液态金属钠凝固过程中微观结构演变及表征的模拟研究
|
摘要
本文采用分子动力学模拟方法,结合双体分布函数、键型指数法和团簇类型指数法(CTIM)等微观结构表征方法,以及基于CTIM的团簇跟踪技术,从微观结构的不同方面,系统研究了液态金属Na在不同条件下凝固过程中微观结构的形成和演变机理。并根据模拟研究的结果,对一些重要实验现象和凝固理论进行了微观解释。
对液态金属Na在不同冷速和熔体初始温度条件下的凝固过程进行了模拟,考察了不同热历史条件对凝固过程微观结构的影响。结果表明,冷速对凝固过程中微观结构的转变起关键性作用,当液态金属Na以1×10~(14) K/s和1×10~(13) K/s的冷速凝固时,形成以二十面体和缺陷二十面体基本原子团为主体的非晶态结构;而在以以1×10~(12) K/s和1×10~(11) K/s的冷速凝固时,形成bcc晶体结构。形成非晶的临界冷速约为10~(13) K/s。不同熔体初始温度对凝固结构晶化程度有明显影响,这种影响随熔体初始温度的降低呈非线性变化关系,但影响程度存在一个上、下限的范围。发现在液固转变温度(T_g和T_c)以上,不同冷速和熔体初始温度热历史条件对微观结构的影响并不明显;但在液固转变温度以下,不同热历史条件对微观结构的影响就明显、充分地表现出来。根据这一特点,有可能建立另一种确定T_g和T_c的新方法。
进一步对包含50000个Na原子的较大体系的快速凝固过程进行了模拟,研究了快速凝固过程团簇结构的形成特性和演变机理。结果表明,液态金属Na和Al在快速凝固过程中,其团簇结构的演变有相似之处,又各有其特征。CTIM与H-A键型指数法相比,更能有效识别两者的差异所在。这展现了CTIM对识别和表征团簇结构的有效性,它将为研究液态金属凝固过程中团簇结构的形成和演变特性提供一条新途径。快速凝固结构中纳米团簇的形成经历了一个复杂的演变过程:从高温液态中极不稳定的较小尺度原子团,经历了过冷液态中相对较稳定的中等尺度原子团,到T_g以下中等尺度原子团相互兼并而形成。金属Na体系比Al更容易形成纳米团簇,并且这些纳米团簇的结构显著不同于那些由气相沉积、离子溅射等方法所获得的团簇结构。
对包含10000个Na原子体系的凝固结晶过程进行了模拟,跟踪研究了结晶过程晶核的形成机理。液态金属Na晶化过程中,体系微观结构的转变从过冷液态中二十面体和缺陷二十面体为主体的结构,经历了T_c附近的缺陷bcc结构,到最后的接近完整bcc结构。团簇的能量和几何因素对凝固过程中最有利形成的微观结构组态同时起关键性作用。体系中晶核的形成会经历很多不同的形核路径,团簇的内部结构和尺寸对临界晶核的形成同时起关键性作用,内部结构的差异会引起临界晶核尺寸的不同。临界晶核呈非球状形貌,并且包含部分亚稳态结构。由模拟所得到的临界晶核尺寸,与经典形核理论的预测差别不大。在过冷液态金属Na恒温晶化过程,通过团簇跟踪分析所获得的结晶量随时间的变化关系,满足Johnson-Mehl-Avrami (JMA)结晶动力学规律。这一方面从原子层次出发验证了基本凝固理论的正确性,另一方面也说明了基于CTIM的团簇跟踪分析方法的有效性。
对包含10000个原子的非晶态金属Na体系等温退火过程进行了模拟,跟踪研究了非晶态金属Na晶化过程形核和长大机理。非晶态金属Na等温退火形核过程中,经历了二十面体和缺陷二十面体团簇结构逐渐解体,接着具有bcc对称性结构的团簇逐渐形成的过程。同时只有当具有bcc对称性结构团簇的尺寸达到某一临界尺寸时,才能成为稳定晶核。非晶态金属Na的晶化过程与其深过冷熔体结晶过程类似,呈现形核、长大和晶粒粗化三个阶段特征。通过对比不同分析方法所得到的结果可见,基于CTIM的团簇跟踪分析更能准确区分晶化过程的不同阶段特征,并为DSC实验不能清楚区分非晶态金属晶化阶段的实验现象,提供了良好的微观解释。
In this thesis, with the molecular dynamics method, the solidification processes of liquid metal Na under different conditions are simulated. By means of the different microstructural description methods of the pair distribution function, bond-type index method, and cluster-type index method (CTIM), and the technique of tracing cluster based on the CTIM, the formation properties and evolution mechanisms of microstructures during the solidification processes of liquid metal under different conditions are deeply studied. According to the computer simulation results, some experimental phenomenons and solidification theories are explained on microstructural level.
