расчет предельных коэффициентов распределения примесей в

82
«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 746, 2006
ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï. 4 /32/
Â.Ì. Àæàæà, Ã.Ï. Êîâòóí, À.Ï. Ùåðáàíü...
Ðàñ÷åò ïðåäåëüíûõ êîýôôèöèåíòîâ ðàñïðåäåëåíèÿ...
ɍȾɄ 669.297
ɊȺɋɑȿɌ ɉɊȿȾȿɅɖɇɕɏ ɄɈɗɎɎɂɐɂȿɇɌɈȼ ɊȺɋɉɊȿȾȿɅȿɇɂə ɉɊɂɆȿɋȿɃ ȼ
ɐɂɊɄɈɇɂɂ ɂ ȽȺɎɇɂɂ
ȼ.Ɇ. Ⱥɠɚɠɚ, Ƚ.ɉ. Ʉɨɜɬɭɧ, Ⱥ.ɉ. ɓɟɪɛɚɧɶ, Ɉ.Ⱥ. Ⱦɚɰɟɧɤɨ, Ⱦ.Ⱥ. ɋɨɥɨɩɢɯɢɧ
ɇɚɰɢɨɧɚɥɶɧɵɣ ɇɚɭɱɧɵɣ ɐɟɧɬɪ “ɏɚɪɶɤɨɜɫɤɢɣ ɮɢɡɢɤɨ-ɬɟɯɧɢɱɟɫɤɢɣ ɢɧɫɬɢɬɭɬ”,
ɭɥ. Ⱥɤɚɞɟɦɢɱɟɫɤɚɹ 1, ɝ. ɏɚɪɶɤɨɜ, 61108, ɍɤɪɚɢɧɚ
E-mail: shcherban@kipt.kharkov.ua
ɉɨɫɬɭɩɢɥɚ ɜ ɪɟɞɚɤɰɢɸ 14 ɧɨɹɛɪɹ 2006 ɝ.
ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɩɪɟɞɫɬɚɜɥɟɧɵ ɪɚɫɱɟɬɵ ɩɪɟɞɟɥɶɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɨɬɞɟɥɶɧɵɯ ɩɪɢɦɟɫɟɣ ɤ0 limB ɜ Zr ɢ Hf
ɦɟɬɨɞɚɦɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɚɧɚɥɢɡɚ ɞɢɚɝɪɚɦɦ ɫɨɫɬɨɹɧɢɹ ɢ ɝɪɚɮɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ ɷɤɫɬɪɚɩɨɥɹɰɢɢ ɥɢɧɢɣ ɫɨɥɢɞɭɫɚ ɢ ɥɢɤɜɢɞɭɫɚ ɧɚ ɧɭɥɟɜɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ. ɉɨɤɚɡɚɧɨ ɫɨɜɩɚɞɟɧɢɟ ɡɧɚɱɟɧɢɣ ɤ0 limB, ɨɩɪɟɞɟɥɟɧɧɵɯ ɷɬɢɦɢ ɪɚɫɱɟɬɧɵɦɢ ɦɟɬɨɞɚɦɢ. ɉɨɥɭɱɟɧɧɵɟ ɞɚɧɧɵɟ ɩɨ ɡɧɚɱɟɧɢɹɦ ɩɪɟɞɟɥɶɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢɫɫɥɟɞɭɟɦɵɯ ɩɪɢɦɟɫɟɣ ɜ Zr ɢ Hf ɪɚɫɲɢɪɹɸɬ ɤɪɭɝ
ɫɢɫɬɟɦ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɯ ɢɧɬɟɪɟɫ ɞɥɹ ɨɰɟɧɤɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɤɪɢɬɚɥɥɢɡɚɰɢɨɧɧɨɣ ɨɱɢɫɬɤɢ ɷɬɢɯ ɦɟɬɚɥɥɨɜ. Ɉɩɪɟɞɟɥɟɧɵ ɬɟɦɩɟɪɚɬɭɪɧɵɟ ɢ ɤɨɧɰɟɧɬɪɚɰɢɨɧɧɵɟ ɩɚɪɚɦɟɬɪɵ ɞɨɫɬɢɠɟɧɢɹ ɩɪɟɞɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɤ0 limB ɩɪɢɦɟɫɟɣ ɜ ɷɬɢɯ ɦɟɬɚɥɥɚɯ.
ɄɅɘɑȿȼɕȿ ɋɅɈȼȺ: ɰɢɪɤɨɧɢɣ, ɝɚɮɧɢɣ, ɤɨɷɮɮɢɰɢɟɧɬɵ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɤɪɢɫɬɚɥɥɢɡɚɰɢɹ, ɞɢɚɝɪɚɦɦɵ ɫɨɫɬɨɹɧɢɹ, ɩɪɢɦɟɫɢ, ɪɚɫɬɜɨɪɢɦɨɫɬɶ, ɪɚɮɢɧɢɪɨɜɚɧɢɟ.
ɂɧɬɟɪɟɫ ɤ ɱɢɫɬɵɦ ɰɢɪɤɨɧɢɸ ɢ ɝɚɮɧɢɸ ɫɜɹɡɚɧ ɩɪɟɠɞɟ ɜɫɟɝɨ ɫ ɲɢɪɨɤɢɦ ɩɪɢɦɟɧɟɧɢɟɦ ɢɯ ɜ ɚɬɨɦɧɨɣ ɷɧɟɪɝɟɬɢɤɟ ɜ ɤɚɱɟɫɬɜɟ ɤɨɧɫɬɪɭɤɰɢɨɧɧɵɯ ɦɚɬɟɪɢɚɥɨɜ – ɨɛɨɥɨɱɟɤ ɬɨɩɥɢɜɧɵɯ ɷɥɟɦɟɧɬɨɜ (Zr) ɢ ɩɨɝɥɨɳɚɸɳɢɯ ɫɬɟɪɠɧɟɣ
ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɢ ɡɚɳɢɬɵ ɚɬɨɦɧɵɯ ɪɟɚɤɬɨɪɨɜ (Hf). ɂɫɩɨɥɶɡɨɜɚɧɢɟ Zr ɢ Hf ɜ ɚɬɨɦɧɨɣ ɷɧɟɪɝɟɬɢɤɟ ɢ ɞɪɭɝɢɯ
ɨɛɥɚɫɬɹɯ ɬɟɯɧɢɤɢ ɬɚɤɢɯ, ɤɚɤ ɤɨɫɦɢɱɟɫɤɨɣ, ɯɢɦɢɱɟɫɤɨɣ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ, ɷɥɟɤɬɪɨɧɢɤɟ ɜɵɞɜɢɝɚɸɬ ɩɨɜɵɲɟɧɧɵɟ
ɬɪɟɛɨɜɚɧɢɹ ɤ ɱɢɫɬɨɬɟ ɷɬɢɯ ɦɟɬɚɥɥɨɜ.
