Si15.5Nb3B7Cu1 and (Fe,Co)86Zr7B6Cu1
alloys. After M€
uller et al. (1996b).
phase is an important parameter, as it is the temperature limit for exchange
coupling between the crystallites of the nanocrystalline soft magnetic alloy.
When the Curie temperature of the amorphous phase is exceeded, the
coercivity increases at an accelerating rate with increased over-temperature.
While the details of this effect will be discussed in the section on the
temperature dependence of magnetic properties, it is clear that the magnetic
character of the alloy can be substantially modified by minor composition
modifications.
The most important parameter for the reduction of losses in soft magnetic materials is a near zero value of magnetocrystalline anisotropy (K1).
Nanocrystalline Soft Magnetic Alloys
227
It has been shown in Section 1.2 that the effective magnetocrystalline
anisotropy can be strongly influenced by the microstructure as described
by the random anisotropy model (more details are found in Section 6.3).
When applied to nanostructure soft magnets, a D6 reduction in coercivity is
found when the grain size is reduced below 100 nm. At the same time,
the effective anisotropy (and therefore coercivity) also depends strongly on
the crystalline phase magnetocrystalline anisotropy, K1 4 . For this reason, the
size, composition, and distribution of the primary crystalline phase are
important as together they contribute to the losses in the material. In the
case of Fe–Si–B–Nb–Cu alloys, the magnetocrystalline anisotropy of
the crystallites is dependent on the composition of the alloy, especially
evident with variation of Si (Chikazumi and Graham, 1997). When the
effective magnetocrystalline anisotropy has been reduced enough, the magnetoelastic anisotropy becomes a dominant factor.
The magnetostrictive coefficient (ls) for nanocrystalline alloys is sensitive to both the nominal composition of the alloy and the annealing
conditions for crystallization. An as-spun ribbon with Fe73.5Si13.5B9Nb3Cu1
composition has a large, positive value of ls ¼ 20 106 (ppm), which is
rapidly reduced when annealed above the primary crystallization temperature to values below 5 ppm (Herzer, 1991). This reduction in ls is due to
the volume fraction-weighted average of positive coefficient from the
amorphous phase (lam
s 20 ppm) and the negative value of the nanocrystalline phase (lcr
s 5 ppm). When the alloy is about 70–80 vol% crystallized,
am
the equation ls ¼ Xlcr
s þ (1 X)ls describes the trend in ls with Si content. It has been noted that the near zero value of ls is found at higher
nominal Si contents in nanocrystalline alloys than expected from polycrystalline a-(Fe,Si) alloys (at 12 at% Si) due to the preferential segregation of
this element to the crystalline phase (Herzer, 1991).
Magnetostrictive coefficients for the alloy series Fe96zSixBzxNb3Cu1
(where 18.5 z 23.5 and x 17.5) show a near constant value for the asspun alloys at 22 ppm, independent of the alloy composition (Herzer,
1996). However, samples crystallized at 540 C for 1 h show a compositional dependence of ls with a broad maximum at x 5 and a near zero
value at x ¼ 16–17. This is important, as the internal stresses can be 1–2 MPa
resulting in magnetoelastic anisotropy near 50–100 J/m3 for amorphous
alloys. In comparison to the 2–3 J/m3 resulting from the exchange averaged
magnetocrystalline anisotropy in the nanocomposite alloys, this would be a
significant and dominating factor if the magnetostriction were not reduced
by nanostructuring. For instance, the relatively large value of coercivity
observed in (Fe,Co)–Zr–B–Cu alloys (see Fig. 4.24b) is a result of the
composition naturally having a large magnetoelastic anisotropy. In this
case, the benefits of very high Curie temperature of the residual amorphous
phase and large saturation magnetization outweigh the increased coercivity,
allowing these materials to be used for high-temperature applications.
228
Matthew A. Willard and Maria Daniil
3.4. Domain structure considerations
As soft magnetic materials are typically used in applications where ease of
switching is a necessity, the magnetic domain structure is an important
design factor for these materials. Magnetic domains in soft magnetic materials form readily when no magnetic field is applied due to the large reduction
in magnetostatic energy when the free magnetic poles are removed from the
surface. In the process, domain walls are formed between the domains.
Switching between large positive and negative magnetic fields results in
domain wall motion, yielding a net change in the magnetization. Nonuniform arrangement of domains within a material can result in larger losses if
impediments to domain wall motion are present in the material (i.e.,
domain wall-pinning sites). These can include nonmagnetic inclusions,
regions of large anisotropy, grain boundaries, or surface effects.
Nanocrystalline soft magnetic alloys possess domain structures indistinguishable from amorphous alloys by optical microscopy techniques,
including features such as stripe domain patterns and stress patterns if
the magnetostriction is nonzero (Schäfer et al., 1991). Sharp domain walls
are observed by Lorentz microscopy for an amorphous (i.e., as-spun)
Fe73.5Si13.5B9Nb3Cu1 alloy (Shindo et al., 2002). After optimal annealing
the domain walls broaden and remain straight, consistent with the magnetic
softening of the alloy. Annealing the material at temperatures exceeding
secondary crystallization (e.g., 923 K and above) results in domains following the grain boundaries of the enlarged grain (<50 nm). Measuring the
domain structure of the optimally annealed sample at temperatures above
the Curie temperature of the intergranular amorphous phase results in a
decoupled domain structure (Hubert and Schafer, 2000).
When contributions from magnetocrystalline anisotropy and magnetostriction have been minimized through proper processing and choice of
composition, induced anisotropies dominate. These anisotropies can be
used to control the domain structure of the material, allowing some amount
of tuning of the hysteresis loop. This type of loop shape adjustment allows
one material to be used for various applications. Annealing the material in a
field (either stress or magnetic) can create an induced magnetic anisotropy as
described in the previous sections. The resulting domain structure in the
best-performing alloys shows a stripe domain configuration. A coherent
rotation switching mechanism can be achieved when the vector normal to
the domain walls of these stripe domains is parallel to the applied switching
field. This reduces the permeability of the material without the necessity of
creating an air gap, a benefit for inductor applications. Transverse magnetic
field annealing of a Co60Fe18.8Si9Nb2.6B9Cu0.6 alloy annealed at 803 K
showed regular domains with 180 domain walls along the direction of
the induced anisotropy (Saito et al., 2006).
Nanocrystalline Soft Magnetic Alloys
229
Unfortunately, not all alloy compositions are well suited for field annealing to control the magnetic domain structure. The embrittlement of many
alloys during the crystallization process limits the stress-annealing technique’s general use. Magnetic field annealing has strong compositional dependences, resulting in small values of induced anisotropy for many Fe-rich
compositions (with significant improvements found in Co-rich alloys)
(Ohodnicki et al., 2008b; Ohodnicki et al., 2008c; Suzuki et al., 2008a).
The induced anisotropies formed by magnetic field annealing have also
been found to change the effective anisotropy as described by Suzuki et al.
(1998). The typical D6 dependence of the coercivity with grain diameter is
reduced to a D3 dependence when a long-range, uniaxial anisotropy (as
found in field annealing) is induced.
4. Phase Transformations, Kinetics,
and Thermodynamics
The rapid solidification and annealing processes that results in an alloy
with nanocomposite microstructure and desirable magnetic properties are the
result of careful consideration of factors that affect the thermodynamics and
kinetics of the transformations in these materials. Important factors to consider include the kinetics of the nucleation and growth processes, the thermodynamics of the crystallization process, and other phase transformations,
resulting in optimized magnetic performance. Understanding crystallization
and other phase transformations can improve our ability to choose the best
annealing temperatures and times to achieve the desired microstructure.
In Section 4.2, phase diagrams for crystallization of the as-spun ribbons
will be discussed for various nanocrystalline alloy systems. Using time–
temperature transformation (TTT) diagrams, Section 4.3 will describe the
crystallization kinetics to show the necessary critical cooling rates for amorphous alloy formation and the crystallization process at different temperatures. Order–disorder transformations that are important in several alloy
systems will be discussed in Section 4.4.
4.1. Thermal analysis techniques
Differential thermal analysis (DTA) and differential scanning calorimetry
(DSC) are standard techniques that have been successfully used to identify
crystallization temperatures for amorphous ribbon samples. In some cases,
the glass transition and Curie temperatures are also observed by these
techniques. The DTA measurement uses a differential temperature between
an unknown sample and reference material to determine when heat is
230
Matthew A. Willard and Maria Daniil
generated or absorbed by the samples. The reference is chosen to have a
similar heat capacity to the unknown, and both materials are contained in
the same furnace so that they are both subjected to the same thermal
environment. Typical measurements by DTA are performed with a constant heating rate (between 1 and 100 K/min) with minimal amounts of
sample, less than 10 mg. The sample should be large enough to provide
adequate signal during heating, which depends on heating rate due to the
thermal activation of the crystallization process. However, it must also be
small enough to avoid temperature gradients through the sample. Typical
temperature ranges are from 300 to 1000 K with a sensitivity of 10–100 mJ/s.
DSC is a similar technique where the power difference required to maintain
the two cups at the same temperature is measured, giving a more accurate
determination of the enthalpy of reactions.
These techniques are used widely because they are a quick and easy way
to identify critical parameters for annealing procedures. By heating the
sample at a constant heating rate, the glass transition and Curie temperatures
can be identified if they are much smaller than the primary crystallization
temperature. Each can be identified by a slope change in the DTA or DSC
signal. Primary and secondary crystallization peaks (labeled Tx1 and Tx2) are
observed as exothermic reactions where the high entropy amorphous phase
is transformed into the low entropy crystalline phase (see Fig. 4.25). An
associated enthalpy change occurs at each crystallization temperature. Studies typically report two different crystallization temperatures for each
4.8
Temperature difference (K)
4.6
4.4
onset
T x1
p
T x1
onset
T x2
p
Tx2
10 K/min
4.2
DH x1
4.0
3.8
3.6
5 K/min
3.4
3.2
3.0
2 K/min
2.8
400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700
Measurement temperature (K)
Figure 4.25 Variation of peak temperature with heating rate in differential thermal
analysis measurements for a Fe4.45Co84.55Zr7B4 as-cast alloy, heated at 2, 5, and 10 K/min.
Nanocrystalline Soft Magnetic Alloys
231
crystallization event, the temperature of crystallization onset and the temperature of peak signal. These temperatures can be separated from each
other by as much as 30–40 K. Since the crystallization process is thermally
activated, the onset and peak temperatures and the enthalpy of reaction are
variable with the heating rate used during the measurement. Slower heating
rates tend to have smaller peaks at lower temperatures than faster heating
rates. Measuring several samples with varying heating rates can provide
information about the activation energy of crystallization (described in
more detail in Section 4.3).
4.2. Primary and secondary crystallization
While it is possible to produce nanocrystalline microstructures by other
transformations (e.g., eutectic or polymorphous) (Lu, 1996), the most
common method for ribbons is by primary crystallization of an amorphous
precursor. In order to achieve a nanocrystalline microstructure with a
specific crystalline phase, we must consider the thermodynamics and kinetics of primary crystallization, which depend on the composition of the alloy
and the processing conditions of the rapidly solidified alloy. Understanding
the thermodynamics can help identify compositions that are favorable for
amorphous alloy formation as well as favorable for primary crystalline phases
that might form during subsequent annealing. Understanding the kinetics of
primary crystallization allows us to identify compositions that are likely to
produce the desired fine-grained microstructure. Properly designed alloys
will allow the formation of beneficial primary crystalline phases, high
nucleation rates, and slow growth of grains, resulting in improved magnetic
properties. This is achievable when crystallization occurs in a multistage
process, with large separation of crystallization temperatures for desirable
primary crystalline phases and unwanted secondary phases. The microstructure obtained by annealing above the primary, but below the secondary
crystallization temperature, consists of nanocrystalline grains embedded in a
residual amorphous matrix phase. Full crystallization of the sample does not
occur at primary crystallization due to elemental partitioning between the
forming crystalline phase and the remaining amorphous phase. The amorphous alloys that successfully form nanocrystalline microstructures typically
possess a large temperature difference between the primary (Tx1) and
secondary crystallization (at Tx2). The larger the range between these
temperatures, the more opportunity exists for optimization of the microstructure by varying annealing conditions.
Table 4.1 shows many classes of nanocrystalline soft magnetic alloys
separated by the primary crystalline phase and observed saturation magnetization. In general, the most suitable phases during primary crystallization
include a-(Fe,Si), a-(Fe,Co,Ni), and g-(Co,Ni,Fe), due to their large
magnetizations and cubic symmetry. For the purpose of this discussion,
232
Matthew A. Willard and Maria Daniil
we will refer to these phases as simple MTM phases. Limited solubility of
the glass-forming elements in these phases is an important factor since ETM
and metalloid elements tend to substantially reduce the magnetization of the
MTM. In some cases, the atomically ordered, cubic, a0 -Fe3Si or a0 -FeCo
intermetallic phases are observed at primary crystallization. If the primary
crystallites are not simple MTM phases (or MTM intermetallics), but instead
are intermetallics of MTM and either ETM and/or metalloid elements, the
performance of the materials is significantly impaired due to the increased
magnetocrystalline anisotropy of these noncubic phases and the deterioration of the desired microstructure.
At temperatures exceeding secondary crystallization, the residual amorphous phase also crystallizes into intermetallic phases and borides, including
Fe2B, Fe3B, Fe23B6, Fe23Zr6, Fe2Zr, and/or Fe3Zr. The secondary crystallization products for a given alloy depend strongly on the composition of the
alloy; however, the microstructure coarsens dramatically for all compositions.
Secondary crystallization degrades the magnetic performance considerably
and in many cases poses the upper temperature limit for potential application
(Willard et al., 2012b). It is essential to avoid secondary crystallization when
annealing the samples during devitrification. Even small volume fractions of
Fe2B crystallites can have a detrimental effect on the magnetic performance.
Two factors are responsible for the degradation. First, the grain sizes tend to
be larger than the primary crystallites, in the range of 50–100 nm, which is
large enough to provide significant domain wall pinning. Second, the magnetocrystalline anisotropy is quite large for Fe2B, K1 ¼ 4.3 MJ/m3 at room
temperature. Both of these effects together result in coercivities in excess of
100 A/m. Structure and characteristics of primary and secondary phases are
discussed in more detail in Section 5.
Early observations of these alloys identified the necessity of both ETMs
and copper as alloying elements to achieve a nanocomposite microstructure
(Kataoka et al., 1989; Noh et al., 1990; Yoshizawa and Yamauchi, 1991). The
most generally accepted microstructure evolution model to achieve nanocomposite microstructure in Fe96zSixBzxNb3Cu1 alloys was refined over
about 10 years (Ayers et al., 1993, 1994, 1997; Hono et al., 1992, 1999). The
model uses nucleation and growth principles to describe the roles of both Nb
and Cu and has been discussed in more detail in the earlier sections.
Due to the complex nature of the roles of each element in the crystallization process, strong variations in crystallization temperature are observed
as the composition is varied. For instance, in Fe96zSixBzxNb3Cu1 alloys
when the total amount of Si þ B is 18.5, the primary and secondary crystallization temperatures tend to increase with increased Si content and a third
crystallization temperature is observed (see Fig. 4.26) (Herzer, 1997). In this
case, primary crystallization forms a-FeSi, secondary crystallization adds
Fe2B and Fe3B, and only at tertiary crystallization is all of the amorphous
phase completely crystallized as a FeNbB phase is formed. At higher Si þ B,
233
Crystallization temperature (K)
Nanocrystalline Soft Magnetic Alloys
Fe96 - zSixNb3Bz - xCu1
1100
Tx3
1000
900
Tx2
800
Tx1
700
z = 18.5
z = 20.5
8
12
z = 22.5
600
0
2
4
6
10
14
16
18
Si content, x (at%)
Figure 4.26 Crystallization temperature variations with Si content in Fe96zSixBzxNb3Cu1 alloys. After Herzer (1997).
the primary crystallization temperature is relatively stable with changes in Si
content, and merged secondary/tertiary crystallization increases with Si
content for Si þ B ¼ 22.5. An important factor for proper microstructure
evolution is the large temperature difference between crystallization of
primary and secondary phases, which is observed for the whole composition
range. Another factor is the formation of a desirable phase at primary
crystallization, which is also found.
Since the magnetic properties are dependent on both the microstructure
and the composition of the crystallized phases, many studies of modified to
the Fe–Si–Nb–B–Cu alloys have been made. As an alloying element, Ga has
been shown to form an a-(Fe,Si,Ga) solid solution (Matsuura et al., 1996).
Similarly, Al additions to Finemet act as substitutional elements for Si in the
crystalline phase (Frost et al., 1999; Lim et al., 1993b). While small additions
of Al have been shown to reduce the coercivity (through reduction in K1),
the magnetization drops rapidly with Al additions. However, improved
performance has been observed in the (Fe,Si,Al)-based alloys at cryogenic
temperatures, an effect attributed to lower magnetocrystalline anisotropy
and magnetostriction (Daniil et al., 2010a). The replacement of Nb by Gd,
examined by Crisan et al., resulted in the formation of RE–Fe–B phases at
secondary crystallization (among other phases) and increased growth kinetics of the primary crystallites (Crisan et al., 2003). Replacement of Si with
Ge showed a significant increase in TCam (Cremaschi et al., 2004a).
The substitution of noble metals, Pt and Pd, for Cu in a Fe–Si–B–Nb–M
alloy results in a substantial decrease in he crystallization onset temperature;
however, the primary crystallization products are Fe3B and a-FeSi with
grain diameters of 20 nm and larger (Conde et al., 1998). The absence of a
234
Matthew A. Willard and Maria Daniil
single a-FeSi phase and the larger grain size indicate that Pt and Pd do not
share the same role as Cu in the crystallization process. The use of M ¼ Ag
showed larger grain sizes (<30 nm) and correspondingly larger coercivities
( 20 A/m) than alloys using Cu (Chau et al., 2005). On the other hand, Au
has been shown to provide good grain refinement and comparable coercivities to Cu-containing alloys (Kataoka et al., 1989). The role of Cu as a
heterogeneous nucleation site and the optimization of the amount of Cu
necessary to maximize magnetic softness have been examined by meticulous
DSC and small-angle neutron scattering experiments (Ohnuma et al.,
2000). These results indicate that the Cu-clustering phenomena are thermally activated and that optimal Cu content is found when the number
density of Cu clusters is maximized at the start of primary crystallization. For
this reason, the optimal Cu content is closely related to the Fe–Si content of
the alloy and heating rate to primary crystallization.
Although Cu or Au is an indispensible element for grain refinement due
to its ability to enable a large number of heterogeneous nucleation sites in
many nanocomposite alloy compositions, the grain growth must also be
controlled to yield the desired microstructure. In the (Fe,Si)–Nb–B–Cu
alloys, this has been accomplished by the use of Nb; however, several other
elements are also good grain growth inhibitors. The ETMs (or refractory
metals) have been shown to provide similar grain growth inhibition
(Kataoka et al., 1989; Yoshizawa and Yamauchi, 1991). In Fe73.5Si13.5B9Nb3xMxCu1 alloys, the variation of the primary crystallization
temperature shows a 50 K increase between ETMs with small atomic radius
(e.g., V or V þ Nb) and those with large atomic radius (e.g., Ta, Zr), as
shown in Fig. 4.27. The atomic radii of these atoms are larger than those of
the MTMs. The effectiveness of these elements in providing nanocrystalline
microstructures is related to the atomic radii, with best results for the largest
atoms, Nb and Ta (Müller and Mattern, 1994). An increased primary
crystallization temperature indicates an increased stability of the amorphous
phase compared to the primary crystalline phase.
MTM variations in an alloy are used to tune the saturation magnetizations,
Curie temperatures, and losses in nanocomposite soft magnets. Varying
the MTM composition can significantly change the primary crystallization
temperatures as illustrated in Fig. 4.28 for Fe73.5xMTMxSi13.5B9Nb3Cu1
alloys. Substitution of Cr for Fe has the strongest effect, with a near linear
increase in Tx1 to 910 K at 10 at% Cr (Hajko, 1997). This trend in primary
crystallization is shared with the trend in activation energy for primary
crystallization observed in Cr-substituted alloys (to 5 at% Cr at least) (Chau
et al., 2006). Slight increases are observed for Ni substitution for Fe; however,
the secondary crystallization temperature is significantly lowered with
increasing Ni content (Agudo and Vázquez, 2005). Alloying with Co tends
to keep a steady primary crystallization temperature between 780 and 800 K
235
Primary crystallization temperature (K)
Nanocrystalline Soft Magnetic Alloys
Fe73.5Si13.5B9Nb3 − xMxCu1
810
800
790
780
770
760
M = V, V + Nb
M = Zr
M = Mo, Mo + Nb
M = Ta
M=W
M = Nb
750
740
1.90
1.95
2.00
2.10
2.05
2.15
Average atomic radius ETM (Å)
Figure 4.27 Effect of early transition metal type and content on the primary crystallization temperatures in Fe73.5Si13.5B9Nb3xMxCu1 alloys (where M ¼ V, Mo, W, Nb,
Ta, Zr) (Borrego and Conde, 1997; Degro et al., 1994; Hernando and Kulik, 1994;
Herzer, 1989; Kulik, 1992; Lim et al., 1993b; Liu et al., 1997b; Mitra et al., 1998;
Rodrı́guez et al., 1999; Yoshizawa and Yamauchi, 1991; Yoshizawa et al., 1988a;
Zhang et al., 1998a; Zorkovská et al., 2000).
Crystallization temperature (K)
Fe73.5 - xMTMxSi13.5B9Nb3Cu1
900
850
800
750
MTM = Cr
MTM = Ni
MTM = Co
700
0
10
20
30
40
50
60
70
80
MTM substitution for Fe (at%)
Figure 4.28 Variation of primary crystallization with magnetic transition metal substitution in Fe73.5xMTMxSi13.5B9Nb3Cu1 alloys, where MTM ¼ Cr (Atalay et al., 2001;
Chau et al., 2006; Conde et al., 1994; Franco et al., 2001b; González et al., 1995; Hajko
et al., 1997), Ni (Agudo and Vázquez, 2005; Atalay et al., 2001), Co (Atalay et al., 2001;
Borrego et al., 2001a; Chau et al., 2004; Gercsi et al., 2006; Gómez-Polo et al., 2001;
Kolano et al., 2004; Mazaleyrat et al., 2004; Yu et al., 1992).
236
Matthew A. Willard and Maria Daniil
Crystallization temperature (K)
until 50% of the Fe has been substituted with Co (Mazaleyrat et al., 2004).
At higher Co contents, the Tx1 drops to below 750 K.
Fe–Zr–B-type nanocomposite alloys do not have the same alloy design
requirements as those containing Si. While Cu has been found to help refine
the microstructure and improve coercivity in some alloys (e.g., Fe–Si–Nb–
B–Cu), it is not a necessary element to achieve the nanocomposite microstructure in others (e.g., Fe–Zr–B or Fe–Co–Zr–B) (Suzuki et al., 1991c).
The effect is attributed to two factors, the lowering of Tx1 (extension of the
a-Fe phase stability) and the refinement of the grain size. The addition of at
least 1 at% Cu has been found to expand the composition range of Fe–Zr–B
alloys that exhibit large permeability (above 104). Microstructure evolution
of these alloys shows a nearly complete rejection of Zr from the crystallizing
a-Fe phase during the crystallization process of Fe–Zr–B alloys (Zhang
et al., 1996c). A trend in Tx1 with ETM radii is observed in Fe–ETM–
Zr–B alloys, having higher crystallization temperatures as the atomic radii is
increased (similar to Fig. 4.27) (Bitoh et al., 1999; Müller et al., 1997). The
stability of the amorphous phase against primary crystallization is also
strengthened by substituting B for Fe in Fe–B–M–Cu and Fe–Nb–B alloys
(Kuhrt and Herzer, 1996; Lee et al., 1994).
When the MTM composition is varied in the Si-free (Fe,Co,
Ni)88Zr7B4Cu1 and (Fe,Co)86Zr7B6Cu1 alloys, the variation in primary
crystallization temperature with MTM substitution is more gradual across
the whole composition range than in Fe73.5xMTMxSi13.5B9Nb3Cu1
alloys. As shown in Fig. 4.29, Tx1 for Fe (8 e/atom) is about 80 K higher
(Fe,Co)86Zr7B6Cu1
(Fe,Co,Ni)88Zr7B4Cu1
(Co,Ni)88Zr7B4Cu1
1000
900
800
700
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
Valence electrons per atom
Figure 4.29 Variation of primary and secondary crystallization with magnetic transition metal substitution in (Fe,Co,Ni)88Zr7B4Cu1 and (Fe,Co)86Zr7B6Cu1 alloys
(Caballero-Flores et al., 2010; Hornbuckle et al., 2012; M€
uller et al., 1996b; Willard
et al., 1999a, 2000, 2007).
Nanocrystalline Soft Magnetic Alloys
237
than for Co (9 e/atom) in (Fe,Co)86Zr7B6Cu1 alloys (Müller et al.,
1996b). Further decreases in Tx1 are observed when Co is substituted for
Ni (10 e/atom) to values below 700 K, indicating a deterioration of the
stability of the amorphous phase against crystallization similar to that found
in the Si-containing alloys (Hornbuckle et al., 2012).
4.3. Crystallization kinetics and phase stability
Above the primary crystallization temperature, the amorphous precursor
alloy crystallizes by an exothermic reaction, resulting in the evolution of a
nanocomposite microstructure. To achieve the best magnetic properties, this
primary crystallization product phase of the supersaturated amorphous solid
solution should be a low anisotropy, high magnetization phase. In most cases,
this restricts the best alloy compositions to MTM-rich alloys (hypoeutectic)
where primary crystallites are cubic phases (e.g., A2, D03, and/or A1 structures). Lower symmetry phases, such as Fe2B, Fe3B, Fe3Zr, etc., tend to have
larger magnetocrystalline anisotropies and smaller saturation magnetizations,
making them undesirable. These phases can be avoided by choosing compositions where the high-symmetry phases form at significantly lower temperatures than the low symmetry phases. Methods of lowering the Tx1 and raising
Tx2 extend the processing window exemplifying the importance of understanding reaction kinetics. In this section, the thermodynamic and kinetic
factors for the crystallization reaction will be discussed.