The solidification processes of liquid metal Na under different cooling rates and initial melt temperatures are simulated. The effects of different thermal history conditions on the microstructures during the solidification processes are investigated. The results show that the cooling rate plays a critical role in the transitions of microstructures. When the cooling rates are 1×10~(14) K/s and 1×10~(13) K/s, the amorphous structures are formed mainly with the icosahedron basic cluster and the defective icosahedron basic cluster. When the cooling rates are 1×10~(12) K/s and 1×10~(11)K/s, the bcc crystal structures are formed. The critical cooling rate for the formation of amorphous Na is about 10~(13) K/s. The initial melt temperature evidently affects the crystallinity of solidification structures. The influence degree is not linearly varying with the decrease of initial melt temperature, and has the upper and lower limits. It is still demonstrated that the effects of different cooling rates and initial melt temperatures on the microstructures of metal Na are very small above the liquid-solid transition temperature (T_g and T_c), but they are fully displayed near the liquid-solid transition points. According to this feature, it possibly provides a new method to determine the T_g and T_c.
The rapid solidification process of liquid metal Na with 50000 atoms is simulated. The formation properties and evolution mechanismes of cluster structures during the rapid solidification process are investigated. The results show that during the rapid solidification process of liquid metal Na and Al, there are some similar in their evolution features of cluster structures, meanwhile many differences. The CTIM can distinguish these differences more exactly than the H-A bond-type index method. The validity of CTIM in describing the cluster structures is confirmed, and it provides a new method of studing the formation properties of clusters during the solidification process. The formation and evolution of nano-clusters in the rapid solidification process have undergone a complicated evolution process: the small unstable cluster is formed in the liquid, through a middle-cluster in the supercooled liquid, and finally the nano-cluster is formed by combing several middle-clusters after T_g. The nano-clusters are formed more easily in liquid metal Na than in Al system, and the configurations of nano-clusters are also obviously different from those obtained by gaseous deposition, ionic spray methods and so on.
The crystallization process during the solidification of liquid metal Na with 10000 atoms is simulated. The formation mechanismes of crystal nuclei are investigated by tracing the evolution of clusters. The results show that during the crystallization process of liquid metal Na, the microstructures transform from the icosahedron or defective icosahedron structure in the supercooled liquid, through the defective bcc structure near the crystallization temperature, and finally to the perfect bcc structure. The energies of clusters and their geometrical constraints interplay the favorable microstructures during the nucleation process. The formation of nucleus may go along many different pathways. The size of cluster and its internal structure both play a crucial role in determining whether it is a critical nucleus. It is also found that the critical nucleus is non-spherical and may include some metastable structures. And the deviation of critical sizes in our simulations from the prediction of classical nucleation theory is not too much. The evolution of the volume fraction of crystal phases during the isothermal crystallization of the supercooled liquid metal Na satisfies the Johnson-Mehl-Avrami (JMA) theory. This verifes the validity of basic solidification theory from the microstructural level, on the other hand, the validity of the technique of tracing cluster based on the CTIM on studying the crystallization process is displayed.