Ɉɞɧɢɦ ɢɡ ɫɩɨɫɨɛɨɜ ɩɨɜɵɲɟɧɢɹ ɱɢɫɬɨɬɵ ɦɟɬɚɥɥɨɜ ɹɜɥɹɟɬɫɹ ɡɨɧɧɚɹ ɩɥɚɜɤɚ ɜ ɜɚɤɭɭɦɟ. ȼɚɠɧɵɦ ɩɚɪɚɦɟɬɪɨɦ,
ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɦ ɩɨɜɟɞɟɧɢɟ ɩɪɢɦɟɫɢ ɩɪɢ ɤɪɢcɬɚɥɥɢɡɚɰɢɨɧɧɨɣ ɨɱɢɫɬɤɟ, ɹɜɥɹɟɬɫɹ ɟɟ ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ (ɄɊ). ɉɨ ɢɡɜɟɫɬɧɵɦ ɡɧɚɱɟɧɢɹɦ ɄɊ ɦɨɠɧɨ ɡɚɪɚɧɟɟ ɤɚɱɟɫɬɜɟɧɧɨ ɨɰɟɧɢɜɚɬɶ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɩɪɨɰɟɫɫɚ ɤɪɢɫɬɚɥɥɢɡɚɰɢɨɧɧɨɣ ɨɱɢɫɬɤɢ ɢ ɞɨɫɬɢɝɚɟɦɭɸ ɱɢɫɬɨɬɭ ɪɚɮɢɧɢɪɭɟɦɨɝɨ ɦɟɬɚɥɥɚ. Ⱦɥɹ ɞɟɬɚɥɶɧɵɯ ɠɟ ɪɚɫɱɟɬɨɜ ɜɥɢɹɧɢɹ ɭɫɥɨɜɢɣ ɧɚɩɪɚɜɥɟɧɧɨɣ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ (ɇɄ) ɧɚ ɝɥɭɛɨɤɭɸ ɨɱɢɫɬɤɭ ɦɟɬɚɥɥɨɜ ɢ ɪɚɫɱɟɬɨɜ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɨɱɢɫɬɤɢ ɜ
ɤɚɱɟɫɬɜɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɜɫɟɝɞɚ ɢɫɩɨɥɶɡɭɸɬɫɹ ɡɧɚɱɟɧɢɹ ɄɊ.
ȼ ɥɢɬɟɪɚɬɭɪɟ ɨɩɟɪɢɪɭɸɬ ɬɪɟɦɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɄɊ. ɗɮɮɟɤɬɢɜɧɵɣ ɄɊ ɩɪɢɦɟɫɢ ɤȼ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ
ɨɬɧɨɲɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɪɢɦɟɫɢ ɜ ɧɚɱɚɥɶɧɨɣ ɢ ɤɨɧɟɱɧɨɣ ɱɚɫɬɢ ɫɥɢɬɤɚ. ȼɟɥɢɱɢɧɚ ɤȼ ɦɨɠɟɬ ɛɵɬɶ ɛɨɥɶɲɟ ɢɥɢ
ɦɟɧɶɲɟ ɟɞɢɧɢɰɵ ɢ ɡɚɜɢɫɢɬ ɨɬ ɭɫɥɨɜɢɣ ɡɚɬɜɟɪɞɟɜɚɧɢɹ – ɫɤɨɪɨɫɬɢ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ ɢ ɫɬɟɩɟɧɢ ɩɟɪɟɦɟɲɢɜɚɧɢɹ
ɠɢɞɤɨɫɬɢ. Ɂɧɚɱɟɧɢɟ ɷɮɮɟɤɬɢɜɧɨɝɨ ɄɊ ɩɪɢɦɟɫɢ ɤȼ ɧɟ ɹɜɥɹɟɬɫɹ “ɢɧɜɚɪɢɚɧɬɨɦ” ɤɨɧɤɪɟɬɧɨɣ ɫɢɫɬɟɦɵ ɨɫɧɨɜɚɩɪɢɦɟɫɶ ɢ, ɩɨ ɷɬɨɣ ɩɪɢɱɢɧɟ, ɜɟɥɢɱɢɧɵ ɤȼ ɞɥɹ ɪɚɡɧɵɯ ɭɫɥɨɜɢɣ ɇɄ ɧɟɥɶɡɹ ɫɪɚɜɧɢɜɚɬɶ ɦɟɠɞɭ ɫɨɛɨɣ ɢ ɢɦɢ ɧɟɥɶɡɹ
ɨɩɟɪɢɪɨɜɚɬɶ ɜ ɩɨɫɬɪɨɟɧɢɢ ɤɚɤɢɯ–ɥɢɛɨ ɡɚɜɢɫɢɦɨɫɬɟɣ, ɤɨɪɪɟɥɹɰɢɣ ɢ ɬ.ɩ. Ɂɧɚɱɟɧɢɹ ɤȼ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ
ɬɨɥɶɤɨ ɞɥɹ ɝɪɭɛɨɣ ɨɰɟɧɤɢ ɩɨɜɟɞɟɧɢɹ ɩɪɢɦɟɫɟɣ ɩɪɢ ɨɱɢɫɬɤɟ ɜɟɳɟɫɬɜɚ. ɗɮɮɟɤɬɢɜɧɵɟ ɄɊ ɩɪɢɦɟɫɟɣ ɤȼ ɨɩɪɟɞɟɥɹɸɬɫɹ ɬɨɥɶɤɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɩɭɬɟɦ.