The majority of nanocrystalline soft magnetic alloys are produced by the
melt spinning technique. At the end of this rapid solidification step, the
desired product is typically a compositionally uniform, metastable amorphous alloy. Standard post-quench processing would promote partial crystallization of the alloy by two thermally activated processes, nucleation and
growth. While this simplistic view captures the main aspects of microstructure evolution of nanocrystalline soft magnetic alloys, the details of heat
flow, thermodynamics, and the nucleation and growth process provide the
necessary guidance to aid in alloy design and performance optimization.
The rate at which heat can be extracted from the liquid limits the range of
possible compositions to produce an amorphous precursor alloy. The primary crystallization product is determined by the thermodynamics of the
alloy system, and the nucleation and growth kinetics shape the ultimate
microstructure evolution. In the end, achieving a fine-grained microstructure requires high nucleation rate (given by large supersaturation or heterogeneous nucleation sites) and low growth rate (given by slow diffusion).
The nucleation of competing crystalline phases from the amorphous
precursor is largely determined by the lowest value of activation energy
barrier to nucleation, DG* (Boettinger and Perepezko, 1985). The influence of heterogeneous nucleation sites and undercooling for each competing phase are prime factors for establishing the value of DG*. The
238
Matthew A. Willard and Maria Daniil
e ) has an abrupt increase with the magnitude of undernucleation rate (N
cooling (DT) which can be described by the classical nucleation theory:
e ¼ fn Cn exp DG
N
kB T
ð1Þ
with preexponential factors for frequency of stable nuclei formation (fn) and
number of atoms in contact with the heterogeneous nucleation site per unit
volume (Cn) (Porter and Easterling, 1992). The exponential dependence of
the nucleation rate with the undercooling temperature is captured in the
activation energy barrier term (DG*). This term in the classical formulation
depends on the solid–liquid interfacial energy (gsl), the driving force for
nucleation (DGv / DT), and a shape factor (b (16p/3) S(y), where S 1)
in the following relation:
DG ¼
bgsl 3
DGv2
ð2Þ
This relationship infers that either lowering gs–l or raising DGv can
reduce the activation energy barrier. The reduction of the solid–liquid
interfacial energy (gs–l) is largely influenced by the introduction of suitable
heterogeneous nucleation sites. An example of successful alloy design taking
advantage of gs–l to improve the nucleation rate is the addition on Cu to Fe–
Si–B–Nb and Fe–Zr–B alloys, resulting in increased number of nuclei and
nucleation rate (Ayers et al., 1994; Hono et al., 1992; Zhang et al., 1996b).
The maximum driving force for nucleation (DGv) can be used for the
determination of the nucleus composition so long as the solid–liquid interfacial energy and shape factors are not a strong function of composition.
This technique was used to analyze the observation that BCC crystallites in
a Co-rich HITPERM alloy were forming due to the Fe enrichment of the
initial nuclei (Goswami and Willard, 2008; Willard et al., 2007). The
density of nuclei has been observed by HRTEM and STM to be 1 1023
to 1 1024 nuclei/m3 after primary crystallization (Goswami and Willard,
2008; Tonejc et al., 1999a). In some cases, the nuclei are present in the asquenched alloys (e.g., Co-rich HITPERM), and other cases, some nuclei
are present in the as-quenched state but further nucleation is required to
account for all of the grains in the coarsened microstructure (e.g., Fe–Sibased alloys) (Goswami and Willard, 2008; Hirotsu et al., 2004).
During the rapid solidification process, surface nucleation can occur if
the solidification rate is too slow. Typically found on the glossy side of the
ribbon (i.e., farthest from the quench wheel, often referred to as the “free”
side of the ribbon), the grains formed by surface nucleation typically grow
with either (1 1 0) or (1 1 1) fiber texture for BCC or FCC grains,
respectively. This effect becomes more pronounced in alloys with greater
Nanocrystalline Soft Magnetic Alloys
239
MTM contents where the amorphous phase is more difficult to form.
Surface crystallization has been found to greatly influence the magnetic
performance of partially crystallized metallic glasses through the magnetostrictive induced anisotropy produced by the stress field from the crystallites (Herzer and Hilzinger, 1986).
Achieving the desired nanocrystalline microstructure requires either
preexisting nuclei or very rapid nucleation rate in the early stages of
crystallization followed by a slow growth rate. The large initial nucleation
rate has been influenced by control of composition (e.g., adding Cu to Fe–
Si–Nb–B), by two-stage annealing (e.g., annealing near but below Tx1
where the driving force for nucleation is highest), and by control of the
heating rate (e.g., Joule heating). The slow growth rate, required in the
latter stages of crystallization, has been accomplished by adding alloying
elements that retard the diffusion of FTMs (e.g., incorporation of ETMs).
The elimination of Cu from Fe–Si–Nb–B–Cu and Fe–Zr–B–Cu alloys
results in a less refined grain size and an over all inferior magnetic performance to Cu-containing compositions. However, Cu is not the only
element found to provide heterogeneous nucleation sites in Fe–Si-based
alloys. Common characteristics of alloying elements that enhance the
nucleation site density (and rate) include elements which have low solubility
in BCC Fe (having positive heats of mixing with Fe) and weak bonding
interactions in the amorphous phase (allowing large mobility at low annealing temperatures). These elements include Cu and Au. Two-stage annealing effects have been studied as a method of improving the grain refinement
of the nanocrystallites (He et al., 2000; Noh et al., 1993). The first stage,
designed to aid nucleation rate with little growth, is performed at temperatures below primary crystallization. The second stage, designed for grain
growth, is similar to the standard (e.g., one-stage) annealing temperature
near or above the primary crystallization.
The growth rate is also a temperature-dependent process, although not
as critically determined by the undercooling of the alloy as the nucleation
rate. In nanocrystalline soft magnetic alloys, the growth rate is largely
determined by the diffusivity of Fe through the intergranular amorphous
phase. The incorporation of ETM elements to Fe–B–Si-based alloys was
found to reduce the growth rate substantially (Kulik, 1992). An increase in
the stability of the remaining amorphous phase was also observed, leading
wider separation of the primary and secondary crystallization temperatures
from 36 K without ETMs to 150 K with 3 at% Nb or Ta. Crystallization
kinetics and tracer diffusion studies show that trap-retarded diffusion of the
larger Nb (or other ETM) atoms in the amorphous matrix phase is the ratelimiting factor for grain growth in Fe–Si–Nb–B–Cu alloys (Damson and
Würschum, 1996).
The composition evolution during grain growth shows marked differences in Fe–Si–Nb–B–Cu- and Fe–Zr–B–Cu-type alloys (Lovas et al.,
240
Matthew A. Willard and Maria Daniil
1998). In the former case, nanocrystalline grains tend to increase their
solubility of Si as the annealing time progresses. In contrast, the Fe–Zr–B–
Cu alloy shows reduction of Zr in the crystalline phase with increasing
annealing time. In both cases, the remaining amorphous phase has increased
stability as indicated by the increased secondary crystallization temperature.
The kinetics of crystallization for nanocrystalline soft magnetic alloys
have been widely studied through controlled isothermal annealing studies
and through constant heating rate studies (McHenry et al., 2003; Yavari and
Negri, 1997). The resulting view of this thermally activated process has
been analyzed by two major methods depending upon the type of data
collected, the Johnson–Mehl–Avrami (JMA) technique for isothermal
kinetics and the Kissinger method for constant heating rate kinetics
(Avrami, 1939, 1940; Johnson and Mehl, 1939; Kissinger, 1956, 1957).
This section describes both of these techniques, the parameters resulting
from these analyses, and a unifying analysis of both techniques.
The isothermal crystallization kinetics has been described by the JMA
equation:
X ¼ 1 exp½kðt t0 Þn
ð3Þ
where X is the volume fraction transformed in time t, n is the Avrami
exponent, and t0 is the transformation onset time (Burke, 1965). The
reaction constant, k, is described by the Arrhenius equation:
k ¼ k0 exp
EA
kB T
ð4Þ
which provides the temperature dependence to the crystallization process.
In this equation, EA is the activation energy for crystallization and k0 is the
reaction rate coefficient. From isothermal crystallization theory, the Avrami
exponent (n) has contributions from the nucleation conditions (p) and the
growth conditions (q). The value of p is 0 when all of the nuclei are present
at the transformation onset and 1 when nucleation occurs throughout the
transformation process. The value of q ranges from 1/2 to 3 dependent on
two factors: (1) the dimensionality of the crystallite growth (values of 1, 2, 3,
respectively, for rod, plate, and sphere morphologies) and (2) the growthlimiting factor (1/2 for diffusion-controlled growth and 1 for interfacecontrolled growth). These two factors are combined, resulting in n ¼ p þ q
values ranging from 1/2 (preexisting nuclei and diffusion-controlled,
rod-like growth) to 4 (continuous nucleation and interface-controlled
sphere-like growth).
The use of the JMA model for kinetics in nanocrystalline soft magnetic
alloys violates two of the simplifying assumptions of the model. First,
in the strictest sense, the model applies to compositionally invariant
241
Nanocrystalline Soft Magnetic Alloys
transformations (e.g., polymorphic reactions). This does not strictly apply to
the nanocrystalline soft magnetic alloys due to the multiphase nature of the
alloys and the preferential segregation of certain elements to each phase. As
an example, during the crystallization of Fe–Si–B–Nb–Cu alloys, crystallites
are enriched in Fe and Si, while the remaining amorphous phase is enriched
in Nb and B. Second, in the later stages of crystallization the model
considers the overlap of diffusion fields between grains that arrest the
transformation. Again, this does not apply to this type of nanocomposite
microstructure, where each grain tends to be isolated from others by the
intergranular amorphous matrix. That being said, the analysis of nanocrystalline soft magnetic alloys by JMA kinetics has been widely used to discuss
primary crystallization with reasonable values of activation energies and
Avrami exponents (in most cases).
A study of the isothermal crystallization kinetics of an alloy with
composition Fe73.5Si15.5B7Nb3Cu1 reported Avrami exponents for a series
of annealing temperatures and annealing times, using DSC and XRD to
determine crystalline volume fractions transformed (X) (Yavari and Negri,
1997). The Avrami exponents were found to change with annealing
time from n ¼ 2.5–3 at early stages of annealing to n ¼ 0.75–1.1 for late
stages. The latter values were too low to be explained by the JMA
kinetics model and were attributed to the inexactness of the DSC estimates
for X and composition gradients formed during the devitrification process
(a point that opposes the assumptions of the JMA model). Nucleation
site saturation effects may also play a role in the observed reduction in n
(Christian, 2002).
Constant heating rate experiments for crystallization of amorphous
alloys have been described by the Kissinger equation:
f
EA
¼ #exp
RTp
Tp2
ð5Þ
with the peak transformation temperature at Tp, constant heating rate of f,
a frequency factor #, and ideal gas constant, R (8.314 J/(K mol)). The
activation energy for crystallization can be determined by measuring the
exothermic crystallization peak temperature (Tp) at various heating rates and
plotting the resulting values as log[T2p/f] versus Tp1. This approach
requires limited time for collecting enough data for analysis of activation
energy, giving it an advantage over the isothermal technique. Kissinger
analysis should only be applied to systems where the peak transformation
temperature is coincident with a constant value of fraction transformed
(which may or may not be true for the nanocomposite alloys). Notwithstanding, the measurements seem to give reasonable values of activation
energy and have been widely applied to nanocomposite alloys. Quantitative
comparison between the JMA and Kissinger kinetics models is possible by
242
Matthew A. Willard and Maria Daniil
Table 4.3 Activation energies for primary crystallization (Ea1) and secondary
crystallization (Ea2) for Fe–Si–B–(Nb,Cu) alloys
Ea1 (kJ/mol)
Ea1 (eV/at) Ea2 (kJ/mol) Ea2 (eV/at)
Fe77.5Si13.5B9
395.8 101.0 4.10 1.05 350.3 59.2 3.63 0.61
Fe76.5Si13.5B9Cu1
247.8 14.2 2.57 0.15 259.3 8.74 2.69 0.10
Fe74.5Si13.5B9Nb3
409.3 43.4 4.24 0.45
–
–
Fe73.5Si13.5B9Nb3Cu1 378.3 66.8 3.92 0.69 443.9 59.6 4.60 0.62
Averages and standard deviations are provided based on values from both Johnson–Mehl–Avrami and
Kissinger analyses (Bigot et al., 1994; Blázquez et al., 2003; Borrego and Conde, 1997; Chau et al., 2004;
Chen and Ryder, 1995; Duhaj et al., 1991; Illeková, 2002; Kane et al., 2000; Kulik, 1992; Leu and Chin,
1997; Panda et al., 2000; Surinach et al., 1995; Varga et al., 1994a; Zhang and Ramanujan, 2005; Zhang
et al., 1998a; Zhou et al., 1994).
taking the time derivative of the JMA isothermal kinetics equation (Damson
and Würschum, 1996):
f¼
@X
¼ nkð1 X Þ½Lnð1 X Þ ðn1Þ=n
@t
ð6Þ
For this reason, the two techniques should give similar activation energy
results. The average activation energies for Fe–Si–B–(Nb,Cu) alloys are
shown in Table 4.3, with values averaged from both JMA and Kissinger
techniques.
Several studies have examined the activation energy for substitution of
ETMs in Fe73.5Si13.5Nb3xMxB9Cu1 alloys. With the small amount of Cu
giving heterogeneous nucleation sites in the early stages of primary crystallization, the strongest contributor to the activation energy is the growth of
the crystallites. For this reason, variation of the ETM content has a substantial effect on the activation energy. A reduction in activation energy has
been observed as Ta and V are substituted for Nb (Borrego and Conde,
1997; Conde and Conde, 1994; Kulik, 1992). Mo substitution has been
found to slightly decrease the activation energy and partial Zr substitution
tends to raise the activation energy (Borrego and Conde, 1997). These
results are consistent with variation of crystallization temperature in Fe73.5Si13.5M3B9Au1 alloys, where M ¼ Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, W
(Duhaj et al., 1991; Kataoka et al., 1989). Figure 4.30 shows the phases
formed in the Fe73.5Si13.5M3B9Au1 alloy series under different isothermal
annealing conditions (3600 s). While Cu was used in the activation energy
studies and Au in Fig. 4.30, the very similar role these elements play in the
kinetics validates comparison. The greatest stability of the amorphous phase
is observed in the Nb-containing alloy, with Mo, Hf, W, and V, providing
an as-spun amorphous phase and primary crystallites with amorphous matrix
after annealing above 700 K for 3600 s. On the other hand, substitution of
243
Nanocrystalline Soft Magnetic Alloys
1400
Annealing temperature (K)
Fe73.5Si13.5ETM3B9Au1
Amorphous
a-(Fe,Si) (A2)
Fe23B6
tann = 3600 s
1200
1000
800
600
400
200
Ti
V
Cr
Zr
Nb
Mo
Hf
Early transition metals
Ta
W
Figure 4.30 Schematic diagram showing phases formed after annealing for 3600 s at
various temperatures for Fe73.5Si13.5M3B9Au1 alloys, where M ¼ Ti, V, Cr, Zr, Nb, Mo,
Hf, Ta, W (Duhaj et al., 1991; Kataoka et al., 1989).
Ti and Zr is found to have poor glass formability, with crystallites in the asspun state. The reduced secondary crystallization observed when Cr substitutes for Nb is consistent with the smaller atomic radius of Cr giving it a
role in alloying in the a-(Fe,Si) crystallites rather than partitioning to the
remaining amorphous phase. Limited substitution of Mo for Nb in Fe73.5Si13.5M3B9Cu1 alloys is shown in Fig. 4.31 (Borrego and Conde, 1997;
Borrego et al., 1998; Liu et al., 1996a; Zhang et al., 1996a). The results are
consistent with the Au-containing alloys in Fig. 4.30.
In alloys that do not contain Si, the activation energy for primary
crystallization has been examined as a function of the MTM content.
Figure 4.32 shows slightly decreased activation energy when Co is substituted for Fe in (Fe,Co,Mn)–M–B–Cu alloys (M ¼ Zr or Nb). Alloys higher
in B content (14–15 at%) showed moderately higher activation energy (near
350 kJ/mol) than alloys with lower B content (4–5 at%) near 290 kJ/mol
(Blázquez et al., 2001, 2005; Conde et al., 2004b; Johnson et al., 2001;
Majumdar et al., 2007). Alloys with composition (Fe,Co,Ni)88Zr7B4Cu1
had intermediate values near 325 kJ/mol, with a drop to near 200 kJ/mol as
the compositions become rich in Ni (>9.2 e/atom) (Hornbuckle et al.,
2012; Willard and Daniil, 2009; Willard et al., 2012c).
Any technique that possesses sensitivity to the crystallization process may
be exploited to examine the crystallization kinetics, including measurements of resistivity, magnetization, heat evolved, and density. Kinetics of
crystallization can be tracked in many ways. Resistivity and magnetization
will be discussed in later sections. The density of an amorphous Fe73.5Si13.5Nb3B9Cu1 alloy was found to be 7150 kg/m3 (El Ghannami et al.,
244
Matthew A. Willard and Maria Daniil
1400
Fe73.5Si13.5ETM3B9Cu1
tann = 3600 s
Annealing temperature (K)
1200
1000
Amorphous
a-(Fe,Si) (A2)
Fe3Si (D03)
Fe2B
Fe23B6
Fe3B (D011)
800
600
400
200
Zr
Nb
Mo
4d early transition metals
Activation energy for Primary crystallization
(kJ/mol)
Figure 4.31 Schematic diagram showing phases formed after annealing for 3600 s at
various temperatures for Fe73.5Si13.5M3B9Cu1 alloys, where M ¼ Nb, Mo, Nb þ Mo
(Borrego and Conde, 1997; Borrego et al., 1998; Liu et al., 1996b; Zhang et al., 1996a).
400
300
200
(Fe,Co)88Zr7B4Cu1
(Fe,Co)83Zr6B5Ge5Cu1
(Fe,Co)83Zr6B10Cu1
(Fe,Co,Mn)78Nb6B15Cu1
(Fe,Co,Mn)78Nb6B16
(Fe,Co,Ni)88Zr7B4Cu1
100
0
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
Valence electrons per atom
Figure 4.32 Activation energy for primary crystallization for (Fe,Co)88Zr7B4Cu1
(open circle: Johnson et al., 2001; Majumdar et al., 2007), (Fe,Co)83Zr6B5Ge5Cu1
(closed circle: Blázquez et al., 2005), (Fe,Co)83Zr6B10Cu1 (half-closed circle:
Blázquez et al., 2005), (Fe,Co,Mn)78Nb6B15Cu1 (opened square: Blázquez et al.,
2001; Conde et al., 2004a), (Fe,Co,Mn)78Nb6B16 (closed square: Blázquez et al.,
2001; Conde et al., 2004a), and (Fe,Ni,Co)88Zr7B4Cu1 (diamonds: Hornbuckle
et al., 2012; Willard et al., 2012c) alloys with variation in valence electrons per atom.
Nanocrystalline Soft Magnetic Alloys
245
1994). Upon crystallization, the density was found to increase by 1–2% as
higher density crystalline phases replace the lower density amorphous phase.
Added usefulness is found when the technique yields information proportional to the fraction of the sample transformed with time or temperature.
For this reason, differential thermal techniques (DTA, DSC), thermomagnetic techniques, resistivity (T/t dependent), in situ X-ray diffraction (T/tdependent), and in situ transmission electron microscopy (T/t dependent) can
provide greater information about the transformations.
In combination, these techniques can provide information about the
time necessary for a transformation to occur and the resulting phases that are
formed. The time-temperature transformation (TTT) diagrams are useful
constructs for examining the crystallization kinetics of amorphous alloys. In
addition to providing information about the time–temperature relationship
for achieving primary crystallization and avoiding secondary crystallization,
such a diagram can also estimate the critical cooling rate necessary for
amorphous alloy formation. An extensive discussion of isothermal and
constant heating rate crystallization kinetics as well as their use for describing
TTT diagrams is found in a recent review (Clavaguera-Mora et al., 2002).
The TTT diagrams for Fe77.5Si13.5B9 and Fe76.5Si13.5B9Cu1 alloys indicate that even relatively low annealing temperatures (below 700 K) result in
partial crystallization of the alloys (Fig. 4.33). The primary crystallization
temperatures cannot be identified since all annealed samples show some sign
of crystallization; an indication that the amorphous phase has little stability
in these alloys (especially true for Fe77.5Si13.5B9). The secondary crystallization temperature is clearly identified for both alloy compositions, exhibiting
shorter times to transformation in the Fe76.5Si13.5B9Cu1 alloys at temperatures above 800 K. However, the secondary crystallization occurs at lower
temperatures for the Fe77.5Si13.5B9 alloy when annealed for 1800 s. This is
consistent with the role of Cu as an aid for crystallite nucleation.
The Fe73.5Si13.5B9Nb3Cu1 alloy has been extensively studied, allowing a
greater degree of detail for its TTT diagram. Figure 4.34 shows the TTT
diagram with clear indication of both primary and secondary crystallization.
It should be noted that the a-(Fe,Si) phase is typically identified at shorter
times and lower temperatures than the ordered a1-Fe3Si phase. This may be
an incidental effect due to an inability to identify the atomic ordering in the
alloy due to Bragg intensity broadening with the small grain size. It may also
be a direct effect related to the lack of ordering that occurs at short times and
low temperatures. It is not clear from experiments whether either of these
(or both) is true. Separation between primary and secondary crystallization
seems to be nearly constant from 102 to 105 s with a value of 150 K. At
the secondary crystallization temperature boundary, the amorphous phase is
identified concurrently with some Fe2B, Fe23B6, or Fe3B phases; however,
at higher temperatures and longer times, the phase is no longer found. The
highest annealing temperatures and longest annealing times tend to show all
of these secondary phases with coarsened a-(Fe,Si) or a1-Fe3Si.
246
Matthew A. Willard and Maria Daniil
1000
Temperature (K)
Fe77.5Si13.5B9
900
800
Amorphous
a-(Fe,Si) (A2)
Fe3Si (D03)
Fe2B
Fe23B6
Fe3B (D011)
700
600
500
1
10
100
1000
Time (s)
10
4
105
106
1000
104
105
106
1000
Temperature (K)
Fe76.5Si13.5B9Cu1
900
800
Amorphous
a-(Fe,Si) (A2)
Fe3Si (D03)
Fe2B
Fe23B6
700
600
500
1
10
100
Time (s)
Figure 4.33 Time–temperature transformation (TTT) diagrams for Fe77.5Si13.5B9
(Kataoka et al., 1989; M€
uller et al., 1992; Noh et al., 1990; Zhang and Ramanujan,
2005, 2006; Zhou et al., 1994) and Fe76.5Si13.5B9Cu1 alloys (Ayers et al., 1998;
Noh et al., 1990; Yoshizawa and Yamauchi, 1990; Zhang and Ramanujan, 2006;
Zhou et al., 1994).
Similar results are found for the Fe73.5Si16.5B6Nb3Cu1 alloy; however,
both primary and secondary crystallization temperatures seem to be shifted
to longer times and higher temperatures. As shown in Fig. 4.35, an additional secondary phase loosely identified as FeNbSi is shown (unknown
crystal structure).
There are noticeable differences between the TTT diagrams of the
Fe73.5Si13.5B9Nb3Cu1 and the Fe91Zr7B2 alloys (see Figs. 4.34 and 4.36).
First, the primary crystallization temperature is much lower than in the Sicontaining alloy. Second, the separation of primary and secondary crystallization is substantially larger. The lower primary crystallization temperature
indicates a stabilization of a-Fe over the amorphous precursor. In the case of
Fe91Zr7B2 alloys, the secondary crystalline phase was identified as Fe3Zr
(possibly with Fe23Zr6 structure). The activation energy for primary
247
Nanocrystalline Soft Magnetic Alloys
1400
Fe73.5Si13.5B9Nb3Cu1
Temperature (K)
1200
1000
800
Amorphous
a-(Fe,Si) (A2)
Fe3Si (D03)
Fe2B
Fe23B6
Fe3B (D011)
600
400
1
10
100
1000
104
105
106
Time (s)
Figure 4.34 Time–temperature transformation (TTT) diagrams for Fe73.5Si13.5B9Nb3Cu1
alloy (Alvarez et al., 2001; Ayers et al., 1998; Chen and Ryder, 1995; Cremaschi et al., 2002;
Crisan et al., 1997; Duhaj et al., 1995; Gorrı́a et al., 1996; Hampel et al., 1995; Herzer, 1993;
Hono et al., 1999; Kataoka et al., 1989; Matta et al., 1995; M€
uller et al., 1992; Noh et al.,
1990; Pascual et al., 1999; Rixecker et al., 1992; Saad et al., 2002; Vázquez et al., 1994;
Wang et al., 1991).
1400
Fe73.5Si16.5B6Nb3Cu1
Temperature (K)
1200
1000
800
Amorphous
a-(Fe,Si) (A2)
Fe3Si (D03)
Fe2B
Fe23B6
Fe3B (D011)
FeNbSi
600
400
1
10
100
1000
104
105
106
Time (s)
Figure 4.35 Time–temperature transformation (TTT) diagrams for Fe73.5Si16.5B6Nb3Cu1
alloy (Bie
nkowski et al., 2004a; Blasing and Schramm, 1994; Gorrı́a et al., 1996; Gupta et al.,
1994; Herzer, 1993; Kulik et al., 1997; Matta et al., 1995; M€
uller et al., 1991; Yoshizawa
and Yamauchi, 1990; Zemčik et al., 1991).
248
Matthew A. Willard and Maria Daniil
1400
Fe91Zr7B2
Temperature (K)
1200
1000
800
600
Amorphous
a-Fe
Fe3Zr
400
10
100
1000
4
10
10
5
6
10
10
7
Time (s)
Figure 4.36 Time–temperature transformation (TTT) diagrams for Fe91Zr7B2 alloy
(Suzuki et al., 1990; Suzuki et al., 1994; Suzuki et al., 1996).
crystallization in similar alloys was in the range of 320–370 kJ/mol, consistent with grain growth of the a-Fe phase and also consistent with the
observed primary crystallization observed in the TTT diagram (Al-Haj
and Barry, 1998; Duhaj et al., 1996; Hsiao et al., 2002).