The isothermal annealing process of amorphous metal Na with 10000 atoms is simulated. The formation and growth of nuclei in amorphous Na are traced. The results show the formations of nuclei undergo the shrink of clusters with icosahedron short-range order structure firstly, and then the bcc symmetric clusters are formed gradually. Only when the sizes of bcc symmetric clusters reach a critical size, they can turn into stable nuclei. The crystallization of amorphous Na exhibits three distinct stages three distinct stages of nucleation, subsequent growth of nuclei and coarsening of crystal grains. Through comparing the results obtained by different analysis methods, it is found that the CTIM can distinguish the different stages of crystallization processes. Our simulation results provide a reasonable explanation at atomic level for the experimental phenomenon that the DSC method cannot exactly reveal the crystallization stages of some amorphous metals.
对液态金属Na在不同冷速和熔体初始温度条件下的凝固过程进行了模拟,考察了不同热历史条件对凝固过程微观结构的影响。结果表明,冷速对凝固过程中微观结构的转变起关键性作用,当液态金属Na以1×10~(14) K/s和1×10~(13) K/s的冷速凝固时,形成以二十面体和缺陷二十面体基本原子团为主体的非晶态结构;而在以以1×10~(12) K/s和1×10~(11) K/s的冷速凝固时,形成bcc晶体结构。形成非晶的临界冷速约为10~(13) K/s。不同熔体初始温度对凝固结构晶化程度有明显影响,这种影响随熔体初始温度的降低呈非线性变化关系,但影响程度存在一个上、下限的范围。发现在液固转变温度(T_g和T_c)以上,不同冷速和熔体初始温度热历史条件对微观结构的影响并不明显;但在液固转变温度以下,不同热历史条件对微观结构的影响就明显、充分地表现出来。根据这一特点,有可能建立另一种确定T_g和T_c的新方法。
进一步对包含50000个Na原子的较大体系的快速凝固过程进行了模拟,研究了快速凝固过程团簇结构的形成特性和演变机理。结果表明,液态金属Na和Al在快速凝固过程中,其团簇结构的演变有相似之处,又各有其特征。CTIM与H-A键型指数法相比,更能有效识别两者的差异所在。这展现了CTIM对识别和表征团簇结构的有效性,它将为研究液态金属凝固过程中团簇结构的形成和演变特性提供一条新途径。快速凝固结构中纳米团簇的形成经历了一个复杂的演变过程:从高温液态中极不稳定的较小尺度原子团,经历了过冷液态中相对较稳定的中等尺度原子团,到T_g以下中等尺度原子团相互兼并而形成。金属Na体系比Al更容易形成纳米团簇,并且这些纳米团簇的结构显著不同于那些由气相沉积、离子溅射等方法所获得的团簇结构。
对包含10000个Na原子体系的凝固结晶过程进行了模拟,跟踪研究了结晶过程晶核的形成机理。液态金属Na晶化过程中,体系微观结构的转变从过冷液态中二十面体和缺陷二十面体为主体的结构,经历了T_c附近的缺陷bcc结构,到最后的接近完整bcc结构。团簇的能量和几何因素对凝固过程中最有利形成的微观结构组态同时起关键性作用。体系中晶核的形成会经历很多不同的形核路径,团簇的内部结构和尺寸对临界晶核的形成同时起关键性作用,内部结构的差异会引起临界晶核尺寸的不同。临界晶核呈非球状形貌,并且包含部分亚稳态结构。由模拟所得到的临界晶核尺寸,与经典形核理论的预测差别不大。在过冷液态金属Na恒温晶化过程,通过团簇跟踪分析所获得的结晶量随时间的变化关系,满足Johnson-Mehl-Avrami (JMA)结晶动力学规律。这一方面从原子层次出发验证了基本凝固理论的正确性,另一方面也说明了基于CTIM的团簇跟踪分析方法的有效性。
对包含10000个原子的非晶态金属Na体系等温退火过程进行了模拟,跟踪研究了非晶态金属Na晶化过程形核和长大机理。非晶态金属Na等温退火形核过程中,经历了二十面体和缺陷二十面体团簇结构逐渐解体,接着具有bcc对称性结构的团簇逐渐形成的过程。同时只有当具有bcc对称性结构团簇的尺寸达到某一临界尺寸时,才能成为稳定晶核。非晶态金属Na的晶化过程与其深过冷熔体结晶过程类似,呈现形核、长大和晶粒粗化三个阶段特征。通过对比不同分析方法所得到的结果可见,基于CTIM的团簇跟踪分析更能准确区分晶化过程的不同阶段特征,并为DSC实验不能清楚区分非晶态金属晶化阶段的实验现象,提供了良好的微观解释。
In this thesis, with the molecular dynamics method, the solidification processes of liquid metal Na under different conditions are simulated. By means of the different microstructural description methods of the pair distribution function, bond-type index method, and cluster-type index method (CTIM), and the technique of tracing cluster based on the CTIM, the formation properties and evolution mechanisms of microstructures during the solidification processes of liquid metal under different conditions are deeply studied. According to the computer simulation results, some experimental phenomenons and solidification theories are explained on microstructural level.
The solidification processes of liquid metal Na under different cooling rates and initial melt temperatures are simulated. The effects of different thermal history conditions on the microstructures during the solidification processes are investigated. The results show that the cooling rate plays a critical role in the transitions of microstructures. When the cooling rates are 1×10~(14) K/s and 1×10~(13) K/s, the amorphous structures are formed mainly with the icosahedron basic cluster and the defective icosahedron basic cluster. When the cooling rates are 1×10~(12) K/s and 1×10~(11)K/s, the bcc crystal structures are formed. The critical cooling rate for the formation of amorphous Na is about 10~(13) K/s. The initial melt temperature evidently affects the crystallinity of solidification structures. The influence degree is not linearly varying with the decrease of initial melt temperature, and has the upper and lower limits. It is still demonstrated that the effects of different cooling rates and initial melt temperatures on the microstructures of metal Na are very small above the liquid-solid transition temperature (T_g and T_c), but they are fully displayed near the liquid-solid transition points. According to this feature, it possibly provides a new method to determine the T_g and T_c.
The rapid solidification process of liquid metal Na with 50000 atoms is simulated. The formation properties and evolution mechanismes of cluster structures during the rapid solidification process are investigated. The results show that during the rapid solidification process of liquid metal Na and Al, there are some similar in their evolution features of cluster structures, meanwhile many differences. The CTIM can distinguish these differences more exactly than the H-A bond-type index method. The validity of CTIM in describing the cluster structures is confirmed, and it provides a new method of studing the formation properties of clusters during the solidification process. The formation and evolution of nano-clusters in the rapid solidification process have undergone a complicated evolution process: the small unstable cluster is formed in the liquid, through a middle-cluster in the supercooled liquid, and finally the nano-cluster is formed by combing several middle-clusters after T_g. The nano-clusters are formed more easily in liquid metal Na than in Al system, and the configurations of nano-clusters are also obviously different from those obtained by gaseous deposition, ionic spray methods and so on.
The crystallization process during the solidification of liquid metal Na with 10000 atoms is simulated. The formation mechanismes of crystal nuclei are investigated by tracing the evolution of clusters. The results show that during the crystallization process of liquid metal Na, the microstructures transform from the icosahedron or defective icosahedron structure in the supercooled liquid, through the defective bcc structure near the crystallization temperature, and finally to the perfect bcc structure. The energies of clusters and their geometrical constraints interplay the favorable microstructures during the nucleation process. The formation of nucleus may go along many different pathways. The size of cluster and its internal structure both play a crucial role in determining whether it is a critical nucleus. It is also found that the critical nucleus is non-spherical and may include some metastable structures. And the deviation of critical sizes in our simulations from the prediction of classical nucleation theory is not too much. The evolution of the volume fraction of crystal phases during the isothermal crystallization of the supercooled liquid metal Na satisfies the Johnson-Mehl-Avrami (JMA) theory. This verifes the validity of basic solidification theory from the microstructural level, on the other hand, the validity of the technique of tracing cluster based on the CTIM on studying the crystallization process is displayed.
The isothermal annealing process of amorphous metal Na with 10000 atoms is simulated. The formation and growth of nuclei in amorphous Na are traced. The results show the formations of nuclei undergo the shrink of clusters with icosahedron short-range order structure firstly, and then the bcc symmetric clusters are formed gradually. Only when the sizes of bcc symmetric clusters reach a critical size, they can turn into stable nuclei. The crystallization of amorphous Na exhibits three distinct stages three distinct stages of nucleation, subsequent growth of nuclei and coarsening of crystal grains. Through comparing the results obtained by different analysis methods, it is found that the CTIM can distinguish the different stages of crystallization processes. Our simulation results provide a reasonable explanation at atomic level for the experimental phenomenon that the DSC method cannot exactly reveal the crystallization stages of some amorphous metals.
引文
[1] 陈 光 ,傅 恒 志 . 非 平 衡 凝 固 新 型 金 属 材 料 . 北 京 :科 学 技 术 出 版 社 ,2004, 1-19
[2] 傅 恒 志 ,柳 百 成 ,魏 炳 波 . 凝 固 科 学 技 术 与 发 展 . 北 京 :国 防 工 业出 版 社 , 2005, 2-69
[3] Alder B J, Wainwright T E. Phase transition for a hard sphere system. J. Chem. Phys., 1957, 27(5): 1208-1209
[4] Finney J L. Random Packing and the structure of simple liquids. Proc. R. Soc. A, 1970, 319(10): 479-493
[5] Steinhardt P J, Nelson D R, and Ronchetti M. Bond-orientational order in liquids and glasses. Rhys. Rev. B, 1983, 28(2): 784-805
[6] Honeycutt J D, Andersen H C. Molecular-dynamics study of melting and freezing of small Lennard-Jones clusters. J. Phys. Chem., 1987, 91(19), 4950-4963
[7] Chen H S. Glassy metals. Rep. Prog. Phys., 1980, 43(4): 353-432
[8] 惠希东, 陈国良. 块体非晶合金. 北京:化学工业出版社. 2007,75-87
[9] Bernal J. A geometrical approach to the structure of liquid. Nature, 1959, 183(17): 141-147
[10] Scott G D. Radial distribution of the random close packing of equal spheres. 1962, 194(9): 956-957
[11] Cohen M H, Turnbull D. Metastability of amorphous structures. 1964, 203(29): 964-964
[12] Sadoc J L, Dixmier J, Ginier A. Theoretical calculation of dense random packings of equal and non-equal sized hard spheres applications to amorphous metallic alloys. J. Non-Cryst. Solids, 1973, 12(1): 46-60
[13] Connel G A N. Dense random packing of hard and compressible spheres. Solid State Commun., 1975, 16(1): 109-112
[14] Barker J A, Hoare M R. Relaxation of the Bernal model. Nature, 1975, 257(11): 120-122
[15] Gaskill G S. A new structural model for transition metal? Metalloid glasses. Nature, 1978, 276(30): 484-485
[16] Miracle D B. A structure model for metallic glass. Nature, 2004, 3(19):697-702
[17] Sheng H W, Luo W K, Alamgir F M, et al. Atomic packing and short-to-medium-range order in metallic glasses. Nature, 2006, 439(26):419-425
[18] 王 广 厚 . 团 簇 物 理 学 . 上 海 : 上 海 科 学 技 术 出 版 社 , 2003, 1-9
[19] 李先芬. 共晶与匀晶系二元合金熔体结构转变及其对凝固的影响: [博士学位论文]. 合肥: 合肥工业大学, 2006, 18-19
[20] 边秀房,王伟民,李辉,马家骥. 金属熔体结构. 上海:上海交通大学出版社,2003, 66-79
[21] Reichert H, Klein O, Dosch H, et al. Observation of five-fold local symmetry in liquid lead. Nature, 2000, 408(14): 839-841
[22] Spaepen F. Condensed-matter science: Five-fold symmetry in liquid. Nature, 2000, 408(14): 781-782
[23] Schenk T, Moritz D H, Simonet V, et al. Icosahedral short-range order in deeply undercooled metallic melts. Phys. Rev. Lett., 2002, 89(7): 075507-4
[24] Steeb S, Entress H. Atom distribution and eleetrical resistivity of molten magnesium-tin alloys. Z. Metallkunde, 1966, 57(11): 803-807
[25] Alblas B P, van der Marel C, Geertsma W, et al. Experimental results for liquid Alkali-group IV alloys. J. Non-Cryst. Solids, 1984, 61(1): 201-206
[26] 潘学民, 边秀房, 秦敬玉, 王伟民. Cu-12%Al 合金熔体内中程有序原子团簇. 物理化学学报, 2001, 17(8): 707-712
[27] 丛红日, 边秀房, 李辉. Al 5 Fe2合金熔体中程有序结构的研究. 化学学报, 2002, 60(2): 287-292
[28] 边秀房,王伟明,潘学民 等. Al-TM 合金熔体的中程有序结构及其演化规律. 化学学报, 2002, 60(7): 1215-1219
[29] 边秀房,潘学民, 秦绪波 等. 金属熔体中程有序结构. 中国科学 E,2002, 32(2): 145-151
[30] Zhou J K, Bian X F, Wang W M, et al. Medium-range order and crystallization in amorphous Al–Ni–Pr alloys. Mater. Lett., 2004, 58(27): 2559-2563
[31] Zhang L, Wu Y S, Bian X F, et al. Short-range and medium-range order in liquid and amorphous Al90Fe5Ce5 alloys. J. Non-Cryst. Solids, 2000, 262(1-3): 169-176
[32] 秦敬玉. 液体 Al-Fe 合金的微观不均匀结构研究: [博士学位论文]. 济南: 山东工业大学, 1998, 70-83
[33] Jónsson H and Andersen H C. Icosahedral ordering in the Lennard-Jones liquid and glass. Phys. Rev. Lett., 1988, 60(22): 2295-2298
[34] Jakse N, Lebacq O, Pasturel A. Ab initio molecular-dynamics simulations of short-range order in liquid Al 80 Mn 20 and Al 80 Ni20 alloys. Phys. Rev. Lett., 2004, 93(20): 207801-4
[35] Jakse N, Pasturel. Local order of liquid and supercooled zirconium by ab initio molecular dynamics. Phys. Rev. Lett., 2003, 91(19): 195501-4
[36] Tomida T, Egami T. Molecular-dynamics study of orientational order in liquids and glasses and its relation to the glass transition. Phys. Rev. B, 1995, 52(5): 3290-3308
[37] Luo W K, Sheng H W, Alamgir F M, et al. Icosahedral short-range order in amorphous alloys. Phys. Rev. Lett., 2004, 92(14): 145502-4
[38] Cozzini S, Ronchetti M. Local icosahedral structures in binary-alloy clusters from molecular-dynamics simulation. Phys. Rev. B, 1996, 53(18): 12040-12049
[39] de la Fuente R O, Soler J M. Structure and stability of an amorphous metal. Phys. Rev. Lett., 1998, 81(15): 3159-3162
[40] Qi D W, Wang S. Icosahedral order and defects in metallic liquids and glasses. Phys. Rev. B, 1991, 44(2): 884-887
[41] Liu R S, Li J Y, Dong K J, et al. Formation and evolution properties of clusters in larger liquid metal system during rapid cooling processes. Mater. Sci. Eng. B, 2002, 94(2-3): 141-148
[42] Liu R S, Dong K J, Tian Z A, et al. Formation and magic number characteristics of clusters formed during solidification processes. J. Phys.: Condens. Matter, 2007, 19(19): 196103-17
[43] Liu R S, Dong K J, Li J Y, at al. Formation and description of nano-clusters formed during rapid solidification processes in liquid metals. J. Non-Cryst. Solids, 2005, 351(6-7): 612-617
[44] Dong K J, Liu R S, Yu A B, et al. Simulation study of the evolution mechanisms of clusters in a large-scale liquid Al system during rapid cooling processes. J. Phys.: Condens. Matter, 2003, 15(6): 743-753
[45] Zheng C X, Liu R S, Dong K J, et al. Simulation study on transition mechanisms of microstructures during forming processes of amorphous metals. Trans. Nonferrous Met. Soc. China, 2001, 11(1): 35-39
[46] Dong K J, Liu R S, Zheng C X, et al. Parallel algorithm of solidification process simulation for large-sized system of liquid metal atoms. Trans.Nonferrous Met. Soc. China, 2003, 13(4): 824-829
[47] 张爱龙,刘让苏,梁佳,郑采星. 冷却速率对液态 Ni 凝固过程中微观结构演变影响的模拟研究. 物理化学学报, 2005,21(4): 347-353
[48] 林艳,刘让苏,田泽安 等. 冷却速率对液态金属 Zn 快速凝固过程中微观结构的影响. 物理化学学报, 2008,24(2): 250-256
[49] Volmer M, Weber A. Nucleus formation in supersaturated systems. Z. Phys. Chem., 1926, 119(1): 277-301
[50] Becher R, D?ring W. The kinetic treatment of nuclear formation in supersatured vapors. Ann. Phys., 1935, 24(2): 719-771
[51] Turnbull D, Fisher J C. Rate of nucleation in condensed systems. J. Chem. Phys., 1949, 17(1): 71-73
[52] 李超. 金属学原理. 哈尔滨:哈尔滨工业大学出版社, 1996, 52-54
[53] 冯端. 金属物理学: 第二卷 相变. 北京:科学出版社, 2000, 111-114
[54] Johnson W A, Mehl R F. Reaction kinetics in processes of nucleation and growth. Trans. AIME, 1939, 135(2): 416-458
[55] Avrami M. Kinetics of phase change I. J. Chem. Phys. 1939, 7(12): 1103-1112
[56] Avrami M. Kinetics of phase change II. J. Chem. Phys. 1940, 8(2): 212-224
[57] Raabe D. 计算材料学. 北京:化学工业出版社. 2002, 3-10
[58] 陈舜麟. 计算材料科学. 北京:化学工业出版社. 2005, 1-9
[59] Mandell M J, McTague J P, Rahman. Crystal nucleation in a three-dimensional Lennard-Jones system. II. Nucleation kinetics for 256 and 500 pacticies. J. Chem. Phys., 1977, 66(7): 3070-3081
[60] Jund P, Caprion D, Jullien R. Is there an ideal quenching rate for an ideal glass? Phys. Rev. Lett., 1997, 79(1): 91-94
[61] Yu D Q, Chen M, Han X. Structure analysis methods for crystalline solids and supercooled liquids. Phys. Rev. E, 2005, 72(5): 051202
[62] O’Malley B, Snook I. Crystal nucleation in the hard sphere system. Phys. Rev. Lett., 2003, 90(8): 085702-4
[63] Kob W. Computer simulations of supercooled liquids and glasses. J. Phys.: Condens. Matter, 1999, 11(10): R85-R115
[64] Rahman A. Correlations in the motion of atoms in liquid argon. Phys. Rev., 1964, 136(2A): A405-A411
[65] Rahman A. Density fluctuations in liquid rubidium. II. Molecular-dynamics calculations. Phys. Rev. A, 1974, 9(4): 1667-1671
[66] Van Duijneveldt J S, Frenkel D. Computer simulation study of free energy barriers in crystal nucleation. J. Chem. Phys., 1992, 96(6): 4655-4668
[67] Halicio?lu T, Pound G M. Calculation of potential energy parameters form crystalline state properties. Phys. Stat. Sol. 1975, 30(2): 619-623
[68] Zhen S, Davies G J. Calculation of the Lennard-Jones n-m potential energy parameters for metals. Phys. Stat. Sol. A, 1983, 78(2): 595-605
[69] Ghatee M H, Sanchooli M. Structural properties of liquid cesium metal by application of cohesive energy density. Fluid Phase Equilib., 2006, 240(1): 22-28
[70] Heine V, Abarenkov V. A new method for the electronic structure of metals. Phil. Mag., 1964, 9(99): 451-465
[71] Shaw R. Optimum Form of a Modified Heine-Abarenkov Model Potential for the Theory of Simple Metals. Phys. Rev., 1968, 174(3): 173-781
[72] Appapillai M, Williams A R. The optimized model potential for thirty-three elements. J. Phys. F: Metal. Phys., 1973, 3(4): 759-770
[73] Harrison W A. Model pseudopotential and the Kohn effect in lead. Phys. Rev., 1965, 139(1A): A179-A185
[74] Jena P, Das T P, Mahanti S D. Pseudopotential calculation of the knight shift and relaxation time in magnesium. Phys. Rev. B, 1970, 2(6): 2264-2267
[75] Hausleitner C, Hafner. A novel hybridised nearly-free-electron tight-binding-bond approach to interatomic forces in disordered transition-metal alloys application to the modelling of metallic glasses. J. Phys.: Condens. Matter, 1990, 2(31): 6651-6657
[76] Woo C H, Wang S, Matsuura M. Electronic structure of metals. I. Energy independent model pseudopotential formalism. J. Phys. F: Metal Phys., 1975, 5(10): 1836-1848
[77] Woo C H, Wang S, Matsuura M. Electronic structure of metals. II. Phonon spectra and Fermi surface distortions. J. Phys. F: Metal Phys., 1975, 5(10): 1849-1859
[78] Wang S, Lai S K. Structure and electrical resistivities of liquid binary alloys. J. Phys. F: Metal. Phys., 1980, 10(12): 2717-2737
[79] Li D H, Li X R, Wang S. Variational calculation of Helmholtz free energies with applications to the sp-type liquid metals. J. Phys. F: Metal. Phys., 1986, 16(3): 309-321
[80] Lai S K, Wang S, Wang K P. A computer “experiment” on the microstructureof amorphous Cr. J. Chem. Phys., 1987, 87(1): 599-603
[81] Li D H, Moore, R A, Wang S. A computer and analytic study of the metallic liquid-glass transition. J. Chem. Phys., 1988, 88(4): 2700-2705
[82] Lu J, Szpunar J A. Glass formation and crystallization of liquid and glass rubidium: A constant-pressure molecular-dynamics study. J. Chem. Phys., 1992, 97(2): 1313-1319
[83] Qi D W, Lu J, Wang S. Crystallization properties of a supercooled metallic liquid. J. Chem. Phys., 1992, 96(1): 513-516
[84] Liu C F, Wang S. On the phase transitions of binary Al 0.86 V0.14 glass. J. Phys.: Condens. Matter, 1992, 4(32): 6729-6734
[85] Jin Z H, Lu K, Gong Y D, et al. Glass transition and atomic structures in supercooled Ga 0.15 Zn 0.15 Mg0.7 metallic liquids: A constant pressure molecular dynamics study. J. Chem. Phys., 1997, 106(21): 8830-8840
[86] Liu R S, Wang S. Anomalies in the structure factor for some rapidly quenched metals. Phys. Rev. B, 1992, 46(18): 12001-12003
[87] Liu R S, Qi D W,Wang S. Subpeaks of the structure factors for rapidly quenched metals. Phys. Rev. B, 1992, 45(1): 451-453
[88] 张海涛, 刘让苏, 侯兆阳 等. 冷速对液态金属 Ga 凝固过程中微观结构演变影响的模拟研究. 2006, 55(5): 2409-2417
[89] 刘让苏, 覃树萍, 侯兆阳 等. 液态金属 In 凝固过程中微观结构转变的模拟研究. 2004, 53(9): 3119-3124
[90] Swope W C, Anderson H C. 10 6 particle molecular-dynamics study of homogeneous nucleation of crystals in supercooled atomic liquid. Phys. Rev. B., 1991, 41(10): 7042-7054
[91] Streitz F H, Glosli J N, Patel M V. Beyond finite-size scaling in solidification simulations. Phys. Rev. Lett., 2006, 96(22): 225701-4
[92] Daw M S, Baskes M I. Embedded atom method:Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B, 1983, 29(12): 6443-6453
[93] Johnson R A. Analytic nearest-neighbor model for FCC metals. Phys. Rev. B, 1989, 37(12): 3924-3931
[94] Foiles S M, Baskes M I, Daw M S. Embedded-atom-method function for the fcc metal Cu, Ag, Au, Ni, Pd, Pt and their alloys. Phys. Rev. B, 1986, 33(12): 7983-7991
[95] Manninen M, Johnson R A. