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利用剩余键的思想, 通过数学推导, 建立定量描述金属熔体结构与黏度关系的物理模型, 提出黏度的微观结构变化特性为熔体剩余键结构尺寸d的演变; 应用建立的模型理论计算液相线以上一定温区镁熔体和铝熔体的运动黏度, 得到函数关系式分别为vMg=3.1710-7+3.0410-7 d和vAl=1.6510-7+1.0510-7d, 这与采用坩埚扭摆振动法的实验测量结果相符合. 该模型从化学结合键角度揭 示了金属熔体的结构微观不均匀性及其黏度的微观物理本质, 为金属熔体黏度的理论计算提供了一种新的途径. 这对于深入认识液态金属的微观结构及其与宏观物性之间的关系具有重要意义.Based on the concept of residual bond, a physical model quantitatively describing the relationship between the melt structure and viscosity of metal is established by mathematical deduction, and the microscopic nature of viscosity is considered to be the evolution of the size d of the residual-bond structure of melt. Using this model, the kinematic viscosityies of the magnesium and aluminum melt in a certain region above the melting point are calculated, and the functional relations vMg=3.1710-7+3.0410-7d and vAl=1.6510-7+1.0510-7d are obtained, which accord with the experimental data measured by the method of crucible rotating oscillation damping. This model reveals the microscopic naturs of the micro-inhomogeneity and viscosity of the melt structure from the view of chemical bond, which provides a new way to calculate the viscosity of melt and is of significance for understanding the relationship between microstructure and macroscopic properties of liquid metal.
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Keywords:
- liquid metals /
- residual bond /
- physical model /
- micro-inhomogeneity of structure
[1] Zhukova L A 2009 The Atomic Structure of Metals and Alloys in Liquid or Amorphous State (Ekaterinburg: USTU-UPI) pp8-149 (in Russian) [Жукова Л A 2009 Aтomнoe Строение Meталлов и Сплавов в Жидком и Аморфном Состояниях（Eкатеринбург: УГТУ-УПИ) c.8-149]
[2] Elanskii G N, Elanskii D G 2006 Structure and Properties of Liquid Metal (Moscow: Metallurgical Industry Press) pp101-131 (in Russian) [Еланский Г Н, Еланский Д Г 2006 Строение и Свойства Металлических Раплавов (Moсква: MГВмИ)c.101-131]
[3] Zu F Q, Zhu Z G, Guo L J, Zhang B, Shui J P, Liu C S 2001 Phys. Rev. B 64 180203
[4] Wang Q, Lu K Q, Li Y X 2001 Chin. Sci. Bull. 46 1431
[5] Iida T, Rodarick I L 1993 The Properties of Liquid Metal (Oxford: Clavendon Press) p148
[6] Bachinskii A I 1960 Science Memoir (Moscow: Soviet Union Academy of Sciences Press) (in Russian) [Бачинский А И 1960 Собранных Труд(Moсква: A Н СССР)]
[7] Frenkel J I 1958 An Introduction to Metal Physics (Moscow: National Press of Physics-Mathematics) pp236-252 (in Russian) [Френкелъ Я И 1958 Ввдение в Теорию Металлов (Moсква: Государственное Издателъство Физико-Математической Литературы)c.236-252]
[8] Banchinkov G M 1947 Theory for Liquid Viscosity (Moscow: National Science and Technology Press) pp7-71 (in Russian) [Панченков Г М 1947 Теория Вязкости Жидкостей (Moсква: ГНТИ)c.7-71]
[9] Baum B A 1979 Metal Liquid-Problem and Assumption (Moscow: Science Press) p120 (in Russian) [Баум Б А 1979 Металлические Жидкости-Проблемы и Гипотезы (Moсква: Наука)c.120]
[10] Popel P S 1988 Ph. D. Dissertation (Ekaterinburg: USTU-UPI) pp280-320 (in Russian) [Попель П С 1988 Диссертация Доктора Физ (Екатеринбург: УрГТУ-УПИ)c.280-320]
[11] Li P J 1994 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) pp64-72 (in Chinese) [李培杰 1994 博士学位论文 (哈尔滨: 哈尔滨工业大学) 第64-72页]
[12] Mi G B, Li P J, He L J, Popel P S 2010 Rare Metal Materials and Engineering 39 1881
[13] Mi G B, Li P J, Ohapkin A V, Konstantinova N Yu, Sabirzianov A A, Popel P S 2011 Acta Phys. Sin. (in Chinese) 60 056601 [弭光宝, 李培杰, Охапкин А В, Константинова Н Ю, Сабирзянов А А, Попель П С 2011 物理学报 60 056601]
[14] Mauro N A, Bendert J C 2011 The Journal of Chemical Physics 135 044502
[15] Bergeron D E, Welford Castleman J A, Morisato T, Khanna S N 2004 Science 304 84
[16] Wessels V, Gangopadhyay A K, Sahu K K, Hyers R W, Canepari S M, Rogers J R, Kramer M J, Goldman A I, Robinson D, Lee J W, Morris J R, Kelton K F 2011 Phys. Rev. B 83 094116
[17] Dahlborg U, Besser M, Calvo-Dahlborg M 2007 Journal of Non-Crystalline Solids 353 3005
[18] Shpilrain E E, Fomin V A, Skovorotko S N 1983 Research of Viscosity for Liquid Metal (Moscow: Science Press) pp10-54 (in Russian) [Шпильрайн З З, Фомин В А, Сковородько С Н 1983 Исследование Вязкости Жидких Металлов (Moсква: Наука)c.10-54]
[19] Wang Y Q, Wu Y Q, Bian X F 2007 Chin. Sci. Bull. 52 1441
[20] Mi G B, Li P J, Ohapkin A V, Konstantinova N Yu, Sabirzianov A A, Popel P S 2011 Acta Phys. Sin. (in Chinese) 60 046601 [弭光宝, 李培杰, Охапкин А В, Константинова Н Ю, Сабирзянов А А, Попель П С 2011 物理学报 60 046601]
[21] Mi G B, Li P J, He L J 2010 Sci. China: Phys. Mech. Astron. 53 1571
[22] Mi G B, Li P J, He L J 2010 Sci. China: Phys. Mech. Astron. 53 1830
[23] Mi G B, Li P J, Popel P S 2010 Sci. China: Phys. Mech. Astron. 53 2054
[24] Mi G B, He L J, Li P J 2009 The Chinese Journal of Nonferrous Metals 19 1372 (in Chinese) [弭光宝, 何良菊, 李培杰 2009 中国有色金属学报 19 1372]
[25] Baum B A, Hassin G A, Tyagunov G V 1984 Liquid Steel (Moscow: Metallurgical Industry Press) p6 (in Russian) [Баум Б А, Хасин Г А, Тягунов Г В 1984 Жидкая Сталь(Moсква: Металлургия)c.6]
[26] Skrebcov A M 2008 Casting Process 5 9 (in Russian) [Скребцов А М 2008 Процессы литья 5 9]
[27] Editorial Board of Professor Chen Xichen Collected Works 2011 The Liquid Structure of Alloys and Solidification Control (Beijing: National Defence Industry Press) pp29-37 (in Chinese) [陈熙琛教授文集编委会 2011 合金液态结构探索和凝固过程控制 (北京: 国防工业出版社) 第29-37页]
[28] Dean J A 1999 Lange's Handbook of Chemistry (15th Ed.) (New York: McGraw-Hill) p6, 124
[29] Mi G B, Li P J, He L J 2009 The Chinese Journal of Nonferrous Metals 19 2074 (in Chinese) [弭光宝, 李培杰, 何良菊 2009 中国有色金属学报 19 2074]
[30] Chhabra R P, Seth D K 1990 Z. Metallkde 81 264
[31] Zhang R L 1993 Empirical Electron Theory of Solids and Molecules (Jilin: Jilin Science and Technology Press) (in Chinese) [张瑞林 1993 固体与分子经验电子理论 (长春: 吉林科学技术出版社)]
[32] Assael M J, Kakosimos K R, Banish M 2006 J. Phys. Chem. Ref. Data 35 285
[33] Kolobnev I F, Krimov V V, Polianskii A P 1957 Caster Manual-Shaped Castings of Aluminium and Magnesium Alloys (Moscow: Mashgr) pp5-8 (in Russian) [Колобнев И Ф, Крымов В В, Полянский А П 1957 Справочник Литейшика-Фасонное Литье из Алюминиевых и Магниевых Сплавов (Moсква: МАШГЗ)c.5-8]
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[1] Zhukova L A 2009 The Atomic Structure of Metals and Alloys in Liquid or Amorphous State (Ekaterinburg: USTU-UPI) pp8-149 (in Russian) [Жукова Л A 2009 Aтomнoe Строение Meталлов и Сплавов в Жидком и Аморфном Состояниях（Eкатеринбург: УГТУ-УПИ) c.8-149]
[2] Elanskii G N, Elanskii D G 2006 Structure and Properties of Liquid Metal (Moscow: Metallurgical Industry Press) pp101-131 (in Russian) [Еланский Г Н, Еланский Д Г 2006 Строение и Свойства Металлических Раплавов (Moсква: MГВмИ)c.101-131]
[3] Zu F Q, Zhu Z G, Guo L J, Zhang B, Shui J P, Liu C S 2001 Phys. Rev. B 64 180203
[4] Wang Q, Lu K Q, Li Y X 2001 Chin. Sci. Bull. 46 1431
[5] Iida T, Rodarick I L 1993 The Properties of Liquid Metal (Oxford: Clavendon Press) p148
[6] Bachinskii A I 1960 Science Memoir (Moscow: Soviet Union Academy of Sciences Press) (in Russian) [Бачинский А И 1960 Собранных Труд(Moсква: A Н СССР)]
[7] Frenkel J I 1958 An Introduction to Metal Physics (Moscow: National Press of Physics-Mathematics) pp236-252 (in Russian) [Френкелъ Я И 1958 Ввдение в Теорию Металлов (Moсква: Государственное Издателъство Физико-Математической Литературы)c.236-252]
[8] Banchinkov G M 1947 Theory for Liquid Viscosity (Moscow: National Science and Technology Press) pp7-71 (in Russian) [Панченков Г М 1947 Теория Вязкости Жидкостей (Moсква: ГНТИ)c.7-71]
[9] Baum B A 1979 Metal Liquid-Problem and Assumption (Moscow: Science Press) p120 (in Russian) [Баум Б А 1979 Металлические Жидкости-Проблемы и Гипотезы (Moсква: Наука)c.120]
[10] Popel P S 1988 Ph. D. Dissertation (Ekaterinburg: USTU-UPI) pp280-320 (in Russian) [Попель П С 1988 Диссертация Доктора Физ (Екатеринбург: УрГТУ-УПИ)c.280-320]
[11] Li P J 1994 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) pp64-72 (in Chinese) [李培杰 1994 博士学位论文 (哈尔滨: 哈尔滨工业大学) 第64-72页]
[12] Mi G B, Li P J, He L J, Popel P S 2010 Rare Metal Materials and Engineering 39 1881
[13] Mi G B, Li P J, Ohapkin A V, Konstantinova N Yu, Sabirzianov A A, Popel P S 2011 Acta Phys. Sin. (in Chinese) 60 056601 [弭光宝, 李培杰, Охапкин А В, Константинова Н Ю, Сабирзянов А А, Попель П С 2011 物理学报 60 056601]
[14] Mauro N A, Bendert J C 2011 The Journal of Chemical Physics 135 044502
[15] Bergeron D E, Welford Castleman J A, Morisato T, Khanna S N 2004 Science 304 84
[16] Wessels V, Gangopadhyay A K, Sahu K K, Hyers R W, Canepari S M, Rogers J R, Kramer M J, Goldman A I, Robinson D, Lee J W, Morris J R, Kelton K F 2011 Phys. Rev. B 83 094116
[17] Dahlborg U, Besser M, Calvo-Dahlborg M 2007 Journal of Non-Crystalline Solids 353 3005
[18] Shpilrain E E, Fomin V A, Skovorotko S N 1983 Research of Viscosity for Liquid Metal (Moscow: Science Press) pp10-54 (in Russian) [Шпильрайн З З, Фомин В А, Сковородько С Н 1983 Исследование Вязкости Жидких Металлов (Moсква: Наука)c.10-54]
[19] Wang Y Q, Wu Y Q, Bian X F 2007 Chin. Sci. Bull. 52 1441
[20] Mi G B, Li P J, Ohapkin A V, Konstantinova N Yu, Sabirzianov A A, Popel P S 2011 Acta Phys. Sin. (in Chinese) 60 046601 [弭光宝, 李培杰, Охапкин А В, Константинова Н Ю, Сабирзянов А А, Попель П С 2011 物理学报 60 046601]
[21] Mi G B, Li P J, He L J 2010 Sci. China: Phys. Mech. Astron. 53 1571
[22] Mi G B, Li P J, He L J 2010 Sci. China: Phys. Mech. Astron. 53 1830
[23] Mi G B, Li P J, Popel P S 2010 Sci. China: Phys. Mech. Astron. 53 2054
[24] Mi G B, He L J, Li P J 2009 The Chinese Journal of Nonferrous Metals 19 1372 (in Chinese) [弭光宝, 何良菊, 李培杰 2009 中国有色金属学报 19 1372]
[25] Baum B A, Hassin G A, Tyagunov G V 1984 Liquid Steel (Moscow: Metallurgical Industry Press) p6 (in Russian) [Баум Б А, Хасин Г А, Тягунов Г В 1984 Жидкая Сталь(Moсква: Металлургия)c.6]
[26] Skrebcov A M 2008 Casting Process 5 9 (in Russian) [Скребцов А М 2008 Процессы литья 5 9]
[27] Editorial Board of Professor Chen Xichen Collected Works 2011 The Liquid Structure of Alloys and Solidification Control (Beijing: National Defence Industry Press) pp29-37 (in Chinese) [陈熙琛教授文集编委会 2011 合金液态结构探索和凝固过程控制 (北京: 国防工业出版社) 第29-37页]
[28] Dean J A 1999 Lange's Handbook of Chemistry (15th Ed.) (New York: McGraw-Hill) p6, 124
[29] Mi G B, Li P J, He L J 2009 The Chinese Journal of Nonferrous Metals 19 2074 (in Chinese) [弭光宝, 李培杰, 何良菊 2009 中国有色金属学报 19 2074]
[30] Chhabra R P, Seth D K 1990 Z. Metallkde 81 264
[31] Zhang R L 1993 Empirical Electron Theory of Solids and Molecules (Jilin: Jilin Science and Technology Press) (in Chinese) [张瑞林 1993 固体与分子经验电子理论 (长春: 吉林科学技术出版社)]
[32] Assael M J, Kakosimos K R, Banish M 2006 J. Phys. Chem. Ref. Data 35 285
[33] Kolobnev I F, Krimov V V, Polianskii A P 1957 Caster Manual-Shaped Castings of Aluminium and Magnesium Alloys (Moscow: Mashgr) pp5-8 (in Russian) [Колобнев И Ф, Крымов В В, Полянский А П 1957 Справочник Литейшика-Фасонное Литье из Алюминиевых и Магниевых Сплавов (Moсква: МАШГЗ)c.5-8]
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