Chen Chen and Ryder have examined the crystallization process of
Finemet on preannealed samples by differential scanning calorimetry
(Chen and Ryder, 1995). They then determined the activation energy for
crystallization as a function of preannealing temperature using a Kissinger
analysis. Their results show a rapid increase in activation energy from 401 to
494 kJ/mol as the preannealing temperature was varied from 400 to 500 C.
The crystallization temperature at 10 K/min was reported as 522 C, but
X-ray diffraction of the samples annealed as low as 480 C shows signs of
crystallization. These results indicate slowing diffusion as the crystallization
process proceeds, consistent with Nb enrichment of the remaining amorphous matrix and the retarded growth of the nanocrystalline grains at
extended annealing times.
4.4. Order–disorder transformations
Long-range atomic ordering has been observed in (Fe,Si)–Nb–B–Cu and
(Fe,Co)–Zr–B–Cu alloys. In the former, the BCC solid solution of Fe with
Si is found to order as the Si content is increased, first by losing the body
centering to form an a2-FeSi phase (B2 structure) and then to a slightly
249
Nanocrystalline Soft Magnetic Alloys
Table 4.4 Two types of superlattice reflections and fundamental reflections
identified for atomic ordering in (Fe,Si) alloys
Structure factors (D03)
S2
S1
F
S2
S1
Fhkl ¼ 4(fA fB)
Fhkl ¼ 4(fB fA)
Fhkl ¼ 4(3 fA þ fB)
Fhkl ¼ 4(fA fB)
Fhkl ¼ 4(fB fA)
D03
Fm3m
(1 1 1)
(2 0 0)
(2 2 0)
(3 1 1)
(2 2 2)
B2
Pm3m
–
(1 0 0)
(1 1 0)
–
(1 1 1)
A2
Im
3m
–
–
(1 1 0)
–
–
F indicates a fundamental reflection, S1 is a superlattice reflection found by B2 ordering, and S2 is an
additional superlattice reflection from D03 ordering.
more complicated a0 -Fe3Si phase with D03 structure. The ordering can be
evident in the saturation magnetization, magnetocrystalline anisotropy,
resistivity, and lattice parameters, so atomic ordering is quite important in
many of the studied alloys (e.g., see Hall, 1959) (Table 4.4).
In (Fe,Si)–Nb–B–Cu alloys, the ordered Fe3Si phase is frequently
reported after primary crystallization. Two types of superlattice reflections
are found with D03 ordering, one set comes when the BCC solid solution
loses its body-centered ordering (A2 transforms to B2) and the second when
further ordering of the Si occurs to form the D03 structure (described in
more detail in Section 5.1). Both sets of superlattice reflections are observed
in D03-ordered samples; however, the size of the diffraction peaks is smaller
than the fundamental peaks and broader due to their nanocrystalline size,
making them difficult to identify in many cases. If only the S1-type superlattice peaks are observed, the FeSi (B2) phase is present (although this is not
typically observed, it may be possible for high Si-content alloys). It is likely
that some diffraction patterns do not have sufficient intensity to show the
atomic ordering (or partial ordering) in the samples even when it is present.
Primary crystallized alloys with composition Fe75.5Si12.5B8Nb3Cu1
show enrichment of remaining amorphous phase in Nb and B as the
crystallites grow in diameter (Van Bouwelen et al., 1993). Slight differences
were observed for the Si content of the remaining amorphous phase and the
crystallized a-(Fe,Si) in this alloy annealed at 776 K for 105 s. The degree of
ordering is both a function of the Si content of the alloy and the annealing
conditions. For a Fe73.5Si13.5B9Nb3Cu1 alloy, the degree of atomic ordering
was determined for various annealing conditions by tracking the ratio of
superlattice to fundamental peaks (of both S1- and S2-types) from X-ray
diffraction experiments (see Fig. 4.37) (Zhang et al., 1998b; Zhu et al.,
1991). A common trend was found in both sets of superlattice reflections,
indicating that B2 ordering and antisite disorder are not likely. Higher Si
content in the crystalline phase (as determined by lattice parameter
250
Matthew A. Willard and Maria Daniil
Long-range order parameter
0.80
0.75
(111) S2
(200) S1
(311) S2
0.70
0.65
0.60
0.55
0.50
480 490 500 510 520 530 540 550 560 570 580 590 600
Annealing temperature (°C)
Figure 4.37 Long-range order parameter for D03 ordering in Finemet-type with
annealing temperature. After Zhang et al. (1998b).
measurements) accompanied the stronger ordering observed at higher
annealing temperatures.
In (Fe,Co)–Zr–B–Cu alloys, the B2-type atomic ordering has been
observed; however, the superlattice reflections are very difficult to determine due to the similar atomic scattering factors of Fe and Co, with the
structure factor being proportional to the difference between the two. For
this reason, special X-ray diffraction techniques must be used to observe the
superlattice reflections (see Willard et al., 1998, 1999b for example).
5. Structural and Microstructural
Characterization
The phases formed during primary crystallization and the composition
of each phase in the nanocomposite microstructure have a strong effect on
the magnetic properties. As an illustration of the importance of crystal
structure and composition of phases on the properties, the coercivities of a
series of Fe73.5xMxSi13.5B9Nb3Cu1 alloys (with M ¼ Cr, Co, Ni) are plotted against composition in Fig. 4.38. Significant increases in coercivity are
observed for (Fe,Cr)-containing alloys occur near 10 at% substitution. In this
case, Cr efficiently reduces the Curie temperature of the intergranular
amorphous phase causing decoupling between grains, which leads to the
rising coercivity. Amount and distribution of Cr are important in this case.
A significant rise in coercivity is also observed for (Fe,Co)-containing alloys
251
Nanocrystalline Soft Magnetic Alloys
Coercivity (A/m)
10,000
1000
Fe73.5 – xMxSi13.5B9Nb3Cu1
M = Ni
M = Co
M = Cr
100
10
1
0.1
1
10
100
M content (at%)
Figure 4.38 Coercivity variation with magnetic transition metal content in
Fe73.5xMxSi13.5B9Nb3Cu1 alloys where M ¼ Cr (Atalay et al., 2001; Chau et al.,
2006; Franco et al., 2001b; Marı́n et al., 2002), Ni (Atalay et al., 2001; Agudo and
Vázquez, 2005), and Co (Atalay et al., 2001; Chau et al., 2004; Gómez-Polo et al.,
2001; Kolano-Burian et al., 2004b; Marı́n et al., 2006; Mazaleyrat et al., 2004).
above 50 at% substitution. In this case, the structure change of the primary
crystalline phase to FCC and/or HCP results in the observed increase in
coercivity (Gómez-Polo et al., 2001). This section discusses typically
observed phases, compositional effects, and the microstructures and domain
structures that are important for understanding extrinsic magnetic properties.
5.1. Crystal structure and phase identification
The nanocomposite microstructure developed during primary crystallization can be formed of several types of crystallites—a feature that largely
determines how we classify the alloy. The structure of the crystalline phase
can have a significant impact on the magnetic properties. Cubic crystallites
that are rich in MTMs are most desirable for primary crystallization due to
their large magnetization and their typically small magnetocrystalline anisotropies. When alloys are rich in Fe (without significant Si content, e.g.,
Fe–Zr–B–(Cu)), they typically form the BCC phase, upon primary crystallization. Substitution of Co for Fe in these alloys can result in the long-range
ordering within the crystallites, producing an a0 -FeCo phase with CsCl
(B2)-type ordering. Ni-rich alloys tend to form an FCC phase, and Co-rich
alloys have been found to have both FCC and hexagonal close-packed
(HCP) structures during primary crystallization. Due to the metastable
nature of the processing, the phase-field boundaries between BCC, FCC,
and HCP phases are typically different from equilibrium.
252
Matthew A. Willard and Maria Daniil
(a)
(b)
(c)
z
y
Figure 4.39 Relationship between crystal structures of common primary crystalline
phases (a) a-Fe (A2), (b) a0 -FeCo (B2), and (c) a0 -Fe3Si (D03).
When Si is substituted for Fe (instead of Co), the ordered phase a0 -Fe3Si
and/or disordered phase a-(Fe,Si) are observed. The disordered phase has the
BCC structure where Fe and Si form a solid solution. While intermediate
ordering between the a0 -Fe3Si and a-(Fe,Si) phases is possible (e.g., the
a2-FeSi phase with B2 structure), it is not commonly reported. The ordered
Fe3Si phase has a D03 crystal structure ðFm3mÞ with a lattice parameter about
twice the size of the disordered BCC phase (near 5.667 Å). In the binary
Fe–Si phase diagram, the Fe3Si phase has substantial solubility for Si extending
to mainly Fe-rich compositions from 25 at% Si in Fe (Massalski, 1990). Two
inequivalent Fe sites are positioned at (1/4, 1/4, 1/4) and (1/2, 1/2, 1/2)
(Wyckoff 8c and 4b) and Si at the (0, 0, 0) sites (Wyckoff 4a). The (1 1 1) and
(2 0 0) superlattice reflections are indicative of the D03 ordering, differentiating it from BCC and B2 crystal structures (see Fig. 4.39). Partial substitution
of Co for Fe in Fe73.5xCoxSi13.5B9Cu1 nanocrystalline alloys showed preferential population of Co on the 8c site by neutron diffraction (resulting in
additional ordering forming an L12 phase) (Gómez-Polo et al., 2002).
Due to the deleterious effect of secondary crystallization on the stability
of the nanocrystalline microstructure, recent studies have focused on understanding these phases. In (Fe,Si)-based alloys, the most common secondary
phases include the tetragonal Fe2B phase, the orthorhombic Fe3B phase,
and the cubic Fe23B6 phase. The former two structures are shown in
Fig. 4.40. The Fe2B phase is an equilibrium phase forming by peritectic
reaction at 1660 K. Its structure (Strukturbericht, C16) consists of stacked
Fe and B layers in a body-centered configuration with B atoms having 10
near neighbors (i.e., 8 Fe in a square anti-prism in a–b plane and 2 B atoms
forming caps along the c-axis—see Fig. 4.40a). The Fe atoms are topologically close packed with a coordination number of 15 in a Frank–Kaspertype configuration.
Both Fe3B and Fe23B6 are metastable phases. While several Fe3B phases
have been reported, the most commonly identified crystal structure during
secondary crystallization is the well-known Fe3C (cementite) prototype
(Strukturbericht, D011). The B atoms in this orthorhombic structure have
eight close Fe near neighbors and one more at about 20% greater distance,
253
Nanocrystalline Soft Magnetic Alloys
(a)
(b)
x
z
y
x
y
Figure 4.40 Crystal structures for two common secondary phases in (Fe,Si)-based
alloys: (a) Fe2B (C16) viewed along [0 0 1]; (b) Fe3B (D011) viewed along [11 0 4]
direction. Large spheres represent Fe atoms and small spheres represent B atoms.
(a)
(b)
z
z
x
x
y
y
Figure 4.41 Crystal structures for two common secondary phases in Fe-based alloys:
(a) Fe23B6 (D84) (large spheres—Fe; small spheres—B), (b) Fe23Zr6 (D8a) (large
spheres—Zr; small spheres—Fe). Lower left shows the arrangement of atoms that
populate the FCC sites for each structure (see text).
forming a tri-capped trigonal prism (illustrated in Fig. 4.40b). The Fe atoms
have a nearly close-packed structure (with B in distorted interstitial sites).
All B atoms are closely networked with Fe in the structure but share close
proximity with other B atoms. In contrast, the Fe23B6 phase (with cubic
Cr23C6 structure (Strukturbericht, D84)) exhibits well-separated B atoms
and a high degree of symmetry (see Fig. 4.41a). In this structure, the FCC
sites are populated with a central Fe atom surrounded by 12 other Fe atoms
in a cuboctahedron and 6 B atoms in an octahedron. All tetrahedral sites
between these clusters are filled with Fe, and all octahedral interstices are
filled with eight Fe atoms in cube formation. This results in B atoms having
a square anti-prism coordination of eight Fe atoms and no near-neighbor B
atoms. The Fe atoms have four inequivalent sites, with three of these sites
254
Matthew A. Willard and Maria Daniil
having Frank–Kasper-like coordination and the final site being the highsymmetry FCC site.
Another secondary phase commonly found in Fe–Zr–B–(Cu) alloys is
the Fe23Zr6 phase (along with Fe23B6). Although Fe23B6 and Fe23Zr6 are
both FCC phases with 116 atoms per unit cell, they are structurally quite
different. The FCC sites in Fe23Zr6 are occupied by a central Fe atom
surrounded by a cube of 8 Fe atoms, an octahedron of 6 Zr atoms, and a
cuboctahedron of 12 more Fe atoms (which share vertices with clusters on
adjacent FCC sites) (see Fig. 4.41b). All octahedral interstices are filled with
four Fe atom tetrahedra. The Zr atoms are arranged with a seven-capped
pentagonal prism configuration with a coordination number of 17 (13 Fe
and 4 Zr atoms). The Fe atoms have four inequivalent sites, two are
icosahedral, one is Frank–Kasper-like, and the final site has the highsymmetry FCC placement. Table 4.5 provides information regarding commonly observed primary and secondary crystalline phases.
The soft a-(Fe,Si) phase is retained after secondary crystallization, but it
coarsens due to the absence of the intergranular amorphous phase at these
temperatures. In an alloy with composition Fe73.5Si13.5B9Nb3Cu1, secondary crystallization resulted in heavily twinned Fe2B at temperatures as low as
580 C (Wang et al., 1991; Zhu et al., 1991). The Fe3B phase was observed
by others after annealing at 600 C for 3.6 ks, and the (Fe,Nb,Si)23B6 phase
was found after annealing at 700 C (Chen and Ryder, 1997).
The nominal composition of the primary crystalline phases is rich in
MTMs, whereas the glass-forming elements, Nb, Zr, B, etc., have been
chosen not only for their aid in rapid solidification to a fully amorphous
alloy but also for their limited solubility in the primary crystalline phase.
However, due to the nonequilibrium processing, some solubility of these
elements is found in the primary crystalline phase. For instance, a lattice
parameter 4% larger than a-Fe is observed in Fe91Zr7B2 alloys after crystallization above the primary crystallization temperature (Suzuki et al., 1991c).
As the annealing temperature is increased, the lattice parameter decreases
toward the a-Fe phase value. Detailed analysis of the composition profiles
through crystallizing grains using APFIM on the similar Fe90Zr7B3 alloy
shows near complete rejection of Zr from the crystallites and retention of
some B, leading to the increased lattice parameter (Zhang et al., 1996c).
A similar effect is observed in other Fe- and (Fe,Co)-based alloys which do
not contain Si (Makino et al., 1995; Willard et al., 2002c, 2007).
In the Fe73.5Si13.5B9Nb3Cu1 alloy, the lattice parameter of the primary
crystalline phase also tends to change with annealing time and temperature.
In this case, Si is enriched in the crystalline phase as annealing progresses
until the lattice parameter of a-(Fe,Si) is near that of 20–23% Si in Fe (which
was also found to be consistent with the observed Curie temperature
(Herzer, 1991)). Thermal expansion coefficients for the a-(Fe,Si), Fe3B,
and Fe2B phases were determined from in situ neutron diffraction studies,
Table 4.5
Primary and secondary crystalline phases identified for typical nanocomposite soft magnetic alloys
Phase
Prototype and
(Strukturbericht)
Space
group
Lattice parameter Pearson
(Å)
symbol
Atom type and
(Wyckoff notation)
a-Fe
g-(Fe,Ni)
a0 -FeCo
W, BCC (A2)
Cu, FCC (A1)
CsCl (B2)
Im3m
Fm3m
Pm3m
a ¼ 2.8664
a¼3.5240 (Ni)
a ¼ 2.8508
cI2
cF4
cP2
a0 -Fe3Si
BiF3 (D03)
Fm3 m
a ¼ 5.6554
cF16
Fe2B
Al2Cu (C16)
I4/mcm
tI12
Fe3B
Fe3C (D011)
Pnma
a ¼ 5.110
c ¼ 4.183
a ¼ 4.439
b ¼ 5.428
c ¼ 6.699
oP16
Fe (2a)
Fe (4a)
Fe (1a)
Co (1b)
Si (4a)
FeI (4b)
FeII (8c)
B (4a)
Fe (8h)
B (4c)
FeI (4c)
FeII (8d)
Fe23B6
Cr23C6 (D84)
Fm3m
a ¼ 10.595
cF116
Fe23Zr6
Mn23Th6(D8a)
Fm3m
a ¼ 11.578
cF116
FeI (4a)
FeII (8c)
B (24e)
FeIII (32f) FeIV (48h)
FeI (4a)
FeII (24d)
Zr (24e)
FeIII (32f1) FeIV (32f2)
Special
positions
xFe ¼ 0.334
xB ¼ 0.3764
zB ¼ 0.4426
xFeI ¼ 0.0388
zFeI ¼ 0.6578
xFeII ¼ 0.1834
yFeII ¼ 0.0689
zFeII ¼ 0.1656
xB ¼ 0.276
xFeIII ¼ 0.381
yFeIV ¼ 0.171
xZr ¼ 0.203
xFeIII ¼ 0.321
xFeIV ¼ 0.178
Lattice parameters and special positions are identified for bulk crystalline samples. Primary phases are identified in bold face (Buschow et al., 1983; Ellis and Greiner, 1941;
Khan et al., 1982; Ohodnicki et al., 2008a).
256
Matthew A. Willard and Maria Daniil
with da/a values of 1.78 105, 1.34 105, and 1.15 105 K1, respectively (Barquı́n et al., 1998). The result for a-(Fe,Si) was somewhat larger
than expected.
5.2. Microstructure and phase distribution
The average grain size is the most important aspect of improving the loss
characteristics of nanocomposite soft magnetic alloys. However, the typical
microstructure for these nanocomposite soft magnetic materials consists of
multiple phases, so the grain size alone does not describe the microstructure.
For example, the high-resolution transmission electron micrograph in
Fig. 4.42 shows several important features not described by the grain
diameter. First, the grains are largely equiaxed, but some are more elongated
than others. Second, the material is not fully crystalline, with an intergranular amorphous phase up to 3 nm in width surrounding the grains. These
are common features of most of the successful alloys of this type, but these
characteristics are not the only ones that are important for refining the
magnetic properties.
The phase and grain size distributions, the compositions of each phase
and their crystal structures, and the fraction of each phase in the optimized
microstructure are terms that should not be ignored due to their importance
in the magnetic performance of the alloys. For example, the partitioning
of elements during crystallization can have a great effect on the microstructure, the Curie temperature of the remaining amorphous phase, and
the magnetization of the alloy. Also, the fraction transformed to the crystalline phase affects the magnetostriction and thermomagnetic properties of
5 nm
Figure 4.42 High-resolution transmission electron micrograph for a
(Fe0.05Co0.95)89Zr7B4 alloy showing 8–12 nm nanocrystalline grains embedded in
1–2 nm-wide amorphous matrix (Goswami and Willard, 2008).
257
Nanocrystalline Soft Magnetic Alloys
the nanocomposite. With more specificity, in Fe–Si–B–Nb–Cu alloys, the
desired grain refinement is not achieved unless both Nb and Cu are added in
small amounts. If Nb is not included, grain growth is not inhibited and
coarsening occurs rapidly (see Fig. 4.43). After the first stage of crystallization of a Fe76.5Si13.5B9Cu1 alloy, the grain size and its standard deviation
were found to be 71 and 22 nm, respectively (Kulik, 1992). When both Nb
and Cu are eliminated from the composition, the average grain size is
further degraded to near 300 nm. Refinement is possible by the substitution
of 3 at% Nb and 1 at% Cu for Fe, resulting in 11 nm grain diameters with
4.5 nm standard deviation. Figure 4.43 shows transmission electron micrographs of Fe73.5Si13.5Nb3B9Cu1 and related alloys, which have been
200
Fe77.5Si13.5B9
Fe73.5Si13.5B9Nb3Cu1
Fe76.5Si13.5B9Cu1
Fe77.5Si13.5B9
Fe74.5Si13.5B9Nb3
Fe77.5Si13.5B9
8 s at 550 °C
Grain diameter (nm)
3600 s at 550 °C
100
Fe76.5Si13.5B9Cu1
50
50 nm
3600 s at 550 °C
Fe76.5Si13.5B9Cu1
Fe73.5Si13.5B9Nb3Cu1
20
50 nm
50 nm
8 s at 550 °C
7200 s at 550 °C
1
10
10
2
3
10
10
4
Annealing time (s)
Figure 4.43 Diagram showing the average grain size as annealing time at 550 C is
varied for Fe73.5Si13.5Nb3B9Cu1, Fe76.5Si13.5B9Cu1, and Fe77.5Si13.5B9 with supporting
transmission electron micrographs for selected samples (Ayers et al., 1998; Willard and
Harris, 2002).
258
Matthew A. Willard and Maria Daniil
annealed for various times at 823 K. The absence of Cu has a far smaller
effect on the grain size than the absence of Nb.
The partitioning of elements in the alloy during the crystallization
process has a significant effect on the resulting microstructure and magnetic
properties. Cu clustering during the early stages of crystallization has been
spatially correlated with a-(Fe,Si) crystallites in Fe73.5Si13.5B9Nb3Cu1 alloys
using APFIM (Hono et al., 1999). The clusters were determined to be FCC
in structure (by EXAFS), enabling them to provide low-energy heterogeneous nucleation sites for the a-(Fe,Si) (Ayers et al., 1998; Sakurai et al.,
1994). As crystallization progresses, Nb has been determined to segregate to
the remaining amorphous phase while Si partitions to the a-(Fe,Si) crystallites. The Nb-enriched intergranular amorphous phase inhibits further grain
growth and the Si-enriched crystallites have lower magnetocrystalline
anisotropy; both aid the performance of the material. The final compositions of each phase, volume fractions transformed, and grain size depend on
the nominal composition of the Fe–Si–Nb–B–Cu alloy and the annealing
conditions (temperature and time) (Herzer, 1993). Annealing for 1 h above
the primary crystallization temperature is generally long enough to allow
nearly all of the available Si to partition to the crystalline phase, leaving the
remaining amorphous phase near an (Fe,Nb)2B composition. The Cu-rich
clusters that form during the early stages of annealing tend to slowly coarsen
over time and are typically found in the intergranular region.
Due to the stability of the ETMs enriched intergranular phase, nanocomposite alloys never reach 100% primary crystalline phase. The fraction
transformed to the crystalline phase has a strong influence on the magnetic
properties of the nanocomposite, especially when the Curie temperature of
the intergranular amorphous phase is near the operation temperature. In the
Fe73.5Si13.5B9Nb3Cu1 alloy, the crystalline fraction transformed and magnetostrictive coefficient of the alloy are intimately linked. This effect is
complex and related to the changing composition of the crystalline and
amorphous phases during crystallization, as well as the individual magnetostrictive coefficients of each phase (Herzer, 1995). Figure 4.44 illustrates
the variation of the magnetostrictive coefficient with crystalline fraction for
a Fe73.5Si13.5B9Nb3Cu1 alloy (Twarowski et al., 1995a). In Fe89Zr7B4
alloys, the volume fraction transformed has been tracked using electron
microscopy for various annealing temperatures for 3600 s (see Fig. 4.45a)
(Malki
nski and Ślawska-Waniewska, 1997). The coercivity is directly
affected by the fraction transformed through the intergranular exchange
interactions which are only weakly ferromagnetic in the amorphous phase
(Tam
C 293 K). The result is a lower coercivity with crystalline fraction
transformed attributed to the compositional changes in the intergranular
amorphous phase that raises the Tam
C (Fig. 4.45b).
The structural correlation length chosen to describe nanocomposite
materials is typically the average grain diameter. In most cases, the standard
259
Nanocrystalline Soft Magnetic Alloys
Magnetostrictive coefficient (ppm)
Fe73.5Si15.5B7Nb3Cu1
20
15
10
5
0
0
10
20
30
40
50
60
70
80
90
Crystalline fraction (%)
Figure 4.44 Magnetostrictive coefficient variation with crystalline fraction transformed in a Fe73.5Si13.5B9Nb3Cu1 alloy (Twarowski et al., 1995a).
deviation is less than 0.5 giving, close agreement between the median and
mean grain sizes (da Silva et al., 2000; Willard et al., 2000). However, the
dependence of the coercivity on grain size having a strong D6 dependence
means that large grains will have a greater influence on the coercivity than
smaller grains. This is especially true for samples with bimodal grain size
distributions, where a small volume fraction of significantly larger grains has
been shown to increase the coercivity by 50% in Fe–Nb–B alloys (Bitoh
et al., 2004). Simulations of nanocomposite Fe86Zr7B6Cu1 alloys show that
breadth in grain size distribution tends to lower the magnetic exchange
length (Lex), resulting in the necessity for smaller average grain sizes to
achieve the same effective magnetocrystalline anisotropy (through the random anisotropy model) (da Silva et al., 2000). The effect is quite significant
with a reduction in Lex by a factor of 3 when the grain diameter standard
deviation is raised from 0.01 to 0.4.
5.3. Magnetic domains and characteristic magnetic lengths
Soft magnetic materials easily form multiple magnetic domains when an
applied magnetic field is removed from the material due to their small
magnetic anisotropy and large magnetization. The reduction in magnetostatic energy is responsible for the formation of domains, which is favorable
despite the added energy cost of the domain walls between the fully
saturated domain regions. In nanostructured magnetic materials, the magnetic exchange length provides a fundamental length scale over which
nanocrystalline grains are coupled. So the magnetic domain does not
260
Matthew A. Willard and Maria Daniil
(a)
Crystalline fraction (%)
80
Fe89Zr7B4
tann = 3600 s
60
40
20
0
400 420 440 460 480 500 520 540 560 580 600 620 640 660
Annealing temperature (°C)
(b)
Fe89Zr7B4
Coercivity (A/m)
1000
100
10
35
40
45
50
55
60
65
70
75
80
85
90
Crystalline fraction (%)
Figure 4.45 (a) Variation of volume fraction transformed with annealing temperature
(3600 s) for Fe89Zr7B4 alloys; (b) effect of volume fraction transformed on the coercivity (Malki
nski and Ślawska-Waniewska, 1997).
necessarily possess a precise direction for the magnetization, rather the
magnetization may slightly vary in orientation across a macroscopic domain
in these materials. This section describes processing steps to control domains
structure, domain configurations and sizes, domain wall motion, and the
fundamental nature of the exchange correlation length.
The configuration of magnetic domains can have a significant impact
on the magnetic performance in soft magnetic materials. As mentioned
in earlier sections, the use of stress or magnetic fields during alloy processing
can greatly influence the domain structure changing the switching mode
from domain wall motion to coherent rotation. The former switching
261
Nanocrystalline Soft Magnetic Alloys
mode gives a square loop with a large remanent magnetization, and the latter
gives a sheared loop with constant permeability over a wide range of fields. With
such a dominant effect on the magnetic behavior, knowledge of the domain
structure is an important factor in nanocrystalline alloy characterization.
The domain structure of nanocrystalline materials is in most ways indistinguishable from metallic glasses with regular, wide domains and wide, welldefined domain walls (Schäfer, 2000). Two distinct domain configurations
are typically found in the as-quenched ribbons of Fe–Si–Nb–B–Cu alloys due
to variations in the stress state of the sample and their large magnetoelastic
anisotropy (Guo et al., 1998, 2001; Schäfer et al., 1991). Regions with largely
tensile stresses show wide domains (from 50 to 100 s mm wide) with an
undulating character to the domain boundaries. In regions with local compressive stress, the domains consist of narrow laminar patterns (10 mm wide)
arranged in a maze-like pattern. The domain structure of as-cast alloys with
composition Fe73.5Si16.5Nb3B6Cu1 showed regions with both of these characteristics within the same micrograph (Grössinger et al., 1990). These
characteristics are also observed in amorphous magnets when the magnetostrictive coefficient is not exactly zero.
After annealing at the optimal annealing temperature, the domains are
largely 180 in character with wide domains at the center of the ribbon (up to
a few mm in width) and narrower closure domains near the ribbon’s edge
(Grössinger et al., 1990). Stress annealing of a Fe73.5Si13.5Nb3B9Cu1 alloy (at
540 C and 150 Mpa for 3.6 ks) was found to produce stripe domains with
spacing of about 100–150 mm in a direction transverse to the ribbon length (see
Fig. 4.46) (Alves and Barrué, 2003; Fukunaga et al., 2002b; Kraus et al., 1992).
Similar results for transverse domains on stress-annealed Fe–Si–Nb–B–Cu
alloys have been reported elsewhere (Fukunaga et al., 2002b; Hofmann
and Kronmüller, 1996; Lachowicz et al., 1997). Transverse domains were
also formed by magnetic field annealing in a saturating field when a Fe73Si16Nb3B7Cu1 alloy was crystallized at 843 K for 1.8 ks (Flohrer et al., 2005).
Transverse
Longitudinal
Ribbon axis
Figure 4.46 Schematic diagram showing the effects of induced anisotropy on magnetic domains (a) longitudinal and (b) transverse domains.
262
Matthew A. Willard and Maria Daniil
The stripe domains in this case were 125–150 mm in width. Stress annealing in a
Fe84Zr3.5Nb3.5B8Cu1 alloy produced the opposite domain configuration from
the Fe–Si–Nb–B–Cu alloys, with wide domains (several hundred microns
wide) parallel to the ribbon length (and therefore the applied stress) (Alves
and Barrué, 2003). In Fe78.8xCoxSi9B9Nb2.6Cu0.6 alloys, a correlation
between thep
induced
ffiffiffiffiffiffiffiffiffiffi anisotropy (Ku) and the domain width (ddw) was observed
with ddw / 4 1=Ku (Saito et al., 2006).
The domain structure of a Fe73.5Si13.5Nb3B9Cu1 alloy annealed at 550 C,
observed using Lorentz microscopy, showed circularly magnetized domains
with 5 mm radius, an expected domain configuration for low anisotropy
materials (Kohmoto et al., 1990). At this annealing condition, the grain size
is about 10 nm insinuating that each domain contains 2.5 105 grains in a
locally uniform anisotropy region. An electron holography study showed
somewhat smaller domain size for an alloy with similar processing; however,
in this case, the magnetic softness of the alloy was demonstrated by tilting the
sample within the remanent magnetic field from the inactive objective lens
(160 A/m) (Shindo et al., 2004). A small in-plane component of the
magnetic field (10–15 A/m) was enough to saturate the sample.
When the sample is annealed above the secondary crystallization temperature (1073 K), the domains are clearly pinned on the coarsened grains,
which are a few hundred nanometers in diameter (Kohmoto et al., 1990).
Shindo et al. who used electron holography on a sample annealed at 973 K
for 3.6 ks found that the domain sizes were smaller than the optimally
annealed condition and the domain walls were immobile due to the formation of Fe–B compounds (see Fig. 4.47e and f) (Shindo et al., 2004). These
results are consistent with the random anisotropy model at small grain sizes
where domain walls are not impeded by the fine grains (Hc / D6). Microstructures consisting of larger grains show domain walls pinned on the grain
boundaries, which is partially due to the formation of secondary crystallization, and illustrate the magnetic hardening of the alloy and the transition
into the Hc / 1/D regime.
Dynamic domain wall motion has been observed for a section of a toroidal
core using differential imaging of magneto-optical Kerr effect microscopy
(Závĕta et al., 1995). The Fe73.5Si16.5B6Nb3Cu1 core was optimally annealed
and measured using an alternating current magnetic measurement system at
1 kHz, while simultaneously observing the domain walls move under different applied field amplitudes. Some regions of the sample were found to have
better domain wall mobility than others with large jumps in wall position
observed as the applied field amplitude was increased.
Further dynamic domain observations were observed using stroboscopic
Kerr microscopy imaging with a time resolution of up to 1.5 ns (Flohrer
et al., 2005, 2006). Magnetic field annealing was used to prepare the
Fe73.5Si16B7Nb3Cu1 cores to different levels of induced anisotropy (near
5, 10, and 29 J/m). Weak induced anisotropy resulted in irregular domain
263
Nanocrystalline Soft Magnetic Alloys
H perpendicular to foil
Some in-plane H
(b)
As-spun
(a)
(d)
500 nm
(e)
(f)
500 nm
Hardly changed
973 K 3.6 ks
823 K 3.6 ks
(c)
Easily switched
500 nm
Figure 4.47 Reconstructed phase images from electron holography measurements of
Fe73.5Si13.5Nb3B9Cu1 thin foils (a,b) as-spun; (c,d) annealed at 823 K; (e,f) annealed at
973 K with (a,c,e) no tilt (b,d,f) 3 , 4 , 6 tilt (160, A/m field). Modified from Shindo
et al. (2004).
patterns and more active switching regions than the stronger induced
anisotropy samples due to high domain nucleation rates (see Fig. 4.48)
(Flohrer et al., 2006). The core losses were noticeably larger for samples
with greater degrees of induced anisotropy which was linked to the wider
domains and smaller amount of domain nucleation at high frequency (and
therefore lower number of switching regions near the domain walls). The
switching behavior of the domains, in this case, was observed to be largely
by coherent rotation of the magnetization (Flohrer et al., 2005). Domain
wall velocities tended to increase with measurement frequency and with
degree of induced anisotropy, with values of 0.75 and 1.4 m/s for moderate and strong Ku, respectively.
Magnetic correlations in the two-phase nanocomposite alloys have been
directly investigated by SANS. These experiments use an external magnetic
field applied perpendicular to the incident neutrons to image a twodimensional scattering profile for the material. The profile is then separated
into two parts, one related to the square of the angle between the scattering
vector and the applied field and the other independent of angle
(Wiedenmann, 1997). The angular-dependent part of the scattering profile
can be directly correlated to the magnetic correlation length of the sample,
while the angular-independent part is related to the structural correlation
(nuclear scattering).
264
Matthew A. Willard and Maria Daniil
50 Hz
1 kHz
5 kHz
10 kHz
Strong
Ku
200 mm
Moderate
Ku
Weak
Ku
Magnetic field,
easy axis,
magneto-optical
sensitivity axis
Specific power loss per cycle
(mWs/kg)
6
Strong Ku
5
4
Moderate Ku
3
Weak Ku
2
nt loss per cyc
ical eddy curre
Specific class
1
le
Specific hysteresis loss per cycle
0
0
2
4
6
8
10
Frequency [kHz]
Figure 4.48 Specific power loss per cycle versus frequency and corresponding domain
images of nanocrystalline Fe73Si16B7Nb3Cu1cores with different strengths of the
induced anisotropy Ku. The domain images are taken around the point of zero magnetic
induction. Domain refinement is distinctive with increasing frequency. Modified from
Flohrer et al. (2006).
Kohlbrecher, Wiedenmann, and Wollenberger found that an optimally
annealed Fe73.5Si15.5B7Nb3Cu1 alloy had strong temperature sensitivity in the
anisotropic scattering intensity as the temperature was varied from 404 to
720 K (Kohlbrecher et al., 1997). This effect was correlated with the difference in magnetization between the crystallites and amorphous matrix phases
which increase as the Curie temperature of the amorphous phase is exceeded
(at 650 K). The presence of a paramagnetic amorphous phase which decouples the ferromagnetic grains, starting slightly below the Curie temperature of
the amorphous phase and increasing in magnitude as the temperature is
increased, has been observed in a less direct manner in the increased coercivity
(Herzer, 1991). This decoupling was also observed by magneto-optic Kerr
effect microscopy measured at 623 K, where domains were observed to be far
more localized and less laminar in shape (Schäfer et al., 1991).
Nanocrystalline Soft Magnetic Alloys
265
Variation in the SANS differential scattering cross section with applied
field revealed a nonuniformity in the spin orientation on the scale of 100 nm
for a Fe73Si16B7Nb3Cu1 alloy with 17 nm grain size (Michels et al., 2005).
These field-annealed samples showed sheared hysteresis loops that saturate
at fields above 10 mT and are made up of domains about 100 mm in size.
For this reason, the nonuniform spin orientation, manifesting itself as a
magnetization ripple, is more closely related to the magnetic exchange
length rather than individual domain configurations (Hasegawa et al.,
1996; Hoffmann, 1969). In Fe89Zr7B3Cu1 alloys with smaller volume
fractions transformed (40%), the dipolar interactions between high magnetization a-Fe grains were observed by SANS (Vecchini et al., 2005). The
effect was not observed in an alloy with same composition but larger
crystalline fraction (near 70%) and was attributed to the large change in
magnetization across the interphase interface. The lower Curie temperature
of the amorphous phase has in Fe–Zr–B alloys also been suggested to give
rise to larger dipolar contributions to the domain ripple in these materials
(Hasegawa et al., 1996).
The random anisotropy model used to describe the magnetic softness in
nanocrystalline materials works on the premise that the grains are not strong
domain wall-pinning centers, since the grains are smaller than the exchange
correlation length. It has been shown (indirectly using SANS) that the
exchange length is much larger than the grain size, but smaller than the
domain size. Using Lorentz microscopy, the magnetic domains in a
Fe44Co44Zr7B4Cu1 alloy have been shown to be much larger than the
grain size without discernible pinning of the domain walls at the grain
boundaries (De Graef et al., 2001). The domain wall width was estimated
to be less than 2 mm using a magnetic force microscope for the Fe91Zr7B2
alloy, giving a exchange correlation length of 500 nm (or equivalently 104
grains) (Suzuki et al., 1997). This value is consistent with the observed
coercivity, but not the calculated exchange length of 50 nm (assuming
3
KFe
1 47 kJ/m ). It is surmised that the discrepancy may be due to the slight
dissolution of Zr and B in the a-Fe grains (as determined by atom probe)
(Hono et al., 1995).
6. Magnetic Property Characterization
The constitutive relationship between magnetic induction (B in Tesla),
magnetization (M in A/m), and magnetic field (H in A/m) is given by
B ¼ m0(H þ M). An attempt to use SI units under the Sommerfeld convention will be made throughout this section. This equation describes the
magnetic behavior of a material and magnetic fields both above and below
the Curie temperature. However, a spontaneous magnetization is only found
266
Matthew A. Willard and Maria Daniil
for the magnetically ordered phase below the Curie temperature, where the
exchange interaction is strong enough to align magnetic moments on adjacent atoms. The saturation magnetization (Ms) is an intrinsic material quantity
dependent on the composition of the phases, comprising the alloy and
established when a large magnetic field is applied to the alloy causing the
alignment of all of the magnetic moments in the material. When small
magnetic fields are applied, a good soft magnetic material possesses large
permeability (m ¼ B/H) and susceptibility (w ¼ M/H). Since soft magnetic
materials require very little H to create large changes in magnetization, the B
and M are sometimes used interchangeably (referring to M erroneously in Tesla
for instance). Due to the nonlinear behavior of a material’s response to an
applied magnetic field, a range of permeabilities are observed as a material is
taken from zero applied field to saturation. Much of this behavior is linked to
changes in the magnetic domain structure that can be greatly affected by the
microstructure.
Soft magnetic materials have been continually improved, most recently
by the development of the materials described in this review. These
improvements include higher saturation magnetization, higher permeability, lower coercivity, and ultimately lower hysteretic and core losses. The
effects of processing and composition on these characteristics will be the
focus of the following sections.
6.1. Magnetic moments and saturation magnetization
The saturation magnetization (Ms) is the maximum magnetic moment per
unit volume for a magnetic material. This intrinsic property is an important
factor for soft magnetic applications, since large values allow miniaturization.
In nanocrystalline soft magnetic alloys, the composition of the alloy, structure
of the crystalline phase, and fraction of crystalline and amorphous phases have
a significant impact on the saturation magnetization of the alloy. Most
prominent among these is the influence of MTM on the saturation magnetization of the alloy. In polycrystalline alloys, this variation was famously
described separately by Slater (1937) and Pauling (1938), with the observation
that a maximum value of saturation magnetization of 1.95 106 A/m
(2.43 T) is found for a Fe65Co35 alloy with BCC structure (Pfeifer and
Radeloff, 1980). A steady decline of magnetization becomes linear with Co
enrichment for contents greater than about 60% Co, which is especially
evident for compositions with FCC crystal structure. The Fe–Co alloys
show a break in their magnetization upon transition from the BCC phase
(left) and the FCC phase (right) in Fig. 4.49. The Fe–Ni alloys show a similar
trend with composition, with peak at slightly higher Fe contents and steady
linear decline of magnetization for Ni contents exceeding about 45% Ni.
Rigid band and virtual bound state models have been used to describe the
267
Nanocrystalline Soft Magnetic Alloys
(a)
Saturation magnetization (T)
2.5
(Fe,Co,Ni)86Zr7B6Cu1
2.0
1.5
1.0
0.5
0
7.8
8.0
8.2
8.4
8.6 8.8 9.0 9.2 9.4 9.6
Valence electrons per atom
9.8 10.0 10.2
(b)
FeCo (BCC)
Saturation magnetization (T)
2.5
FeNi
2.0
FeCo (FCC)
1.5
(Fe,Co)86B6Zr7Cu1
(Fe,Co)84B9Nb7
(Fe,Co)83Si1B8Nb7Cu1
(Fe,Co)79.4Si9B9Nb2.6
(Fe,Co)78.8Si9B9Nb2.6Cu0.6
(Fe,Co)71.5Si10Nb4B13.5Cu1
(Fe,Co)73.5Si13.5B9Nb3Cu1 (1)
(Fe,Co)73.5Si13.5B7Nb3Cu1 (2)
(Fe,Co)73.5Si13.5B7Nb3Cu1 (3)
(Fe,Co)73.5Si15.5B7Nb3Cu1
(Fe,Ni)78.8Si9B9Nb2.6Cu0.6
(Fe,Cr)73.5Si13.5B9Nb3Cu1
1.0
(Fe,Co)
Si £ 9 at%
(Fe,Cr)
0.5
Si £ 1 at%
(Fe,Ni)
Si ³ 10 at%
0
7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0 10.2
Valence electrons per atom
Figure 4.49 Variation of saturation magnetization with magnetic transition metal
uller et al., 2000)
content for (a) (Fe,Co,Ni)86Zr7B6Cu1 alloys ( BCC, þ FCC) (M€
and (b) (Fe,Co)79.4xSi9B9Nb2.6Cux (x ¼ 0, 0.6) (Ohnuma et al., 2003b; Yoshizawa
et al., 2003, 2004) (square, diamond), (Fe,Co)73.5Si13.5Nb3B9Cu1 (circles), (Fe,
Co)73.5Si15.5Nb3B7Cu1 (rt pointing triangles (Chau et al., 2004, 2006; Kolano-Burian
et al., 2004a; Mazaleyrat et al., 2004; M€
uller et al., 1996b)), (Fe,Co)86Zr7B6Cu1
(downward triangles (M€
uller et al., 2000)), (Fe,Co)83Si1B8Nb7Cu1 (triangle
(Yoshizawa and Ogawa, 2005)), and (Fe,Co)71.5Si10Nb4B13.5Cu1 (lt pointing triangles
(Inoue and Shen, 2003)), (Fe,Ni)78.8Si9B9Nb2.6Cu0.6 ( (Ohnuma et al., 2003b;
Yoshizawa et al., 2003, 2004)) alloys.
268
Matthew A. Willard and Maria Daniil
filling of electronic bands during the alloying process and its effect on the
saturation magnetization of the material (OHandley, 2000).
The variation of the saturation magnetization of nanocrystalline alloys
with MTM content is compared to the Slater–Pauling curve for polycrystalline alloys in Fig. 4.49a. Interestingly, the alloys without the substitutional
element, Si, show a very similar behavior, exhibiting a peak in the saturation
magnetization at about 40% Co substituted for Fe. The transition from
BCC to FCC with composition is shifted to higher Co content with greater
stabilization of the BCC phase as exhibited by the shift in observed BCC
phase to higher Co content compared with polycrystalline alloys (see
discussion of BCC stabilization in Ohodnicki et al., 2009). The saturation
magnetization remains lower than the crystalline alloys of the same MTM
content, which is expected as the composition is made up in part of
nonmagnetic elements, which dilute the magnetization. As the material
has a nanocomposite microstructure, each phase contributes to the magnetization weighed by the respective phase fraction and their individual
magnetizations. In most cases, the saturation magnetization is increased
upon crystallization due to the relatively small values of magnetization
observed in most amorphous alloys.
In (Fe,Co,Ni)–Si–B–Nb–Cu alloys, the saturation magnetization does
not show the same peak behavior as observed in the alloys without Si (see
Fig. 4.49b) (Yoshizawa et al., 2003). Rather than slightly increasing with
increased Co or Ni content, the saturation magnetization shows a flat
saturation magnetization with Co alloying and reduced magnetization
with Ni alloying. The strong drop in magnetization for Fe–Ni alloys at
about 3:1 ratio of Fe:Ni is similar to the trend observed in polycrystalline
alloys, resulting from the magnetic phase instability at the transition
between BCC and FCC compositions (termed Invar effect for the resulting
invariance in thermal expansion coefficient for these alloys) (Chikazumi and
Graham, 1997). Similar invariance in thermal expansion coefficient has not
been discussed with regard to these alloys. Substitution of transition metals
in Fe–M–Si–Nb–B–Cu-type alloys results in the substitution of the Fe(4b)
sites for MTMs (M ¼ Co and Ni) and Fe(8c) sites for ETMs (M ¼ Ti, V, Cr,
and Mn) in the D03 nanocrystallites (Gómez-Polo et al., 2003). Neutron
diffraction experiments were conducted to establish this connection, which
has a direct effect on the magnetization as a function of composition.
Much of the work done in nanocrystalline alloy design has focused on
increasing magnetization while simultaneously decreasing coercivity.
Reduced coercivity has been demonstrated by the substitution of Al in
Fe–Si–Nb–B–Cu and Fe–Zr–B–(Cu) alloys (Lim et al., 1993b; Moya et al.,
1998). However, this substitution results in reduced magnetization, a trend
also observed in crystalline alloys with similar substitutions (Fig. 4.50)
(Bozorth, 1959). Higher contents of Al and Si result in greater reduction of
magnetization, especially evident in the Al/Si-rich Fe87zAlxSizxNb3B9Cu1
269
Nanocrystalline Soft Magnetic Alloys
Saturation magnetization (T)
2.0
1.5
1.0
0.5
Fe87 – z Alx Siz - x Nb3B9Cu1 Tann = 823 K
Fe73.5 – x Alx Si13.5Nb3B9Cu1 Tann = 793 K
Fe90 – x Zr7B3Six
Fe87Zr7B3Al2Cu1 Tann = 873 K
Fe73.5 – xAlx Si13.5Nb3B9Cu1 Tann = 823 K
Fe90 – x Zr7B3Alx
Fe88 – x Zr7B5Alx Tann = 777–819 K
0
0
2
4
6
8
10
12
14
16
x, Al/Si content (at.%)
Figure 4.50 Effect of Al content on the saturation magnetization for (Fe,Al,
Si)87M3B9Cu1 alloys where M ¼ Nb or Mo (Borrego et al., 2001b; Daniil et al.,
2010a; Szumiata et al., 2005; Tate et al., 1998; Todd et al., 2000; Zorkovská et al.,
2002) and (Fe,Al,Si)90Zr7B3(Cu) alloys with 0 < Al < 15 at% (Hison et al., 2006; Inoue
et al., 1996; Kováč et al., 2002).
and Fe73.5xAlxSi13.5Nb3B9Cu1 alloys (Borrego et al., 2001b; Daniil
et al., 2010a; Szumiata et al., 2005; Tate et al., 1998; Todd et al., 2000;
Zorkovská et al., 2000). Despite the reduced magnetization, a nanocrystalline
Fe63Si17.5Al6Nb3B9Cu1 alloy was recently shown to provide lower coercivity
and higher magnetization than the commercially available Cryoperm-10 alloy
for cryogenic applications (Daniil et al., 2010a).
Although the type of ETM does not seem to have a strong impact on the
saturation magnetization, the saturation magnetization tends to decrease
steadily with the amount of ETM in the alloy. This effect is shown in
Fig. 4.51, where several combinations of Nb, Mo, V, and U are shown to
reduce the magnetization from the ETM-free value of 1.5 T by a factor
that greatly exceeds a dilution effect. The Curie temperature of the amorphous phase continually decreases with increasing ETM content (see
Fig. 4.54); however, it remains large enough to have little impact on the
saturation magnetization at room temperature.
6.2. Temperature dependence of magnetization and Curie
temperatures
Ferromagnetic order relies on positive exchange interactions between magnetic moments in the material to promote parallel alignment of those
moments. At sufficiently high temperatures, all ferromagnetic materials
270
Saturation magnetization (T)
Matthew A. Willard and Maria Daniil
1.5
1.0
Fe76.5 - xMxSi13.5B9Cu1
no ETM
M = Nb + Mo
M = Nb + V
M = Nb
M=U
0.5
0
0
1
2
3
4
5
6
7
8
9
M content, x (at.%)
Figure 4.51 Effect of early transition metal content on saturation magnetization for
Fe76.5xMxSi13.5B9Cu1 alloys (where M ¼ Nb, Nb þ Mo, Nb þ V, U) (Conde et al.,
1997; Konč et al., 1995; Wang et al., 1997; Yoshizawa and Yamauchi, 1990).
become paramagnetic due to the thermal disruption of the coupling between
magnetic moments. The temperature at which the magnetic order is lost in
the material is called the Curie temperature. Below the Curie temperature,
the spontaneous magnetization acts as the order parameter for ferromagnetism
(a higher-order phase transformation). At the Curie temperature, the magnetization is reduced to zero as thermal switching of the magnetization occurs.
The Curie temperature is higher in materials where the exchange coupling is
stronger and when the atomic moments are larger; however, the variation of
Curie temperature with composition is dependent on many complicating
factors, including the types of magnetic atoms, their coordination and symmetry in their local environment, and their bonding characteristics (especially
localized bonding and bond lengths). Due to natural variations in these
characteristics, amorphous alloys tend to have lower Curie temperatures
than crystalline alloys with similar MTM ratios.
Measurement of the saturation magnetization with temperature gives
important information about magnetic ordering and limitations of a given
material for environments other than near room temperature. Obviously,
the magnetization must remain large at the operation temperature for
any soft magnetic material, with no exception for nanocomposites. In
Fig. 4.52, the saturation magnetization alone limits some alloys to near room
temperature applications (e.g., (Fe,Si)-based alloys), while the saturation
magnetization is quite large to high temperatures for others (e.g., especially
(Fe,Co)-based alloys). Thermomagnetic experiments are especially important for nanocomposite materials due to the requirement of good exchange
271
Nanocrystalline Soft Magnetic Alloys
Magnetization (A m2/kg)
150
100
Fe44.5Co44.5Zr7B4
50
Fe77Co5.5Ni5.5Zr7B4Cu1
Co83.6Fe4.4Zr3.5Hf3.5B4Cu1
Fe88Zr7B4Cu1
Fe73.5Si13.5Nb3B9Cu1
0
200
300
400
500
600
700
800
900
1000
1100
Measurement temperature (K)
Figure 4.52 Saturation magnetization variation with measurement temperature for
Fe-based, (Fe,Si)-based, and (Fe,Co)-based alloys.
coupling between grains to maintain the exchange softening condition
throughout the alloy. The details of this will be discussed in the next section;
however, the fact that the Curie temperature of the amorphous matrix is the
limiting factor for their high-temperature operation is the motivation for
our detailed discussion of Tam
C and the following discussion of theoretical
models.
Two theories help us to understand the interaction of atomic moments—
the Weiss mean field theory and the Heisenberg exchange theory. By the
Weiss mean field theory, the moments are brought to alignment by an
(nonphysical) internal magnetic field (i.e., mean field) that acts to align the
moments in the absence of an applied field. The mean field is used to
approximate the interaction of the surrounding widespread environment on
individual moments in the material. This leads to the spontaneous magnetization observed in ferromagnetic materials. The Heisenberg exchange theory,
on the other hand, considers the alignment of the magnetic moments due to
quantum mechanical exchange interactions between near-neighbor atoms
(local environment). Heisenberg exchange can be used to describe ferromagnets, ferrimagnets, and antiferromagnets by consideration of size of
magnetic moments and sign of the exchange interaction. Combined use of
these models gives us insight into the magnitude of the Curie temperature and
its composition dependence.
Using the Weiss mean field theory to describe the internal magnetization, the Langevin function (or Brillouin function) can be applied to
calculate the reduced magnetization as a function of temperature. Although
this method results in a transcendental equation, it can be solved numerically to estimate the Curie temperature:
272
Matthew A. Willard and Maria Daniil
mA Happ mA lW m0 Ms ðT Þ
m0 Ms ðT Þ
¼ tanh
þ
kB T
m0 Ms ð0K Þ
kB T
ð7Þ
In this equation, the atomic moment mΑ experiences an applied magnetic field Happ and mean field lWm0Ms(T), where lW is the Weiss mean
field constant. An extension of this model has been used to estimate the
dependence of magnetization with temperature for amorphous alloys, using
a modified Brillouin function to reflect the distributions of exchange interaction that occur due to the varied interatomic distances found in amorphous alloys (Gallagher et al., 1999; Handrich, 1969; Kobe and Handrich,
1970). This method has been used to estimate Curie temperatures for the
amorphous phase when the T am
C exceeds the crystallization temperatures
(see Hornbuckle et al., 2012; Willard, 2000).
The Heisenberg exchange model provides a Hamiltonian
(Hex) to describe
X ! !
Jij Si Sj , where Si are
the exchange energy in the system as Hex ¼ 2
i<j
total spin angular momenta and Jij is the exchange energy between the ith and
jth atomic moments. When Jij is positive or negative, the spins prefer parallel or
antiparallel configurations, respectively. Strictly speaking, the Heisenberg
Hamiltonian applies to materials with localized magnetic moments only
(e.g., oxide magnets). However, when combined with the Weiss mean field
model, it can be extended for macroscopic calculations of the exchange
energy, specifically the Weiss mean field
can befficlarified in terms of exchange
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
interactions by lW m0 Ms ðT Þ ¼ 2zJij SðS þ 1Þ=m0 Nv m2A , where Nv is the
number of moments per volume (1028–1029 m3) and z is the number of
near-neighbor moments. An extension of the Curie law results in Ms(T) ¼ C
(Happ þ lWm0Ms(T))/T, where C ¼ m0Nvm2A/3kB and kB is Boltzmann’s constant. Using these expressions, the Curie temperature can be estimated using
TC ¼
2zJij SðS þ 1Þ
3kB
ð8Þ
While the estimated values of Curie temperatures using this equation
tend to be much higher than experimentally observed, the proportionality
of the exchange energy with the Curie temperature can be used to explain
compositional trends in amorphous and crystalline alloys. The empirical
relationship of the exchange energy with the ratio of atomic separation to
3d atomic orbital diameter, or Bethe–Slater curve, has its foundation in the
band theory of solids. The Curie temperature dependence on composition
is therefore dependent on the interatomic effects (via Jij) and the size of the
local atomic moments (via S(S þ 1)), which ultimately are affected by the
coordination number of magnetic atoms, the distance between these atoms,
and the localized bonding. The exchange stiffness (Aex) used in the definition of the exchange correlation length, a defining length scale for the
Nanocrystalline Soft Magnetic Alloys
273
exchange softening which is critically important to nanocrystalline soft
magnet performance, can also be described using the Heisenberg exchange
theory with Aex ¼ zJijS2/2a, where a is the lattice constant.
For ferromagnetic alloys at temperatures far below the Curie temperature (T/TC < 0.5), the magnetization drops more quickly with temperature
than expected by the mean field model described above. This has been
explained by the decay of magnons (spin waves) in the alloy and is better
described by the Bloch T3/2 law:
3=2
Ms ð0K Þ Ms ðT Þ
T
¼ 1 C3=2
Ms ð0K Þ
TC
ð9Þ
where C3/2 is a proportionality constant. The nanocrystalline alloy Fe73.5
Si13.5B9Nb3Cu1 has been observed to follow the Bloch T3/2 law between
80 and 230 K (Zbroszczyk, 1994). The addition of a (T/TC)5/2 term was
found to extend the Law’s applicability to the temperature range 1.5–300 K
(Guo et al., 1993; Holzer et al., 1999). Spin wave stiffnesses were determined from this analysis to have values between 100 and 161 meV Å2 with
tendency to increase in value for samples annealed at higher temperatures
(Guo et al., 1993; Kiss et al., 2003; Zbroszczyk, 1994). The resulting
exchange stiffness (Aex) was determined to be near 5.7–7.2 1012 J/m
for nanocrystalline Fe73.5Si13.5B9Nb3Cu1 samples (Holzer et al., 1999; Konč
et al., 1995).
Being a two-phase material, nanocrystalline soft magnetic alloys possess a
more complex temperature dependence of magnetization, which is dependent on the processing conditions (e.g., microstructure and phase evolution)
and composition of each phase. At low temperatures, both amorphous matrix
and nanocrystalline phases are fully exchange coupled. The Curie temperature of the amorphous matrix phase is lower than that of the crystalline phase
due to alloying with nonmagnetic elements, local coordination of magnetic
atoms (OHandley, 2000), and distributed exchange that varies the exchange
interaction (Gallagher et al., 1999). Dependent on the distribution and
separation distance between crystallites, partial or total decoupling of the
crystalline phase has been observed as the temperature has been raised through
the Curie temperature of the amorphous phase. Hardening of the nanocomposite alloy is typically observed above this temperature. However, for
sufficiently small grains and high temperatures, superparamagnetic behavior
can be observed. These topics will be discussed in this section and Section 6.4
in the context of standard thermomagnetic analyses.
Improvements in the Curie temperature of the amorphous phase result
from substituting some Co for Fe in nanocomposite soft magnetic alloys.
Substitution of Co for Fe in a (Fe1xCox)73.5Si13.5B9Nb3Cu1 alloy results in
increased Tam
C to from 593 K for x ¼ 0 to about 720 K for x ¼ 60 (see
Fig. 4.53a) (Fernández et al., 2000; Gercsi et al., 2006). Further increase
274
Matthew A. Willard and Maria Daniil
(a)
1000
Curie temperature (K)
(Fe,M)3Si
(Fe1 - xMx)73.5Si13.5B9Nb3Cu1
800
600
400
M = Co
M = Cr
M = Mn
M = Ni
200
(Fe,Co)3Si
(Fe,Cr)3Si
(Fe,Mn)3Si
(Fe,V)3Si
7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0
Valence electrons per atom
(b)
Curie temperature (K)
1400
1200
1000
800
600
400
200
8.0
8.2
8.4
(Fe,Co)82Nb3Ta1Mo1B13
(Fe,Co)89Zr7B3Cu1
(Fe,Co)84Zr3.5Nb3.5B8Cu1
(Fe,Co)86Zr7B6Cu1
(Fe,Co)86Hf7B6Cu1
(Fe,Co)88Zr7B4Cu1
(Fe,Co)90Zr10
(Fe,Co,Ni)88Zr7B4Cu1
(Co,Ni)88Zr7B4Cu1
8.6
8.8
9.0
9.2
9.4
Valence electrons per atom
9.6
9.8
10.0
Figure 4.53 Effect of magnetic transition metal on amorphous phase Curie temperature in (a) Fe73.5xMxSi13.5Nb3B9Cu1 alloys (where M ¼ Cr (Chau et al., 2006; Conde
et al., 1994; Hajko et al., 1997; Malki
nski and Ślawska-Waniewska, 1996; Marı́n et al.,
2002; Randrianantoandro et al., 1997), Mn (Kolat et al., 2002), Co (Borrego et al.,
2001a; Chau et al., 2004; Gómez-Polo et al., 2001; Mazaleyrat et al., 2004) and Ni
(Agudo and Vázquez, 2005)) and (b) (Fe,Co)90Zr10, (Fe,Co,Ni)88Zr7B4Cu1, (Fe,
(Fe,Co)89Zr7B3Cu1,(Fe,Co)84(Nb,Zr)7B8Cu1,
and
(Fe,
Co)86(Hf,Zr)7B6Cu1,
Co)82(Nb,Ta,Mo)5B13 (Caballero-Flores et al., 2010; Hornbuckle et al., 2012;
M€
uller et al., 1996b; Suzuki et al., 2002b; Willard et al., 1999a; Willard et al., 2000;
Willard et al., 2007). Curie temperatures above secondary crystallization temperatures
are approximate. For comparison, the Curie temperatures of (Fe,M)3Si (M ¼ Co, Cr,
Mn, V) intermetallic phases are shown in (a) (Chakravarti et al., 1991; Mahmood et al.,
2004; Niculescu et al., 1979; Nishino et al., 1993; Waliszewski et al., 1994).
275
Nanocrystalline Soft Magnetic Alloys
in Co substitution did not result in further increases in Tam
C . When Ni was
substituted instead of Co, the Tam
C only showed a small improvement with
small amounts of Ni substitution and then a slow reduction for further
additions. Reductions in Tam
C accompany the substitution of Cr or Mn for
Fe in (Fe1xMx)73.5Si13.5B9Nb3Cu1 alloys, with a more rapid decrease in
magnetic ordering temperature for Mn substitution. Both of these alloying
elements couple antiferromagnetically with the Fe, resulting in the destabilization of the ferromagnetic order. Similar results have been reported for
(Fe,M)3Si alloys where M ¼ Co, Cr, Mn, and V (see Fig. 4.53a)
(Chakravarti et al., 1991; Mahmood et al., 2004; Niculescu et al., 1979;
Nishino et al., 1993; Waliszewski et al., 1994).
The ETMs are essential to formation of the nanocrystalline microstructure in (Fe,Si)-based alloys. For this reason, some amount of ETM must be
added to the alloy to keep the coercivity low; however, the magnetization
and Curie temperatures are both reduced as the amount of ETM is
increased. In Fig. 4.54, the Curie temperature of the amorphous phase is
plotted for many Fe76.5x(Si,B)22.5ETMx(Cu,Au)1 alloys with varying
Amorphous phase Curie temperature (K)
750
Fe76.5 - x(Si,B)22.5ETMx(Cu,Au)1
no ETM
Nb
V + Nb
Zr + Nb
Mo + Nb
Hf + Nb
Ta + Nb
W + Nb
700
650
600
550
500
450
0
1
2
3
4
5
6
7
8
9
ETM content (at.%)
Figure 4.54 Effect of early transition metals on the Curie temperature of the amorphous phase in Fe76.5x(Si,B)22.5ETMx(Cu,Au)1 alloys (Agudo and Vázquez, 2005;
Barandiarán et al., 1993; Chau et al., 2004; Conde and Conde, 1995a; Degro et al.,
1994; Franco et al., 2001a; GómezPolo et al., 1997; Hakim and Hoque, 2004; Hampel
et al., 1992; Hernando and Kulik, 1994; Herzer, 1989, 1991; Kataoka et al., 1989; Kulik
et al., 1994; Lovas et al., 1998; Mattern et al., 1994; Mitra et al., 2002; M€
uller et al.,
1991, 1992; Noh et al., 1991; Panda et al., 2003; Pe˛kala et al., 1995b; Ponpandian et al.,
2003; Rodrı́guez et al., 1999; Surinach et al., 1995; Tonejc et al., 1999b; Yoshizawa
and Yamauchi, 1990, 1991).
276
Matthew A. Willard and Maria Daniil
Saturation magnetization (T)
1.6
1.4
1.2
1.0
0.8
0.6
Fe89Zr7B4 813 K
0.4
Fe86Zr7B6Cu1 573 K
Fe86Zr7B6Cu1 773 K
0.2
Fe86Zr7B6Cu1 823 K
Fe86Zr7B6Cu1 873 K
0
250
300
350
400
450
500
550
600
650
700
750
800
Measurement temperature (K)
Figure 4.55 Saturation magnetization variation with measurement temperature for
Fe89Zr7B4 and Fe86Zr7B6Cu1 alloys (Ślawska-Waniewska et al., 1994; Suzuki et al.,
1991c).
ETM type. A reduction in T am
C is observed at a nearly constant rate of 30 K
per at% ETM substitution for Fe, regardless of the type of ETM used.
Many Fe-based samples tend to have Curie temperatures for the asspun amorphous phase near room temperature (see Fig. 4.55). As the
Fe86Zr7B6Cu1 alloy is annealed above the primary crystallization temperature, partitioning of the Zr and B to the remaining amorphous phase
changes the composition of that phase, resulting in an increased TC am.
The unusual behavior of increasing Tam
C with reduced Fe content has
been observed in Fe–B amorphous alloys and has been attributed to the
local coordination of glass-forming elements in the alloy (see Bhattacharya
et al., 2012 for details). However, even in the partially crystallized alloys, the
crystallites do not always exhibit the Curie temperature of a-Fe of 1043 K.
This is due to the nonequilibrium compositions found in the crystalline
phase, with greater amounts of B and Zr that tend to reduce the Curie
temperature. Due to the low Curie temperature of the amorphous phase in
Fe–M–B alloys, thermomagnetic measurements of the as-spun alloys have
been used as sensitive probes of the crystallization kinetics for primary
crystallization. Both isothermal and constant heating rate experiments
have been performed and activation energies for primary crystallization
have been determined using JMAK and Kissinger kinetics, respectively
(Hsiao et al., 1999; Hsiao et al., 2002).
In contrast, Tam
C in the HITPERM-type alloys tends to increase well
above 800 K with increasing Co content resulting in estimated peak values
above 1000 K (see Fig. 4.53b). This increase in Curie temperature can be
277
Nanocrystalline Soft Magnetic Alloys
Fe86-xCoxHf7B6Cu1
Saturation magnetization (T)
1.5
1.0
298 K
373 K
473 K
573 K
673 K
773 K
873 K
948 K
Above T x2
0.5
0
0
10
20
30
40
50
60
70
80
90
Co content (at.%)
Figure 4.56 Saturation magnetization as a function of Co content and measurement
temperature for (Fe,Co)88Hf6B6Cu1 alloys (Liang et al., 2007).
linked to both the increased magnetic moments and the generally larger
exchange interaction expected for Fe–Co compositions. These values do
not follow trends observed in crystalline (Fe,Co)-based alloys, due to the
generally lower values of Tam
C found in Co-free compositions. In general,
the very high Tam
C for (Fe,Co)-based alloys allows high operation temperatures, only limited by the breakdown of the nanocrystalline microstructure
at the secondary crystallization temperature (Willard et al., 2012a).
Similar to the (Fe,Co)–Zr–B–Cu alloys reported in Section 6.1, the
saturation magnetization shows a peak value at about 35% substitution of
Co for Fe in (Fe,Co)86Hf7B6Cu1 alloys. As the measurement temperature is
increased, a shift in the peak magnetization value to higher Co contents is
observed (see Fig. 4.56). Considering the operation temperature should not
exceed secondary crystallization, the peak value at the maximum operation
temperature of 773 K is found for the alloy with even amounts of Co and Fe
(Liang et al., 2007). The magnetization does not show strong degradation
for alloys measured above Tx2; however, the coercivity of these alloys was
substantially degraded for these samples.
Several types of nanocomposite soft magnetic alloys have been found to
possess only short-range magnetic order at cryogenic temperatures (i.e.,
spin-glass behavior). For example, in Fe91xZr8RuxCu1 alloys, the spinglass phenomenon was observed in the as-spun amorphous alloy and spindependent magnetoresistance was found in the nanocomposite alloy with
x ¼ 10 (Suzuki et al., 2002a). This result was attributed to the reduction of
amorphous phase Curie temperature by alloying with Ru which contributed to the spin-dependent scattering in the nanocomposite alloy.
278
Matthew A. Willard and Maria Daniil
6.3. Magnetic anisotropy and magnetostriction
Magnetic anisotropy is found in all magnetic materials to varying extents
with origins from atomic arrangements, shape of the magnet, magnetoelastic, or induced during processing (e.g., stress or magnetic field annealing).
Each contributes to the overall loss of the material as the magnetization is
switched from one saturated direction to another, which means that reduction of all sources of magnetic anisotropy is desirable for optimal soft magnet
performance.
In crystalline materials, the magnetocrystalline anisotropy, due to the
coupling of the atomic magnetic moments with the crystal lattice, is a
dominant factor. The behavior is described by a series of magnetocrystalline
anisotropy constants (i.e., K1, K2, etc.) with angular dependence described
by the symmetry of the crystalline lattice. For materials with tetragonal or
hexagonal crystal lattices, the energy density is described by
EKu ¼ Ku1 sin 2 y þ Ku2 sin 4 y
ð10Þ
where y is the angle between the uniaxial direction and the magnetization
vector. Similarly for cubic crystal structures:
EK ¼ K1 a21 a22 þ a22 a23 þ a23 a21 þ K2 a21 a22 a23
ð11Þ
where ai are the direction cosines between the magnetization vector and the
principal axes of the crystalline lattice. The magnetocrystalline anisotropy
constants are dependent on temperature and composition and tend to have
reduced values as the order of the angular dependence is increased. In many
cases, the first magnetocrystalline anisotropy term is the largest and most
important.
As the magnetization of the alloy changes directions, the shape of the
sample changes (d‘=‘), resulting in a magnetoelastic contribution to the overall
anisotropy of the material. The saturation magnetostrictive coefficient (ls)
creates an additional anisotropy term (Ks) with form: Ks ¼ 3/2 lss, where s is
the stress in the sample (tensile). For a uniaxial stress state, Ks replaces Ku1 and
y is the angle between the stress direction and the magnetization vector.
The magnetostatic energy is a result of the formation of a magnetic field
external to the magnetized material produced by the magnetization of the
material. A demagnetizing field within the material results from the formation of the external field and the need to preserve the constitutive relationships between the field B, H, and M (via Faraday’s law). The shape
anisotropy energy density (Es) results from the demagnetizing effect and
has the form:
Es ¼
m0 Ms2 Na cos 2 c þ Na sin 2 c
2
ð12Þ
279
Nanocrystalline Soft Magnetic Alloys
for a prolate spheroid with major equatorial axis a and minor axis b, c is the
angle between the polar axis and the magnetization direction, and Na is the
demagnetizing factor for the equatorial axis. In ribbon-shaped samples (e.g.,
suitable for measurement in a vibrating sample magnetometer), the shape
anisotropy is dominant due to the small contributions from exchange
averaged magnetocrystalline anisotropy and relatively random orientation
of local stresses (lowering the magnetoelastic contribution). The macroscopic shape anisotropy is not a material property (being dependent on
sample geometry) and can be largely eliminated by creating a wound ribbon
core. Powder cores use the shape anisotropy to lower the overall permeability of the composite material, important for use in inductor applications.
Nanocrystalline soft magnetic alloys possess magnetic anisotropy values
far lower than expected from polycrystalline materials, resulting in
extremely small values of coercivity. Herzer performed a systematic study
of the grain size dependence on coercivity, where he employed a random
anisotropy model to describe the results (Herzer, 1990). The random
anisotropy model was first developed to describe the large anisotropy
found in rare earth iron amorphous alloys (Harris et al., 1973) and was
further refined by describing the effects in terms of magnetic correlation and
structural correlation lengths (Alben et al., 1978). By this model, the
coercivity of perfectly random amorphous materials was found to be proportional to the sixth power of the structural correlation length to magnetic
correlation length ratio. Noting the fact that the grains were exchange
coupled through the residual amorphous matrix, a random anisotropy
model was applied to show that the coercivity was proportional to the
grain size to the sixth power (Herzer, 1992).
In general, the magnetic energy of a nanostructured material is the sum
of the exchange and anisotropy energies (E ¼ Eex þ Ea):
Eex ¼ A
X ð
i;a
2
d x rmai 3
Vi
ð
Iij
d2 xmi mj
hi;ji d
Sij
X
ð13Þ
where mi(x) is the space-dependent magnetization unit vector within grain
i of volume Vi and A is the intragranular exchange constant (Löffler et al.,
1999). The first term represents the exchange energy within a single phase
and the second term refers to the exchange between neighboring grains
through the interface Sij of width d and intergranular exchange Iij. The
anisotropy energy has the form:
Ea ¼ K
Xð
i
d 3 xð m i n i Þ 2
ð14Þ
Vi
where ni is the direction of the easy anisotropy axis (varying with random
orientation for each grain) (Löffler et al., 1999). In small grains, the
280
Matthew A. Willard and Maria Daniil
exchange energy dominates, and in large grains, the anisotropy energy
dominates. The dividing line between these sizes is the magnetic domain
wall width, which is intimately related to the magnetic exchange correlation
length (L0).
The random anisotropy model applies when the following three
requirements are met: (a) the magnetic correlation length is greater than
the structural correlation length, (b) the grains have random orientation, and
(c) the grains are exchange coupled. The use of the random anisotropy
model for nanocomposite materials relies on scaling arguments and statistical
considerations (Suzuki and Cadogan, 1998), which are naturally met when
these three conditions are satisfied. The magnetic exchange correlation
length (L0) indicates the minimum size scale over which the atomic
moments must remain aligned due to exchange forces. The magnitude of
this fundamental magnetic material parameter can be found by
L0 ¼
pffiffiffiffiffiffiffiffiffiffiffiffi
A=K1
ð15Þ
where A is the exchange stiffness and K1 is the first magnetocrystalline
anisotropy constant. For perspective, the 180 Bloch wall has a value
dB ¼ pL0. A resulting L0 of 35 nm was calculated for Fe–Si-based alloys
and a dB of nearly 100 nm.
When the structural correlation length of the material (i.e., grain size) is
much smaller than the exchange correlation length, the magnetic moments
in each individual grain cannot relax into the local easy direction dictated by
the grain orientation. This results in an averaging of the local magnetocrystalline anisotropy over the exchange correlation volume. In this case, the
easiest magnetization direction is not determined by the magnetocrystalline
anisotropy, as it is in micron-sized polycrystalline materials, rather it is
determined by statistical fluctuations of the grains within the exchange
correlation length. Using a random walk type, random anisotropy model,
an effective magnetocrystalline anisotropy p
(hK
ffiffiffiffiffi1i), representing the material
response can be determined as hK1 i ¼ K1 = N with N being the number of
grains within the exchange correlation length. The natural reduction in the
magnetocrystalline anisotropy reflected in hKi results in an increased
exchange
length for the nanocrystalline material defined as
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Lex ¼ A=hK1 i, which can have values of hundreds of nm when D is
reduced below 10 nm. The value of N in a cubic volume with sides Lex can
be estimated by the relation: N ¼ (Lex/D)3.
Using the definitions of hK1i, Lex, and N, the effective anisotropy can be
determined in terms of the crystalline materials parameters, K1, A, and D:
hK 1 i ¼
K14 D6
A3
ð16Þ
281
Nanocrystalline Soft Magnetic Alloys
The more general equation for n-dimensional system has the form:
hK1 i ¼ K1
D
pffiffiffiffiffiffiffiffiffiffiffiffi
A=K1
!2n=ð4nÞ
ð17Þ
yielding D2/3, D2, and D6 dependences for n ¼ 1, 2, and 3, respectively
(Herzer, 1991). Interestingly, due to dimensional constraints alone, a nanowire will have a reduced exchange softening (D2/3) compared to thin films
(D2) and bulk materials (D6). These dependencies are shown in Fig. 4.57a,
which follows this equation for an (Fe,Si)-based alloy with parameter values
for Fe80Si20 found in Table 4.6. In each of the three cases (n ¼ 1, 2, 3), the
(a)
Effective K1, áK1ñ (J m-3)
106
104
1-D
102
2-D
100
10-2
3-D
10-4
1
10
Grain size, D (nm)
100
(b)
Exchange length, Lex (nm)
106
3D
105
104
103
2D
102
1D
10
1
10
100
Grain size, D (nm)
Figure 4.57 Schematic diagrams of (a) the exchange averaged magnetocrystalline
anisotropy and (b) the exchange length as a function of grain size for 3D, 2D, and 1D
solutions of the random anisotropy model below the natural exchange length (red dot)
and the 3D solution for large grain sizes. Parameter values for these calculations are
found in Table 4.6 for the Fe80Si20 phase.
282
Matthew A. Willard and Maria Daniil
Table 4.6 Calculations using the multiphase, 3D random anisotropy model for
several different samples
Fe80Si20
3
K1 (J/m ) Crystalline phase
magnetocrystalline
anisotropy
L0 (nm)
Natural exchange
length
ls (ppm) Magnetostrictive
coefficient
hKi (J/m3) Effective anisotropy
Lex (nm) Effective exchange
length
Hc (A/m) Coercivity
mi
Permeability
m0Ms (T) Saturation
magnetization
8.2 10
Fe
3
Fe50Co50 Fe70Co30
47 10 5.9 103 1.1 104
3
35
15
41
30
6
4.4
80
45
2.3
2085
2600
62
0.7
3780
8.1
1120
1.21
832
260 103 612
1.23
2.0
0.18
2.10
3.5 106 297 103
2.4
2.45
Assuming D ¼ 10nm, (1 Vam) ¼ 0.75, and A ¼ 1011 J/m. Where Hc ¼ pchKi/m0Ms and mi ¼ pmM2s /
m0hKi and pc ¼ 0.64 and pm ¼ 0.5 (Herzer, 1995; Pfeifer and Radeloff, 1980; Suzuki et al., 2008b).
definitions of Lex and hK1i are the same; however, the exchange coupled
volume is reduced to N ¼ (Lex/D)2 for 2D and N ¼ Lex/D for 1D. For this
example, the natural exchange length (L0) was found to be 32 nm and the
nanocrystalline exchange length (Lex) varied as shown in Fig. 4.57b.
The total magnetocrystalline anisotropy energy is unchanged by the averaging; however, the fluctuations are diminished leading to lower coercivity and
higher permeability for the nanocomposite alloy. Since the fluctuations of the
anisotropy are the important factors in considering magnetization switching,
the coercivity and initial permeability can be calculated using these equations
(and a coherent magnetization rotation model (Stoner and Wohlfarth, 1948))
with good accuracy for grain sizes less than 40 nm using the relations:
H C ¼ aC
hK i
m0 Ms
aC
K14 D6
m M2
and mi ¼ am 0 s
3
m0 Ms A
hK i
am
m0 Ms2 A3
K14 D6
ð18Þ
when the dimensionless parameters aC and am have values of 0.13 and 0.5,
respectively (Herzer, 1990). The 3D solution for the effective anisotropy
was used in the coercivity and permeability equations above; however, the
2D, 1D, and equations using uniform anisotropies can also be used (as
demonstrated in Fig. 4.58). When these grains with cubic anisotropy are
randomly oriented, the squareness of the hysteresis loop is enhanced,
reflecting the strong exchange coupling and the dominance of exchange
energy over anisotropy energy in the alloy (resulting in remanence ratios
283
Coercivity, Hc (A/m)
Nanocrystalline Soft Magnetic Alloys
103
1D
102
2D
101
100
3D
10-1
1 nm
100 nm
10 mm
1 mm
Grain size, D
Figure 4.58 Calculated coercivity as a function of grain size for 3D, 2D, and 1D
solutions of the random anisotropy model below the natural exchange length (apex)
and the 3D solution for large grain sizes. Using equations from Table 4.7 with Vam ¼ 0,
j ¼ 1, no Ku, and parameter values from Table 4.6 (Fe80Si20).
(Mr/Ms) exceeding 0.83) (Herzer et al., 2005). A large degree of scatter is
experimentally observed in the coercivity even for a single grain size
(Herzer, 2005). This is due in part to the intimate relationship between
alloy composition and processing. Producing the nanocomposite microstructure inevitably requires changes in composition of the phases in the
alloy, with variations in the annealing temperatures, annealing times, and
alloy compositions resulting in varied volume fractions transformed and
compositions of the crystallites and residual amorphous phases.
Reduction in coercivity by exchange softening has also been modeled
using a domain wall-pinning formalism (Chikazumi and Graham, 1997).
Due to spatial fluctuations in the local domain wall energy (gw), the
magnetization sees different amounts of resistance to motion by an applied
field, resulting in a coercivity determined by the maximum value of spatial
fluctuation (with wavelength, L) (Herzer, 1990):
HC ¼
1
@gw
2m0 Ms @x max
pffiffiffiffiffiffiffiffiffi
AK1
m0 Ms L
ð19Þ
For small grains, the spatial wavelength parameter, L, is equal to the
exchange length, Lex, and the magnetocrystalline anisotropy, K1, is replaced
by the exchange averaged hKi. Grains exceeding the domain wall width (or
about pLex) tend to follow a 1/D relationship describing a well-known
domain wall pinning on grain boundaries (Mager, 1952). The experimental
comparison of coercivity and initial permeability against grain size for
D > 150 nm shows good agreement using the following relations:
284
Matthew A. Willard and Maria Daniil
pffiffiffiffiffiffiffiffiffi
AK1
m Ms2 D
and mi ¼ am p0 ffiffiffiffiffiffiffiffiffi
H C ¼ aC
m0 Ms D
AK1
ð20Þ
when the dimensionless parameters aC and am have values of 2.6 and 0.05,
respectively (Herzer, 1990). A similar argument is given considering the
coherent rotation previously considered for nanocrystalline grains. When
the grain size and exchange length are approximately the same, the magnetocrystalline anisotropy is not averaged over the exchange length and the
coercivity and initial permeability are commensurately deteriorated:
H C ¼ aC
K1
m M2
and mi ¼ am 0 s
m0 Ms
K1
ð21Þ
resulting in a maximum value of coercivity and minimum value of
permeability (Herzer, 1990).
To this point, the random anisotropy model has been applied to nanocrystalline materials without consideration of the multiphase nature of these
materials. Multiphase solutions of the random anisotropy model are necessary to describe (1) magnetic hardening at elevated temperatures (near the
Curie temperature of the amorphous phase where grains start to decouple)
and (2) magnetic hardening during the initial stages of crystallization (small
volume fractions of crystallites in large amorphous matrix) (Suzuki and
Cadogan, 1998). An extension of the random anisotropy model to multiphase materials was provided by Herzer, considering the problem from the
perspective of the spatial fluctuations of the mean square amplitude of
the anisotropy energy (hE2a i) and its effect on the effective magnetocrystalline anisotropy (hK1i) (Herzer, 1995). In this case, the volume of the ith
phase (Oi) determines the structural correlation length which is compared to
the exchange coupled volume (Vex) to determine its affect on hE2a i. The
following expression gives the general mean square amplitude of the anisotropy energy:
Ea2 ¼
X
Oi <Vex
N i ðO i K i Þ2 þ
X
Oi Vex
Ni ðVex Ki Þ2
ð22Þ
where Ki is the magnetocrystalline anisotropy of the ith phase, Oi ¼ aD3i ,
and Vex ¼ aL3ex (a is a geometric
factor between 0.5 and 1) (Herzer, 1995).
qffiffiffiffiffiffiffiffiffiffi
Ea2 =Vex and the definition Ni ¼ viVex/Oi
Using the relation hK1 i ¼
(where Ni is the frequency with which the anisotropy changes within the
exchange coupled volume), we find
"
hK 1 i ¼
X
vi D3i Ki2 X
vi Ki2 A3=2
þ
3=2
Di <Lex A
Di Lex D3 hK i3
1
i
#2
ð23Þ
285
Nanocrystalline Soft Magnetic Alloys
This expression reduces to the aforementioned effective magnetocrystalline anisotropy when a crystalline phase with Ki ¼ K1 and amorphous phase
with Ki ¼ 0 are the only two phases in the material and the dimensions of
each phase never exceed Lex. Not only does this formulation allow us to
consider multiple magnetic materials, but it also allows consideration of
grain size distributions. Solutions for three important cases using the multiphase solution of the random anisotropy model are (A) when all grains are
less than the magnetic exchange length; (B) when all grains are exactly the
same size as the exchange length; and (C) when all grains are larger than the
exchange length. The solutions for each are shown here:
A: ∑
⟨ ⟩
B:
∑
C
∑
ð24Þ
When largest grains are less than the exchange length, the usual D6
dependence from the random anisotropy model is observed. When the
grains are all the size of the exchange length, the maximum coercivity is
observed, with the effective K equaling the root mean square of the types of
grains in the material. For samples with minimum grain size larger than the
exchange length, a D6/7 power law is observed. The two regimes are
observed in the (Fe,Si)–(Nb,Mo)–B–Cu samples shown in Fig. 4.59a, with
the transition between D6 and D6/7 at about 55 nm. As previously mentioned, the reduced dimensionality of thin films results in the observed D2
dependence as shown in Fig. 4.59b. Deviations from the D6 dependence
(e.g., Fe–Zr–B–Cu in Fig. 4.59a) due to uniform anisotropies will be
discussed later in this section.
The situation is more complicated when grain size distributions are
considered. For narrow distributions (with standard deviations s near
0.01), the result is identical to those cases just described. For wider grain
size distributions (s 0.4), the transition between power law regions is
broadened significantly (da Silva et al., 2000). In this case, a gradation of
the power laws between D6 and D6/7 is found even when the mean grain
size is half of the natural exchange length, resulting in accelerated deterioration of the coercivity as the standard deviation is increased. For this
reason, the distribution of grain size can be extremely important. This is
especially evident when a bimodal distribution of grain sizes is observed, and
can have a significant impact on the coercivity of the material. Fifty
percentage larger coercivity values were reported when a small volume
fraction of relatively large grains (40 nm) was taken into consideration
for its effect on coercivity, despite the vast majority of the grains being less
than 20 nm (Bitoh et al., 2004).
286
Matthew A. Willard and Maria Daniil
(a)
104
Coercivity (A/m)
103
102
D3
10
D6
1
Fe–Zr–B–Cu
(Fe,Si)–(Nb,Mo)–B–Cu
10-1
10
10
1000
Grain diameter (nm)
(b)
105
Coercivity (A/m)
104
10
D2
3
102
D3
Fe91Zr7B2
Fe78PxC18 – xGe3Si0.5Cu0.5
Fe90Zr7B2Cu1
Fe73.5Si13.5B9Nb3Cu1
Fe66Ni11Co11Zr7B4Cu1
Fe67Ni11Co11Zr7B4
10
1
10-1
10
100
Grain diameter (nm)
Figure 4.59 (a) Variation of coercivity with grain diameter for ribbon samples of
(Fe,Si)–(Nb,Mo)–B–Cu (D6)and Fe–Zr–B–Cu (D3) alloys (del Muro et al., 1994;
Gómez-Polo et al., 1996; He et al., 1994; Herzer, 1990, 1993; Kulik and Hernando,
1996; Kulik et al., 1994, 1997; Liu et al., 1997a; Majumdar and Akhtar, 2005; Mattern
et al., 1995; Mazaleyrat and Varga, 2001; M€
uller et al., 1991, 1992; Panda et al., 2003;
Suzuki and Cadogan, 1999; Suzuki et al., 1996; Todd et al., 1999, 2000; Xiong et al.,
2001; Zhou et al., 1996). (b) Variation of coercivity with grain diameter in thin film
samples of Fe73.5Si13.5Nb3B9Cu1 and Fe66xNi11Co11Zr7B4Cux alloys (D2) (Baraskar
et al., 2007; Yamauchi and Yoshizawa, 1995) and ribbon samples with uniaxial anisotropy of Fe78PxC18xGe3Si0.5Cu0.5, Fe91Zr7B2, and Fe90Zr7B2Cu1 alloys (D3) (Suzuki
et al., 1998).
Nanocrystalline Soft Magnetic Alloys
287
Another benefit of this formulation is the extension of the random
anisotropy model to describe magnetic hardening at elevated temperatures
and during the initial stages of crystallization. In the first case, the magnetic
hardening results from decoupling of the grains as the Curie temperature of
the intergranular amorphous matrix is exceeded. In the latter case, the small
volume fraction of isolated grains in a large amorphous matrix is addressed.
In these cases, the exchange coupling between the grains has been phenomenologically adjusted to simulate elevated temperatures using various relations for exchange stiffnesses, including Aam ¼ gAcr by Hernando et al.
(1998a,b), a relation of the exchange stiffnesses defined through a definition
of the spin
crystalline
and amorphous coupling pairs
protation
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiangle between
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
j0 ¼ D= Acr =hK i þ L= Aam =hK i by Suzuki and Cadogan (1998), and
an effective exchange stiffness Aeff ¼ (1 Vam)1/3/Acr þ (Vam)1/3/Aam by
Löffler et al. (1999). The results give surprisingly similar values of effective
anisotropy:
"
#6
ð1 Vam Þ4 4 6 1
ð1 Vam Þ1=3 1
pffiffiffiffiffiffiffiffi
K1 D pffiffiffiffiffiffiffi þ
hK i ¼
j6
Acr
Aam
ð25Þ
where Acr and Aam are the exchange stiffness of the crystalline and amorphous phases, respectively, j is a geometric/statistical parameter with value
near 1, and Vam is the volume fraction of the amorphous matrix phase.
These considerations are extremely important when discussing the hightemperature performance of nanocomposite materials (see Section 6.4).
Consideration of localized random anisotropy with long-range induced
anisotropy was first discussed by Alben et al. (1978) resulting in coercivity
with a grain size to the third power dependence (as opposed to grain size to
the sixth without induced anisotropy). Reduced power-law dependence on
grain size is also found in lower dimensional systems as first discussed by
Hoffmann for magnetization ripple in thin films (Hoffmann, 1968).
Uniform anisotropies (induced or magnetoelastic in origin) tend to dominate in nanocomposite alloys in a similar way to amorphous alloys due to
their small local anisotropies. The remanance ratio (Mr/Ms) has been
observed to change from 0.5 for samples with strong induced anisotropy
(indicative of uniaxial anisotropy dominance) to above 0.83 for samples
with random anisotropy dominance in Fe-based nanocrystalline alloys
(Suzuki and Cadogan, 1998). For this reason, uniform anisotropies can be
an important tool to modify the magnetic behavior from sharp magnetic
switching to energy storage behaviors.
Many electronic devices use inductor core to store magnetic energy
(e.g., choke coils, reactors, etc.). For these applications, large saturation
magnetization, low core losses, and consistent, low permeabilities over a
wide frequency range are important factors. Gapped ferrite cores have been
288
Matthew A. Willard and Maria Daniil
used for these applications; however, continued miniaturization of magnetic components using ferrites has become problematic due to the large
leakage fluxes at the gap (Fukunaga et al., 2000). For these reasons, induced
anisotropy has become an important field of study.
The generalization of the random anisotropy model to consider uniform
uniaxial anisotropy (Ku) in addition to exchange averaged local anisotropies
was approximated in the large Ku limit by Suzuki and Cadogan (Suzuki
et al., 1998). Later, an exact solution to the quartic equation describing the
combined anisotropy contributions was shown by Ito (2007). The solution
shows that power-law scaling for grain size dependence of effective anisotropy (hKi) is strongly dependent on the ratio of the uniform anisotropy (Ku)
to random anisotropy (hK1i) contributions. When Ku/hK1i > 2, the
uniform anisotropy dominates and the power law is reduced from D6 to
D3 dependence (Suzuki et al., 2008b). Such a change has been observed in
Fe-based nanocrystalline alloys and is thought to be responsible for their
reduced sensitivity to exchange softening. This results in the D3 dependence
of coercivity observed in the Fe–Zr–B–Cu alloys shown in Fig. 4.59a and b.
The formulae for the use of the multiphase random anisotropy model
considering cases with and without a uniform uniaxial anisotropy are
provided in Table 4.7.
A uniaxial induced anisotropy results in sheared hysteresis loops, effectively lowering the permeability of the alloy without the necessity of an air
gap. The anisotropy energy is typically determined from these sheared loops
as the area between the upper branches of the flattened hysteresis loops (first
quadrant) for the field-annealed and non-field-annealed samples (Lovas
et al., 1998). The origin of the magnetic field annealing induced anisotropy
has been attributed to the directional ordering of the magnetic and nonmagnetic elements in the Fe–Si–Nb–B–Cu alloys (Yoshizawa and
Yamauchi, 1989). Induced anisotropies tend to have an effect when their
anisotropy values exceed the averaged magnetocrystalline anisotropy hKi
(e.g., 5 J/m3 for 10 nm a-(Fe,Si) grains). As a result, slightly lower
coercivities were observed for field-annealed samples; an effect attributed
to the reduction in spatial fluctuations for domain wall pinning and the
simplified domain wall configuration (Herzer, 1992).
The lower bound for coercivity reduction solely by grain size refinement is near 0.5 A/m and is determined by anisotropies with origin other
than magnetocrystalline, including surface roughness, magnetoelastic coupling, induced anisotropies, etc. (Herzer, 1991). For this reason, successive
refinement of grain size does not result in continued lowering of the
anisotropy unless all forms of anisotropy can be reduced simultaneously.
In nanocrystalline soft magnetic alloys, where the magnetocrystalline
anisotropy energy has been exchange averaged, the magnetization process is
largely determined from the contributions of magnetoelastic energy and
demagnetization effects (magnetostatic energy).
Table 4.7 Effective magnetic anisotropy for 1D, 2D, and 3D exchange coupled volumes, without and with consideration of uniform
anisotropies (Ku)
Two phases: hKi ( J/m3)
3D (no Ku)
2D (no Ku)
1D (no Ku)
3D (w/Ku)
"
#6
ð1 Vam Þ4 4 6 1
ð1 Vam Þ1=3 1
pffiffiffiffiffiffiffiffi
K1 D pffiffiffiffiffiffiffi þ
j6
Acr
Aam
"
#2
2
ð1 Vam Þ 2 2 1
ð1 Vam Þ1=2 1
pffiffiffiffiffiffiffiffi
K1 D pffiffiffiffiffiffiffi þ
j2
Acr
Aam
"
#2=3
ð1 Vam Þ4=3 4=3 2=3 1
ð1 Vam Þ1 1
pffiffiffiffiffiffiffi þ
pffiffiffiffiffiffiffiffi
K1 D
j2=3
Acr
Aam
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
pffiffiffi
u
ð1 Vam Þ2 D6 K14 1 u f 1=3
4Ku2 16 3 2A3 Ku4 ð1 Vam Þ4 D12 K18
ffiffiffi þ
hK i ¼
þ
þ t p
þ
4j6 A3
3
4j12 A6
2 3 3 2A3
3f 1=3
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
pffiffiffi
u
1 u f 1=3 8Ku2 16 3 2A3 Ku4 ð1 Vam Þ4 D12 K18
h
ffiffiffi þ
þ
þ pffiffi
þ t p
3
12
6
1=3
3
3
2j A
2 3 2A
4 g
3f
pffiffiffi
f 1=3
4Ku2 16 3 2A3 Ku4 ð1 Vam Þ4 D12 K18
ffiffi
ffi
þ
þ
þ
g¼ p
3
4A6
3f 1=3
3 3 2A 3
9
f ¼ 128Ku6 A
þ 27ð1 Vam Þ4 Ku4 K18 D12 A12 =j12
q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffiffiffi
þ 27 256ð1 Vam Þ4 Ku10 K18 D12 A12 =j12 þ 27ð1 Vam Þ8 Ku8 K116 D24 A6 =j24
(Continued)
Table 4.7 Effective magnetic anisotropy for 1D, 2D, and 3D exchange coupled volumes, without and with consideration of uniform
anisotropies (Ku)—cont’d
Two phases: hKi ( J/m3)
h¼
2D (w/Ku)
1D (w/Ku)
8ð1 Vam Þ2 j12 D6 A6 Ku2 K14 þ ð1 Vam Þ6 D18 K112
j18s
A9ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3
2
1 ð1 Vam ÞD2 K12
ð1 Vam Þ2 D4 K14 5
2þ
þ
4K
hK i ¼ 4
u
j2 A
j4 A2
2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u
u 1=3
p
pffiffiffi
ffiffiffi
3
2
3K 4
u f 1=3 8K 2 16 3 2A3 K 4 h1
A
1u
f
4K
16
2
1
1
1
u
u
u
u
t
t
pffiffiffi þ
pffiffiffi þ
þ
þ
þ pffiffiffiffi
hK i ¼
1=3
1=3
3
3
g1
2 3 3 2A 3
2 3 3 2A 3
3f
3f
1
1
pffiffiffi
1=3
f1
4Ku2 16 3 2A3 Ku4
ffiffiffi þ
g1 ¼ p
þ
1=3
3
3 3 2A 3
3f1
9
f1 ¼ 128Ku6 Aq
þ
27ð1 Vam Þ4 K18 D4 A7 =j4
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
pffiffiffiffiffi
þ 27 256ð1 Vam Þ4 Ku6 K18 D4 A16 =j4 þ 27ð1 Vam Þ8 K116 D8 A14 =j8
h1 ¼
2ð1 Vam Þ2 D2 K14
j2 A
Reduces to single-phase models by selecting Vam ¼ 0. F is a geometric and statistical parameter with value near 1.
Nanocrystalline Soft Magnetic Alloys
291
A major contributor is the magnetoelastic energy, which is proportional
to the magnetostrictive coefficient and the internal stress in the alloy.
While internal stresses (evaluated by an impedanciometry technique) were
found to be significantly reduced during the crystallization process in
Fe73.5Si16.5Nb3B6Cu1 alloys, from 15 MPa in the as-cast sample to
0.2 MPa in a sample annealed at 580 C (Carara et al., 2002). However,
achieving the lowest core losses requires near zero values of magnetoelastic
anisotropy not merely reduced stress fields. Fortunately, the nanocomposite
nature of the microstructure provides a way of tuning the magnetostriction
in a way that is not possible in single-phase soft magnetic alloys. The local
compositions of the nanocrystalline and residual amorphous phases in the
alloy can be adjusted by small variations in the nominal composition of the
alloy and by adjustments of the annealing conditions. In this way, the large
positive value of magnetostrictive coefficient observed in most amorphous
alloys can be reduced, as the alloy is partially devitrified.
As the magnetization of the alloy changes (in direction or magnitude),
the shape of the sample changes (d‘=‘ and/or dV/V ), resulting in a
magnetoelastic contribution to the overall anisotropy of the material. We
call this stress dependence of the magnetocrystalline anisotropy, “magnetostriction.” Due to the polycrystalline nature of the microstructure and the
low magnetocrystalline anisotropy of nanocrystalline soft magnetic alloys,
the linear magnetostrictive coefficient (ls) can be obtained using a strain
gage to measure the d‘=‘ as a saturating magnetic field is rotated within the
sample (Claassen et al., 2002). The relationship between the ls and the
change in shape d‘=‘ is simply:
d‘ 3
1
¼ ls cos 2 y ‘ 2
3
ð26Þ
where y is the angle between the magnetization direction and the strain
gage direction (Datta et al., 1984). Capacitance, dilatometers, and transverse
susceptibility methods are also used to determine magnetostrictive coefficients for this class of materials (Kaczkowski et al., 1996; Vlasák et al., 2003).
The saturation magnetostriction coefficient has been found to vary widely
with Si content in Fe–Si–Nb–B–Cu alloys, with values ls ¼ þ1.4 ppm for
Fe73.5Si13.5Nb3B9Cu1 (Tann ¼ 580 C) and ls ¼ 0.3 ppm for Fe73.5
Si16.5Nb3B6Cu1 (Tann ¼ 550 C) (Herzer, 1995; Polak et al., 1992). The
effect has been attributed to a balancing of the negative magnetostriction
coefficient for the crystalline phase (lcr
s 3 ppm) and a positive magnetostriction coefficient for the amorphous matrix phase (lam
s 12 17 ppm),
yielding an effective magnetostrictive coefficient (leff
)
with
near zero value
s
for the nanocomposite alloy (Herzer, 1992; Twarowski et al., 1995b). The
leff
s is found as the weighted average of the ls and the volume fraction of each
am
cr
phase: leff
s ¼ (1 x)ls þ xls , where x is the volume fraction transformed
292
Matthew A. Willard and Maria Daniil
Magnetostrictive coefficient (ppm)
30
Fe73.5Si13.5B9Nb3Cu1
tann = 3600 s
(a)
(b)
Fe73.5Si15.5B7Nb3Cu1
tann = 3600 s
(c)
Fe73.5Si16.5B6Nb3Cu1
tann = 3600 s
25
20
15
10
5
0
-5
700
800
900
1000 750
800
850
900
650
700
750
800
850
900
Annealing temperature (K)
Figure 4.60 Magnetostrictive coefficients plotted against annealing temperature for
(a) Fe73.5Si13.5Nb3B9Cu1 (Agudo and Vázquez, 2005; Herzer, 1993; Kulik et al., 1994,
1995; Lim et al., 1993b; Todd et al., 2000; Vázquez et al., 1994; Yoshizawa and
Yamauchi, 1990; Zbroszczyk et al., 1995), (b) Fe73.5Si15.5Nb3B7Cu1 (Herzer, 1992;
M€
uller et al., 1991; Nielsen et al., 1994; Twarowski et al., 1995a; Yoshizawa et al.,
1994), and (c) Fe73.5Si16.5Nb3B6Cu1 alloys (Carara et al., 2002; Herzer, 1994b; Kulik
et al., 1997; M€
uller et al., 1991; Nielsen et al., 1994; Tejedor et al., 1998). Different
symbols are used per reference except in (a) where average results are used (error bars
indicate standard deviations).
(Hernando et al., 1997; Herzer, 1991). An additional parameter (6xlsurf
s /D,
where D is the grain diameter) for interfacial contributions was found to be
necessary in some cases to achieve an accurate leff
s (Murillo et al., 2004;
Ślawska-Waniewska et al., 1997; Szymczak et al., 1999). The lsurf
in these
s
cases was found to be quite small (in the range 0.1–0.7 ppm). The annealing
conditions and composition of the alloy have a profound effect on the
effective magnetostrictive coefficient for the nanocomposite. In Fig. 4.60,
the change in magnetostrictive coefficients with annealing temperature is
plotted for several very similar Fe73.5(Si,B)22.5Nb3Cu1compositions. When
the sample is amorphous, the magnetostrictive coefficient is large. As the
alloys are annealed at temperatures near the primary crystallization temperature for 3600 s, the magnetostrictive coefficient reaches near zero values,
which vary depending on the nominal composition of the alloy.
In general, a near zero value of magnetostrictive coefficient can be
achieved when the Si to Si þ B ratio is near 0.7 and when the sample is
annealed at temperatures that allow a large volume fraction crystallized. These
results for Fe73.5(Si,B)22.5Nb3Cu1 are summarized in Fig. 4.61, which shows
lam
(filled circles) with large values across the composition range and a
s
lowering trend with increased Si content. It also shows reduced leff
s as the
annealing temperature is increased to the primary crystallization temperature.
293
Nanocrystalline Soft Magnetic Alloys
Magnetostrictive coefficient (ppm)
20
763–773 K
783–793 K
798–803 K
813 K
823 K
15
838–843 K
853–863 K
873–883 K
>893 K
10
5
0
Fe73.5Si22.5B22.5 – xNb3Cu1
tann = 3600 s
0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85
Si/(Si + B)
Figure 4.61 Magnetostrictive coefficient plotted against Si/(Si þ B) for a series of
Fe73.5(Si,B)22.5Nb3Cu1 alloys annealed at various temperatures for 3600 s (Agudo and
Vázquez, 2005; Carara et al., 2002; Herzer, 1992, 1993; Herzer, 1994b; Kulik, 1995;
Kulik et al., 1994, 1997; Lim et al., 1993b; M€
uller et al., 1991; Nielsen et al., 1994; Noh
et al., 1991; Tejedor et al., 1998; Todd et al., 2000; Twarowski et al., 1995b; Vázquez
et al., 1994; Yoshizawa and Yamauchi, 1990; Yoshizawa et al., 1988a, 1994;
Zbroszczyk et al., 1995).
While, in most magnetic amorphous alloys, the magnetostrictive coefficient is proportional to the square of the magnetization, nanocrystalline soft
magnetic alloys provide a class of materials where the magnetostrictive
coefficient can be near zero up to m0Ms above 1.5 T (Makino et al.,
1995). This is an advantage of nanocomposite alloys over amorphous alloys,
broadening the potential composition ranges for optimal magnetic performance. However, many substitutions that enhance the saturation magnetization possess commensurately large magnetostrictive coefficient, including
the obvious substitution of Co for Fe in these alloys.
A sharp rise in magnetostrictive coefficient with Co substitution for Fe is
observed in nanocrystalline (Fe,Co)86–88Zr7B4-6Cu1 and (Fe,Co)73.5Si13.5–15.5
Nb3B7-9Cu1 alloys (see Fig. 4.62). The peak value was near 18 ppm for (Fe,
Co)73.5Si13.5–15.5Nb3B7-9Cu1 alloys with nearly 50% substitution of Co for
Fe (Kolano-Burian et al., 2004b; Müller et al., 1996b). In (Fe,Co)86–
88Zr7B4–6Cu1 alloys, the peak value was 40 ppm near 70% substitution
of Co for Fe (Müller et al., 2000; Willard et al., 2002b). Substitution of Ni
for Fe in Fe73.5xNixSi13.5Nb3B9Cu1 results in increased magnetostrictive
coefficients (above 13 ppm) for 10 x 40 when the alloys have been
annealed to promote partial crystallization (Vlasák et al., 2003). Adjustment
of the magnetostrictive coefficient has also been achieved by varying the
ETM content in Fe-based alloys. Figure 4.63 shows the near zero
294
Matthew A. Willard and Maria Daniil
Magnetostrictive coefficient (ppm)
(a)
(Fe,Co) BCC
(Fe,Co) FCC
(Fe,Ni) BCC
(Fe,Ni) FCC
(Fe,Co,Ni) BCC
(Fe,Co,Ni) FCC
(Co,Ni) FCC
40
30
20
10
0
Large symbol: MTM86Zr7B6Cu1
Small symbol: MTM88Zr7B4Cu1
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8 10.0
Valence electrons per atom
(b)
Magnetostrictive coefficient (ppm)
20
15
10
5
0
(Fe1 – xCox)73.5Si15.5B7Nb3Cu1
(Fe1 – xCox)73.5Si13.5B9Nb3Cu1
-5
0
10
20
30
40
50
60
70
80
Co content, x (at.%)
Figure 4.62 Effect of magnetic transition metal on magnetostrictive coefficient in (Fe,
uller et al., 2000) and (Fe,Co,Ni)88Zr7B4Cu1 (Willard et al.,
Co,Ni)86Zr7B6Cu1 (M€
2002a) alloys.
magnetostrictive coefficient can be produced in samples with 50–75% Nb
substituted for Zr and concomitant increase in B to maintain glass formability. Similar alloy design ideas have been used in (Fe,Co,Ni)-based alloys
(Knipling et al., 2012).
The sign of the magnetostrictive coefficient (l) is an important indicator
of the magnetic material’s response to a stress field. When l > 0, an applied
tensile stress field results in an increase in the magnetization along the
applied stress direction and under the application of an applied field.
Reversing the sign of l (or applying a compressive stress field) results in a
295
Magnetostrictive coefficient (ppm)
Nanocrystalline Soft Magnetic Alloys
(Fe89Zr7B3Cu1)1 – x(Fe83Nb7B9Cu1)x
(Fe90Zr7B3)1 – x(Fe84Nb7B9)x
Fe85Nb3.5Hf3.5B7Cu1
Fe89Hf7B4
1.0
0.5
0
-0.5
-1.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
x, Nb/Hf substitution for Zr
Figure 4.63 Variation of magnetostrictive coefficient with Nb or Hf substitution for
Zr in Fe–M–B–(Cu) alloys (Makino et al., 1995; Makino et al., 2000; Wu et al., 2001).
lowering of the magnetization magnitude. These phenomena are called
Villari effects (or piezomagnetic effects) and result in induced anisotropy,
especially when applied during annealing (see Section 2.2).
6.4. Exchange interactions and interphase coupling
The previous discussion of the reduction in coercivity by microstructure
refinement is predicated on the assumption that the randomly oriented grains
are sufficiently exchange coupled through the intergranular amorphous
matrix phase. In Section 6.2, the Curie temperature of the amorphous matrix
(TCam) was shown to be 593 K for a Fe73.5Si13.5Nb3B9Cu1 alloy annealed at
793 K for 1 h. For operation temperatures exceeding TCam, the coercivity of
the nanocomposite material rises quickly from less than 1 A/m at 473 K to
80 A/m at 673 K (see Fig. 4.64B) (Herzer, 1991). The increased coercivity
with measurement temperature reflects a reduced exchange coupling
between grains, through the amorphous intergranular region, reducing the
effectiveness of the exchange interaction to create a lowered average anisotropy, hKi. The domain structure changes from broad stripe domains to an
irregular domain pattern as the temperature passes from below to above TCam
(Schäfer et al., 1991). So long as the temperature is not increased to the
secondary crystallization temperature (i.e., no allowance for change in microstructure or phases), the increase in coercivity is fully reversible when the
material’s temperature is reduced (Willard et al., 2012a).
In general, the magnetic behavior of the nanocomposite is dominated by
the intergranular amorphous phase when TCam is exceeded, due to reduced
exchange interactions between grains. The coercivity shows a significant peak
296
Matthew A. Willard and Maria Daniil
(a)
T cm (Ta 753 K)
a
Coercivity (A/m)
400
793 K Fe72Si13.5Nb4.5B9Cu1
803 K Fe72Si13.5Nb4.5B9Cu1
813 K Fe72Si13.5Nb4.5B9Cu1
793 K Fe73.5Si13.5Ta3B9Cu1
773 K Fe73.5Si13.5Ta3B9Cu1
753 K Fe73.5Si13.5Ta3B9Cu1
300
T cm (Nb 793 K)
a
200
T acm (Ta 773 K)
T acm (Ta 793 K)
100
0
400
450
500
550
600
650
700
750
800
Measurement temperature (K)
(b)
10000
Fe73.5Si13.5Nb3B9Cu1
tann = 3600 s @ Tann
Coercivity (A/m)
1000
793 K
773 K
813 K
848 K
873 K
100
10
1
T cm (appro)
a
0.1
250 300 350 400 450 500 550 600 650 700 750 800 850 900
Measurement temperature (K)
Figure 4.64 Coercivity against measurement temperature for (a) Fe72Si13.5
Nb4.5B9Cu1 (squares) and Fe73.5Si13.5Ta3B9Cu1 (triangles). Annealing conditions are
shown in parenthesis and amorphous phase Curie temperatures (with ETM and Tann
indicated) are also shown. (b) Fe73.5Si13.5Nb3B9Cu1 (Herzer, 1991, 1993; Kim et al.,
1996; Kulik and Hernando, 1994; Mazaleyrat and Varga, 2001).
as the measurement temperature is increased (see Fig. 4.64a). The rise in
coercivity occurs when anisotropy and magnetostatic energies become dominant over exchange energy. The temperature at which peak coercivity is
observed is slightly higher than the Tam
C determined from thermomagnetic
experiments. The differences in the Curie temperatures for the two alloys
shown in Fig. 4.64a are consistent with the variation in Tam
C with ETM
content (see Fig. 4.54). When temperatures are sufficiently high, the grains
completely decouple, resulting in superparamagnetic behavior and a resulting
decrease in the coercivity. Samples prepared with low enough annealing
297
Nanocrystalline Soft Magnetic Alloys
temperatures tend to have greater amounts of intergranular amorphous phase,
resulting in more complete decoupling at lower operation temperatures with
commensurately lower temperatures for the onset of superparamagnetism (see
Fe72Si13.5Nb4.5B9Cu1 (793/803 K) and Fe73.5Si13.5Ta3B9Cu1 (753 K) data in
Fig. 4.64a). There are several proposed reasons for the observed peak in
coercivity and its temperature dependence, including exchange penetration
through the intergranular amorphous phase, superferromagnetism, and dipolar interactions (Hernando and Kulik, 1994; Herzer, 1995; Škorvánek and
O’Handley, 1995).
From a practical standpoint, the increase in coercivity is quite small over
a wide temperature range in (Fe,Si)-based alloys (see Fig. 4.60b) and is
limited by the Curie temperature of the residual amorphous phase for all
compositions (Willard et al., 2012a). While the increase in coercivity based
on these thermal effects is reversible, it can be a limitation for hightemperature use of the alloys. The main limiting factor for the alloys
shown in Fig. 4.64b, however, is not the coercivity rise. Rather, the
saturation magnetization decreases sufficiently with temperature to make
it the limiting factor (see Fig. 4.52).
This effect can be explained using the critical exponent equation for the
thermomagnetic response of the nanocomposite material with the exchange
averaged anisotropy equation for hKi. Realizing that the exchange stiffness (A)
weakens most rapidly as the operation temperature is increased and that it
depends on (m0Ms(T ))2, the following proportionality is found (Herzer, 1989):
hK i / ðm0 Ms ðT ÞÞ6 /
TCam T
TCam
6b
ð27Þ
When this holds true, Eq. (25) can be used to describe the full multiphase
dependency of the effective anisotropy with operation temperature
(through the weakening of the exchange stiffness of the amorphous matrix
(Aam)). Figure 4.65a shows the effective anisotropy with three levels of
decoupling: fully coupled (5 1012 J/m), partially coupled (1012 J/m),
and decoupled grains (5 1013 J/m). As the grains lose exchange coupling,
the anisotropy energy dominates magnetic switching. Magnetostatic and
magnetocrystalline sources of anisotropy raise the coercivity in a reversible
way, leading to deteriorated performance of the magnetic material at
operation temperatures near Tam
C . Similar results are observed if thin film
or nanowire forms of the effective anisotropy are considered.
Examination of the critical exponent (b) for the saturation magnetization
as a sample is heated to the Curie temperature (TC) helps to determine the
value of TC. Such an analysis finds proportionality between the reduced
magnetization (i.e., saturation magnetization (Ms (T )) at a given temperature divided by the saturation magnetization at absolute zero (Ms (0 K))) and
the reduced temperature to a fractional exponent:
298
Matthew A. Willard and Maria Daniil
(a)
áK1ñ (J/m3)
80
Aam = 5 ´ 10–13
60
40
Aam = 1 ´ 10-12
20
Aam = 5 ´ 10-12
0.2
0.4
0.6
0.8
1.0
Fraction amorphous phase, Vam
(b)
110
70%
100
90
áK1ñ (J/m3)
80
70
60
75%
50
40
80%
30
20
10
90%
transformed
0
0.2
0.3 0.4
1
2
Exchange stiffness (10
3
-12
4 5
10
2
J/m )
Figure 4.65 (a) Calculated effective anisotropy variation (Eq. 25) with fraction amorphous phase for 3D exchange coupled nanocomposites. (b) Variation of effective
anisotropy with exchange stiffness for several volume fractions of crystalline phase
(K1 ¼ 104 J/m3, Acr ¼ 1011 J/m2, j ¼ 1, and D ¼ 10 nm).
m0 Ms ðT Þ ¼ m0 Ms ð0K Þ
TC T
TC
b
ð28Þ
The critical exponent is found to be b ¼ 1/2 using the mean field model.
Analysis of thermomagnetic data collected for an as-spun Fe73.5Si13.5B9Nb3Cu1 alloy, showed a critical exponent, b ¼ 0.36, and a Curie
temperature of the amorphous phase (Tam
C ) of 593 K (Herzer, 1991). Samples of the same compositions, annealed at 520 C for 1 h to partially
crystallize the ribbon, show two Curie temperatures, Tam
C remains at
593 K and the Curie temperature of the a-(Fe,Si) phase (TxC) at about
873 K. The value of TxC is lower than the 1043 K expected for a-Fe and
Nanocrystalline Soft Magnetic Alloys
299
is consistent with 20–23 at% Si in a a-(Fe,Si) phase. The alloy Fe66Cr8Si13B9Cu1 shows that Cr reduces Tam
C to 490 K but does not significantly
change the critical exponent (b ¼ 0.364) (Ślawska-Waniewska et al., 1992).
Similar substitution of Mn (up to 5 at%) for Fe in (Fe,Si)-based nanocrystalline alloys results in lower Tam
C and subsequently reduced exchange
coupling through the residual amorphous phase (Gómez-Polo et al.,
2005; Hsiao et al., 2001).
The variation of hK1i with Aam is shown in Fig. 4.65b for Vcr from 0.7
to 0.9. Smaller Aam is equivalent to higher temperature of the nanocomposite, with Aam < 1012 J/m2, indicating decoupling of the grains, so higher
temperatures trend to the left in Fig. 4.65b. By this method, we see that
significant increases in hK1i are observed in the typical range of crystallite
volume fractions 0.7 Vcr 0.8 for this class of nanocomposite alloys.
Larger volume fractions transformed result in smaller hK1i as the grains
are decoupled, indicating a potential benefit for high-temperature use.
However, mean intergranular amorphous phase thickness (L) also decreases
with increasing Vcr, resulting in L < 0.4 nm for Vcr ¼ 0.9, which may be
inadequate to prevent significant grain coarsening, ultimately limiting the
practicality of this approach for improving high-temperature performance.
The most effective way to improve the high-temperature performance
of nanocomposite soft magnetic materials has been MTM substitutions,
especially Co for Fe. In nanocrystalline (Fe1xCox)84Zr3.5Nb3.5B8Cu1
alloys, a coercivity of less than 60 A/m is observed for operation temperatures up to 773 K when x is near 0.4–0.5 (Gercsi et al., 2006). The x ¼ 0.3
alloy had the lowest coercivity over the temperature range from 573 to
773 K, with a value between 40 and 45 A/m. Similar results are reported in
(Fe1xCox)86Hf7B6Cu1 alloys, which show increased coercivity as the Co
content is increased, from less than 20 A/m at x ¼ 0.2 to near 50 A/m for
x ¼ 0.9 (see Fig. 4.66) (Liang et al., 2005). The Fe-based alloy showed
significant persistent increase in coercivity across the whole temperature
range. Each Co-containing alloy showed a slight increase in coercivity as
the temperature increased up to the secondary crystallization temperature
( 875 K) where the coercivity experienced a large irreversible increase due
to deterioration of the intergranular amorphous matrix (quite evident in
Fig. 4.66 for alloys with closed symbols).
Compared with (Fe,Si)-based alloys, the rate of coercivity increase with
temperature is quite small for (Fe,Co)-based alloys; however, the overall
coercivity is much larger due to the increased magnetostrictive effects as Co
content is increased. Similar Co substitution into (Fe,Si)-based alloys
resulted in large increases in coercivity at about 600 K due to the partial
decoupling of nanocrystalline grains at Tam
C (i.e., superferromagnetic behavior). For temperatures exceeding 600 K, the coercivity of (Fe,Co)-based
alloys is lower than (Fe,Si)-based alloys (comparing Figs. 4.66 and 4.64a).
Additionally, the (Fe,Co)-based alloys maintain a strong saturation
300
Matthew A. Willard and Maria Daniil
(Fe1 – xCox)86Hf7B6Cu1
Tann = 823 K
tann = 3600 s
Coercivity (A/m)
100
x=0
x = 0.2
x = 0.4
x = 0.5
10
x = 0.6
x = 0.8
x = 0.85
x = 0.9
250 300 350 400 450 500 550 600 650 700 750 800 850 900 950
Measurement temperature (K)
Figure 4.66 Effect of measurement temperature on coercivity of (Fe1xCox)86
Hf7B6Cu1 alloys annealed at 823 K for 3600 s (Liang et al., 2005).
70
(Fe1 – xCox)86Hf7B6Cu1
Fe77Co5.5Ni5.5Zr7B4Cu1
Coercivity (A/m)
60
50
Tmeas = 723 K
40
30
20
Tmeas = 298 K
10
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Co content, x
Figure 4.67 Comparison of coercivities measured at 298 and 723 K for a series of
(Fe1xCox)86Hf7B6Cu1 alloys (Liang et al., 2005). A Fe77Co5.5Ni5.5Zr7B4Cu1 alloy is
shown for comparison (Knipling et al., 2009).
magnetization as the temperature is increased, making them more suitable
for high-temperature applications.
At room temperature, the coercivity tends to increase with increasing
Co content in (Fe1xCox)86Hf7B6Cu1 alloys (see Fig. 4.67). The increase is
likely related to the increased magnetostrictive coefficient, similar to polycrystalline Fe–Co and (Fe,Co)-based amorphous alloys (see OHandley,
1977). For alloys measured at 723 K, the coercivity is increased at all
compositions, with the largest increase observed for the Co-free alloy.
301
Nanocrystalline Soft Magnetic Alloys
6
10
Finemet (FT-1M)
Finemet (FT-1L)
Finemet (stress ann.)
Finemet (400m powder) 60% packed
Co-based amorphous alloy
Fe-based amorphous alloy
Mn–Zn ferrite
Ni–Zn ferrite
Fe powder core
4–79 Mo permalloy
Fit of Snoek’s limit
Relative permeability
105
4
10
103
102
10
1
3
10
4
10
10
5
10
6
10
7
10
8
10
9
Switching frequency (Hz)
Figure 4.68 Comparison of relative permeability with varied switching frequencies
for several soft magnetic materials (Chikazumi and Graham, 1997; Mazaleyrat and
Varga, 2000; Thornley and Kehr, 1971; Yoshizawa et al., 1988b).
This is due to the low Curie temperature of the intergranular amorphous
matrix and decoupling effects. Alloying additions that raise Tam
C consequently improve the soft magnetic performance at elevated temperatures.
The substitution of equal amounts of Ni and Co for Fe has recently shown
improved high-temperature performance for a low-Co alloy composition,
where the magnetostriction can be more easily controlled giving better
energy efficiency.
The high-temperature magnetic performance of Fe73.5xCoxSi13.5B9Nb3Cu1 alloys showed improved permeability above 573 K for
x ¼ 30 over no substitution (Gómez-Polo et al., 2002). The observed
improvements were observed at temperatures exceeding the Curie temperature of the amorphous phase (Tam
C ) and were attributed to exchange
penetration from the ferromagnetic crystalline phase through the thin,
paramagnetic intergranular amorphous phase. The room temperature values
of coercivity were found to increase with Co substitution from 3.6 A/m
(x ¼ 0) to 14.8 A/m (x ¼ 45) at 1 kHz and magnetic field amplitude of
48 A/m. Low coercivity values (below 15 A/m) were observed for x ¼ 30
at an applied magnetic induction value of 0.5 T at low frequency and
operation temperatures up to 773 K (Mazaleyrat et al., 2004). Higher
coercivity values deteriorated the soft magnetic performance of alloys
with x 30, which was attributed to the increasing positive values of
magnetostrictive coefficients which tend to dominate the losses in these
alloys. When these alloys are annealed at temperatures exceeding the
secondary crystallization temperature, boride phases form resulting in
302
Matthew A. Willard and Maria Daniil
much larger coercivities. For example, the Fe2B phase, which is a secondary
crystallite for (Fe,Si)- and Fe-based nanocrystalline alloys, has K1 430 kJ/m3
(with Lex 5 nm) (Herzer, 1996).
The thermomagnetic phenomenon, superparamagnetism, results from
the thermal activation of exchange coupled moments in particles (Bean and
Livingston, 1959). The unique magnetic behavior observed includes lack of
hysteresis (i.e., zero coercivity) and universal curve behavior for magnetization plotted against Ms H/T. Samples of Fe66Cr8Si13B9Cu1 annealed at
temperatures between 803 K for 1.2 ks were found to possess superparamagnetic behavior when measured at temperatures between 523 and 773 K,
but not at 423 K (Ślawska-Waniewska et al., 1992). The Curie temperature
of the amorphous phase was determined to be 490 K by thermomagnetic
analysis, indicating that at the lowest measurement temperature, the sample
was fully ferromagnetic (both phases). At higher temperatures, Tam
C is
exceeded and the grains fully decouple due to the low volume fraction
transformed (18 vol%) and resulting large distance between adjacent
grains (Lachowicz et al., 2002). The mean field approximation described
above can be used to describe superparamagnetism in this case, replacing the
atomic moment with a super-moment consisting of all of the exchange
coupled moments in the grain. A spherical grain with diameter 10 nm (as
observed in this alloy) has a volume of 525 nm3, which compares favorably to the volume of each superparamagnetic moment from the best fit to
the experimental data (548 nm3). Superparamagnetism was not observed in
Fe73.5Si13.5B9Nb3Cu1 until temperatures much higher than TC am, rather
superferromagnetism was observed due to the stronger interactions between
particles (Ślawska-Waniewska et al., 1993). At sufficiently high temperatures (exceeding 600 K), superparamagnetic behavior was observed in a
Fe72Si13.5B9Nb4.5Cu1 annealed at 803 K for 3.6 ks (Kim et al., 1996).
At temperatures below 50 K, spin-glass and spin-freezing effects have
been observed in Fe73.5Cr5B10Nb4.5Cu1 alloys (Škorvánek and Wagner,
2004). This has been characterized by strong irreversibility between zero
field cooled and field cooled conditions.
6.5. Static hysteresis and AC core losses
High permeability is desirable for applications where the core material
switches under low-field conditions, such as common-mode chokes or
ground fault interrupts. Low permeability is necessary for high-frequency
power transformers in power electronics applications or interface transformers for telecommunications. In both instances, common characteristics
that improve performance include low losses, high resistivity, and good
thermal stability. Control of permeability and reduction of core loss are two
engineering aspects of these materials that are important for application and
will be discussed in this section.
Nanocrystalline Soft Magnetic Alloys
303
Magnetostatic effects (e.g., powders) and induced magnetic anisotropy (via
stress or magnetic field annealing) can be used to tune the permeability during
alloy processing. In both cases, the magnetic domains can play an important role
in the switching. Magnetic domains are easily formed in soft magnetic materials
due to their large magnetizations and small values of magnetic anisotropy,
which aid in reduction of magnetostatic energy. To saturate the material, a
magnetic field must be applied to sweep the unfavorably oriented domains out
of the material and then rotate the remaining favorably oriented domain into
the magnetic field direction. From the demagnetized state, small, applied
magnetic fields cause reversible domain wall motion until the domain walls
reach pinning centers in the material. Additional field is required to move the
domain walls away from the pinning centers, which results in irreversible
domain wall motion (a large contributor to the coercivity). When all of the
domain walls are swept from the material, the magnetization then rotates into
the applied field direction as the field is further increased. A magnetic hysteresis
loop results from cycling the magnetic field between large positive and large
negative fields. When this is done slowly, the area swept out by the loop is
minimized and it is referred to as the static hysteretic loss. High-frequency
switching results in larger losses due to the formation of eddy currents, which
screens out the applied field and confines the switching to the material’s surface.
The total core losses of a material switched at high frequencies are
dependent on the amplitude of the applied field, the hysteresis loss, the
excitation frequency, and geometry of the sample, in addition to eddy
currents. In Fig. 4.68, the permeability of various state-of-the-art soft
magnetic materials is shown for low-field switching at various frequencies.
Transverse field annealing has been found to lower the permeability (e.g.,
shearing the hysteresis loop) in Fe73.5Si13.5Nb3B9Cu1 alloys, while longitudinal field annealing gives better squareness to the loop and increases the
maximum permeability (Herzer, 1995). For powder cores, the distributed
air gap causes a reduced permeability due to the effect of the demagnetizing
field. At high enough frequencies, the magnetic resonance of the material
reduces the permeability at the Snoek limit (marked in Fig. 4.68).
The core losses are well described by their contributions from frequencyinsensitive sources (e.g., hysteretic losses) and frequency-sensitive sources
(e.g., classical and excess or anomalous eddy current losses). To this point,
the discussion of coercivity has largely referred to frequency-insensitive measurements carried out by vibrating sample magnetometry. The area of a
hysteresis loop is the hysteretic loss, and it is closely related to the width of
the loop (i.e., coercivity). The nanocrystalline alloys presented here generally
have low hysteretic losses due to their fine-grained microstructure in combination with their low magnetoelastic anisotropy. The eddy current losses in this
class of materials begin to show their significance at frequencies approaching
tens to hundreds of kilohertz. The eddy
to increase when the
pcurrents
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffitend
ffi
skin depth of the material (i.e., dm re =pf m0 m) is smaller than half the
304
Matthew A. Willard and Maria Daniil
ribbon thickness. While some work has been done on amorphous alloys to
reduce the ribbon thickness in attempts to increase the operation frequency,
little work has been done on nanocrystalline materials (Beatrice et al., 2008).
As a general principle, the eddy current losses can be described by
Pcv /
d 2 f 2 B2
re
where d is the ribbon thickness, f is the switching frequency, B is the
magnetic induction amplitude, and re is the electrical resistivity. From
this equation, it is clear that the rapidly solidified nanocomposite ribbons
have advantageous thicknesses (d 18–25 mm) and modest resistivities
(100–130 mO cm), which help to limit the eddy current losses. An additional eddy current term is dominant at frequencies in the tens kHz which is
due to the fast magnetization switching near domain walls (called excess
eddy current losses) (Ferrara et al., 2000; Willard et al., 2005).
Figure 4.69 shows the core losses for several state-of-the-art soft magnetic materials. The core losses naturally increase as the magnetic induction
amplitude is increased (or commensurately the magnetic field strength), due
to the progressively increased area swept out by larger minor hysteresis loops
(Fig. 4.69a). As the material starts to saturate, the magnetization of the
material provides less of the increase to induction (and the magnetic field
provides more). This requires significantly more energy resulting in a sharp
rise in the core losses near saturation. The core losses also increase as the
frequency is increased due to dynamic domain wall motion and eddy
current losses (Fig. 4.69b). In both parts of Fig. 4.69, the (Fe,Si)-based
nanocrystalline alloys have the lowest losses for a given magnetic induction
amplitude (in A) or switching frequency (in B). This is due to the exchange
softening of the magnetocrystalline anisotropy due to the refined microstructure, the near zero magnetostrictive coefficients due to the balanced
components from the phases in the nanocomposite, and the high resistivity
of the residual amorphous phase allowing reduced eddy currents.
The coercivity (Hc), saturation magnetization (Ms), and initial susceptibility (w0) have been used to determine the switching behavior of Fe73.5
Si13.5B9Nb3Cu1 alloys in the as-cast and annealed conditions using the ratio
w0 Hc/Ms (Zbroszczyk, 1994). Coherent rotation was calculated to have a
value of 0.21 and domain wall motion a value of 0.008 (Herzer, 1990;
Hofmann et al., 1992), the latter comparing favorably with experimental
data for optimally annealed samples (0.0079) (Zbroszczyk, 1994).
6.6. Magnetocaloric effect
The magnetocaloric effect is an adiabatic temperature change in a material
due to a change in applied magnetic field (Pecharsky and Gschneidner, 1999).
It can be used to perform solid-state cooling in adiabatic demagnetization
305
Nanocrystalline Soft Magnetic Alloys
(a)
10
f = 50 Hz (sine)
Core loss (W/kg)
1
0.1
0.01
Supermendur
80 Permalloy
Fe–3.5 at% Si
Fe78Si9B13
Fe86Zr7B6Cu1
Fe73.5Si13.5Nb3B9Cu1
0.001
0.2
0.5
1
2
Maximum induction amplitude (T)
(b)
Core loss (W/kg)
105
10
4
Fe–3.5 at% Si
Mn–Zn ferrite
Fe44.5Co44.5Zr7B4
Fe78Si9B13
10
3
Fe86Zr7B6Cu1
Fe73.5Si13.5Nb3B9Cu1
10
2
10
Bm = 0.2 T (sine)
1
1
10
100
1000
Switching frequency (kHz)
Figure 4.69 (a) Comparison of core losses with applied induction amplitude for
several soft magnetic materials using sinusoidal waveforms and a switching frequency
of 50/60 Hz (Gutfleisch et al., 2011; Suzuki et al., 1991a) and (b) with frequency for
several soft magnetic materials using sinusoidal waveforms and an applied induction
amplitude of 0.2 T (Suzuki et al., 1991a; Willard and Daniil, 2009; Yoshizawa and
Yamauchi, 1989).
refrigerators, exhibiting maximum efficiency when the magnetic refrigerant
materials possess small coercivity, strong temperature dependence of magnetization near the operation temperature, and (especially) large magnetic
contribution to the entropy (under an isothermal magnetic field, DSM). In
conventional magnetocaloric materials, materials containing elements
with large atomic moments are used to maximize the DSM; rare earthcontaining compounds are typically used (e.g., diluted paramagnetic salts
(near 0 K); elemental Gd, magnetic garnets, and Gd5(Ge,Si)4; (Pecharsky
and Gschneidner, 1997); etc.). Although these materials have large intrinsic
306
Matthew A. Willard and Maria Daniil
magnetic entropy, they are also quite expensive and in high demand for many
other energy applications.
The use of nanostructured materials for magnetocaloric applications was
posed by McMichael et al. (1992) and specifically to (Fe,Si)-based alloys by
Kalva (1992). In principle, the advantage of nanocrystalline materials lies in
their small grain size that can act as superparamagnetic (or superferromagnetic) clusters when thermally activated. The large moments from these
clusters provide large magnetic entropy as the blocking temperature is
approached (near the Curie temperature of the amorphous phase). An
improvement in magnetocaloric entropy change was observed in a
Co66Si12Nb9B12Cu1 alloy annealed at 843 K, exhibiting a maximum
DSM of 0.035 emu/(g K) for a field change of 0.1 T and at a temperature
of 125 K (Didukh and Ślawska-Waniewska, 2003). Under these processing conditions, the alloy consisted of 7.4 nm grains embedded in an
amorphous matrix with a volume fraction of crystallites 5–7%. The
peak in DSM was consistent with the amorphous phase Curie temperature,
which decoupled the well-separated grains in the material resulting in
superparamagnetic behavior. The maximum DSM shifted to lower temperatures for higher volume fraction transformed.
However, in most nanocrystalline soft magnetic alloys, the magnetocaloric effect is reduced when samples are partially crystallized. For example, a
Fe68.5Mo5Si13.5B9Nb3Cu1 alloy showed deterioration of the DSM after
partial crystallization (Franco et al., 2006b). In amorphous alloys, substitution of 5 at% Co for Fe in a Fe83Zr6B10Cu1 alloy resulted in increased
magnetocaloric entropy (from 1.4 to 1.6 J/kg K); however, the Curie
temperature of the amorphous phase was also increased (from 400 to
485 K) (Franco et al., 2006a). Recent studies of dual substitution of Co
and Ni for Fe in a Fe88Zr7B4Cu1 amorphous alloy show a similar trend with
alloying, but with larger values of magnetic entropy change (CaballeroFlores et al., 2010). In the relaxed amorphous state, the magnetocaloric
properties of this material were favorable when compared to Gd5(Ge,Si)4
materials due to their lower coercivity (and much lower materials cost).
6.7. Giant magnetoimpedance
The giant magnetoimpedance (GMI) effect was first reported by Panina and
Mohri in a Fe4.3Co68.2Si12.5B15 alloy when they observed a change in AC
impedance (Z ¼ R þ ioL) as high as 60% by the application of an AC
current (I ¼ I0 exp(iot)) to an electrically conducing magnetic material
under an applied DC bias field (HDC) (Panina and Mohri, 1994). The strong
field sensitivity of this effect makes it suitable for sensor applications. The
effect itself was attributed to a combination of skin depth and sensitive field
dependence of circumferential or transverse permeability. Such effects have
since been observed to depend strongly on the magnetostrictive coefficient
Nanocrystalline Soft Magnetic Alloys
307
and the subsequent domain structure formed in materials with wire and
ribbon morphologies (Barandiarán and Hernando, 2004; Guo et al., 2001).
The frequency (o ¼ 2pf) dependence is highly influenced by the electrical
resistivity (re) through the skin depth (dm ¼ (re/pfm)1/2) and the permeability (m), especially for f greater than a few MHz. This is due to the formation
of eddy currents in the center of the ribbon cross section, causing the AC
currents to flow closer to the ribbon surface and resultant switching by
magnetization rotation. For f less than a few MHz and low applied fields, the
GMI effect is dominated by domain wall displacements.
The total impedance (Z) has been found to decreases rapidly with applied
magnetic field when the magnetic material possesses a small, negative value of
magnetostrictive coefficient (ls 107) (Phan and Peng, 2008). The
domain structure for a material with this characteristic has a core with axial
magnetization surrounded by a shell of circumferential domains with a stripe
domain pattern. At low fields, the core saturates along the applied field
direction. With increasing field, the circumferential domains align with the
field direction by a coherent rotation process, thereby reducing the impedance. The inductive component of an AC wire voltage can be decreased by
50% for an applied field as low as a few hundred A/m by this method. This
process is dependent on both magnetic field amplitude and frequency. Setup
for making this type of measurement is described by Knobel et al. (1997).
Nanocrystalline Fe73.5Si13.5B9Nb3Cu1 alloys with near zero magnetostrictive coefficient showed similar, large total magnetoimpedance (Zm)
with contributions from magnetoresistance (Rm) and from magnetoreactance (Xm), where Zm(f,H) ¼ Rm(f,H) þ i Xm(f,H) (Chen et al., 1996). The
composition series Fe74SixB22xCu1Nb3 (x ¼ 4–18) and annealing temperature dependence of GMI showed that peaks in the permeability and MI
ratio coincide, with highest field sensitivity of 23%/Oe and 67% MR ratio
for an x ¼ 16 alloy after annealing at 570 C (Ueda et al., 1997). The peak in
GMI ratio for nanocrystalline Fe73.5Si13.5B9Nb3Cu1, Fe90Hf7B3, and
Fe90Zr7B3 alloys peaked between 100 and 500 kHz with values of 10%,
25%, and 27%, respectively (Knobel et al., 1997). The difference was
attributed to the influence on the transverse permeability (implied through
the negative magnetostrictive coefficients) for the Fe-based alloys and the
near zero value for the (Fe,Si)-based alloy. Higher frequency measurements,
to 5 MHz, resulted in an increase of both field sensitivity (40%/Oe) and
maximum GMI ratio (640%) for nanocrystalline Fe71Al2Si14B8.5Nb3.5Cu1
alloys (Phan et al., 2006). This effect was also reported for Fe88Zr7B4Cu1
nanocrystalline alloys, with GMI ratio of 409% at 10 MHz (Chen et al.,
1997). No reports have been made on the GMI of HITPERM-type alloys,
likely due to their lower permeability.
The application of similar amorphous materials as current and field
sensors has been investigated (Valenzuela et al., 1996, 1997). Maximum
GMI sensitivity was found for the frequency range 50–500 kHz and AC
308
Matthew A. Willard and Maria Daniil
current amplitudes of 8–15 mA. Sensors made from (Fe,Si)-based nanocrystalline alloys sandwiched around a copper lead showed optimal performance for small values of ribbon length-to-width ratio and relative
permeability (controlled by stress annealing) (Bensalah et al., 2006).
Frequency-modulated GMI sensors with 15%/Oe sensitivity over the
field range 2 Oe have been demonstrated using a nanocrystalline ribbon
core (Wu et al., 2005).
7. Other Physical Properties
7.1. Mechanical and magnetoelastic properties
Few studies have focused on the mechanical properties of nanocrystalline
soft magnetic alloys. Typical alloys of this type are thin and narrow and quite
brittle after annealing, making standard techniques for measuring bulk
mechanical properties difficult. Despite these limitations, some studies of
alloy microhardness, nanohardness, and relative strain at fracture have been
investigated. A recent study of the amorphous precursor ribbons of Fe73.5
Si13.5Nb3B9Cu1 alloys shows tensile strengths of 2000 MPa and a high
notch toughness of 89 MPam1/2 (El-Shabasy et al., 2012).
Many connections between magnetization and strain behavior in magnetic
alloys have been observed under the application of varying combinations of
magnetic or stress fields or applied torques. Most important among these
include magnetostrictive effects (i.e., shape change due to changing magnetization), DE effect (i.e., mechanical softening due to changing stress), and
Villari effect (i.e., magnetization changing due to applied stress field). The
following section will describe some of the experimental results of these effects
in nanocrystalline soft magnetic alloys. More detailed descriptions of these
effects (and others) can be found elsewhere (Kaczkowski, 1997; OHandley,
2000). Magnetostrictive effects are a major source of hysteretic losses in
nanocomposite alloys, so these properties have been discussed in Section 6.3.
The magnetomechanical coupling coefficient (km) provides information
about the suitability of a given magnetostrictive material for transducer
applications by defining the amount of magnetic energy that is converted
to mechanical energy. This may be accomplished by measuring the permeability under an oscillating magnetic field for (1) a freely vibrating sample
(mt) and (2) a mechanically fixed sample (ms), resulting in: k2m ¼ (1 ms)/mt.
Experimentally, this value may be determined using a resonant/antiresonant
magnetoimpedance technique (Kaczkowski, 1997). The low magnetocrystalline anisotropy, high saturation magnetization, and high electrical resistivity found in nanocrystalline soft magnetic alloys make them good
candidates for transducer applications. However, the magnetostrictive coefficient must be increased substantially (to above 15 ppm) to provide the
309
Nanocrystalline Soft Magnetic Alloys
70
25
65
20
55
50
15
45
40
35
10
30
25
5
20
Magnetostriction, ls (ppm)
Coupling coefficient, km (%)
60
15
10
0
0
50 100 150 200 250 300 350 400 450 500 550 600
Annealing temperature, T (°C)
Figure 4.70 Maximum values of the magnetomechanical coupling coefficient (km) of
the Fe73.5Si15.5B7Nb3Cu1 samples annealed in vacuum and saturation magnetostriction
(ls) of the Fe73.5Si13.5B9Nb3Cu1 samples annealed in air versus annealing temperature
(Tann) for 3600 s. Modified from Kaczkowski et al. (1995) and M€
uller et al. (1992).
necessary large values of km. For this reason, different processing conditions
will be optimal for transducer applications than for power conditioning and
conversion applications, where nearly zero magnetostriction is desired.
Magnetomechanical coupling coefficients as high as km ¼ 0.62 were found
for Fe73.5Si13.5Nb3B9Cu1 samples annealed below the primary crystallization temperature and dropped quickly as the nanocrystalline microstructure
developed due to reduced magnetostrictive coefficients (see Fig. 4.70)
(Kaczkowski et al., 1995).
The DE effect was measured using a vibrating reed method by Bonetti and
Del Bianco on a Fe73.5Si13.5Nb3B9Cu1 alloy as a function of both annealing
and measurement temperatures (Bonetti and Del Bianco, 1997). The change
in elastic modulus (DE) was evaluated by DE/E ¼ (E Emin)/Emin, where E
is the elastic modulus when a saturating magnetic field is applied and Emin is
the lowest value of elastic modulus measured at a constant magnetic field. The
Emin value was observed to coincide with the anisotropy field of the magnetic
hysteresis (Gutiérrez et al., 2003). By this method, amorphous samples had
typical values of DE/E between 0.05 and 0.08. Annealed samples
(Tann > 700 K) showed improved magnetoelastic coupling with DE/E values
in excess of 1.1, which quickly dropped as the temperature was increased to
800 K (e.g., crystallization of the sample). Similarly, by comparing conventionally annealed and Joule annealed samples, the maximum in DE/E was
found in relaxed amorphous samples (e.g., low internal stresses and large
positive magnetostriction) (Bonetti et al., 1996). The elastic (Young’s)
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Matthew A. Willard and Maria Daniil
modulus of a Fe73.5Si13.5Nb3B9Cu1 alloy was found to not vary appreciably
under the application of a magnetic field for an as-cast sample, exhibiting a
value of between 150 and 160 GPa (Kaczkowski et al., 1997). After annealing
above the primary crystallization temperature, the elastic modulus at magnetic
saturation was found to vary between 160 and 180 GPa (slightly less than
BCC-Fe 210 GPa).The elastic modulus of Fe64Ni10Si13Nb3B9Cu1 at magnetic saturation was found to be between 177 and 186 GPa for the amorphous phase depending on the relaxation annealing conditions and between
184 and 209 GPa after partial crystallization, resulting in improved km
(Gutiérrez et al., 2003). The largest coupling coefficients (km 0.85) coincided with the largest values of DE/E (0.61), for this alloy composition
annealed just prior to crystallization (at 460 C).
The magnitude of elastic softening due to the DE effect can be correlated
with the magnetostrictive coefficient by the relation:
DE l2s Es
F
¼
K
E
where K is the anisotropy constant, and F is a factor that depends on the easy
axis distribution and applied field (Hogsdon et al., 1995). The shape of DE
versus applied field plots is directly related to the anisotropy, domain
structure, and saturation magnetostriction (through the above relation)
and therefore can help interpret switching in these alloys (Atalay et al.,
2001). From the shape and magnitude of the DE versus magnetization plots,
the motion of 180 domain walls was found to dominate as Fe73.5
Si16.5Nb3B6Cu1 samples were annealed at temperatures to 620 C.
Magnetoelastic effects were examined on a Fe73.5Si16.5Nb3B6Cu1 toroidal core which was subjected to varying applied compressive stresses during
hysteresis measurement (Bie
nkowski et al., 2004b). A Villari point (where
(dB/ds)Η ¼ 0) was observed for samples with low crystalline volume fractions, inferring a change in the sign of the magnetostrictive coefficient. For
the sample with optimal soft magnetic performance (Tann ¼ 580 C for 1 h),
the magnetic induction was reduced as the compressive stress was increased
to 10 MPa for all applied fields.
The class of nanocrystalline soft magnetic alloys, as a whole, exhibits
significant embrittlement after crystallization, requiring that toroidal cores
be wound to their final shape prior to crystallization. The use of Joule
annealing to partially devitrify a Fe73.5Si13.5Nb3B9Cu1 alloy has been attributed with improved ductility after crystallization. A comparative study
between the strain-at-fracture (ef) values of conventionally annealed and
Joule annealed samples resulted in about a factor of 2 increase (from 0.05
to 0.13) (Allia et al., 1994). Both of these values are much lower than the
0.18 value for the as-cast ribbon, which has significant flexibility (but
limited ductility). Skorvanek and Gerling found that ef was reduced for a
311
Nanocrystalline Soft Magnetic Alloys
10.5
Coble creep
Hall–Petch
Microhardness, Hv (GPa)
10.0
9.5
9.0
8.5
8.0
7.5
7.0
FeMoSiB
FeMoSiB/FeCuSiB
6.5
6.0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
D-0.5 (1/nm0.5)
Figure 4.71 Variation in microhardness with D1/2 for (Fe0.99 M0.01)78Si9B13 alloys
where M ¼ Mo, Cu (Liu et al., 1993a; Liu et al., 1993b).
Fe73.5Si13.5Nb3B9Cu1 alloy annealed at temperatures below the onset of
primary crystallization, which was attributed to an increase in the density of
the amorphous phase (reduction in free volume) (Škorvánek and Gerling,
1992). They further studied a partially crystallized sample (545 C for 1 h)
under neutron irradiation and found little change in ef with neutron fluence
(remaining at 0.04 over the range 1017 to 1019 nth/cm2). Similar studies
on the embrittled amorphous alloys showed a restoration of the high degree
of ef (to near 1) for alloys annealed at 300 and 400 C. The author’s
conclusion from these findings was that the residual amorphous phase was
not solely responsible for the brittle behavior in the nanocrystalline alloys.
Large relative strain at fracture (above 0.35) was observed in Co-rich
(Co1xFex)89Zr7B4 alloys after primary crystallization (Daniil et al.,
2010b; Heil et al., 2007). Analysis of the fracture surfaces showed increased
microvoid coalescence dimple size with enrichment in Co. Materials with
this large ef are capable of processing after annealing, giving a greater
flexibility in the processing route for cores; however, the improved
mechanical performance seems to be limited to x > 0.1 (Fig. 4.71).pffiffiffiffi
A linear dependence of the microhardness values with 1= D was
observed for Fe77.22Mo0.78Si9B13 and Fe77.22Cu0.78Si9B13 samples with
varied grain diameters (D) between 30 and 200 nm, and an inverse dependence was found for grains smaller than 30 nm (Liu et al., 1993a,c). This
result shows behavior consistent with the Hall–Petch relationship for grains
pffiffiffiffi1
with diameter greater than 45 nm, namely, sy ¼ sy0 þ f D , where
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Matthew A. Willard and Maria Daniil
sy is the yield stress (proportional to the hardness, Hv), sy0 is the stress
necessary to make dislocations mobile (lattice friction stress), and f is a
constant. For grains with diameter less than 45 nm, Coble creep may be
the dominant deformation mechanism where sc ¼ A/D þ BD3 (where sc is
the creep stress (again proportional to the hardness, Hv) and A and B are
constants) (Chokski et al., 1989; Lu et al., 1991; Masumura et al., 1998).
While these relationships are consistent with other nanocrystalline materials,
a thorough investigation of the mechanical property variation with grain
size has not been performed on this class of materials.
7.2. Electrochemistry and oxidation
Experiments have been conducted by annealing in an oxygen atmosphere
and by immersion in acid solutions to establish the oxidation and corrosion
properties of nanocrystalline soft magnetic alloys. Conventional methods for
annealing to promote crystallization are conducted in an inert atmosphere to
avoid the deleterious effects of oxidation on the saturation magnetization.
Marino et al. found that annealing nanocrystalline samples of Fe73.5
Si13.5NbxB10.5xCu1 (x ¼ 0, 3, 5) in an oxygen atmosphere at 400 C resulted
in the formation of a passivating oxide layer (Mariano et al., 2003). High Nb
content samples showed faster oxidation; however, slower weight gain during
oxidation was observed for lower Nb content samples, indicating that the
passivating layer was more efficient at preventing further oxidation.
A Fe74Si13.5Nb3B8.5Cu1 alloy was investigated by immersion in a 0.1 M
H2SO4 solution for evaluation of the corrosion resistance of the alloy. The
corrosion rate (evaluated as weight loss over a fixed immersion time) was
found to be larger for the as-spun (1.1–1.2 104 g/(cm2 h)) than for the
nanocrystalline alloy (0.1–0.3 104 g/(cm2 h)) (Souza et al., 1999). Similar studies of a Fe80Zr3.5Nb3.5B12Cu1 alloy showed a much higher corrosion
rate than for the (Fe,Si)-based alloy in both the as-spun alloy (2.1 104 g/
(cm2 h)) and the nanocrystalline sample (5.8 104 g/(cm2 h)) (Souza
et al., 2002). The improvement in corrosion resistance in the (Fe,Si)based alloy was attributed to the SiO2-passivating oxide which was found
to form on the surface of the ribbon; the Fe-based alloy did not possess this
characteristic. The substitution of Co for Fe in (Fe,Si)-based and Fe-based
alloys resulted in an improvement of corrosion resistance to H2SO4, but to a
smaller extent than the substitution of Si (May et al., 2005). In Fe73.5xCrxSi13.5Nb3B9Cu1 (x ¼ 0, 2, 4, 6) alloys, increased Cr substitution (i.e., x ¼ 4, 6)
was found to substantially improve the oxidation resistance during immersion
in a 0.1 M Na2SO4 solution (Pardo et al., 2001).
The potentiodynamic method was used to examine the corrosion
behavior of Fe73.5AlxSi13.5xNb3B9Cu1 (x ¼ 0, 1, 2) alloys using 1 M
NaCl with a pH of 9.0 (Alvarez et al., 2001). Two anodic peaks—
corresponding to dissolution of Fe2þ from the a-(Fe,Si) grains and residual
Nanocrystalline Soft Magnetic Alloys
313
amorphous phases, respectively—were observed for all three compositions
prior to the creation of a passivating silica layer. No significant effect of Al
on the corrosion resistance of the alloy was observed. In Fe64xCo21NbxB15
alloys, short etching with dilute HNO3 was found to dissolve a-Fe precipitates, which formed during rapid solidification processing, giving a
sensitive method for evaluating surface crystallization (Kraus et al., 1997).
While the glass-forming ability of Fe–M–B alloys is improved for M ¼ Zr or
Hf over Nb, the latter has better resistance to oxidation. For this reason, the
Fe–Zr–B and Fe–Hf–B alloys require inert atmosphere during melt
processing.
Transmission electron microscopy and atom probe microscopy require
thinning of the ribbon samples to dimensions less than a few hundred
nanometers. One technique for reducing the sample thickness is the use
of electrochemical polishing. In some studies, a 90% glacial acetic acid and
10% perchloric acid (HClO4) solution at room temperature has been used as
an electrolyte during electropolishing or jet polishing for TEM sample
preparation (Millán et al., 1995). Other studies have used a perchloric acid
and methanol solution (at 35 C) for electrochemically thinning TEM
specimens (Chen and Ryder, 1997; Moon and Kim, 1994). Twin jet
electrochemical polishing 5–10% perchloric acid-acetic acid solution has
also be used for thinning (Conde and Conde, 1995b; Houssa et al., 1999).
However, in most cases, TEM foils can be prepared by direct ion milling of
the ribbons for plan view samples due to their 25 mm thickness (Makino
et al., 2003; Miglierini et al., 1999; Wu et al., 2001).
7.3. Resistivity and magnetoresistance
The resistivity of soft magnetic materials is an important parameter due to its
direct influence on the core losses via eddy current mechanisms, which are
especially important at high switching frequencies. The resistivity can be
substantially larger than conventional soft magnetic alloys due to the amorphous intergranular phase surrounding the nanocrystalline grains. This is
one reason for the reduced losses compared with 3% Si steel (see
Section 6.5). It is important to note that the resistivity is sensitive to
composition and processing conditions that effect the amorphous matrix.
The resistivity of a Fe73.5Si13.5Nb3B9Cu1 alloy was found to increase
about 5% upon primary crystallization at a constant heating rate due to the
formation of (Fe,Si) crystallites (Barandiarán et al., 1993). In alloys where
the Nb content was reduced below 2 at%, the resistivity was found to
decrease upon crystallization, an effect that is amplified as the Nb content
approaches zero (Pe˛kala et al., 1995a). With increasing grain size from 30 to
90 nm in Fe77.22Si9B13Cu0.78 alloys, the resistivity was found to decrease by
a factor of 3 from 126 to 44 mO cm (Liu et al., 1993c). In contrast,
crystallization of the Fe86Zr7B6Cu1 alloy caused a reduction of the resistivity
314
Matthew A. Willard and Maria Daniil
by about 10% when the sample was heated through the crystallization
temperature (Barandiarán et al., 1993). Typical values of room temperature
electrical resistivity for Fe–Si–B–Nb–Cu and Fe–Zr–B–Cu alloys with
optimal magnetic performance are 115–125 mO cm and 50–60 mO cm,
respectively (Herzer, 1996; Knobel et al., 1997). Prior to crystallization,
the resistivity is typically higher with values of 160 8 and 145 7 mO cm
for Fe73.5Si13.5Nb3B9Cu1 and Fe86Zr7B6Cu1, respectively (Barandiarán
et al., 1993).
The magnetoresistive effect is defined as (Dre/re0) ¼ (rek re?)/re0,
where rejj and re? are the resistivities in the longitudinal and transverse
saturating fields and re0 is the resistivity in zero applied field. When the
volume fraction of crystallites in Fe73.5Si15.5Nb3B7Cu1 exceeds 50%, a
negative ferromagnetic anisotropy of resistivity is observed (Kuźmi
nski et al.,
1994). Similar results were earlier reported for a Fe–Cr–Si–Nb–B–Cu
alloy (Ślawska-Waniewska et al., 1993). Small spin-dependent magnetotransport was observed in Fe81Zr8Cu1Ru10 alloys with nanocrystalline
microstructure (Suzuki et al., 2002a). These alloys have an ordinary magnetoresistance in the as-cast state and show anisotropic magnetoresistance (most
prominent at 130 K) only after the nanocrystalline microstructure is formed by
annealing (indicating strong ferromagnetic coupling through the amorphous
matrix).
8. Conclusions
Over the past 20 years, nanocrystalline soft magnetic alloys have
proven an important test bed for nanoscience and nanotechnology. The
rapid commercialization of this class of materials is a testament to their
technologically interesting characteristics. The breadth and depth of the
body of research presented in this chapter illustrate continued interest and
progress in the development of new materials for future generations of high
efficiency magnetic materials. With the growing interest in sustainable
energy, magnetic materials innovations will surely play an important role,
with nanocomposite materials at the forefront.
Materials with widely varying compositions have been shown to possess
improved magnetic performance when formed with nanocomposite microstructures. For high-frequency applications, Fe–Si–Nb–B–Cu alloys have
shown lower losses and higher magnetization than ferrites and amorphous
alloys. Their magnetizations (near 1.2–1.35 T) are higher than other
extremely low loss materials, such as permalloy and Co-based amorphous
alloys, allowing components using them to be reduced in size. In applications where higher magnetizations are required, the Fe–Zr–B alloys are
advantageous, exhibiting lower losses than permalloys and Fe-based
Nanocrystalline Soft Magnetic Alloys
315
amorphous alloys. The Fe-based compositions and processing into thin
ribbon morphologies provides an ease of manufacture for these materials
will low raw materials cost. For high temperatures, the use of (Fe,Co)–Zr–B
or (Fe,Co,Ni)–Zr–B alloys shows improved performance against FeCo
alloys due to their nanocomposite microstructures.
Future research in this area will likely address issues in mechanical
performance of the alloys, processability of ribbons in air, and further
improvements in high magnetization/low core loss alloys. The richness of
the scientific phenomena found in these alloys, along with the large degree
of tunable magnetic properties, will drive new innovations in this class of
soft magnetic alloys for years to come.
ACKNOWLEDGMENTS
The authors would like to thank the Office of Naval Research for support of this work.
M. A. W. would also like to thank the many collaborators and colleagues who through
conversations over the years have greatly influenced his thoughts about nanocrystalline
exchange coupled alloys.
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