перколяция и фазовый переход в аморфном углероде

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«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 781, 2007
ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï.3 /35/
Ì.Ñ. Áûøêèí, À.Ñ. Áàêàé, À.À. Òóðêèí
Ïåðêîëÿöèÿ è ôàçîâûé ïåðåõîä â àìîðôíîì ...
ɍȾɄ . 539.216:546.26-152
ɉȿɊɄɈɅəɐɂə ɂ ɎȺɁɈȼɕɃ ɉȿɊȿɏɈȾ ȼ ȺɆɈɊɎɇɈɆ ɍȽɅȿɊɈȾȿ.
ɆɈɅȿɄɍɅəɊɇɈ-ȾɂɇȺɆɂɑȿɋɄɈȿ ɆɈȾȿɅɂɊɈȼȺɇɂȿ
Ɇ.ɋ. Ȼɵɲɤɢɧ, Ⱥ.ɋ. Ȼɚɤɚɣ, Ⱥ.Ⱥ. Ɍɭɪɤɢɧ
ɇɇɐ ɏɚɪɶɤɨɜɫɤɢɣ ɮɢɡɢɤɨ-ɬɟɯɧɢɱɟɫɤɢɣ ɢɧɫɬɢɬɭɬ, ɭɥ. Ⱥɤɚɞɟɦɢɱɟɫɤɚɹ 1
61108 ɏɚɪɶɤɨɜ, ɍɤɪɚɢɧɚ
E-mail byshkin@kipt.kharkov.ua
ɉɨɫɬɭɩɢɥɚ ɜ ɪɟɞɚɤɰɢɸ 10 ɫɟɧɬɹɛɪɹ 2007 ɝ.
ɉɪɨɜɟɞɟɧɨ ɦɨɥɟɤɭɥɹɪɧɨ-ɞɢɧɚɦɢɱɟɫɤɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ, ɩɨɥɭɱɟɧɧɨɝɨ ɡɚɤɚɥɤɨɣ ɪɚɫɩɥɚɜɚ. Ɉɛɧɚɪɭɠɟɧɵ
ɨɫɨɛɟɧɧɨɫɬɢ ɧɚ ɡɚɜɢɫɢɦɨɫɬɢ ɫɜɨɣɫɬɜ ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ ɨɬ ɞɚɜɥɟɧɢɹ. ɉɨɤɚɡɚɧɨ, ɱɬɨ ɩɪɢ ɬɨɦ ɞɚɜɥɟɧɢɢ, ɩɪɢ ɤɨɬɨɪɨɦ
ɨɛɧɚɪɭɠɢɜɚɸɬɫɹ ɨɫɨɛɟɧɧɨɫɬɢ ɮɢɡɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ, ɩɨɹɜɥɹɟɬɫɹ ɩɟɪɤɨɥɹɰɢɨɧɧɵɣ ɤɥɚɫɬɟɪ, ɨɛɪɚɡɨɜɚɧɧɵɣ
ɚɬɨɦɚɦɢ ɜ sp3 ɤɨɧɮɢɝɭɪɚɰɢɢ, ɢ ɫɤɚɱɤɨɨɛɪɚɡɧɵɦ ɨɛɪɚɡɨɦ ɦɟɧɹɟɬɫɹ ɤɨɪɪɟɥɹɰɢɹ ɤɨɧɮɢɝɭɪɚɰɢɣ ɫɨɫɟɞɧɢɯ ɚɬɨɦɨɜ. ɇɚɣɞɟɧɧɵɟ
ɡɧɚɱɟɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɢ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ 30-40% ɢ ɞɚɜɥɟɧɢɹ 13 Ƚɉɚ, ɩɪɢ ɤɨɬɨɪɵɯ ɧɚɛɥɸɞɚɸɬɫɹ ɨɫɨɛɟɧɧɨɫɬɢ,
ɯɨɪɨɲɨ ɫɨɝɥɚɫɭɸɬɫɹ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɞɪɭɝɢɯ ɚɜɬɨɪɨɜ.
ɄɅɘɑȿȼɕȿ ɋɅɈȼȺ: ɫɬɟɤɥɨɜɚɧɢɟ, ɩɟɪɤɨɥɹɰɢɹ, ɮɚɡɨɜɵɣ ɩɟɪɟɯɨɞ, ɚɬɨɦɧɚɹ ɤɨɧɮɢɝɭɪɚɰɢɹ, ɧɚɧɨɤɪɢɫɬɚɥɥ
Ɇɧɨɠɟɫɬɜɨ ɫɬɪɭɤɬɭɪɧɵɯ ɮɨɪɦ ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ (aC) ɜɨɡɦɨɠɧɨ ɛɥɚɝɨɞɚɪɹ ɪɚɡɧɨɨɛɪɚɡɢɸ ɜɨɡɦɨɠɧɵɯ
ɤɨɧɮɢɝɭɪɚɰɢɣ ɟɝɨ ɷɥɟɤɬɪɨɧɧɵɯ ɨɛɨɥɨɱɟɤ: ɚɬɨɦ ɭɝɥɟɪɨɞɚ ɦɨɠɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ sp3 , sp2 ɢ sp1 ɝɢɛɪɢɞɢɡɚɰɢɹɯ. ɋ
ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ aC -ɧɟɷɪɝɨɞɢɱɧɚɹ ɢ ɧɟɪɚɜɧɨɜɟɫɧɚɹ ɫɢɫɬɟɦɚ. ɉɪɢ ɬɟɦɩɟɪɚɬɭɪɚɯ T < 1000 K
ɫɬɪɭɤɬɭɪɧɵɟ ɪɟɥɚɤɫɚɰɢɨɧɧɵɟ ɩɪɨɰɟɫɫɵ ɜ aC ɩɪɨɢɫɯɨɞɹɬ ɱɪɟɡɜɵɱɚɣɧɨ ɦɟɞɥɟɧɧɨ. ɉɨɷɬɨɦɭ ɦɧɨɝɢɟ ɮɨɪɦɵ aC
ɞɨɫɬɚɬɨɱɧɨ ɭɫɬɨɣɱɢɜɵ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɣ ɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɜ ɪɚɡɥɢɱɧɵɯ ɩɪɢɥɨɠɟɧɢɹɯ.
ɉɪɢ ɜɵɫɨɤɨɣ ɩɥɨɬɧɨɫɬɢ aC ɹɜɥɹɟɬɫɹ ɢɡɨɥɹɬɨɪɨɦ, ɢɦɟɟɬ ɡɧɚɱɢɬɟɥɶɧɭɸ ɬɜɟɪɞɨɫɬɶ, ɜɵɫɨɤɭɸ
ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ, ɛɨɥɶɲɭɸ ɲɢɪɢɧɭ ɡɚɩɪɟɳɟɧɧɨɣ ɡɨɧɵ, ɬ.ɟ. ɟɝɨ ɫɜɨɣɫɬɜɚ ɫɯɨɞɧɵ ɫɨ ɫɜɨɣɫɬɜɚɦɢ ɚɥɦɚɡɚ, ɬɨɝɞɚ
ɤɚɤ ɩɪɢ ɧɢɡɤɨɣ ɩɥɨɬɧɨɫɬɢ ɫɜɨɣɫɬɜɚ ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ ɫɯɨɞɧɵ ɫɨ ɫɜɨɣɫɬɜɚɦɢ ɝɪɚɮɢɬɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ
ɚɦɨɪɮɧɵɣ ɭɝɥɟɪɨɞ ɪɚɡɞɟɥɹɸɬ ɧɚ ɚɥɦɚɡɨɩɨɞɨɛɧɵɣ ɢ ɝɪɚɮɢɬɨɩɨɞɨɛɧɵɣ. Ⱥɥɦɚɡɨɩɨɞɨɛɧɵɟ ɫɜɨɣɫɬɜɚ ɚɦɨɪɮɧɨɝɨ
ɭɝɥɟɪɨɞɚ ɨɛɵɱɧɨ ɩɪɨɹɜɥɹɸɬɫɹ ɜ ɫɥɭɱɚɟ ɛɨɥɶɲɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɚɬɨɦɨɜ ɜ “ɚɥɦɚɡɧɨɣ” sp3 ɤɨɧɮɢɝɭɪɚɰɢɢ, ɬ.ɟ. 4-ɯ
ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ. ɗɬɚ ɮɨɪɦɚ ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ ɩɪɢɜɥɟɤɚɟɬ ɨɫɨɛɨɟ ɜɧɢɦɚɧɢɟ, ɬɚɤ ɤɚɤ ɱɚɫɬɨ
ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɰɟɥɟɣ, ɜ ɤɚɱɟɫɬɜɟ ɡɚɳɢɬɧɵɯ ɩɨɤɪɵɬɢɣ ɢɥɢ ɤɚɬɨɞɧɨɝɨ ɦɚɬɟɪɢɚɥɚ. Ɉɛɡɨɪ ɫɜɨɣɫɬɜ
ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɪɚɛɨɬɚɯ [1,2].
Ȼɨɥɶɲɨɟ ɪɚɡɧɨɨɛɪɚɡɢɟ ɫɬɪɭɤɬɭɪ aC ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ, ɢɫɩɨɥɶɡɭɹ ɦɟɬɨɞɵ ɨɫɚɠɞɟɧɢɹ ɚɬɨɦɨɜ ɢɥɢ ɢɨɧɨɜ.
Ɍɟɬɪɚɝɨɧɚɥɶɧɵɣ ɚɦɨɪɮɧɵɣ ɭɝɥɟɪɨɞ ɫ ɛɨɥɶɲɨɣ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ɚɬɨɦɨɜ (ta-C) ɩɨɥɭɱɚɸɬ ɩɪɢ ɨɫɚɠɞɟɧɢɢ ɚɬɨɦɨɜ
ɫ ɷɧɟɪɝɢɹɦɢ ɜ ɢɧɬɟɪɜɚɥɟ ɨɬ 20 ɞɨ 500 ɷȼ. Ⱥɬɨɦɧɨɟ ɨɩɢɫɚɧɢɟ ɦɟɯɚɧɢɡɦɚ ɨɫɚɠɞɟɧɢɹ ɚɬɨɦɨɜ ɩɪɨɞɨɥɠɚɟɬ
ɨɛɫɭɠɞɚɬɶɫɹ ɭɠɟ ɨɤɨɥɨ 30 ɥɟɬ. ȼɵɫɨɤɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ sp3 ɚɬɨɦɨɜ ɜ ta-C ɨɛɴɹɫɧɹɸɬ ɫɥɟɞɭɸɳɢɦɢ ɦɨɞɟɥɹɦɢ:
ɧɟɝɥɭɛɨɤɨɟ ɜɧɟɞɪɟɧɢɟ Ʌɢɮɲɢɬɰɚ [3] ɢ ɫɜɹɡɚɧɧɨɟ ɫ ɧɢɦ ɦɟɬɚɫɬɚɛɢɥɶɧɨɟ ɭɜɟɥɢɱɟɧɢɟ ɩɥɨɬɧɨɫɬɢ Ɋɨɛɟɪɬɫɨɧɚ [1],
ɜɵɛɨɪɨɱɧɨɟ ɜɵɛɢɜɚɧɢɟ Ɋɚɣɧɤɚ ɢ Ʉɭɪɚ [4] ɢ ɮɚɡɨɜɵɣ ɩɟɪɟɯɨɞ ɆɤɄɟɧɡɢ [2,5], ɢɧɞɭɰɢɪɨɜɚɧɧɵɣ ɧɚɩɪɹɠɟɧɢɟɦ,
ɤɨɬɨɪɨɟ ɫɨɡɞɚɟɬ ɜɧɟɞɪɟɧɧɵɣ ɚɬɨɦ.
Ɋɟɡɭɥɶɬɚɬɵ ɩɪɨɜɟɞɟɧɧɨɝɨ ɧɟɞɚɜɧɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ [6,7] ɦɟɬɨɞɨɦ ɦɨɥɟɤɭɥɹɪɧɨɣ ɞɢɧɚɦɢɤɢ (ɆȾ)
ɩɨɞɞɟɪɠɢɜɚɸɬ ɢɞɟɸ ɨ ɫɭɳɟɫɬɜɨɜɚɧɢɢ ɮɚɡɨɜɨɝɨ ɩɟɪɟɯɨɞɚ ɜ aC. ȼ ɪɚɛɨɬɟ [7] ɛɵɥɨ ɜɩɟɪɜɵɟ ɜɵɫɤɚɡɚɧɚ ɢɞɟɹ ɨ
ɫɭɳɟɫɬɜɨɜɚɧɢɢ ɫɜɹɡɢ ɦɟɠɞɭ ɬɨɩɨɥɨɝɢɟɣ ɤɥɚɫɬɟɪɨɜ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ ɜ ɠɢɞɤɨɫɬɢ ɢ ɫɬɟɤɥɟ ɫ
ɮɚɡɨɜɵɦɢ ɩɪɟɜɪɚɳɟɧɢɹɦɢ. ɗɬɚ ɢɞɟɹ ɧɚɲɥɚ ɩɨɞɬɜɟɪɠɞɟɧɢɟ ɜ ɪɚɛɨɬɟ [8], ɝɞɟ ɛɵɥɨ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɭɫɬɨɣɱɢɜɨɫɬɶ
ɤɪɢɫɬɚɥɥɢɬɨɜ ɚɥɦɚɡɚ, ɜɧɟɞɪɟɧɧɵɯ ɜ ɩɟɪɟɨɯɥɚɠɞɟɧɧɭɸ ɠɢɞɤɨɫɬɶ ɭɝɥɟɪɨɞɚ, ɡɚɜɢɫɢɬ ɨɬ ɫɭɳɟɫɬɜɨɜɚɧɢɹ
ɩɪɨɬɟɤɚɸɳɟɝɨ ɤɥɚɫɬɟɪɚ ɫɨɫɟɞɧɢɯ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ. Ɉɞɧɚɤɨ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɣ ɜɨɩɪɨɫ ɨ
ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɮɚɡɨɜɨɝɨ ɩɟɪɟɯɨɞɚ ɜ aC ɨɫɬɚɥɫɹ ɧɟɢɡɭɱɟɧɧɵɦ ɜ ɞɨɥɠɧɨɣ ɦɟɪɟ.
ȼ ɷɬɨɣ ɪɚɛɨɬɟ ɩɪɨɜɨɞɢɬɫɹ ɆȾ ɢɫɫɥɟɞɨɜɚɧɢɟ aC. Ɉɫɧɨɜɧɚɹ ɰɟɥɶ ɪɚɛɨɬɵ – ɩɪɨɜɟɪɢɬɶ ɫɭɳɟɫɬɜɨɜɚɧɢɟ
ɮɚɡɨɜɨɝɨ ɩɟɪɟɯɨɞɚ ɜ ɚɦɨɪɮɧɨɦ ɭɝɥɟɪɨɞɟ. ɋɥɨɠɧɨɫɬɶ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ aC – ɧɟɪɚɜɧɨɜɟɫɧɚɹ ɧɟɷɪɝɨɞɢɱɧɚɹ
ɫɢɫɬɟɦɚ, ɢ, ɡɧɚɱɢɬ, ɫɬɚɧɞɚɪɬɧɵɟ ɦɟɬɨɞɵ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ ɧɟɩɪɢɝɨɞɧɵ ɞɥɹ ɟɟ ɢɫɫɥɟɞɨɜɚɧɢɹ. ɋɬɪɭɤɬɭɪɚ aC
ɡɚɜɢɫɢɬ ɨɬ ɤɢɧɟɬɢɤɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɢ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɷɤɫɩɟɪɢɦɟɧɬɚ, ɱɬɨ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɟɬ ɧɚ
ɮɢɡɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ aC.
ɆȿɌɈȾ ɆɈȾȿɅɂɊɈȼȺɇɂə
Ⱦɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢɫɩɨɥɶɡɨɜɚɥɫɹ ɦɟɬɨɞ ɆȾ. ȼ ɦɨɞɟɥɢɪɭɟɦɨɣ ɹɱɟɣɤɟ ɫɨɞɟɪɠɚɥɨɫɶ N = 13824 ɚɬɨɦɚ. ɇɚ
ɝɪɚɧɢɰɚɯ ɹɱɟɣɤɢ ɡɚɞɚɜɚɥɢɫɶ ɩɟɪɢɨɞɢɱɟɫɤɢɟ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ. ɍɪɚɜɧɟɧɢɹ ɇɶɸɬɨɧɚ, ɨɩɢɫɵɜɚɸɳɢɟ
ɤɥɚɫɫɢɱɟɫɤɨɟ ɞɜɢɠɟɧɢɟ ɚɬɨɦɨɜ, ɪɟɲɚɥɢɫɶ ɩɪɢ ɩɨɦɨɳɢ ɚɥɝɨɪɢɬɦɚ ȼɟɪɥɟɬɚ [10] ɫ ɲɚɝɨɦ ɩɨ ɜɪɟɦɟɧɢ,
ɢɡɦɟɧɹɸɳɢɦɫɹ ɜ ɩɪɟɞɟɥɚɯ 0,4 – 0,7 ɮɫ. ȼɨ ɜɪɟɦɹ ɜɵɱɢɫɥɟɧɢɣ ɜ ɹɱɟɣɤɟ ɩɨɞɞɟɪɠɢɜɚɥɨɫɶ ɩɨɫɬɨɹɧɧɨɟ ɞɚɜɥɟɧɢɟ.
ɇɚ ɤɚɠɞɨɦ ɲɚɝɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɜɵɱɢɫɥɹɥɫɹ ɬɟɧɡɨɪ ɧɚɩɪɹɠɟɧɢɣ ɢ ɧɚɯɨɞɢɥɨɫɶ ɞɚɜɥɟɧɢɟ
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Ì.Ñ. Áûøêèí, À.Ñ. Áàêàé, À.À. Òóðêèí
«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 781, 2007
P
2( E k ;) / 3V ,
(1)
ɝɞe ; Tr (S ) / 2 - ɜɢɪɢɚɥ, S - ɬɟɧɡɨɪ ɧɚɩɪɹɠɟɧɢɹ, ɚ Ek 2k BT 3 - ɫɪɟɞɧɹɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɚɬɨɦɨɜ ɜ
ɫɬɪɭɤɬɭɪɟ. Ⱦɥɹ ɤɨɧɬɪɨɥɹ ɞɚɜɥɟɧɢɹ ɢ ɬɟɦɩɟɪɚɬɭɪɵ ɩɪɢɦɟɧɹɥɫɹ ɚɥɝɨɪɢɬɦ Ȼɟɪɟɧɞɫɟɧɚ [11].
Ȼɨɥɶɲɚɹ ɱɚɫɬɶ ɜɵɱɢɫɥɟɧɢɣ ɛɵɥɚ ɩɪɨɢɡɜɟɞɟɧɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɷɦɩɢɪɢɱɟɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɚ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɚɬɨɦɨɜ ɭɝɥɟɪɨɞɚ, ɩɪɟɞɥɨɠɟɧɧɨɝɨ Ɍɟɪɫɨɮɮɨɦ [12]. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɷɬɨɝɨ
ɩɨɬɟɧɰɢɚɥɚ ɧɟ ɬɪɟɛɭɟɬ ɛɨɥɶɲɢɯ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɪɟɫɭɪɫɨɜ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɚɬɶ ɨɬɧɨɫɢɬɟɥɶɧɨ ɯɨɪɨɲɨ
ɨɬɨɠɠɟɧɧɵɟ ɫɬɪɭɤɬɭɪɵ. ɉɨɫɥɟ ɬɨɝɨ, ɤɚɤ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɟɠɚɬɨɦɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ Ɍɟɪɫɨɮɮɚ ɛɵɥɢ
ɩɨɥɭɱɟɧɵ ɫɬɪɭɤɬɭɪɵ ɭɝɥɟɪɨɞɚ, ɷɬɢ ɫɬɪɭɤɬɭɪɵ ɛɵɥɢ ɭɪɚɜɧɨɜɟɲɟɧɧɵ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɟɬɨɞɚ ɠɟɫɬɤɢɯ ɫɜɹɡɟɣ
(tight-binding: TB) [13]. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɦɟɠɚɬɨɦɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɷɬɢɦ ɦɟɬɨɞɨɦ, ɭɱɢɬɵɜɚɟɬɫɹ
ɩɟɪɟɤɪɵɬɢɟ ɨɪɛɢɬɚɥɟɣ ɜɚɥɟɧɬɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɢ ɩɨɬɨɦɭ ɫɱɢɬɚɟɬɫɹ, ɱɬɨ ɦɟɬɨɞ Ɍȼ ɬɨɱɧɟɟ ɨɩɢɫɵɜɚɟɬ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɚɬɨɦɨɜ ɭɝɥɟɪɨɞɚ, ɱɟɦ ɷɦɩɢɪɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ. Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɫɢɥ ɢ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɚɬɨɦɨɜ ɧɚɯɨɞɢɥɚɫɶ ɦɚɬɪɢɰɚ ɩɥɨɬɧɨɫɬɢ F ɩɪɢ ɩɨɦɨɳɢ O(N) ɦɟɬɨɞɚ [14] ɤɚɤ ɪɟɡɭɥɶɬɚɬ ɪɟɲɟɧɢɹ
ɡɚɞɚɱɢ ɧɟɨɝɪɚɧɢɱɟɧɧɨɣ ɨɩɬɢɦɢɡɚɰɢɢ
(2)
: tr (3F 2 2 F 3 )( H KI )) o min ,
ɝɞɟ ɇ - ɝɚɦɢɥɶɬɨɧɢɚɧ, K - ɯɢɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ. Ⱦɥɹ ɦɢɧɢɦɢɡɚɰɢɢ ɩɪɢɦɟɧɹɥɫɹ ɦɟɬɨɞ ɫɨɩɪɹɠɟɧɧɵɯ
ɝɪɚɞɢɟɧɬɨɜ. Ⱦɟɬɚɥɢ ɢɫɩɨɥɶɡɨɜɚɧɧɨɝɨ O(N) ɦɟɬɨɞɚ ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɪɚɛɨɬɟ [15], ɨɞɧɚɤɨ ɦɵ ɦɨɞɢɮɢɰɢɪɨɜɚɥɢ
ɚɥɝɨɪɢɬɦ ɞɥɹ ɫɨɯɪɚɧɟɧɢɹ tr(F)=2N=const. ɗɬɨɬ ɦɨɞɢɮɢɰɢɪɨɜɚɧɧɵɣ O(N) ɦɟɬɨɞ ɬɪɟɛɨɜɚɥ ɜɫɟɝɨ ɥɢɲɶ 2-3
ɢɬɟɪɚɰɢɢ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (2) ɫ ɞɨɩɭɫɬɢɦɨɣ ɨɲɢɛɤɨɣ 0,001 ɷȼ/ɚɬɨɦ.
Ɇɨɞɭɥɶ ɨɛɴɟɦɧɨɝɨ ɫɠɚɬɢɹ K (c11 2c12 ) / 3 ɧɚɯɨɞɢɥɫɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɪɚɜɧɨɦɟɪɧɨɝɨ ɫɠɢɦɚɸɳɟɝɨ
ɧɚɩɪɹɠɟɧɢɹ. Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɦɨɞɭɥɹ ɫɞɜɢɝɚ P c44 (c11 c12 ) / 2 ɩɪɢɦɟɧɹɥɨɫɶ ɩɪɢɡɦɚɬɢɱɟɫɤɨɟ ɧɚɩɪɹɠɟɧɢɟ,
ɫɨɯɪɚɧɹɸɳɟɟ ɨɛɴɟɦ [16]. Ɇɨɞɭɥɶ ɘɧɝɚ ɧɚɯɥɞɢɥɫɹ ɩɨ ɮɨɪɦɭɥɟ
(3)
Y 9 KP /( P 3K ) .
Ʉɨɨɪɞɢɧɚɰɢɨɧɧɨɟ ɱɢɫɥɨ ɚɬɨɦɚ ɧɚɯɨɞɢɥɨɫɶ ɩɭɬɟɦ ɩɨɞɫɱɟɬɚ ɤɨɥɢɱɟɫɬɜɚ ɫɨɫɟɞɧɢɯ ɚɬɨɦɨɜ, ɧɚɯɨɞɹɳɢɯɫɹ ɨɬ ɧɟɝɨ
ɧɚ ɪɚɫɫɬɨɹɧɢɢ ɧɟ ɛɨɥɟɟ 0,18 ɧɦ, ɬ.ɟ. ɜ ɩɟɪɜɨɣ ɤɨɨɪɞɢɧɚɰɢɨɧɧɨɣ ɫɮɟɪɟ.
ɊȿɁɍɅɖɌȺɌɕ ɆɈȾȿɅɂɊɈȼȺɇɂə
Ɏɨɪɦɢɪɨɜɚɧɢɟ ɤɜɚɡɢɪɚɜɧɨɜɟɫɧɵɯ ɫɬɪɭɤɬɭɪ
ɋɬɪɭɤɬɭɪɵ aC ɛɵɥɢ ɫɮɨɪɦɢɪɨɜɚɧɵ ɡɚɤɚɥɤɨɣ ɪɚɫɩɥɚɜɚ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɞɚɜɥɟɧɢɹ. ɗɬɭ ɮɨɪɦɭ aC
ɧɚɡɵɜɚɸɬ ɤɜɚɡɢɪɚɜɧɨɜɟɫɧɨɣ [9]. ȼ ɭɡɤɨɦ ɢɧɬɟɪɜɚɥɟ ɬɟɦɩɟɪɚɬɭɪ, ɧɚɯɨɞɹɳɢɦɫɹ ɥɢɲɶ ɧɟɡɧɚɱɢɬɟɥɶɧɨ ɧɢɠɟ
ɬɟɦɩɟɪɚɬɭɪɵ ɫɬɟɤɥɨɜɚɧɢɹ [8], ɤɜɚɡɢɪɚɜɧɨɜɟɫɧɵɣ aC ɛɥɢɡɨɤ ɤ ɫɜɨɟɦɭ ɭɫɥɨɜɧɨɦɭ ɪɚɜɧɨɜɟɫɢɸ, ɢ ɩɨɬɨɦɭ ɜ ɷɬɨɦ
ɢɧɬɟɪɜɚɥɟ ɬɟɦɩɟɪɚɬɭɪ ɮɚɡɨɜɵɣ ɩɟɪɟɯɨɞ ɞɨɥɠɟɧ ɫɨɩɪɨɜɨɠɞɚɬɶɫɹ ɫɤɚɱɤɨɨɛɪɚɡɧɵɦ ɢɡɦɟɧɟɧɢɟɦ
ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɞɚɜɥɟɧɢɹ. ȼ ɧɚɲɢɯ ɜɵɱɢɫɥɟɧɢɹɯ ɢɫɩɨɥɶɡɨɜɚɥɚɫɶ ɫɤɨɪɨɫɬɶ
ɨɯɥɚɠɞɟɧɢɹ 1 K/ɩɫ.
ɋɜɨɣɫɬɜɚ ɩɨɥɭɱɟɧɧɵɯ ɫɬɪɭɤɬɭɪ aC ɢ ɢɯ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɞɚɜɥɟɧɢɹ ɢɫɫɥɟɞɨɜɚɥɚɫɶ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɡɧɚɱɟɧɢɢ
ɬɟɦɩɟɪɚɬɭɪɵ. Ⱦɥɹ ɫɬɪɭɤɬɭɪ, ɨɯɥɚɠɞɟɧɧɵɯ ɞɨ ɬɟɦɩɟɪɚɬɭɪ 2500, 2800 ɢ 3100 K, ɡɚɜɢɫɢɦɨɫɬɶ ɚɬɨɦɧɨɝɨ ɨɛɴɟɦɚ V
ɢ ɫɪɟɞɧɟɣ ɚɬɨɦɧɨɣ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɢ Z ɨɬ ɞɚɜɥɟɧɢɹ P ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 1 ɫɩɥɨɲɧɵɦɢ ɥɢɧɢɹɦɢ. Ɇɨɠɧɨ
ɭɜɢɞɟɬɶ ɢɡɦɟɧɟɧɢɟ ɧɚɤɥɨɧɚ ɡɚɜɢɫɢɦɨɫɬɟɣ Z(P)(ɪɢɫ. 1ɚ) ɢ V(P) (ɪɢɫ. 1ɛ) ɩɪɢ ɞɚɜɥɟɧɢɢ 27,5 Ƚɉɚ. Ȼɵɥɨ
ɩɪɨɢɡɜɟɞɟɧɨ ɛɨɥɶɲɨɟ ɤɨɥɢɱɟɫɬɜɨ ɞɪɭɝɢɯ ɤɨɦɩɶɸɬɟɪɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ, ɩɨɞɨɛɧɵɯ ɨɩɢɫɚɧɧɨɦɭ ɜ ɪɚɛɨɬɟ, ɢ ɜɫɟ
ɨɧɢ ɬɚɤɠɟ ɨɛɧɚɪɭɠɢɜɚɥɢ ɨɫɨɛɟɧɧɨɫɬɢ ɧɚ ɡɚɜɢɫɢɦɨɫɬɹɯ ɫɜɨɣɫɬɜ ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ ɨɬ ɞɚɜɥɟɧɢɹ ɩɪɢ ɞɚɜɥɟɧɢɢ
ɩɪɢɦɟɪɧɨ ɪɚɜɧɨɦ 30 Ƚɉɚ. Ɋɟɡɭɥɶɬɚɬɵ ɨɞɧɨɝɨ ɢɡ ɬɚɤɢɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 1 ɩɭɧɤɬɢɪɧɨɣ ɥɢɧɢɟɣ. ȼ
ɷɬɨɦ ɷɤɫɩɟɪɢɦɟɧɬɟ ɫɬɪɭɤɬɭɪɵ ɫɬɟɤɥɚ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɞɚɜɥɟɧɢɹ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɫɠɚɬɢɟɦ ɫɬɟɤɥɚ ɩɪɢ
ɬɟɦɩɟɪɚɬɭɪɟ 3500 K, ɩɨɥɭɱɟɧɧɨɝɨ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɨɯɥɚɠɞɟɧɢɟɦ ɪɚɫɩɥɚɜɚ ɩɪɢ ɞɚɜɥɟɧɢɢ 20 Ƚɉɚ. ȼɢɞɧɨ, ɱɬɨ
ɡɚɜɢɫɢɦɨɫɬɢ Z(P) ɢ V(P) ɤɚɱɟɫɬɜɟɧɧɨ ɧɟ ɦɟɧɹɸɬɫɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɬɟɪɦɢɱɟɫɤɨɣ ɩɪɟɞɵɫɬɨɪɢɢ ɢ ɨɛɧɚɪɭɠɢɜɚɸɬ
ɨɫɨɛɟɧɧɨɫɬɢ ɩɪɢ 30 Ƚɉɚ.
ȼɨ ɜɫɟɯ ɩɨɥɭɱɟɧɧɵɯ ɫɬɪɭɤɬɭɪɚɯ ɫɬɟɤɥɚ ɫɭɦɦɚɪɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɨɞɧɨ- ɢ ɞɜɭɯ- ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ
- ɤɨɧɰɟɧɬɪɚɰɢɹ 4-ɯ
ɛɵɥɚ ɦɟɧɶɲɟ 0,5 %, ɢ ɩɨɬɨɦɭ ɫɪɟɞɧɹɹ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɶ Z | 3 c 4 , ɝɞɟ c 4
ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ. ɇɚ ɪɢɫ. 1ɜ ɩɨɤɚɡɚɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɚɬɨɦɨɜ ȿ
ɨɬ ɞɚɜɥɟɧɢɹ. ɇɚ ɡɚɜɢɫɢɦɨɫɬɢ E(P) ɬɚɤɠɟ ɜɢɞɧɚ ɨɫɨɛɟɧɧɨɫɬɶ ɩɪɢ 27,5 Ƚɉɚ.
ɋɬɪɭɤɬɭɪɵ ɫɬɟɤɥɚ, ɭɪɚɜɧɨɜɟɲɟɧɧɵɟ ɦɟɬɨɞɨɦ ɠɟɫɬɤɢɯ ɫɜɹɡɟɣ
Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɪɟɡɭɥɶɬɚɬ ɤɨɦɩɶɸɬɟɪɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɛɨɥɟɟ ɩɪɚɜɞɨɩɨɞɨɛɧɨ ɨɩɢɫɵɜɚɥ ɫɜɨɣɫɬɜɚ
ɪɟɚɥɶɧɨɝɨ ɭɝɥɟɪɨɞɚ, ɫɬɪɭɤɬɭɪɵ aC, ɩɨɥɭɱɟɧɧɵɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɷɦɩɢɪɢɱɟɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
ɚɬɨɦɨɜ Ɍɟɪɫɨɮɮɚ, ɛɵɥɢ ɭɪɚɜɧɨɜɟɲɟɧɧɵ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɛɨɥɟɟ ɬɨɱɧɨɝɨ ɩɨɬɟɧɰɢɚɥɚ, ɦɟɬɨɞɨɦ Ɍȼ.
ɍɪɚɜɧɨɜɟɲɢɜɚɧɢɟ ɩɪɨɢɡɜɨɞɢɥɨɫɶ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɨɛɴɟɦɟ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ 2100 K. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ
ɦɟɬɨɞɨɦ Ɍȼ ɬɪɟɛɭɟɬ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɤɨɦɩɶɸɬɟɪɧɨɝɨ ɜɪɟɦɟɧɢ, ɱɟɦ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɷɦɩɢɪɢɱɟɫɤɨɝɨ
ɩɨɬɟɧɰɢɚɥɚ. ȼɪɟɦɹ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ ɛɵɥɨ ɫɪɚɜɧɢɬɟɥɶɧɨ ɦɚɥɟɧɶɤɢɦ, 0,3 ɩɫ. ɇɟɫɦɨɬɪɹ ɧɚ ɭɦɟɧɶɲɟɧɢɟ
ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɧɚ ɩɪɨɬɹɠɟɧɢɢ ɜɫɟɝɨ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ, ɜ ɤɨɧɰɟ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ ɧɟ ɛɵɥɨ ɡɚɦɟɬɧɨɝɨ
83
Ïåðêîëÿöèÿ è ôàçîâûé ïåðåõîä â àìîðôíîì ...
ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï. 3 /35/
3.4
Ɂɚɤɚɥɤɚ, T=2525 K
Ɂɚɤɚɥɤɚ, T=2800 K
Ɂɚɤɚɥɤɚ, T=3100 K
ɋɠɚɬɢɟ, T=3500 K
3.45
Ʉɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɶ
Ʉɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɶ
ɢɡɦɟɧɟɧɢɹ ɞɚɜɥɟɧɢɹ ɢɥɢ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɢ. Ɋɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɬɪɭɤɬɭɪ ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ,
ɭɪɚɜɧɨɜɟɲɟɧɧɵɯ ɦɟɬɨɞɨɦ ɠɟɫɬɤɢɯ ɫɜɹɡɟɣ, ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 2 ɢ ɪɢɫ. 3.
3.40
3.35
25
30
Ɂɚɤɚɥɤɚ, T=2525 K
Ɂɚɤɚɥɤɚ, T=2800 K
Ɂɚɤɚɥɤɚ, T=3100 K
ɋɠɚɬɢɟ, T=3500 K
-7.01
-7.02
25
30
35
Ɂɚɤɚɥɤɚ, T=2525 K
Ɂɚɤɚɥɤɚ, T=2800 K
ɛ
-7.04
-7.05
-7.06
ɜ
20
25 30 35
Ⱦɚɜɥɟɧɢɟ, Ƚɉɚ
5
15
20
Y
K+300 Ƚɉɚ
900
-7.03
-7.07
15
25
6.31
Ⱦɚɜɥɟɧɢɟ, Ƚɉa
Ɋɢɫ. 2. ɆȾ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɟ ɦɟɬɨɞɨɦ Ɍȼ.
Ɂɚɜɢɫɢɦɨɫɬɶ ɚ) ɫɪɟɞɧɟɣ ɚɬɨɦɧɨɣ
ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɢ ɢ ɛ) ɚɬɨɦɧɨɝɨ ɨɛɴɟɦɚ
ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ ɨɬ ɞɚɜɥɟɧɢɹ.
ɏ – ɭɪɚɜɧɨɜɟɲɢɜɚɥɚɫɶ ɫɬɪɭɤɬɭɪɚ, ɨɯɥɚɠɞɟɧɧɚɹ ɞɨ
2500 Ʉ, { - ɭɪɚɜɧɨɜɟɲɢɜɚɥɚɫɶ ɫɬɪɭɤɬɭɪɚ,
ɨɯɥɚɠɞɟɧɧɚɹ ɞɨ 2700 Ʉ.
ɛ
Ⱦɚɜɥɟɧɢɟ, Ƚɉɚ
10
6.53
6.09
20
25
35
Ⱦɚɜɥɟɧɢɟ, Ƚɉɚ
Ɉɛɴɟɦ, A3/ɚɬɨɦ
7.0
6.9
6.8
6.7
6.6
6.5
6.4
6.3
6.2
6.1
6.0
20
10
15
20
Ⱦɚɜɥɟɧɢɟ, Ƚɉɚ
6.75
40
Ɋɢɫ.1. ɆȾ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ
ɩɨɬɟɧɰɢɚɥɚ Ɍɟɪɫɨɮɮɚ. Ɂɚɜɢɫɢɦɨɫɬɶ ɨɬ
ɞɚɜɥɟɧɢɹ: a) ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɶ, ɛ) ɨɛɴɟɦ ɢ
ɜ) ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
ɚɬɨɦɨɜ ɚɋ.
ɍɩɪɭɝɢɟ ɦɨɞɭɥɢ, Ƚɉɚ
3
a
5
a
Ɉɛɴɟɦ, Ⱥ /ɚɬɨɦ
3.2
3.30
3.25
E-1,5kBT, ɷȼ/ɚɬɨɦ
3.3
800
700
6.08
6.36
6.63
6.9
Ɉɛɴɟɦ, A /ɚɬɨɦ
3
Ɋɢɫ. 3. ɍɩɪɭɝɢɟ ɦɨɞɭɥɢ ɫɬɪɭɤɬɭɪ aC ɩɨɫɥɟ Ɍȼ
ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ. † ɦɨɞɭɥɶ ɘɧɝɚ Y, ɏ – ɦɨɞɭɥɶ
ɨɛɴɟɦɧɨɝɨ ɫɠɚɬɢɹ B.
84
«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 781, 2007
Ì.Ñ. Áûøêèí, À.Ñ. Áàêàé, À.À. Òóðêèí
Ⱦɜɚ ɡɧɚɱɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɨɰɟɧɢɬɶ ɜɥɢɹɧɢɟ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɨɲɢɛɤɢ ɧɚ
ɮɨɪɦɭ ɩɨɥɭɱɟɧɧɵɯ ɡɚɜɢɫɢɦɨɫɬɟɣ. ɉɨɧɹɬɧɨ, ɱɬɨ ɫɜɨɣɫɬɜɚ ɫɬɪɭɤɬɭɪ ɩɨɫɥɟ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ ɡɚɜɢɫɹɬ ɨɬ ɫɜɨɣɫɬɜ
ɫɬɪɭɤɬɭɪ ɞɨ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ, ɬ.ɟ. ɡɚɜɢɫɹɬ ɨɬ ɢɫɬɨɪɢɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɬɪɭɤɬɭɪ, ɤɚɤ ɢ ɞɨɥɠɧɨ ɛɵɬɶ ɜ ɫɢɫɬɟɦɚɯ ɫ
ɧɚɪɭɲɟɧɧɨɣ ɷɪɝɨɞɢɱɧɨɫɬɶɸ. ɇɚ ɪɢɫ. 2 ɜɢɞɧɨ ɢɡɦɟɧɟɧɢɟ ɭɝɥɚ ɧɚɤɥɨɧɚ ɡɚɜɢɫɢɦɨɫɬɟɣ ɩɪɢ ɞɚɜɥɟɧɢɢ 12-14 Ƚɉɚ.
ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɩɪɢ ɷɬɢɯ ɞɚɜɥɟɧɢɹɯ ɫɠɢɦɚɟɦɨɫɬɶ ɢɫɩɵɬɵɜɚɟɬ ɫɤɚɱɨɤ.
ɉɨɫɥɟ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɹ 2-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ ɜ ɫɬɪɭɤɬɭɪɚɯ ɭɜɟɥɢɱɢɥɚɫɶ ɞɨ 3%.
Ȼɵɥɢ ɧɚɣɞɟɧɵ ɭɩɪɭɝɢɟ ɦɨɞɭɥɢ ɭɪɚɜɧɨɜɟɲɟɧɧɵɯ ɫɬɪɭɤɬɭɪ. ɇɚ ɪɢɫ. 3 ɩɨɤɚɡɚɧɵ ɡɚɜɢɫɢɦɨɫɬɢ ɭɩɪɭɝɢɯ ɦɨɞɭɥɟɣ ɨɬ
ɚɬɨɦɧɨɝɨ ɨɛɴɟɦɚ. ɉɪɢ ɞɚɜɥɟɧɢɢ 10-12 Ƚɉɚ ɦɟɧɹɟɬɫɹ ɯɚɪɚɤɬɟɪ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɚɬɨɦɧɨɝɨ ɨɛɴɟɦɚ ɫɞɜɢɝɨɜɨɝɨ
ɭɩɪɭɝɨɝɨ ɦɨɞɭɥɹ ɢ ɦɨɞɭɥɹ ɘɧɝɚ Y, ɬɨɝɞɚ ɤɚɤ ɦɨɞɭɥɶ ɨɛɴɟɦɧɨɝɨ ɫɠɚɬɢɹ B ɨɫɬɚɟɬɫɹ ɝɥɚɞɤɨɣ ɮɭɧɤɰɢɟɣ ɞɚɜɥɟɧɢɹ
ɢ ɨɛɴɟɦɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɫɥɟ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ ɫɬɪɭɤɬɭɪ ɦɟɬɨɞɨɦ Ɍȼ ɨɫɨɛɟɧɧɨɫɬɢ ɮɢɡɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɧɟ
ɢɫɱɟɡɥɢ, ɚ ɧɚɨɛɨɪɨɬ ɫɬɚɥɢ ɛɨɥɟɟ ɡɚɦɟɬɧɵɦɢ.
Ⱦɨɥɹ ɚɬɨɦɨɜ, Q
ɋɬɪɭɤɬɭɪɧɵɟ ɢ ɩɟɪɤɨɥɹɰɢɨɧɧɵɟ ɫɜɨɣɫɬɜɚ
ȼ ɪɚɛɨɬɟ [7] ɛɵɥ ɩɪɟɞɫɤɚɡɚɧ ɩɟɪɟɯɨɞ ɝɪɚɮɢɬɨɩɨɞɨɛɧɨɝɨ
ɭɝɥɟɪɨɞɚ ɜ ɚɥɦɚɡɨɩɨɞɨɛɧɵɣ ɢ ɫɜɹɡɚɧɧɵɟ ɫ ɷɬɢɦ ɩɟɪɟɯɨɞɨɦ
ɨɫɨɛɟɧɧɨɫɬɢ ɜ ɩɨɜɟɞɟɧɢɢ ɮɢɡɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɚɋ ɩɪɢ ɬɚɤɨɦ
ɉɨɬɟɧɰɢɚɥ Ɍɟɪɫɨɮɮɚ
ɡɧɚɱɟɧɢɢ ɫɪɟɞɧɟɣ ɚɬɨɦɧɨɣ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɢ, ɩɪɢ
ɉɨɫɥɟ Ɍȼ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ
ɤɨɬɨɪɨɣ ɫɨɫɟɞɧɢɟ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɟ ɚɬɨɦɵ ɨɛɪɚɡɭɸɬ
0.4
ɛɨɥɶɲɨɣ ɤɥɚɫɬɟɪ, ɩɪɨɧɢɡɵɜɚɸɳɢɣ ɜɫɸ ɫɬɪɭɤɬɭɪɭ, ɬ.ɟ. ɤɨɝɞɚ
ɤɨɧɰɟɧɬɪɚɰɢɹ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ
ɞɨɫɬɢɝɚɟɬ
ɩɨɪɨɝɚ
ɩɪɨɬɟɤɚɧɢɹ.
Ɇɵ
ɧɚɯɨɞɢɦ
ɤɥɚɫɬɟɪɵ
4-ɯ
ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ ɜ ɫɬɪɭɤɬɭɪɚɯ ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ
0.2
ɢ ɩɨɤɚɡɵɜɚɟɦ, ɱɬɨ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɫɭɳɟɫɬɜɭɟɬ ɤɨɪɪɟɥɹɰɢɹ
ɦɟɠɞɭ ɧɚɣɞɟɧɧɵɦɢ ɨɫɨɛɟɧɧɨɫɬɹɦɢ ɫɜɨɣɫɬɜ ɚɦɨɪɮɧɨɝɨ
ɭɝɥɟɪɨɞɚ ɢ ɩɟɪɤɨɥɹɰɢɨɧɧɵɦɢ ɫɜɨɣɫɬɜɚɦɢ ɟɝɨ ɫɬɪɭɤɬɭɪ.
Ⱦɥɹ ɛɨɥɶɲɢɯ ɫɥɭɱɚɣɧɵɯ ɫɟɬɟɣ ɨɬɧɨɲɟɧɢɟ ɤɨɥɢɱɟɫɬɜɚ
ɭɡɥɨɜ ɜ ɧɚɢɛɨɥɶɲɟɦ ɤɥɚɫɬɟɪɟ ɤ ɩɨɥɧɨɦɭ ɤɨɥɢɱɟɫɬɜɭ ɭɡɥɨɜ
0
ɫɬɪɟɦɢɬɫɹ ɤ ɧɭɥɸ ɧɚ ɩɨɪɨɝɟ ɩɪɨɬɟɤɚɧɢɹ [17]. Ⱦɨɥɹ ɚɬɨɦɨɜ
0
10
20
30
40
ɫɬɪɭɤɬɭɪɵ Q, ɩɪɢɧɚɞɥɟɠɚɳɢɯ ɧɚɢɛɨɥɶɲɟɦɭ ɤɥɚɫɬɟɪɭ,
Ⱦɚɜɥɟɧɢɟ, Ƚɉɚ
ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 4 ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɞɚɜɥɟɧɢɹ.
ɉɟɪɤɨɥɹɰɢɨɧɧɵɣ ɤɥɚɫɬɟɪ ɫɭɳɟɫɬɜɭɟɬ ɩɪɢ ɛɨɥɶɲɨɦ ɞɚɜɥɟɧɢɢ
ɢ
ɧɟ ɫɭɳɟɫɬɜɭɟɬ ɩɪɢ ɦɚɥɟɧɶɤɨɦ ɞɚɜɥɟɧɢɢ. ȼɢɞɧɨ, ɱɬɨ ɜɫɟ
Ɋɢɫ.4. ɉɟɪɤɨɥɹɰɢɨɧɧɵɟ ɫɜɨɣɫɬɜɚ ɫɬɪɭɤɬɭɪ aC ɞɨ ɢ
ɧɚɣɞɟɧɧɵɟ
ɜ ɷɬɨɣ ɪɚɛɨɬɟ ɨɫɨɛɟɧɧɨɫɬɢ ɫɜɨɣɫɬɜ ɚɦɨɪɮɧɨɝɨ
ɩɨɫɥɟ Ɍȼ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ. Ⱦɨɥɹ ɚɬɨɦɨɜ ɜ ɫɚɦɨɦ
ɛɨɥɶɲɨɦ ɤɥɚɫɬɟɪɟ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ
ɭɝɥɟɪɨɞɚ, ɤɚɤ ɞɨ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ (ɪɢɫ. 1), ɬɚɤ ɢ ɩɨɫɥɟ
ɩɨɤɚɡɚɧɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɞɚɜɥɟɧɢɹ
ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ (ɪɢɫ. 2, 3), ɧɚɯɨɞɹɬɫɹ ɩɪɢ ɬɟɯ ɡɧɚɱɟɧɢɹɯ
ɞɚɜɥɟɧɢɹ, ɨɛɴɟɦɚ ɢ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɢ, ɩɪɢ ɤɨɬɨɪɵɯ ɨɛɪɚɡɭɟɬɫɹ ɩɟɪɤɨɥɹɰɢɨɧɧɵɣ ɤɥɚɫɬɟɪ.
ɑɬɨɛɵ ɫɜɹɡɚɬɶ ɬɨɩɨɥɨɝɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɫ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɦɢ, ɪɚɫɫɦɨɬɪɢɦ ɤɨɪɪɟɥɹɰɢɢ ɤɨɧɮɢɝɭɪɚɰɢɣ
ɞɜɭɯ ɫɨɫɟɞɧɢɯ ɚɬɨɦɨɜ. Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ wik ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɫɨɫɟɞ i-ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɝɨ ɚɬɨɦɚ ɹɜɥɹɟɬɫɹ
k-ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɦ. ɇɚ ɪɢɫ. 5 ɩɨɤɚɡɚɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɪɪɟɥɹɬɨɪɚ w44 w34
ɨɬ ɞɚɜɥɟɧɢɹ. ȼɢɞɧɨ, ɱɬɨ ɩɪɢ
ɞɚɜɥɟɧɢɢ 27,5 Ƚɉɚ, ɩɪɢ ɤɨɬɨɪɨɦ ɨɛɪɚɡɭɟɬɫɹ ɩɟɪɤɨɥɹɰɢɨɧɧɵɣ ɤɥɚɫɬɟɪ (ɪɢɫ. 4) ɢ ɧɚɛɥɸɞɚɸɬɫɹ ɨɫɨɛɟɧɧɨɫɬɢ
ɮɢɡɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ (ɪɢɫ. 1), ɤɨɪɪɟɥɹɬɨɪ ɢɡɦɟɧɹɟɬɫɹ ɫɤɚɱɤɨɦ, ɱɬɨ ɹɜɥɹɟɬɫɹ ɩɪɢɡɧɚɤɨɦ ɮɚɡɨɜɨɝɨ ɩɟɪɟɯɨɞɚ
ɩɟɪɜɨɝɨ ɪɨɞɚ.
ɉɚɪɧɵɯ ɤɨɪɪɟɥɹɬɨɪɨɜ wik ɧɟ ɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɨɩɢɫɚɧɢɹ ɛɥɢɠɧɟɝɨ ɩɨɪɹɞɤɚ. Ɇɵ ɧɚɯɨɞɢɥɢ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ,
ɱɬɨ ɭ ɫɥɭɱɚɣɧɨɝɨ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɝɨ ɚɬɨɦɚ ɜɫɟ ɫɨɫɟɞɢ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɟ, ɢ ɜɨ ɜɫɟɦ ɢɧɬɟɪɜɚɥɟ
ɢɫɩɨɥɶɡɭɟɦɵɯ ɡɧɚɱɟɧɢɣ ɞɚɜɥɟɧɢɹ ɢ ɬɟɦɩɟɪɚɬɭɪɵ ɷɬɚ ɜɟɪɨɹɬɧɨɫɬɶ ɛɵɥɚ ɡɚɦɟɬɧɨ ɦɟɧɶɲɟ, ɱɟɦ w44 4 . ɗɬɨ ɬɚɤɠɟ
ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜ ɫɬɪɭɤɬɭɪɚɯ ɧɟ ɩɪɨɢɡɨɲɥɨ ɫɭɳɟɫɬɜɟɧɧɨɣ ɚɥɦɚɡɧɨɣ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ.
ɇɚ ɪɢɫ. 6 ɦɵ ɩɨɤɚɡɵɜɚɟɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹ n(s) ɤɥɚɫɬɟɪɨɜ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ ɩɨ ɪɚɡɦɟɪɭ ɩɪɢ
ɧɟɫɤɨɥɶɤɢɯ ɡɧɚɱɟɧɢɹɯ ɞɚɜɥɟɧɢɹ ɜɛɥɢɡɢ ɩɨɪɨɝɚ ɩɪɨɬɟɤɚɧɢɹ. Ⱦɥɹ ɫɥɭɱɚɣɧɨɣ ɫɦɟɫɢ ɭɡɥɨɜ ɧɚ ɩɨɪɨɝɟ ɩɪɨɬɟɤɚɧɢɹ
n( s ) v s W , ɜ ɬɪɟɯɦɟɪɧɨɣ ɫɢɫɬɟɦɟ W | 2,18 [27] . ɂɡ ɪɢɫ. 6 ɜɢɞɧɨ, ɱɬɨ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɣ ɡɚɤɨɧ ɧɚɪɭɲɚɟɬɫɹ
ɩɪɢ ɦɚɥɟɧɶɤɢɯ s, ɱɬɨ ɯɨɪɨɲɨ ɜɢɞɧɨ ɩɪɢ s<5. ɂɡ ɷɬɨɝɨ ɦɵ ɞɟɥɚɟɦ ɜɵɜɨɞ, ɱɬɨ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɦ ɚɬɨɦɚɦ
ɷɧɟɪɝɟɬɢɱɟɫɤɢ ɧɟ ɜɵɝɨɞɧɨ ɨɛɴɟɞɢɧɹɬɶɫɹ ɜ ɦɚɥɟɧɶɤɢɟ ɤɥɚɫɬɟɪɵ. ɇɚɪɭɲɟɧɢɟ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɝɨ ɡɚɤɨɧɚ
ɩɪɨɢɫɯɨɞɢɬ ɛɥɚɝɨɞɚɪɹ ɧɚɥɢɱɢɸ ɛɥɢɠɧɟɝɨ ɩɨɪɹɞɤɚ ɜ ɫɬɪɭɤɬɭɪɟ ɚɬɨɦɨɜ ɭɝɥɟɪɨɞɚ, ɚ ɢɦɟɧɧɨ ɛɥɚɝɨɞɚɪɹ
ɤɨɪɪɟɥɹɰɢɹɦ ɦɟɠɞɭ ɤɨɧɮɢɝɭɪɚɰɢɹɦɢ ɛɥɢɡɤɨɪɚɫɩɨɥɨɠɟɧɧɵɯ ɚɬɨɦɨɜ. ɉɪɢ ɢɫɩɨɥɶɡɭɟɦɨɣ ɬɟɦɩɟɪɚɬɭɪɟ
85
Ïåðêîëÿöèÿ è ôàçîâûé ïåðåõîä â àìîðôíîì ...
ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï. 3 /35/
ɤɨɧɮɢɝɭɪɚɰɢɢ ɚɬɨɦɨɜ ɜ ɫɬɪɭɤɬɭɪɟ ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ ɩɨɫɬɨɹɧɧɨ ɦɟɧɹɸɬɫɹ, ɢɡ-ɡɚ ɱɟɝɨ ɤɥɚɫɬɟɪɵ 4-ɯ
ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ ɩɨɫɬɨɹɧɧɨ ɦɟɧɹɸɬ ɫɜɨɣ ɪɚɡɦɟɪ, ɪɚɡɛɢɜɚɹɫɶ ɧɚ ɦɚɥɟɧɶɤɢɟ ɤɥɚɫɬɟɪɵ, ɢ ɜɧɨɜɶ
ɨɛɴɟɞɢɧɹɹɫɶ ɜ ɛɨɥɶɲɢɟ. ɉɨɷɬɨɦɭ ɟɫɥɢ ɟɫɬɶ ɧɚɪɭɲɟɧɢɟ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɝɨ ɡɚɤɨɧɚ ɩɪɢ s § 5, ɬɨ ɜ ɦɟɧɶɲɟɣ
ɫɬɟɩɟɧɢ ɨɧɨ ɟɫɬɶ ɢ ɩɪɢ s § 100, ɨɞɧɚɤɨ ɫɥɚɛɚɹ ɫɬɚɬɢɫɬɢɤɚ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɧɟ ɩɨɡɜɨɥɹɟɬ ɷɬɨɝɨ ɭɜɢɞɟɬɶ. ɉɪɢ
ɜɨɡɧɢɤɧɨɜɟɧɢɢ ɛɨɥɶɲɨɝɨ ɩɟɪɤɨɥɹɰɢɨɧɧɨɝɨ ɤɥɚɫɬɟɪɚ ɤɨɥɢɱɟɫɬɜɨ ɭɡɥɨɜ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɢ
ɧɟɜɵɝɨɞɧɵɯ ɦɚɥɟɧɶɤɢɯ ɤɥɚɫɬɟɪɚɯ, ɪɟɡɤɨ ɭɦɟɧɶɲɚɟɬɫɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɵ ɫɜɹɡɵɜɚɟɦ ɫɤɚɱɤɨɨɛɪɚɡɧɨɟ
ɢɡɦɟɧɟɧɢɟ ɤɨɪɪɟɥɹɬɨɪɨɜ ɫ ɜɨɡɧɢɤɧɨɜɟɧɢɟɦ ɩɟɪɤɨɥɹɰɢɨɧɧɨɝɨ ɤɥɚɫɬɟɪɚ.
0.02
1000
100
0
n(s)
w44-w34
0.01
0.01
10
0.02
0.03
1
20
25
30
Ⱦɚɜɥɟɧɢɟ, Ƚɉɚ
35
0.1
Ɋɢɫ.5. ɉɚɪɧɵɟ ɤɨɪɪɟɥɹɰɢɢ ɜ ɩɟɪɜɨɣ
ɤɨɨɪɞɢɧɚɰɢɨɧɧɨɣ ɫɮɟɪɟ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɞɚɜɥɟɧɢɹ
ɜ ɫɬɪɭɤɬɭɪɚɯ ɚɋ ɞɨ Ɍȼ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ.
1
10
s
100
Ɋɢɫ.6. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɤɥɚɫɬɟɪɨɜ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ
2,18
ɩɨ ɪɚɡɦɟɪɭ. ɋɩɥɨɲɧɨɣ ɥɢɧɢɟɣ ɩɨɤɚɡɚɧɚ ɮɭɧɤɰɢɹ 1700 ˜ s
Ʉɨɧɰɟɧɬɪɚɰɢɹ sp3 ɚɬɨɦɨɜ, %
ɋɊȺȼɇȿɇɂȿ ɋ ɗɄɋɉȿɊɂɆȿɇɌɈɆ
ɇɚ ɪɢɫ. 7 ɞɚɧɨ ɫɪɚɜɧɟɧɢɟ ɩɨɥɭɱɟɧɧɨɣ ɜ ɷɬɨɣ
60
Ɇɚɝɧɟɬɪɨɧɧɨɟ ɧɚɩɵɥɟɧɢɟ
Ab initio
ɗɬɚ ɪɚɛɨɬɚ
ɪɚɛɨɬɟ
ɡɚɜɢɫɢɦɨɫɬɢ
ɤɨɧɰɟɧɬɪɚɰɢɢ
4-ɯ
ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ ɨɬ ɜɧɭɬɪɟɧɧɟɝɨ ɧɚɩɪɹɠɟɧɢɹ
ɜ ɫɬɪɭɤɬɭɪɟ aC ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɪɟɡɭɥɶɬɚɬɚɦɢ ɩɨ
ɦɚɝɧɟɬɪɨɧɧɨɦɭ ɧɚɩɵɥɟɧɢɸ ɩɥɟɧɨɤ ɚɋ [18,19], ɚ ɬɚɤɠɟ ɫ
50
ɪɟɡɭɥɶɬɚɬɚɦɢ ab initio ɦɨɞɟɥɢɪɨɜɚɧɢɹ [6]. Ɉɞɢɧ ɢɡ
ɦɟɬɨɞɨɜ ɫɨɡɞɚɧɢɹ aC – ɷɬɨ ɩɥɚɜɥɟɧɢɟ ɮɭɥɥɟɪɢɬɚ [20];
40
ɩɨɪɨɝɨɜɨɟ
ɞɚɜɥɟɧɢɟ
ɚɥɦɚɡɨɩɨɞɨɛɧɨɝɨ
30
ɞɥɹ
ɭɝɥɟɪɨɞɚ
ɜ
ɷɬɨɦ
ɮɨɪɦɢɪɨɜɚɧɢɹ
ɷɤɫɩɟɪɢɦɟɧɬɟ
ɫɨɫɬɚɜɥɹɟɬ 8 Ƚɉɚ ɢ ɯɨɪɨɲɨ ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɩɨɥɭɱɟɧɧɵɦ
20
ɧɚɦɢ ɩɨɪɨɝɨɜɵɦ ɞɚɜɥɟɧɢɟɦ 10-14 Ƚɉɚ. Ɂɚɦɟɬɢɦ, ɱɬɨ
ɧɚɣɞɟɧɧɨɟ ɡɧɚɱɟɧɢɹ ɞɚɜɥɟɧɢɟ ɛɥɢɡɤɨ ɤ ɞɚɜɥɟɧɢɸ ɜ
10
ɬɪɨɣɧɨɣ ɬɨɱɤɟ ɪɚɜɧɨɜɟɫɢɹ ɝɪɚɮɢɬ-ɚɥɦɚɡ-ɠɢɞɤɨɫɬɶ (P =
2 4 6 8 10 12 14 16 18 20 22
ɇɚɩɪɹɠɟɧɢɟ, Ƚɉɚ
Ɋɢɫ.7. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɧɰɟɧɬɪɚɰɢɢ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ
ɚɬɨɦɨɜ ɜ ɫɬɪɭɤɬɭɪɟ ɚɋ ɨɬ ɜɧɭɬɪɟɧɧɟɝɨ ɧɚɩɪɹɠɟɧɢɹ.
Ÿ - ɧɚɩɵɥɟɧɢɟ ɦɚɝɧɟɬɪɨɧɧɵɦ ɪɚɫɩɵɥɟɧɢɟɦ [18,19] ,
Ŷ – an-inito ɦɨɞɟɥɢɪɨɜɚɧɢɟ[6],
Ɣ – ɫɬɪɭɤɬɭɪɵ ɭɪɚɜɧɨɜɟɲɟɧɧɵɟ ɦɟɬɨɞɨɦ Ɍȼ
13 Ƚɉɚ, T = 3700 K) [21].
ɑɚɳɟ ɜɫɟɝɨ ɤɨɧɰɟɧɬɪɚɰɢɹ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ
ɚɬɨɦɨɜ ɜ ɚɥɦɚɡɨɩɨɞɨɛɧɨɦ ɭɝɥɟɪɨɞɟ ɡɧɚɱɢɬɟɥɶɧɨ ɜɵɲɟ,
ɱɟɦ ɜ ɝɪɚɮɢɬɨɩɨɞɨɛɧɨɦ. ɗɬɨ ɯɨɪɨɲɨ ɜɢɞɧɨ ɢɡ ɪɢɫ. 7.
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ
ɜ
ɚɥɦɚɡɨɩɨɞɨɛɧɨɦ
ɚɋ
ɛɵɥ
ɨɛɧɚɪɭɠɟɧ ɩɢɤ Ɋɚɦɚɧɨɜɫɤɨɝɨ ɪɚɫɫɟɹɧɢɹ ɩɪɢɦɟɪɧɨ ɩɪɢ
1150 ɫɦ , ɤɨɬɨɪɵɣ ɧɟɤɨɬɨɪɵɟ ɚɜɬɨɪɵ ɫɜɹɡɵɜɚɸɬ ɫ ɧɚɥɢɱɢɟɦ ɚɥɦɚɡɧɵɯ ɤɪɢɫɬɚɥɥɢɱɟɫɤɢɯ ɜɤɥɸɱɟɧɢɣ [18, 22-25].
-1
86
Ì.Ñ. Áûøêèí, À.Ñ. Áàêàé, À.À. Òóðêèí
«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 781, 2007
ȼ ɪɚɛɨɬɟ [8] ɛɵɥɚ ɢɫɫɥɟɞɨɜɚɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɚɥɦɚɡɧɵɯ ɧɚɧɨɤɪɢɫɬɚɥɥɨɜ, ɜɧɟɞɪɟɧɧɵɯ ɜ ɩɟɪɟɨɯɥɚɠɞɟɧɧɭɸ
ɠɢɞɤɨɫɬɶ ɭɝɥɟɪɨɞɚ, ɢ ɛɵɥɨ ɨɛɧɚɪɭɠɟɧɨ, ɱɬɨ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ ɦɟɧɟɟ 5000 K ɢɯ ɭɫɬɨɣɱɢɜɨɫɬɶ ɨɩɪɟɞɟɥɹɟɬɫɹ
ɫɭɳɟɫɬɜɨɜɚɧɢɟɦ ɜ ɫɬɪɭɤɬɭɪɟ ɠɢɞɤɨɫɬɢ ɩɟɪɤɨɥɹɰɢɨɧɧɨɝɨ ɤɥɚɫɬɟɪɚ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ. ȼ ɫɬɪɭɤɬɭɪɚɯ
aC ɧɚ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɢ ɨɬ ɞɚɜɥɟɧɢɹ ɦɵ ɧɟ ɨɛɧɚɪɭɠɢɥɢ ɡɚɦɟɬɧɨɝɨ ɫɤɚɱɤɚ, ɩɨɫɤɨɥɶɤɭ ɜɪɟɦɹ
ɨɬɠɢɝɚ ɛɵɥɨ ɫɥɢɲɤɨɦ ɦɚɥɟɧɶɤɢɦ ɞɥɹ ɨɛɪɚɡɨɜɚɧɢɹ ɜ ɷɬɢɯ ɫɬɪɭɤɬɭɪɚɯ ɧɚɧɨɤɪɢɫɬɚɥɥɨɜ ɚɥɦɚɡɚ. ɉɨ-ɜɢɞɢɦɨɦɭ,
ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɞɥɢɬɟɥɶɧɨɦ ɨɬɠɢɝɟ ɜ ɬɟɯ ɫɬɪɭɤɬɭɪɚɯ ɚɋ, ɜ ɤɨɬɨɪɵɯ ɫɭɳɟɫɬɜɭɟɬ ɩɟɪɤɨɥɹɰɢɨɧɧɵɣ ɤɥɚɫɬɟɪ, ɛɭɞɭɬ
ɨɛɪɚɡɨɜɵɜɚɬɶɫɹ ɭɫɬɨɣɱɢɜɵɟ ɤɪɢɫɬɚɥɥɢɬɵ ɚɥɦɚɡɚ, ɢɡ-ɡɚ ɱɟɝɨ ɧɚ ɡɚɜɢɫɢɦɨɫɬɹɯ ɨɬ ɞɚɜɥɟɧɢɹ ɛɭɞɭɬ ɢɡɦɟɧɹɬɶɫɹ
ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɶ, ɩɥɨɬɧɨɫɬɶ, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɢ ɞɪɭɝɢɟ ɫɜɨɣɫɬɜɚ ɚɋ (ɭɩɪɭɝɢɟ, ɨɩɬɢɱɟɫɤɢɟ ɢ ɷɥɟɤɬɪɢɱɟɫɤɢɟ).
ȼɕȼɈȾɕ
1. Ɉɛɧɚɪɭɠɟɧɵ ɨɫɨɛɟɧɧɨɫɬɢ ɧɚ ɡɚɜɢɫɢɦɨɫɬɹɯ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ aC ɨɬ ɞɚɜɥɟɧɢɹ. ɇɟɡɚɜɢɫɢɦɨ ɨɬ
ɫɩɨɫɨɛɚ ɩɪɢɝɨɬɨɜɥɟɧɢɹ aC ɩɪɢ ɞɚɜɥɟɧɢɢ ɩɪɢɦɟɪɧɨ 30 Ƚɉa ɫɤɚɱɤɨɦ ɢɡɦɟɧɹɟɬɫɹ ɧɚɤɥɨɧ ɡɚɜɢɫɢɦɨɫɬɟɣ
ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɢ, ɷɧɟɪɝɢɢ ɫɜɹɡɢ ɢ ɭɞɟɥɶɧɨɝɨ ɨɛɴɟɦɚ ɚɦɨɪɮɧɨɝɨ ɭɝɥɟɪɨɞɚ ɨɬ ɞɚɜɥɟɧɢɹ. ɉɨɤɚɡɚɧɨ, ɱɬɨ ɩɪɢ
ɷɬɨɦ ɞɚɜɥɟɧɢɢ ɨɛɪɚɡɭɟɬɫɹ ɩɟɪɤɨɥɹɰɢɨɧɧɵɣ ɤɥɚɫɬɟɪ 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ ɢ ɩɚɪɧɵɟ ɤɨɪɪɟɥɹɬɨɪɵ
ɢɡɦɟɧɹɸɬɫɹ ɫɤɚɱɤɨɦ.
2. ɋɨɜɩɚɞɟɧɢɟ ɨɛɧɚɪɭɠɟɧɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ ɩɟɪɤɨɥɹɰɢɨɧɧɨɝɨ ɤɥɚɫɬɟɪɚ ɧɚɛɥɸɞɚɟɬɫɹ ɧɟ
ɬɨɥɶɤɨ ɩɪɢ ɆȾ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɫ ɩɨɦɨɳɶɸ ɷɦɩɢɪɢɱɟɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɚ Ɍɟɪɫɨɮɮɚ, ɧɨ ɢ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɩɨ
ɦɟɬɨɞɭ ɠɟɫɬɤɢɯ ɫɜɹɡɟɣ Ɍȼ. ɉɨɫɥɟ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ ɫɬɪɭɤɬɭɪ ɚɋ ɦɟɬɨɞɨɦ Ɍȼ ɩɪɢ ɞɚɜɥɟɧɢɢ ɩɪɢɦɟɪɧɨ 13 Ƚɉa
ɨɞɧɨɜɪɟɦɟɧɧɨ ɫ ɢɡɦɟɧɟɧɢɟɦ ɧɚɤɥɨɧɚ ɡɚɜɢɫɢɦɨɫɬɟɣ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɢ, ɷɧɟɪɝɢɢ ɫɜɹɡɢ ɢ ɭɞɟɥɶɧɨɝɨ ɨɛɴɟɦɚ ɨɬ
ɞɚɜɥɟɧɢɟ ɧɚɛɥɸɞɚɥɫɹ ɫɤɚɱɨɤ ɭɩɪɭɝɨɝɨ ɫɞɜɢɝɨɜɨɝɨ ɦɨɞɭɥɹ ɢ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɨɫɬɢ.
3. ɉɪɟɞɥɨɠɟɧɨ ɨɛɴɹɫɧɟɧɢɟ ɫɜɹɡɢ ɩɟɪɤɨɥɹɰɢɨɧɧɨɝɨ ɮɟɧɨɦɟɧɚ ɫ ɨɫɨɛɟɧɧɨɫɬɹɦɢ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɯ
ɫɜɨɣɫɬɜ ɢ ɫɤɚɱɤɨɨɛɪɚɡɧɵɦ ɢɡɦɟɧɟɧɢɟɦ ɤɨɪɪɟɥɹɬɨɪɨɜ: 4-ɯ ɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɦ ɚɬɨɦɚɦ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢ
ɜɵɝɨɞɧɨ ɨɛɪɚɡɨɜɵɜɚɬɶ ɛɨɥɶɲɢɟ ɤɥɚɫɬɟɪɵ.
4. ɉɨɥɭɱɟɧɧɵɟ ɪɟɡɭɥɶɬɚɬɵ ɭɤɚɡɵɜɚɸɬ ɧɚ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɮɚɡɨɜɨɝɨ ɩɟɪɟɯɨɞɚ ɜ aC. ɇɚɣɞɟɧɧɵɟ ɡɧɚɱɟɧɢɹ
ɞɚɜɥɟɧɢɟ 13 Ƚɉa ɢ ɤɨɧɰɟɧɬɪɚɰɢɢ sp3 ɚɬɨɦɨɜ 30–40%, ɩɪɢ ɤɨɬɨɪɵɯ ɧɢɡɤɨɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɣ aC ɩɟɪɟɯɨɞɢɬ ɜ
ɜɵɫɨɤɨɤɨɨɪɞɢɧɢɪɨɜɚɧɧɵɣ, ɯɨɪɨɲɨ ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ.
ȼ ɞɚɥɶɧɟɣɲɟɣ ɪɚɛɨɬɟ ɩɥɚɧɢɪɭɟɬɫɹ ɩɪɢɦɟɧɢɬɶ ɦɟɬɨɞ ɦɨɥɟɤɭɥɹɪɧɨɣ ɞɢɧɚɦɢɤɢ ɞɥɹ ɢɡɭɱɟɧɢɹ ɧɚɧɨɫɬɪɭɤɬɭɪ
ɭɝɥɟɪɨɞɚ ɢ ɧɚɧɨɫɬɪɭɤɬɭɪɧɵɯ ɦɚɬɟɪɢɚɥɨɜ.
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PERCOLATION AND PHASE TRANSITION IN AMORPHOUS CARBON. MOLECULAR-DYNAMICAL
SIMULATION
M.S. Byshkin, A.S. Bakai, A.A. Turkin
National Science Center Kharkov Institute of Physics and Technology, 61108 Kharkov, Ukraine
E-mail: byshkin@kipt.kharkov.ua
The molecular-dynamical investigation of amorphous carbon formed by quenching the melt is performed. The peculiarities are found
on the pressure dependences of physical properties of amorphous carbon. It is shown, that these peculiarities are observed at the
pressure value at which the percolation cluster of atoms in sp3 configuration arises and correlation of configurations of neighboring
atoms changes in jump-like manner. The values of concentration of 4-fold coordinated atoms 30-40 % and pressure 13 GPa, at which
the peculiarities are observed, are in a good agreement with results of other authors.
KEY WORDS: glass transition, percolation, phase transition, atom configuration, nanocrystal.