Ɉɞɧɢɦ ɢɡ ɜɚɠɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɪɨɰɟɫɫɨɜ ɇɄ ɹɜɥɹɸɬɫɹ ɪɚɜɧɨɜɟɫɧɵɟ ɄɊ ɩɪɢɦɟɫɟɣ ɤ0ȼ, ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɸɬɫɹ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɦɢ ɫɜɨɣɫɬɜɚɦɢ ɨɫɧɨɜɧɨɝɨ ɤɨɦɩɨɧɟɧɬɚ Ⱥ ɢ ɩɪɢɦɟɫɢ ȼ ɩɪɢ ɫɤɨɪɨɫɬɢ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ,
ɪɚɜɧɨɣ ɢɥɢ ɛɥɢɡɤɨɣ ɧɭɥɸ. Ɋɚɜɧɨɜɟɫɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɪɢɦɟɫɢ ɤ0ȼ ɪɚɜɟɧ ɨɬɧɨɲɟɧɢɸ ɪɚɜɧɨɜɟɫɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɣ ɞɚɧɧɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɞɜɭɯ ɫɨɫɟɞɫɬɜɭɸɳɢɯ ɮɚɡɚɯ, ɚ ɧɟ ɤɨɧɰɟɧɬɪɚɰɢɣ ɜɨɨɛɳɟ. ɏɨɬɹ ɧɚ ɩɪɚɤɬɢɤɟ ɪɚɜɧɨɜɟɫɧɨɟ ɡɚɬɜɟɪɞɟɜɚɧɢɟ ɪɟɞɤɨ ɞɨɫɬɢɝɚɟɬɫɹ, ɬ.ɤ. ɫɤɨɪɨɫɬɶ ɞɢɮɮɭɡɢɢ ɜ ɬɜɟɪɞɨɦ ɫɨɫɬɨɹɧɢɢ ɨɛɵɱɧɨ ɦɚɥɚ,
ɞɥɹ ɨɰɟɧɤɢ ɪɚɮɢɧɢɪɭɸɳɟɝɨ ɞɟɣɫɬɜɢɹ ɇɄ ɜɟɳɟɫɬɜɚ ɮɭɧɞɚɦɟɧɬɚɥɶɧɭɸ ɢ ɩɪɚɤɬɢɱɟɫɤɭɸ ɰɟɧɧɨɫɬɶ ɤɚɤ ɨɩɨɪɧɵɣ
ɫɩɪɚɜɨɱɧɵɣ ɦɚɬɟɪɢɚɥ ɢɦɟɸɬ ɢɦɟɧɧɨ ɪɚɜɧɨɜɟɫɧɵɟ ɄɊ ɩɪɢɦɟɫɟɣ ɤ0ȼ. Ɋɚɜɧɨɜɟɫɧɵɟ ɡɧɚɱɟɧɢɹ ɤ0ȼ ɨɩɪɟɞɟɥɹɸɬɫɹ,
ɤɚɤ ɩɪɚɜɢɥɨ, ɢɡ ɞɜɨɣɧɵɯ ɞɢɚɝɪɚɦɦ ɫɨɫɬɨɹɧɢɹ (Ⱦɋ) ɨɫɧɨɜɚ – ɩɪɢɦɟɫɶ, ɢɥɢ ɷɤɫɬɪɚɩɨɥɹɰɢɟɣ ɧɚ ɧɭɥɟɜɭɸ ɫɤɨɪɨɫɬɶ
ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɩɪɟɞɟɥɹɟɦɵɯ ɷɮɮɟɤɬɢɜɧɵɯ ɄɊ ɩɪɢɦɟɫɟɣ ɤȼ.
ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɞɨ ɨɛɥɚɫɬɢ ɩɪɟɞɟɥɶɧɨ ɪɚɡɛɚɜɥɟɧɧɵɯ ɪɚɫɬɜɨɪɨɜ ɥɢɧɢɢ ɥɢɤɜɢɞɭɫɚ ɢ ɫɨɥɢɞɭɫɚ Ⱦɋ ɧɟ
ɩɪɹɦɨɥɢɧɟɣɧɵ ɢ ɜɟɥɢɱɢɧɚ ɤ0ȼ ɡɚɜɢɫɢɬ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɪɢɦɟɫɧɨɝɨ ɷɥɟɦɟɧɬɚ. ɉɪɢ ɩɪɟɞɟɥɶɧɨɦ ɠɟ ɫɧɢɠɟɧɢɢ
ɫɨɞɟɪɠɚɧɢɹ ɩɪɢɦɟɫɧɨɝɨ ɷɥɟɦɟɧɬɚ ɤ0ȼ ɛɭɞɟɬ ɫɬɪɟɦɢɬɶɫɹ ɤ ɫɜɨɟɦɭ ɩɨɫɬɨɹɧɧɨɦɭ ɩɪɟɞɟɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ ɤ0 limB,
ɨɩɪɟɞɟɥɟɧɢɟ ɤɨɬɨɪɨɝɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɡɧɚɱɢɬɟɥɶɧɵɣ ɢɧɬɟɪɟɫ ɩɪɢ ɝɥɭɛɨɤɨɣ ɨɱɢɫɬɤɟ ɦɟɬɚɥɥɨɜ.
Ⱦɥɹ Zr ɢ Hf ɩɪɟɞɟɥɶɧɵɟ ɄɊ ɩɪɢɦɟɫɟɣ ɤ0 limB ɢɡɜɟɫɬɧɵ ɞɥɹ ɧɟɦɧɨɝɢɯ ɷɥɟɦɟɧɬɨɜ ɢ ɱɚɫɬɨ ɥɢɲɶ ɨɪɢɟɧɬɢɪɨɜɨɱɧɨ. Ɍɚɤ, ɜ ɰɢɪɤɨɧɢɢ ɨɩɪɟɞɟɥɟɧɵ ɡɧɚɱɟɧɢɹ ɤ0 limB ɬɨɥɶɤɨ ɞɥɹ ɬɚɤɢɯ ɩɪɢɦɟɫɟɣ, ɤɚɤ (Al, Fe, V, Cu, Nb, Mo, Sn,
Pt). Ⱦɥɹ ɝɚɮɧɢɹ ɤɨɥɢɱɟɫɬɜɨ ɩɪɢɦɟɫɟɣ ɫ ɢɡɜɟɫɬɧɵɦ ɡɧɚɱɟɧɢɟɦ ɤ0 limB ɡɧɚɱɢɬɟɥɶɧɨ ɲɢɪɟ (B, C, Al, Si, Ti, V, Cr,
Mn, Fe, Co, Ni ɢ ɞɪ.) [1 ɫ. 285-260, 2 ɫ. 285, 3]. Ɉɞɧɚɤɨ ɫɩɟɤɬɪ ɜɚɠɧɵɯ ɩɪɢɦɟɫɧɵɯ ɷɥɟɦɟɧɬɨɜ ɜ Zr ɢ Hf ɧɟ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɭɤɚɡɚɧɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ ɢ ɡɧɚɧɢɟ ɩɪɟɞɟɥɶɧɵɯ ɄɊ ɤ0 limB ɞɪɭɝɢɯ ɩɪɢɦɟɫɟɣ ɜ ɷɬɢɯ ɦɟɬɚɥɥɚɯ ɬɚɤɠɟ
ɩɪɟɞɫɬɚɜɥɹɟɬ ɩɪɚɤɬɢɱɟɫɤɢɣ ɢɧɬɟɪɟɫ.
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Ðàñ÷åò ïðåäåëüíûõ êîýôôèöèåíòîâ ðàñïðåäåëåíèÿ...
ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï. 4 /32/
ɐɟɥɶɸ ɞɚɧɧɨɣ ɪɚɛɨɬɵ ɹɜɥɹɟɬɫɹ ɪɚɫɱɟɬ ɩɪɟɞɟɥɶɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɪɢɦɟɫɟɣ ɤ0 limB ɜ ɰɢɪɤɨɧɢɢ ɢ ɝɚɮɧɢɢ ɫ ɩɨɦɨɳɶɸ ɤɜɚɞɪɚɬɢɱɧɨɣ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɥɢɧɢɣ ɫɨɥɢɞɭɫɚ ɢ ɥɢɤɜɢɞɭɫɚ ɞɢɚɝɪɚɦɦ ɫɨɫɬɨɹɧɢɹ
ɞɜɨɣɧɵɯ ɫɢɫɬɟɦ ɢ ɦɟɬɨɞɨɦ ɝɪɚɮɢɱɟɫɤɨɣ ɷɤɫɬɪɚɩɨɥɹɰɢɢ ɷɬɢɯ ɥɢɧɢɣ ɜ ɨɛɥɚɫɬɢ ɦɚɥɵɯ ɤɨɧɰɟɧɬɪɚɰɢɣ.
ɆȿɌɈȾɂɄȺ ɊȺɋɑȿɌɈȼ
Ⱦɥɹ ɪɚɫɱɟɬɨɜ ɤ0 limB ɜ ɰɢɪɤɨɧɢɢ ɢ ɝɚɮɧɢɢ ɩɪɢɦɟɧɹɥɫɹ ɦɟɬɨɞ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɚɧɚɥɢɡɚ ɢ ɝɪɚɮɢɱɟɫɤɨɣ ɷɤɫɬɪɚɩɨɥɹɰɢɢ ɬɟɦɩɟɪɚɬɭɪɧɨ-ɤɨɧɰɟɧɬɪɚɰɢɨɧɧɵɯ ɤɪɢɜɵɯ ɪɚɫɬɜɨɪɢɦɨɫɬɢ ɩɪɢɦɟɫɢ ɜ ɠɢɞɤɨɣ ɢ ɬɜɟɪɞɨɣ ɮɚɡɚɯ ɜ ɬɨɱɤɟ
ɢɯ ɩɟɪɟɫɟɱɟɧɢɹ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ ɩɥɚɜɥɟɧɢɹ ɱɢɫɬɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɌɆȺ, ɬ.ɟ. ɤɨɝɞɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɪɢɦɟɫɢ ȼ ɫɬɪɟɦɢɬɫɹ ɤ ɧɭɥɸ [1, 4-6].
ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɮɨɪɦɚ ɥɢɧɢɣ ɫɨɥɢɞɭɫɚ ɢ ɥɢɤɜɢɞɭɫɚ ɞɢɚɝɪɚɦɦ ɫɨɫɬɨɹɧɢɹ (Ⱦɋ) ɡɚɜɢɫɢɦɨɫɬɢ ɬɟɦɩɟɪɚɬɭɪɵ
ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɪɢɦɟɫɢ ɫ ɞɨɫɬɚɬɨɱɧɨɣ ɬɨɱɧɨɫɬɶɸ ɜɵɪɚɠɚɸɬɫɹ ɩɨɥɢɧɨɦɚɦɢ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ:
TS
2
pSB ˜ x*SB
qSB ˜ x*SB TMA ,
(1)
TL
2
pLB ˜ x*LB
q LB ˜ x*LB TMA ,
(2)
ɝɞɟ x*SB, x*LB - ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɪɢɦɟɫɟɣ ɜ ɬɜɟɪɞɨɣ ɢ ɠɢɞɤɨɣ ɮɚɡɚɯ ɜ ɚɩɩɪɨɤɫɢɦɢɪɭɸɳɢɯ ɭɪɚɜɧɟɧɢɹɯ, ɚɬ. %; pSB,
qSB, pLB, qLB - ɤɨɷɮɮɢɰɢɟɧɬɵ ɪɟɝɪɟɫɫɢɢ.
ɍɪɚɜɧɟɧɢɹ (1) ɢ (2) ɜɜɟɞɟɧɢɟɦ ɪɚɡɧɨɫɬɢ ɬɟɦɩɟɪɚɬɭɪ ɌɆȺ – ɌS = 'TS ɢ ɌɆȺ – ɌL = 'TL, ɩɪɟɨɛɪɚɡɭɸɬɫɹ ɤ ɜɢɞɭ:
*2
* ,
(3)
'TS pSB ˜ xSB
q SB ˜ xSB
'TL
2
p LB ˜ x*LB
q LB ˜ x*LB.
(4)
ɉɨɫɤɨɥɶɤɭ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ ɪɚɜɧɨɜɟɫɧɵɣ ɄɊ ɤ0ȼ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɢɡɨɬɟɪɦɢɱɟɫɤɨɟ ɨɬɧɨɲɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɪɢɦɟɫɢ x*SB/x*LB, ɞɨɥɠɧɨ ɫɨɛɥɸɞɚɬɶɫɹ ɪɚɜɟɧɫɬɜɨ 'T = 'TL = 'T MA. ɂɡ ɭɪɚɜɧɟɧɢɣ (3) ɢ (4) ɜɵɜɨɞɢɬɫɹ
ɹɜɧɨɟ ɜɵɪɚɠɟɧɢɟ ɪɚɜɧɨɜɟɫɧɨɝɨ ɄɊ ɤɚɤ ɮɭɧɤɰɢɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɪɢɦɟɫɢ:
k 0B
p LB ˜ x*LB q LB .
*
pSB ˜ xSB
q SB
(5)
ɉɪɟɞɟɥɶɧɵɣ ɄɊ ɩɪɢɦɟɫɢ ɤ0 limB ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɚɤ ɩɪɟɞɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɪɚɜɧɨɜɟɫɧɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɤ0ȼ ɩɪɢ Ɍ o ɌɆȺ ɢɥɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɪɢɦɟɫɢ (ɯ*L,S B) o 0. ɗɬɨ ɡɧɚɱɟɧɢɟ ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɭɱɟɧɨ ɢɡ (5) ɩɪɢ
(ɯ*L,S B) o 0:
k 0lim B
q LB .
q SB
(6)
ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɨɩɢɫɚɧɧɵɣ ɜɵɲɟ ɦɟɬɨɞ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɚɧɚɥɢɡɚ ɥɢɧɢɣ ɫɨɥɢɞɭɫɚ ɢ ɥɢɤɜɢɞɭɫɚ
Ⱦɋ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤ0 limB ɩɪɢɦɟɫɟɣ ɜ Zr ɢ Hf ɧɟ ɜɵɹɜɥɹɟɬ ɡɚɜɢɫɢɦɨɫɬɢ ɄɊ ɩɪɢɦɟɫɟɣ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɢ ɧɟ ɨɩɪɟɞɟɥɹɟɬ ɡɧɚɱɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɣ ɩɪɢɦɟɫɟɣ, ɩɪɢ ɤɨɬɨɪɵɯ ɞɨɫɬɢɝɚɸɬɫɹ ɩɪɟɞɟɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ. ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɜ ɨɛɵɱɧɨɦ ɩɪɟɞɫɬɚɜɥɟɧɢɢ Ⱦɋ ɧɟɥɶɡɹ ɩɨɥɭɱɢɬɶ ɫɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɬɟɦɩɟɪɚɬɭɪɨɣ ɢ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ɜ ɨɛɥɚɫɬɢ ɫɜɟɪɯɱɢɫɬɵɯ ɜɟɳɟɫɬɜ. ɉɨɥɭɱɟɧɧɵɟ ɚɩɩɪɨɤɫɢɦɢɪɭɸɳɢɟ ɭɪɚɜɧɟɧɢɹ ɩɨɡɜɨɥɹɸɬ ɪɟɲɢɬɶ ɷɬɭ ɡɚɞɚɱɭ ɝɪɚɮɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ. Ⱦɥɹ ɷɬɨɝɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɨɥɭ– ɢ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢɣ ɦɚɫɲɬɚɛ
ɢɡɨɛɪɚɠɟɧɢɹ. ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɨɫɭɳɟɫɬɜɢɬɶ ɝɪɚɮɢɱɟɫɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ Ⱦɋ ɜ ɨɛɥɚɫɬɢ ɫɜɟɪɯɧɢɡɤɢɯ ɤɨɧɰɟɧɬɪɚɰɢɣ
ɩɪɢɦɟɫɟɣ.
Ƚɪɚɮɢɱɟɫɤɢɣ ɦɟɬɨɞ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɷɤɫɬɪɚɩɨɥɹɰɢɢ ɥɢɧɢɣ ɫɨɥɢɞɭɫɚ ɢ ɥɢɤɜɢɞɭɫɚ ɧɚ ɧɭɥɟɜɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ
ɩɪɢɦɟɫɢ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɩɚɪɚɦɟɬɪɵ (¨ɌɆȺ ɢ x*LB) ɞɨɫɬɢɠɟɧɢɹ ɡɧɚɱɟɧɢɣ ɤ0 limB. Ɍɚɤɚɹ ɷɤɫɬɪɚɩɨɥɹɰɢɹ
ɬɚɤɠɟ ɩɨɡɜɨɥɹɟɬ ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɹ ɩɪɟɞɟɥɶɧɵɯ ɄɊ ɩɪɢɦɟɫɟɣ ɤ0 limB ɜ ɨɛɥɚɫɬɢ ɫɜɟɪɯɱɢɫɬɨɝɨ ɜɟɳɟɫɬɜɚ, ɤɨɬɨɪɵɟ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɞɥɹ ɤɚɠɞɨɣ ɫɢɫɬɟɦɵ ɨɫɧɨɜɚ – ɩɪɢɦɟɫɶ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɨɣ. Ⱦɥɹ ɧɢɡɤɢɯ ɤɨɧɰɟɧɬɪɚɰɢɣ ɩɪɢ ɢɡɨɛɪɚɠɟɧɢɢ ɜ ɤɨɨɪɞɢɧɚɬɚɯ 'TɆȺ = f (lg x*L,B) ɥɢɧɢɢ ɫɨɥɢɞɭɫɚ ɢ ɥɢɤɜɢɞɭɫɚ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɨɞɧɚ
ɨɬ ɞɪɭɝɨɣ ɧɚ ɪɚɫɫɬɨɹɧɢɢ, ɤɨɬɨɪɨɟ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ:
lg k0 limB
lg x*SB lg x*LB.
(7)
ȼɵɪɚɠɟɧɢɟ (7) ɩɨɡɜɨɥɹɟɬ ɜɵɩɨɥɧɢɬɶ ɝɪɚɮɢɱɟɫɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɪɢɦɟɫɢ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɢ ɨɩɪɟɞɟɥɢɬɶ ɩɪɟɞɟɥɶɧɨɟ ɟɝɨ ɡɧɚɱɟɧɢɟ ɤ0 limB.
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Â.Ì. Àæàæà, Ã.Ï. Êîâòóí, À.Ï. Ùåðáàíü...
«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 746, 2006
ɊȿɁɍɅɖɌȺɌɕ ɂ ɂɏ ɈȻɋɍɀȾȿɇɂȿ
ȼɵɲɟɩɪɢɜɟɞɟɧɧɵɟ ɜɵɤɥɚɞɤɢ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɞɥɹ ɪɚɫɱɟɬɨɜ ɤ0 limB ɜ ɰɢɪɤɨɧɢɢ ɢ ɝɚɮɧɢɢ. Ʉɨɷɮɮɢɰɢɟɧɬɵ
ɪɟɝɪɟɫɫɢɢ ɪɚɫɫɱɢɬɵɜɚɥɢɫɶ ɫ ɩɨɦɨɳɶɸ ɤɨɦɩɶɸɬɟɪɚ ɩɨ ɪɚɡɪɚɛɨɬɚɧɧɨɦɭ ɚɥɝɨɪɢɬɦɭ ɦɟɬɨɞɨɦ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ ɩɨ ɜɡɹɬɵɦ ɢɡ Ⱦɋ [7 Ɍ.1 ɫ. 110-703, Ɍ.2 ɫ. 874-914, Ɍ.3 ɫ. 411-672] ɩɚɪɚɦ ɡɧɚɱɟɧɢɣ: ɌS(i), xSB(i) ɢ TL(j), xLB(j); i,
j = 1, 2, 3 ….
ȼ ɬɚɛɥɢɰɟ ɩɪɢɜɟɞɟɧɵ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɟɝɪɟɫɫɢɢ ɞɥɹ ɥɢɧɢɣ ɫɨɥɢɞɭɫɚ ɢ ɥɢɤɜɢɞɭɫɚ ɜ ɫɢɫɬɟɦɚɯ Zr,
Hf – B ɢ ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ ɮɨɪɦɭɥɟ (6) ɡɧɚɱɟɧɢɹ ɤ0 limB ɞɥɹ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɷɥɟɦɟɧɬɨɜ – ɩɪɢɦɟɫɟɣ. ȼ ɬɚɛɥɢɰɟ
ɩɪɟɞɫɬɚɜɥɟɧɵ ɩɪɢɦɟɫɢ ɫ ɨɝɪɚɧɢɱɟɧɧɨɣ ɪɚɫɬɜɨɪɢɦɨɫɬɶɸ ɜ Zr ɢ Hf ɜ ɬɜɟɪɞɨɣ ɮɚɡɟ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɬɚɛɥɢɰɵ, ɞɥɹ
ɛɨɥɶɲɢɧɫɬɜɚ ɩɪɢɦɟɫɟɣ ɜ Zr, Hf ɡɧɚɱɟɧɢɹ ɤ0 limB ɡɧɚɱɢɬɟɥɶɧɨ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɟɞɢɧɢɰɵ, ɱɬɨ ɞɨɥɠɧɨ ɩɪɢɜɨɞɢɬɶ ɤ
ɡɚɦɟɬɧɨɦɭ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɸ ɢɯ ɩɪɢ ɧɚɩɪɚɜɥɟɧɧɨɣ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ, ɧɚɩɪɢɦɟɪ, ɩɪɢ ɡɨɧɧɨɣ ɩɥɚɜɤɟ. ȼɜɢɞɭ ɡɧɚɱɢɦɨɫɬɢ ɫɢɫɬɟɦɵ Zr – Hf [7 Ɍ.2 ɫ. 923] , ɨɛɥɚɞɚɸɳɟɣ ɧɟɨɝɪɚɧɢɱɟɧɧɨɣ ɪɚɫɬɜɨɪɢɦɨɫɬɶɸ ɜ ɬɜɟɪɞɨɦ ɫɨɫɬɨɹɧɢɢ ɢ
ɧɟ ɤɨɪɪɟɤɬɧɨɫɬɶɸ ɩɪɢɦɟɧɟɧɢɹ ɞɚɧɧɨɝɨ ɦɟɬɨɞɚ ɤ ɬɚɤɢɦ ɫɢɫɬɟɦɚɦ, ɧɢɠɟ ɩɪɟɞɫɬɚɜɥɟɧ ɪɚɫɱɟɬ ɪɚɜɧɨɜɟɫɧɵɯ ɄɊ ɤ0ȼ
ɨɞɧɨɝɨ ɜ ɞɪɭɝɨɦ ɩɨ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɦ ɩɚɪɚɦɟɬɪɚɦ ɢɡ ɜɵɪɚɠɟɧɢɹ [1]:
ɤ0ȼ = exp[¨HɆȼ . (ɌɆB – TMA) / R . TMA . TMB],
(8)
ɝɞɟ ɌɆȼ – ɬɟɦɩɟɪɚɬɭɪɚ ɩɥɚɜɥɟɧɢɹ ɩɪɢɦɟɫɧɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ȼ, ¨HɆȼ – ɷɧɬɚɥɶɩɢɹ ɩɥɚɜɥɟɧɢɹ ɤɨɦɩɨɧɟɧɬɚ ȼ,
R – ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ.
Hf
Ɉɩɪɟɞɟɥɟɧɧɵɟ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɡɧɚɱɟɧɢɹ ɪɚɜɧɨɜɟɫɧɵɯ ɄɊ ɫɥɟɞɭɸɳɢɟ: k 0ZrHf 1,2 ɢ k 0 Zr
0,82 . Ⱦɥɹ ɪɚɫɱɟɬɨɜ ɛɪɚɥɢɫɶ ɫɥɟɞɭɸɳɢɟ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ: ɌɆZr = 2125 K, ¨HɆZr = 23,0 ɤȾɠ·ɦɨɥɶ-1,
ɌɆHf = 2495 K, ¨HɆHf = 21,77 ɤȾɠ·ɦɨɥɶ-1, R = 8,31 ɤȾɠ·ɤɦɨɥɶ-1·ɝɪɚɞ-1 [1].
Ɍɚɛɥɢɰɚ. Ɂɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɟɝɪɟɫɫɢɢ ɭɪɚɜɧɟɧɢɣ ɥɢɧɢɣ ɫɨɥɢɞɭɫɚ ɢ ɥɢɤɜɢɞɭɫɚ ɜ ɫɢɫɬɟɦɚɯ
Zr, Hf – B ɢ ɡɧɚɱɟɧɢɹ ɩɪɟɞɟɥɶɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɪɢɦɟɫɟɣ k0 limB
ɋɢɫɬɟɦɚ
pSB
qSB
pLB
qLB
ɤ0 limB
Zr – Cr
3,9586
- 101,2225
- 0,1172
- 16,4299
0,16
Zr – Ag
- 2,3822
- 80,4422
0,4379
- 53,4391
0,66
Zr – B
- 0,0878
- 18,8300
- 0,0592
- 3,2073
0,17
Zr – Ge
- 51,6459
- 524,1336
- 0,5779
- 29,9242
0,06
Zr – Be
- 0,3050
- 32,7129
- 0,3205
- 18,2500
0,55
Zr – Th
5,6695
- 54,0352
- 0,1259
- 10,4266
0,19
Zr – Ni
- 41,3201
-158,9187
0,3953
- 46,1247
0,26
Zr – Co
-138,3829
- 91,3122
- 0,7256
- 9,1872
0,1
Zr – Sb
3,5312
- 71,5902
- 0,9650
- 8,0960
0,12
Zr – Bi
0,9168
- 51,0357
- 0,1873
- 17,8367
0,35
Zr – Si
-351,2328
- 42,4122
- 0,0966
- 26,8139
0,63
Zr – Ti
- 0,0205
- 4,4895
- 0,0440
- 1,1935
0,27
Zr – Mn
- 3,4509
- 56,7022
- 0,3765
- 18,8390
0,33
Hf – Au
- 1,6235
- 68,9545
- 0,2126
- 16,0279
0,23
Hf – Cu
- 7,9823
-113,6168
- 0,1846
- 28,3098
0,25
Hf – Os
0,8046
- 68,0924
0,2791
- 41,4923
0,61
Hf – Re
0,9505
- 28,4502
- 0,1727
- 10,6340
0,37
Hf – Ru
1,2555
- 61,7604
- 0,0943
- 16,8802
0,27
Hf – Ge
-271,9821
-101,8796
- 2,7905
-21,0319
0,2
Hf – Be
- 21,5795
- 51,3608
- 0,2226
- 16,0413
0,3
Hf – Th
- 4,4577
- 26,1268
- 0,1092
- 5,7390
0,22
85
Ðàñ÷åò ïðåäåëüíûõ êîýôôèöèåíòîâ ðàñïðåäåëåíèÿ...
ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï. 4 /32/
ɇɚ ɪɢɫ. 1, 2 ɩɪɟɞɫɬɚɜɥɟɧɵ ɛɢɧɚɪɧɵɟ Ⱦɋ ɜ ɩɨɥɭí ɢ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬɚɯ ɫɢɫɬɟɦ Zr – Bi, Zr - Cr,
Hf – Os, Hf – Au.
ɚ
ɛ
ɜ
ɝ
Zr
Ɋɢɫ. 1. Ȼɢɧɚɪɧɵɟ ɞɢɚɝɪɚɦɦɵ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦ Zr – Bi, Zr – Cr ɢ k 0 li m
Zr
Bi
, k 0 lim C r , ɨɩɪɟɞɟɥɟɧɧɵɟ ɦɟɬɨɞɨɦ ɝɪɚɮɢɱɟɫɤɨɣ
ɷɤɫɬɪɚɩɨɥɹɰɢɢ: ɚ, ɜ – Ⱦɋ ɫɢɫɬɟɦ Zr – Bi, Zr – Cr ɜ ɩɨɥɭɥɨɝɚɪɢɮɦɢɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬɚɯ; ɛ, ɝ – Ⱦɋ ɫɢɫɬɟɦ Zr – Bi, Zr – Cr ɜ
ɥɨɝɚɪɢɮɦɢɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬɚɯ
ɚ
ɛ
ɜ
ɝ
Hf
Hf
Ɋɢɫ. 2. Ȼɢɧɚɪɧɵɟ ɞɢɚɝɪɚɦɦɵ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦ Hf – Os, Hf – Au ɢ k 0 li m
, k 0 li m A u , ɨɩɪɟɞɟɥɟɧɧɵɟ ɦɟɬɨɞɨɦ ɝɪɚɮɢɱɟɫɤɨɣ ɷɤɫɬɪɚɩɨɥɹɰɢɢ: ɚ, ɜ – Ⱦɋ ɫɢɫɬɟɦ Hf – Os, Hf – Au ɜ ɩɨɥɭɥɨɝɚɪɢɮɦɢɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬɚɯ; ɛ, ɝ – Ⱦɋ ɫɢɫɬɟɦ Hf – Os, Hf –
Au ɜ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬɚɯ
Os
86
Â.Ì. Àæàæà, Ã.Ï. Êîâòóí, À.Ï. Ùåðáàíü...
«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 746, 2006
Ɍɚɦ ɠɟ ɩɪɟɞɫɬɚɜɥɟɧɵ ɝɪɚɮɢɱɟɫɤɢɟ ɡɚɜɢɫɢɦɨɫɬɢ ɪɚɜɧɨɜɟɫɧɵɯ ɡɧɚɱɟɧɢɣ ɄɊ ɷɬɢɯ ɩɪɢɦɟɫɟɣ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ:
ɤ0ȼ = f ('T, x*LB) ɢ ɨɩɪɟɞɟɥɟɧɵ ɢɯ ɡɧɚɱɟɧɢɹ ɜ ɩɪɟɞɟɥɶɧɨɦ ɫɥɭɱɚɟ, ɬ.ɟ. ɩɪɟɞɟɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɄɊ ɤ0 limB ɷɬɢɯ ɩɪɢɦɟɫɟɣ. ɇɚ ɪɢɫ. 2ɝ ɥɢɧɢɢ ɫɨɥɢɞɭɫɚ ɢ ɥɢɤɜɢɞɭɫɚ ɹɜɥɹɸɬɫɹ ɩɚɪɚɥɥɟɥɶɧɵɦɢ. ɗɬɨ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɬɨɦ, ɱɬɨ ɜ ɨɛɥɚɫɬɢ ɨɱɟɧɶ ɧɢɡɤɢɯ ɤɨɧɰɟɧɬɪɚɰɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤ0ȼ ɭɠɟ ɧɟ ɢɦɟɟɬ ɫɭɳɟɫɬɜɟɧɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ
Hf
ɤɨɧɰɟɧɬɪɚɰɢɢ ɢ ɢɞɟɧɬɢɱɟɧ ɫɜɨɟɦɭ ɩɪɟɞɟɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ k0lim
. Ⱦɥɹ ɫɢɫɬɟɦ Zr – Bi, Zr - Cr, Hf – Os ɜɡɹɬɚ
Au 0,23
ɛɨɥɟɟ ɲɢɪɨɤɚɹ ɨɛɥɚɫɬɶ ɬɟɦɩɟɪɚɬɭɪ, ɜɩɥɨɬɶ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ ɷɜɬɟɤɬɢɤɢ. ɉɨɷɬɨɦɭ ɧɚ ɪɢɫ. 1,2 ɦɨɠɧɨ ɜɢɞɟɬɶ ɢɡɦɟɧɟɧɢɟ ɡɧɚɱɟɧɢɣ ɪɚɜɧɨɜɟɫɧɵɯ ɄɊ k 0ZBr i
Zr
ɧɢɣ k0lim Bi
Zr
0, 35 , k 0lim Cr
Hf
0,16 , k0limOs
Zr
0 , 6 , k 0 Cr
Hf
0, 27 , k0Os
0, 66 ɩɪɢ ɷɜɬɟɤɬɢɤɟ, ɞɨ ɢɯ ɩɪɟɞɟɥɶɧɵɯ ɡɧɚɱɟ-
0,61 . ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɢɧɬɟɪɜɚɥɚɯ ɬɟɦ-
ɩɟɪɚɬɭɪ ɪɚɜɧɨɜɟɫɧɵɟ ɄɊ ɩɪɢɦɟɫɟɣ Bi ɢ Cr ɜ Zr ɭɦɟɧɶɲɚɸɬɫɹ ɜ ɫɬɨɪɨɧɭ ɫɜɨɢɯ ɩɪɟɞɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɩɪɢɦɟɪɧɨ ɜ
2 ɪɚɡɚ, ɜ ɬɨ ɜɪɟɦɹ, ɤɚɤ ɞɥɹ Os ɜ Hf ɬɚɤɨɟ ɢɡɦɟɧɟɧɢɟ ɫɨɫɬɚɜɥɹɟɬ ɜɟɥɢɱɢɧɭ < 10 %.
ɂɡ ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɪɢɫɭɧɤɨɜ (ɪɢɫ. 1ɚ,ɜ ɢ ɪɢɫ. 2ɚ,ɜ) ɬɚɤɠɟ ɜɢɞɧɨ, ɱɬɨ ɩɪɟɞɟɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɄɊ ɭɤɚɡɚɧɧɵɯ
ɩɪɢɦɟɫɟɣ ɤ0 limB ɜ ɰɢɪɤɨɧɢɢ ɢ ɝɚɮɧɢɢ ɞɨɫɬɢɝɚɸɬɫɹ ɩɪɢ 'TɆȺ< 10 K ɢ ɤɨɧɰɟɧɬɪɚɰɢɹɯ ɩɪɢɦɟɫɟɣ ɯ*ȼ < 0,1 ɚɬ. %,
ɬ.ɟ. ɩɪɢ ɬɚɤɢɯ ɤɨɧɰɟɧɬɪɚɰɢɹɯ ɩɪɢɦɟɫɟɣ ɢɯ ɄɊ ɫɬɪɟɦɹɬɫɹ ɤ ɩɨɫɬɨɹɧɧɵɦ ɩɪɟɞɟɥɶɧɵɦ ɡɧɚɱɟɧɢɹɦ. Ⱦɥɹ ɞɪɭɝɢɯ
ɩɪɢɜɟɞɟɧɧɵɯ ɜ ɬɚɛɥɢɰɟ ɩɪɢɦɟɫɟɣ, ɩɪɟɞɫɬɚɜɥɟɧɢɟ Ⱦɋ ɜ ɩɨɥɭɥɨɝɚɪɢɮɦɢɱɟɫɤɨɦ ɦɚɫɲɬɚɛɟ ɨɩɪɟɞɟɥɹɟɬ ɬɚɤɢɟ ɠɟ
ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɞɨɫɬɢɠɟɧɢɹ ɤ0 limB. ɇɟɨɛɯɨɞɢɦɨ ɬɚɤɠɟ ɨɬɦɟɬɢɬɶ ɯɨɪɨɲɟɟ ɫɨɜɩɚɞɟɧɢɟ ɡɧɚɱɟɧɢɣ ɤ0 limB, ɩɨɥɭɱɟɧɧɵɯ ɦɟɬɨɞɨɦ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɚɧɚɥɢɡɚ ɤɪɢɜɵɯ Ⱦɋ ɢ ɨɩɪɟɞɟɥɟɧɧɵɯ ɦɟɬɨɞɨɦ ɝɪɚɮɢɱɟɫɤɨɣ ɷɤɫɬɪɚɩɨɥɹɰɢɢ
ɥɢɧɢɣ L ɢ S ɫ ɭɱɟɬɨɦ ɜɵɪɚɠɟɧɢɹ (7), ɪɢɫ. 1 ɛ,ɝ ɢ ɪɢɫ. 2 ɛ,ɝ.
ȼɕȼɈȾɕ
ɉɪɟɞɫɬɚɜɥɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ ɩɪɟɞɟɥɶɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤ0 limB ɨɬɞɟɥɶɧɵɯ ɩɪɢɦɟɫɟɣ
ɜ Zr ɢ Hf ɦɟɬɨɞɚɦɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɚɧɚɥɢɡɚ ɤɪɢɜɵɯ Ⱦɋ ɢ ɦɟɬɨɞɨɦ ɝɪɚɮɢɱɟɫɤɨɣ ɷɤɫɬɪɚɩɨɥɹɰɢɢ ɢɯ ɧɚ ɧɭɥɟɜɭɸ
ɤɨɧɰɟɧɬɪɚɰɢɸ. Ɉɬɦɟɱɟɧɨ ɫɨɜɩɚɞɟɧɢɟ ɡɧɚɱɟɧɢɣ ɤ0 limB, ɨɩɪɟɞɟɥɟɧɧɵɯ ɷɬɢɦɢ ɪɚɫɱɟɬɧɵɦɢ ɦɟɬɨɞɚɦɢ. Ⱦɥɹ ɨɬɞɟɥɶɧɵɯ ɩɪɢɦɟɫɟɣ ɝɪɚɮɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ ɜɵɹɜɥɟɧɚ ɡɚɤɨɧɨɦɟɪɧɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫ
ɤɨɧɰɟɧɬɪɚɰɢɟɣ. Ɉɩɪɟɞɟɥɟɧɵ ɩɚɪɚɦɟɬɪɵ ɞɨɫɬɢɠɟɧɢɹ ('ɌɆȺ, Ʉ ɢ ɯ*ȼ, ɚɬ. %) ɩɪɟɞɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɤ0 limB ɩɪɢɦɟɫɟɣ ɜ ɰɢɪɤɨɧɢɢ ɢ ɝɚɮɧɢɢ.
ɋɉɂɋɈɄ ɅɂɌȿɊȺɌɍɊɕ
1. Ȼɚɪɬɟɥ ɂ., Ȼɭɪɢɧɝ ɗ., ɏɚɣɧ Ʉ., Ʉɭɯɚɪɠ Ʌ. Ʉɪɢɫɬɚɥɥɢɡɚɰɢɹ ɢɡ ɪɚɫɩɥɚɜɨɜ. ɋɩɪɚɜ. ɢɡɞ.: ɉɟɪ. ɫ ɧɟɦ. - Ɇ.: Ɇɟɬɚɥɥɭɪɝɢɹ, 1987.
- 320 ɫ.
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CALCULATION OF THE LIMITING DISTRIBUTION COEFFICIENTS OF ADMIXTURES IN
ZIRCONIUM AND HAFNIUM
V.M. Azhazha, G.P. Kovtun, A.P. Shcherban’, O.A. Datzenko, D.A. Solopikhin
National Science Center “Kharkov Institute of Physics and Technology”
Academicheskaya st.1, Kharkov, 61108, Ukraine
In the present work the results of accounts the limiting distribution coefficients ɤ0 limB of separate impurities in zirconium and hafnium are presented. The calculations are carried out using the method mathematical analysis of liquidus and solidus curves of diagram states and graphical method of extrapolation these curves at zero concentration. It is shown coincidence of values ɤ0 limB determined by these settlement methods. The received data on values the limiting distribution coefficients of researched impurities in Zr
and Hf are expanded a circle of the systems which represent interest for estimation the efficiency of purification these metals by crystallization methods. It has been determined the temperature and concentration parameters achievement of limiting values ɤ0 limB considered impurities in these metals.
KEY WORDS: zirconium, hafnium, distribution coefficients, directional crystallization, diagram states, admixtures, solvency, purification.