10 lnvar alloys masayiki shiga

340
lnvar alloys
Masayuki Shiga
Even though the study of the ‘invar problem’ has a long
history, the origins of the thermal expansion anomaly and
of some exotic behaviors
understood.
of invar have not yet been fully
Over the past few years, however, theoretical
understanding
of the invar problem
as a result of progress
in computer
first principle band calculations
estimate quantitatively
has been greatly improved
methods.
In particular,
have made it possible to
the thermal expansion coefficient
of
invar alloy.
Address
Department of Materiils Science and Engineering,
Kyoto University, Sakyo-ku, Kyoto 606-01, Japan; e-mail:
shiga@magma.mtl.kyoto-u.ac.jp
Current
Opinion
in Solid State & Materials Science 1996,
Figure
l:340-340
0 Current Science
Ltd ISSN
coherent-potential
high spin
T,
low spin
Curie temperature
TN
Nobel temperature
1
1359-0266
Abbreviations
CPA
HS
LS
Now, many other alloys and compounds that show a similar
thermal expansion
anomaly have been found and are
called invar-type alloys. Research on the invar problem is
currently focused on the following areas: firstly, research
for applications;
secondly, discoveries of new invar-type
alloys or compounds
and of anti-invar (which possesses
an enhanced thermal expansion coefficient); thirdly, new
experiments
to reveal the mechanism of invar anomalies;
and fourthly, theoretical studies on the invar problem, and
in particular, calculations of the electronic structure, total
energy and effects of spin fluctuations on thermodynamic
properties. This review highlights these research areas;
comprehensive
data and references on this problem can
be found in other reviews [1,2].
approximation
-AV
V
Introduction
The invar alloy, FebsNi35, is well known as the material
which has a very small thermal expansion
coefficient
around room temperature
(<2x lOdK-1
compared
to
most metallic materials which have a thermal expansion
coefficient
of 10-20x lOAK-1) and is widely used in
industrial applications
(e.g. in precision instruments
such
as shadow masks of cathode ray tubes for color televisions).
In addition to the thermal expansion anomaly, Fe-rich fee
Fe-Ni alloys show many other anomalous properties, such
as large negative pressure effects on the magnetization
and on the Curie temperature
(the transition temperature
between ferromagnetic
and paramagnetic
phases), a large
forced volume magnetostriction
(the volume expansion
induced by an applied magnetic field), and an anomalous temperature
dependence
of the elastic constants.
Furthermore,
deviation
of the spontaneous
magnetic
moment from the Slater-Pauling
curve, a large high field
susceptibility, and a large residual resistivity are observed.
These anomalous
properties
are known collectively
as
the ‘invar anomaly’ or ‘invar effect’. Since its discovery
by Guillaume in 1898 (Guillaume
named this alloy invar
because its length is invariant with temperature),
invar
has attracted much attention
not only from engineers
but also from physicists. Interest is focused particularly
in the field of magnetism,
because the origin of the
thermal expansion
anomaly is intimately
related to the
magnetism of metals, which is not yet fully understood.
T
Schematic
Dashed
diagram of the invar-type thermal expansion
anomaly.
curved indicates thermal expansion for the hypothetical
paramagnetic state. The difference between the two curves
corresponds to the spontaneous volume magnetostriction. T, is the
Curie (or Nobel) temperature.
Applications
Invar alloys have long been used as the material for
precision instruments.
Applications have recently tended
to spread into electronic
devices.
In addition
to use
in these rather small devices, invar alloys are used as
structural components,
for instance, in LNG (liquefied
natural
gas) containers
and core wires of long-distance
power cables. In most cases, FebsNiss-based
alloys are
used, although a third or further elements
are sometimes added to improve their physical, mechanical
and
chemical properties,
depending
upon the purpose and
the environment
of the application. Here, I review some
recent articles on applications of invar alloys, comparing
the effects of Mn, Cr, and Co on the thermal expansion
Invar allloys Shiia
behavior of Fe-Ni
invar 131, the glass-metal
characteristics
[4], and the weldability [Sl.
bonding
Figure 2
341
substances
do not show such a pronounced
anomaly
but exhibit
only a tiny thermal
expansion
anomaly
at the Curie (or Ntel) temperature,
as seen typically
in Fe and Ni. What is the factor that causes the
giant volume magnetostriction,
which gives rise to the
invar-type thermal expansion anomaly? This question is
essential for understanding
the invar problem and will be
discussed in the following sections. Furthermore,
it has
been pointed out that some alloys or compounds that have
similar compositions
to invar, show an enhanced thermal
expansion coefficient in the paramagnetic
state known as
‘anti-invar’ behavior. In this section, I review the materials
that exhibit the invar-type
thermal expansion anomaly
and, in addition, those that exhibit anti-invar behavior.
Fe-rich fee iron alloys: classical invar
0.508
1
0
I
1
I
200
400
Temperature
600
(Kl
800
Temperature dependence of the unit cell volume (V) for YzFel~ (01,
YlFe, ,Co,s (0) and Y2FeI 7C1 ,s (n). The Curie temperatures are
marked by arrows. (Published with permission from I81.I
Figure 3
Al
2.5 1 o-2,
t
Fe rich fee iron alloys such as FebsNi35 and Fe3Pt are
sometimes known as classical invar alloys and have been
intensively
studied from various viewpoints.
Countless
ternary or multicomponent
alloys, such as Fe-Ni-Co
(super invar) and Fe-Co-Cr
(stainless invar), have been
developed for practical uses. As the local atomic arrangements of amorphous
alloys are near to a close-packed
structure,
such as fee, it is likely that the origin of
the electronic
and magnetic
states of Fe atoms play
a crucial role in invar behavior.
Several ternary Fe
alloys, such as Fe-Ni-Mn
and Fe-Ni-Cr,
have been
investigated
in order to reveal the role of Fe atoms and
the associated complicated magnetic characteristics from a
basic viewpoint. Most of the papers on these alloys were
published a long time ago and will be found in the review
papers cited in 111.
Ferromagnetic intermetallic compounds
Temperature (K)
Thermal expansion of Nd2FeI 7Nx with decreasing temperature,
just after nitriding; Al/lo denotes the fractional change in length.
(Published with permission from [Q].)
New invar-type alloys and anti-invar
So far, many alloys and intermetallic
compounds,
exhibiting a thermal expansion anomaly similar to that of
FebsNiJs invar, have been found. This anomaly is caused
by a large volume expansion
accompanying
the onset
of spontaneous
magnetization
or the onset of sublattice
magnetization
of antiferromagnets.
which is known as the
spontaneous volume magnetostriction.
When spontaneous
volume magnetostriction
is large enough to cancel the
normal thermal expansion caused by lattice vibrations, we
have a very small or even a negative expansion coefficient
as shown schematically
in Figure 1. One should note,
however, that most ferromagnetic
(or antiferromagnetic)
Many ferromagnetic
intermetallic
compounds
show the
invar-type
thermal
expansion
anomaly.
&Fez
has a
large spontaneous
volume magnetostriction,
although the
thermal expansion coefficient at room temperature
is not
very small, owing to the rather high Curie temperature. By
substituting
Zr with Nb, the Curie temperature decreases
and the thermal expansion coefficient becomes small or
negative depending
upon the Nb content [6]. Recently,
the magnetic
properties
of rare-earth-iron
compounds
were intensively
studied
after the discovery
of the
magnificent permanent
magnet NdzFel4B. Some of them
were found to exhibit
invar-type
thermal expansion.
It is well known that NdzFel4B
itself has the invar
characteristics (71. It was found that the Curie temperature
of RzFel7 (R = rare earth) compounds can be increased by
introducing
C or N atoms interstitially,
leading to great
interest in their carbides and nitrides as new materials
for rare-earth permanent
magnets with low R and high
Fe contents. It is interesting
that these compounds have
a large spontaneous
volume magnetostriction
and exhibit
a remarkable
thermal expansion
anomaly, as shown in
Figures 2 and 3 [8,9]. Some ferromagnetic Mn compounds,
such as MnB, exhibit a remarkable
thermal expansion
anomaly. Wada and I [lo] showed that the Mnl,Co,B
342
Metals and alloys
system exhibits typical invar-type
x=0.5, as seen in Figure 4.
thermal
expansion
at
Figure 4
Al/l (1 O-3)
Mn ,&o
XB
of color cathode-ray
tubes, this leads to difficulties
or
inconvenience.
Therefore. non-magnetic
invar-type alloys
are desired. Antiferromagnetic
Cr-based alloys have been
studied most intensively
for this purpose. It was found
that Cr-Fe-Mn
alloys have almost no thermal expansion
coefficient at room temperature
[13], however, they have
not yet been corrmercially
used because of their poor
workability (i.e. if is difficult to process them by rolling
or machining).
Some Mn alloys or compounds exhibit a remarkable thermal expansion anomaly accompanied by antiferromagnetic
spin ordering. The Mn-Ge alloy is antiferromagnetic
and
shows an invar-type thermal expansion anomaly. It was
found that the 23at% Ge alloy has a thermal expansion
coefficient of nearly zero at room temperature
[ 141, that is,
it is a non-ferromagnetic
invar alloy. This alloy is, however,
also too brittle to use in practical applications.
Instead of
the effort to seek non-ferromagnetic
invar alloys, which are
free from the effect of a magnetic field, no commercially
valuable alloys have yet been found.
I
0
I
200
400
600
800
1 ooc
T W)
Thermal expansion curve of Mn,_xCo,B;
Al/l denotes the fractional
change in length. Arrows indicate the Curie temperatures
[lo].
Ferromagnetic amorphous alloys
During the past decade, a lot of data on metallic amorphous materials have been accumulated.
Among them,
alloys
Fe-rich
amorphous
ferromagnetic
most
exhibit the invar-type thermal expansion anomaly. It is
believed that the local atomic arrangements
of amorphous
alloys are near to a close-packed
structure,
such as
fee. Therefore,
it is likely that the origin of the invar
anomalies
in these materials
is the same as that of
Fe-rich fee alloys. In fact, the concentration
dependence
of spontaneous
magnetization
and the Curie temperature
of amorphous alloys show a close similarity to those for the
Fe-N; system. Recently, the invar behavior of amorphous
Yl_,Fe,
[l l] and La(Fe,All_x)lA
[12*] alloys has been
reported.
Antiferromagnetic
invar
Invar alloys keep their volume constant as the temperature
changes.
As Fe-Ni
invar is ferromagnetic,
however.
the dimension
(i.e. length)
is sensitive
to magnetic
fields caused by ordinary anisotropic
magnetostriction.
In some practical applications,
such as shadow masks
Laves phases, RMn2, have interesting magnetic properties
in many respects, including magnetovolume
effects [15].
Among them, YMnZ exhibits a drastic volume change
of about 5% at the Ntel temperature,
TN, as shown in
Figure 5, which is the largest volume magnetostriction
so
far reported. However, the magnetic transition of Yhlnz
from the antiferromagnetic
state to the paramagnetic
one
is of the first order and we cannot expect a small thermal
expansion coefficient. Rather, one should note that the
thermal expansion
coefficient
above TN is remarkably
large. This enhancement
of the thermal expansion
coefficient may be regarded as an ‘anti-invar’
effect, as
described below. Other RMn2 compounds
carrying Mn
moments
exhibit a similar thermal expansion
anomaly
at the magnetic
transition
temperature,
although
the
magnitude of the spontaneous
volume magnetostriction
is
smaller than that of YMnZ. The large volume shrinkage in
Rhlnz compounds above TN is ascribed to the collapse of
Mn moments at TN.
Anti-invar
It is now believed
that temperature
variation of the
magnitude
of local magnetic moments or the amplitude
of spin fluctuations
plays a crucial role for determining
the thermal expansion coefficient
in metallic magnetic
systems (see below). According to the theory of spin Huctuations (which predicts the existence of local magnetic
moments,
whose magnitude
increases
with increasing
temperature).
we can expect an increase of magnetic
moments with increasing temperature
in the paramagnetic
phase, giving rise to an enhancement
of the thermal
expansion coefficient. Some scientists call this ‘anti-invar’
behavior (although it is not a popular technical term). The
anti-invar effect is most clearly found in YMnz compounds
[16]. Figure 6 shows the thermal expansion coefficient
of Y(hlnl_,AI,)Z
compounds
at room temperature
as a
Invar alloys Shiga
343
Figure 6
Figure 5
a(i) 7.90
YMn,
7.80-
0
200
400
600
800
1 oat
T(K
Temperature dependence of the lattice parameter (a, in A) of
YMnp A huge volume change of about 5% is observed at the
magnetic transition temperature from the antiferromagnetic to the
paramagnetic state. Above the transition temperature, the thermal
expansion coefficient is very large, about 50 x 10-B K-1. (Published
with permission from [161.)
function of Al composition, x. The thermal expansion coefficient of YMnZ is enormously large, being 50 x 104 K-l
but rapidly decreases when Mn is replaced by small
amounts of Al, approaching a normal value for the thermal
expansion coefficient. This enhancement
of the thermal
expansion coefficient was explained as a result of thermal
evolution of the amplitude
of spin fluctuations
after the
collapse of local magnetic moments of Mn just above TN
[16]. On the other hand, by substituting
Al with Mn,
Mn moments are stabilized and the amplitude
of spin
fluctuations
remains constant against temperature,
giving
rise to the normal thermal expansion for x > 0.1.
By plotting
the temperature
dependence
of thermal
expansion coefficients of antiferromagnetic
fee Fel_,Mn,
[ 17.1 and FesoNi,Mns+x
[ 181 along a scale normalized
by the melting temperature,
together with other normal
metals, it has been shown that the thermal expansion of
these antiferromagnetic
alloys is strongly enhanced above
TN due to the anti-invar effect (Fig. 7) Moroni et a/. [ 19.1
have shown that anti-invar
behavior is widely observed
in strongly paramagnetic
systems such as ZrVz, ZrZn~
and TiBez, for which they performed self-consistent
band
calculations
and estimated
the magnetic contribution
to
thermal expansion.
Models for invar effects and experimental
evidence
The origin of invar effects has been intensively
debated
for a couple of decades. I should say that we have not
yet reached the final solution. One reason for confusion
is that the definition of invar effects or invar anomalies
is not clear. I believe that the essential
character of
0
1.0
YMn2
YA12
Concentration (x) dependence of the the-1
expansion coefficient of
Y (MNI_,,Alx)~ at room temperature. The broken line is extrapolated
from x (a) > 0.2. This figure clearly shows that the thermal expansion
coefficient is enhanced more than twice by spin fluctuations.
(Published with permission from [161.).
invar alloys is an extraordinarily
large spontaneous volume
magnetostriction,
which is commonly observed in invar
type alloys and compounds.
There
are many other
anomalies in the classical Fe-Ni invar alloys, such as their
deviation from the Slater-Pauling
curve. However, most
of them are specific to the Fe-Ni system and are not
observed even in Fe-Pt invar. The origin of the deviation
from the Slater-Pauling
curve for Fe-Ni invar is still a
controversial
problem. Here, I discuss the origin of large
spontaneous
volume magnetostriction.
At the first stage of this long debate, the invar problem
was discussed on the basis of the local-moment
model.
Assuming a strong volume dependence
of the exchange
integral between
neighboring
local magnetic moments,
it is possible to explain the large spontaneous
volume
magnetostriction.
However, it became evident that 3d
electrons in transition
metals are of itinerant character;
therefore,
the magnetovolume
coupling should also be
discussed on the basis of an itinerant electron model.
The origin of spontaneous
volume magnetostriction
is
explained
as follows: the exchange interaction
causes a
ferromagnetic
or antiferromagnetic
spin polarization of 3d
bands, which leads to an increase in the kinetic energy
of the 3d electrons. This energy loss can be reduced by
344
Metals and alloys
splitting should be proportional
to <Sl>G=, no distinct
volume change
is observed
for nearly local moment
systems such as bee Fe, whose temperature
dependence
of <SLY> is described by curve b (Fig. 8). When <S1,?>
decreases considerably
with increasing temperature
but
below T,, as shown by curve c, we can expect the
invar-like
thermal expansion
anomaly to occur. <$,z>
increases with increasing temperature
in the paramagnetic
region by thermal excitations
of spin fluctuations;
an
anti-invar-like
enhanced thermal expansion coefficient is
expected. Some authors claim that the change of <S1,%- in
Fe-Ni and FeJPt invar can be described by excitation of
low-spin (LS) from the high spin (HS) states, which are
characteristic electronic states of fee Fe [Zl). However, it
is not easy to detect the decrease of the amplitude of spin
fluctuations or excitation of the LS state directly.
Figure 7
0.08
t
Icc-Mn
A
0.06
Fiaure 8
0.02
:s,*>
Tc
15
;:
0
0
0.2
0.4
0.6
T/T,
0.8
1
MC
--q-
d
Product of the melting temperature
(T,) and the thermal expansion
coefficients
(a) versus the reduced temperature
(T/T,) for different
fee metals and alloys. The dashed curve represents
the average of
e
J
these metals. One can see that the thermal expansion of fee Fe-Mn
alloys and fee Fe is highly enhanced.
(Published with permission from
T
f17’1.1
Schematic
representations
spin fluctuation
amplitude,
volume expansion because the 3d bandwidth is reduced
or the density of states is increased
by the volume
expansion. In fact, a precise band calculation, for instance
of bee Fe, has shown that the volume expansion
due
to band polarization
should be as large as several per
cent [ZO]. However, such a large volume change is not
always observed
in metallic ferromagnets
at the Curie
temperature
(T,) except for invar-type
alloys, implying
that a simple band theory for magnetism
(the Stoner
model) does not properly describe the electronic state of
itinerant electron ferromagnets at high temperatures.
The
apparent lack of the large volume change at T, can be
explained by assuming that the effective 3d band splitting
does not change at T, but persists as local magnetic
moments
above T,. The concept of spin fluctuations
gives a unified picture for localized moment and itinerant
electron models, where the magnitude
of local moments
can be defined as the amplitude of the longitudinal
spin
fluctuations
at each atomic site, <St,z> (where S is the
spin quantum
number and L denotes ‘local’ at atomic
sites). For most metallic magnets, <Sr,z> remains almost
constant below and above the Curie temperature, as shown
schematically
by curve b in Figure 8. On the other
hand, as the volume expansion due to effective 3d band
of temperature
dependencies
&L%.
(a) Localized moment
of the local
system:
(b) nearly localrzed moment systems like bee Fe; (e) invar-type; (d)
weakly itinerant ferromagnets;
and (e) nearly ferromagnetic
metals.
For (c-e). <SL% increases with increasing temperature
grving rise to an enhancement
of the thermal expansion
‘anti-lnvar effect’.
above T,,
known as the
Several experiments
have been performed to detect the
change of spin polarization of 3d bands or the excitation
of LS states. Kisker et nl. [ZZ] carried out spin-resolved
and angle-resolved
photoemission
on ordered
FeJPt
with synchrotron
radiation
at below and above the
Curie temperature
and detected
a difference
between
the two temperatures.
They ascribed
this difference
to the change of the density
of states between
the
spin-polarized
(ferromagnetic)
state and the non-polarized
(paramagnetic)
state. A similar experiment
was carried
out for Fe#iJj
invar alloy [23] and nearly the same
result as found for FejPt
was obtained.
StPhler et (I/.
[24] have
dependence
carried out measurements
of the temperature
of the circular
magnetic
X-ray dichroism
for ordered FeTzPt28 invar at a low temperature
(11OK)
and just below
the Curie
temperature
(41OK:). ‘They
found
a temperature-dependent
change
of the
magnetic
Invar alloys Shiga
absorption profile that differed from the pure amplitude
reduction due to the reduced magnetization,
implying a
change of the spin splitting in the low-lying unoccupied
p states. Buchholz ef of. [25*]have carried out infrared
(IR) emission spectroscopy
at energies 9-33mRy
in the
temperature
range 430-8OOK on single crystals of FeNi
and FePt invar. They found a drastic decrease of the
IR absorption in the energy range 23-33 mRy, whereas at
low energies, around 9 mRy, the absorption is temperature
independent.
These two results are not direct evidence
of the change in 3d band splitting,
but are discussed
within the framework of the model of HS-LS transitions
by comparing
them with spin-polarized
band-structure
calculations [25*].
In principle, paramagnetic
neutron scattering experiments
can give an estimation of <S$>. However, scanning a wide
range of the momentum
and energy space is necessary
for a reliable estimation.
Because of this difficulty, no
new measurement
to estimate <SL%= has been reported
since the pioneering
work on Fe65Ni35 by Collins [26]
and on Fe3Pt by Ziebeck ef a/.[27]. In contrast, inelastic
neutron
scattering
experiments
have been carried out
intending
to find the ‘hidden excitations’,
which were
proposed by Ishikawa et a/.[28]to explain the fact that the
magnetization
of the invar alloys decreases more rapidly
with temperature than can be explained on the basis of the
measured spin wave dispersion relations. Lynn and Rosov
[29] have carried out polarized inelastic neutron scattering
experiments
on the amorphous
ferromagnetic
Feg,jBrd
invar alloy and found
longitudinal
spin fluctuations
separated
from the transverse
(spin wave) excitations.
However,
a similar excitation
was observed
in the
non-invar ferromagnetic
amorphous alloy Fe~Ni~P&.
Therefore,
the unusual longitudinal
magnetic excitation
might be characteristic
of ferromagnet
amorphous alloys
but not of the invar alloy. In fact, by means of precise
inelastic neutron scattering experiments
on ordered and
disordered
Fe72Ptza single crystals below Tc, they did
not find any excitations other than the ordinary transverse
spin wave excitations, although they confirmed that the
zero-temperature
spin wave stiffness constants (98 meVA2
and 107meVA2 for the disordered
and ordered alloys,
respectively)
are significantly
higher than those determined by magnetization
measurements
[30]. Dumpich et
a/.[31] have measured the temperature
dependence
of
magnetization
of evaporated
Fe-Ni invar alloy films and
determined
the stiffness constant. They have shown that
the stiffness constant for the as-prepared
Fe6sNi35 film
(130 meV &‘) lies close to that determined
from spin-wave
dispersion curves (140meVA2)
and that a value for the
annealed film (77 meV AZ) is comparable with that for bulk
Fe6sNi35 invar alloy. They claimed that the difference in
the stiffness constants between neutron and magnetization
measurements
is not an intrinsic invar characteristic
but
may be caused by a partial or premartensitic
transformation
(a martensitic transformation
is a phase transition without
long distance atomic movements:
premartensitic
refers
345
to the phenomena
observed just before a martensite
transition begins) caused by inhomogeneity.
A theoretical
approach to this problem was attempted
[32], which was
successful in qualitative but not quantitative
terms.
Band calculations and theoretical aspects
Developments
in the technique
for calculating the electronic structure of metals and compounds give us reliable
information
on the electronic
structure
without introducing any adjustable
parameter. For disordered
alloys
such as Fe-Ni
invar, however, the lack of periodicity
makes it difficult to execute the first-principle calculations.
In order to have information
on Fe6sNi35 invar, the
electronic
structure
of ordered Fe3Ni alloy has been
calculated.
The first attempt was made by Williams ef
a/. [33]. They calculated
the total energy of Fe3Ni as
a function
of the unit cell volume and showed that
the spin-polarized
(ferromagnetic)
state has a larger unit
cell volume than the non-magnetic
state and that the
energy difference
between
them is very small. They
pointed
out that the thermal expansion
anomaly
of
the invar alloy can be ascribed to thermal excitations
of the small-volume
non-magnetic
state. Moruzzi [34]
calculated
the total energy (E) of Fe3Ni as a function
of volume (V) and magnetization
(Ml, that is, E(M,V),
and showed that energy versus volume curves display a
low-spin state centered at low volume and a high-spin
state at high volume.
On the basis of this calculation, he described
a qualitative
understanding
of the
thermal properties
of invar alloys. For a quantitative
description
of their thermal properties,
the effect of
spin fluctuations
should be taken into account. Mohn
et al.[35] calculated other properties and the magnetic
contribution
to the thermal expansion coefficient on the
basis of phenomenological
spin fluctuation theory using
the E(M,V) surface obtained by the fixed-spin-moment
method. The calculation
was extended
to a tetragonal
distorted lattice and the connection
between martensitic
transformation
and the invar effects was discussed [36].
The real Fe-Ni invar alloy is, of course, a disordered
alloy. The coherent-potential
approximation
(CPA) can
describe an electronic state of disordered alloys. Hasegawa
and Kanamori
[37] first applied CPA calculations
to
Fe-Ni alloys using a model density of states. Recently,
Schriiter eta/.[38*‘1 calculated the electronic structure and
thermal evolutions of the magnetic and structural binding
surfaces of fee Fe-Ni alloys using CPA combined with the
Korringa-Kohn-Restocker
band calculation scheme. The
results of their calculations are shown in Figure 9. On the
basis of these binding surfaces, they successfully explained
many aspects of invar effects, including the connection
to
martensitic transformation.
Calculations
of the electronic
structure
and the total
energy have been performed for Fe3Pt invar. Podgorny
[39] obtained the E(M,V) curve for ordered FeJPt, showing double minima in the energy surface as observed in
FelNi. He explained the essential features of the ground
346
Metals and alloys
Figure 9
5.5
0.0
6.3
6.4
6.5
6.6
6.7
6.8
6.9
0.0
6.3
6.4
6.5
6.4
6.5
6.6
6.7
6.8
6.9
6.6
6.7
6.8
6.9
a (IMJ.)
2.5
2.0
1.5
1.0
0.5
‘.:\ i
A
6.3
6.4
6.5
6.6
4(&U.)
6.7
6.8
6.9
0.0
-6.3
a (a.&)
2.5
2.5
2.0
1.5
1.0
0.5
nn
_.-
6.3
6.4
6.6
6.6
l@&)
6.7
6.6
6.9
0.0
6.3
2.5
2.5
2.0
20
1.5
1.5
1.0
1.0
0.5
0.5
0.0
6.3
6.4
6.5
6.6
6.7
6.8
6.9
_.-
6.4
L5
6.6
6.7
6.8
6.9
6.4
S.5
65
a (ML)
6.7
6.8
6.9
00
6.3
&ding
surfaces (energy contour maps in the momen~voiume space) for the disordered Fe,Nit,
system in the fee structure obtained by (a-g)
KKR-CPA
calculations and (h) augmented spherical wave (ASW) calculatrons. Contour lines are at 0.5 mRy intervals; a IS the lattice parameter
in atomic units. it is clearly shown that upon changing x, the system gradually transforms from (a) Fe so Ni 40, which is magnetic with an energy
minimum located at a=6625atomic
units, M=l.6
&atom
to (g) Fe 7s Ni ss, which is non-magnetic with an energy minimum at a=6.457atomrc
units, M=Ou6/atom
(where M is the magnetrc moment per atom). (h) shows the binding surface of ordered FesNi. (Published wrth permrssron
from [38**1.)
imar alloys Shiga
state properties of FeJPt invar. Uhl et al. [40**] calculated
the total energy of Fe3Pt as a function of the volume
and the magnetic moment arranged in both collinear and
non-collinear
spiral structure and explained the thermal
expansion
coefficient
by taking spin fluctuations
into
account.
Conclusions
Applications
of invar alloys are extending to the field of
high technology, and in particular, to electronic devices,
because their thermal expansion coefficient is controllable
(i.e. alloys with any thermal expansion coefficient may be
prepared by changing the composition). However, research
in this field is rather specific. Many invar-type alloys and
compounds have been discovered. Although most of them
present difficulties for applications in many respects, they
provide fruitful information
for understanding
the invar
problem. With regard to the origin of the large spontaneous
volume magnetostriction
of invar, the long debate is focusing on the model based on the theory of spin fluctuations.
This model states that an appreciable
decrease of the
amplitude of longitudinal spin fluctuations with decreasing
spontaneous
magnetization
causes a shrinkage of volume.
Results of precise band calculations
support this view,
even in the quantitative
respect. Experimental
evidence
to probe this model without ambiguity is needed. The
theory of spin fluctuations
predicts an enhancement
of
the thermal expansion
coefficient
in the paramagnetic
state of invar-type
alloys. Careful analysis of thermal
expansion has indeed revealed this enhancement
effect.
Despite progress, there are still unsolved problems. The
existence and the mechanism of ‘hidden excitations’ are
still controversial. The origin of low temperature anomalies
found in FebsNi35 invar (such as a sudden increase of
the bulk modulus [41]) has not yet been understood. The
reason why softening
of longitudinal
phonon modes is
not observed by neutron scattering experiments,
contrary
to a remarkable softening in the bulk modulus, is also a
puzzling problem [42]. It seems that there are relaxation
processes in magnetovolume
or magnetoelastic
coupling
within a wide range of the energy spectrum. Thus, the
study of invar alloys is still providing challenging problems
in the field of metallic magnetism.
References
and recommended
reading
Papers of particular interest, published within the annual period of review,
havs been highlighted as:
.
l*
Shiga M: lnvsr alloys. In Electronic and Magneric Properties of
Metals and Ceramics, Materials Science and Technology, vd.
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1993:159-210.
2.
Wassermann EF: INVAR: moment-volume instsbility in transition
metals and alloys In Handbook of Magnetic Materials, vol 5.
Edited Buschow KHJ. Amsterdam: North-Holland; 1990:237-322.
3.
Lea JH, Kim HJ, Kang IK, Kim HS, Ahn HG: Effects of Mn. Cr and
Co on the thermel expansion behaviors of Fe-Ni invar alloys. J
Korean lnst Met Meter 1993, 31:867-872.
of glass-cemmic to metal
4.
Ashcroft IA, Derby B: Chamcterizethm
bonds. J Mater Sci lQQ4,29:4436-4446.
5.
Han YH: leser beem welding of diuimlier meteis In
Proceedings 07 the 2nd European Conference and Joining
Technology, Italy. 1 984:16-l
8.
6.
Shiga M, Nakamura Y: Megnetovolume effects and
lnver chsrecten of Zrt_xNbxFes. J Phys Sot Jpn 1979,
47:1446-l
451.
z
Buschow KHJ: Invar effects in R2Fo14B compounds (R44
Nd, Sm, Gd. Er). J Less-Common Met 1886, 1 l&349-353.
8.
Andretw A V. De Boer FR. Jacobs TH. Buschow KHJ: Thermal
expansion 6nomeiies and spontane&~s magnetostrictlon
in R2Fe&
intermeb llic compounds phvsica B 1991,
9.
Algarabel PA, ibarra MR: inver behevior and in situ obsetvstfon
of the nftridlng process in R2FeITNx intermeteilics. J Magn
Magn Mater 1892, 110:323-326.
10.
Wada H, Shii
M: Thermel expenslon anomaly and
inver effects of Mn,_xCoxB. J Magn Magn Mater 1 QQ2,
104-107:1925-1926.
11.
Fujita A, Suzuki T, Kataoka N, Fukamiihi K: Themvelaxpsnsion
and Inverse-megnetk-susceptibiiity
anomalies in amorphous
Y-Fe dloys phvs Rev 8 1994, 5661 QQ-6202.
Ce,
175361-369.
12.
.
Fukarnichi K, Chiang TH, Matsubara E, Waseda Y: Atomic
stNrctums, megnetovoiume
end pressure effects in amorphous
LdFexAit,)ts
eiioys conslstlng of icosehedml clusters. Sci
Rep R/TV 1995, A41 R-40.
This may bs ths first exampb of a quasicrystal invar-type alloy. Details of
crystal structure anafysis, magnetic properties and other thermal properties
are investigated.
13.
Fukamiii K Saito H: On new nonferromeQnetfc B.C.C. CrFe-Mn invar alloys. Phys Status Solidi A-Appl Res 1972,
lO:K129-131.
14.
Masumoto H, Kikuchi M, Nakayarna T: Non-ferromagnetic
lnvartype alloys in the Mn-Ge system Trans J/M 1963, 24:42-46.
15.
Shiga M: Msgnetism and spln fiuctuetions of Laves phase
Physica B 1986, 149:293-305.
manganese compounda
16.
Shiga M, Wada H, Nakamura H, Yoshimura K, Nakamura Y:
ChamcterNtic spin fluctuetions in Y(Mnt_xAtx)s. J Phys f 1987,
17:1781-1793.
17.
.
Schneider T. Acet M, Rellinghauss B, Wassermann EF, Pepperhoff
W: Anttferromagnetfc Invar and anti-invar in Fe-Mn alloys. Pbys
Rev B 1995, 51:8917-8921.
This work dearly shows ths enhancement of the thermal expansion
coefficient of Fe-Mn alloys by precise measurements of thermal expansion
up to 115OK.
18.
Acet M. Z&hres H. Wassermann EF Peoosrhoff W: Hiahtemperstun
moment-volume
insMblli& and anti-in&r of y-Fe.
Phys Rev B 1994,49:6012-6017.
19.
Moroni EG, Lerch P, Jarfborg T: An&lnvar behavior in enhanced
.
pammagnets. f’bys Rev B 1994,49:11979-11965.
The enhancement of the thermal expansion coefficient in strongly
paramagnetic ZrVs, ZrZns and TiBes was quantitatively explained in terms
of spin fluctuation theory based on the total energy calculations for these
compounds.
20.
Janak JF, Willis
compressibility
21.
Moruui VL: Theory of invar. Solid State Commun 1992,
03:739-743.
22.
Kisker E, Wassermann EF, Carbone C: Evidence for the highspin to low-spin state transition in ordered FesPt invar. Phys
Rev Len 1987,5&l
704-1707.
23.
Carbone C, Sohal GS, Akai H, Kisker E, Wassermann
EF: Spin-polarized angle-resolved
UV photoelectron
soecboscoov studv of the electronic structure of disordered
ferromsQn&
Fe&Nlo.ss
invar alloy. So/id State Commun
1969.72:1111-1115.
24.
Stiihler S, Kniilb M. Schijtz G, Fischer P, Welzel-Gerth S,
Buchholz B: Tempemture dependence of the circular magnetfc
x-ray dichroism in the fnvar alloy Fe@txs. J Appl Phys 1993,
73:6064-6065.
25.
.
Buchhob 8, Wassermann EF, Pepperhoff W, Acet M: IR
spectroscopy on FeNi and FePt invsr alloys. J Appl Phys 1994,
75:7012-7014.
of special interest
of outstanding interest
1.
347
AR: Giant internal magnetic pressure and
anomelies. Phys Rev B 1976, 14:4199-4204.
348
Metals and alloys
This may be the first experiment of IR spectroscopy on invar alloys as a
function of temperatures. The result is helpful for intemretation of thermal
excitations of the electron system.
26.
Collins MF: A maasuremant by neutron scattering of magnetic
moments In a paramaQnetlc iron-nlckel alloy. Proc Phys Sot
1 Q65, 86:Q73-976.
27
Ziebeck KRA, Webster PJ, Brown PJ, Capellmann H: The invar
effect and spin fluctuatfons in disordered FesPL I Magn Magn
Mater 1 Q63, 36:151-l 59.
28.
lshikawa Y, Onodera S, Tajima K: MaQnetfc excitations in
tnvar alloys, FessNiss and FesPL J Magn Magn Mater 1 Q79,
10:183-190.
29.
Lynn JW, Rosov N: Polarization analysis of the magnetic
excitations in invar and non-invar amorphous alloys. J Appl
Phys 1 QQ3, 73:536Q-5371.
30.
Rosov N, Lynn J W, K&etner J, Wassermann EF, Chanopadhyay T,
Bach H: Temparature dependence of the magnetic excitations
In ordered and disordered Fer2pt2a J Appl Phys 1 QQ4,
75:6072-6074.
31.
Dumpich G, Kiistner J, Kirschbaum U, Miihlbauer H, Liang J.
Liiback Th, Wassermann EF: Invar behavior of fee Fet_xNi, thln
films. Phys Rev B 1QQ2,46:9256-9261.
32.
Valiev EZ, Menshikov AZ: Longitudinal spin fluctuations (hidden
magnetic excftations) in invar alloys J Megn Magn Mater 1 QQ5,
147:18Q-191.
33.
Williams AR, Moruui VL, Gelatt CD, Kiibler J: The theory of invar
and Heusler alloys. J Magn Magn Mater 1Q63, 31-34:66-94.
34.
Moruui VL: High-spin and low-spin states in inver and related
alloys. Phys Rev B 1 QQO, 41:693Q-6946.
35.
Mohn P, Schwan K, Wagner D: MaQnetoelastic anomalies
Fe-N1 invar alloys. Phys Rev B 1 QQl, 43:3318-3324.
in
36.
Entel P, Hoffmann E, Mohn P, Schwas K, Morruzi VL: Firstprinciple calculations of the instability leading to the lnvar
effect. Phys Rev B lQQ3,47:0706-0720.
37.
Hasegawa H, Kanamori J: An application of the coherent
potential approximation to ferromagnetic alloys J Phys Sot
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36.
..
Schroter M, Ebert H, Akai H, Entel P, Hoffmann E, Reddy GG:
First-principles investigations of atomic disorder effects on
magnetic and structural instabilities in transition-metal alloys.
Phys Rev B 1995, 52:188-209.
This paper shows that the theoretical understanding of FeesNiBs invar is
approaching the final goal of understanding the origin of its thermal expansion anomaly. Authors took account of both atomic disorder and spin
fluctuation effects in their first-principle calculation of electronic structures.
39.
Podgomy M: Magnetic instabilities in FesR and in the fee Ni-Fe
system. Phys Rev B 1QQ2, 46:62Q3-6302.
40.
..
Uhl M, Sandratekii LM, Kiibler J: Spin fluctuations in YFe and in
FesPt fnvar from local-density-functional
calculatfons. Phys Rev
B 1 QQ4,50:2Ql-301.
This paper may be the best theoretical study so far published on FesPt
invar. Authors have successfully explained the thermal expansion of FeoF’t
and yFe by taking into account the effects of longitudinal and transverse
spin fluctuations in the total energy calculations as a function of the volume
and the magnetic moment arranged in spiral structure.
41.
Shiga M, Makita K, Uematsu K, Muraoka Y. Nakamura Y:
Magnetoelastlclty
of Fe-Ni and Fess(Nit_xMn,)ss invar alloys:
II. Low-temparature
anomaly. J Phys - Condens Matter 1991,
3:3577-3590.
42.
Endoh Y: Lattice dynamics in ferromagnetic
Magn Mater 1979, 10:177-182.
invar alloys. J Magn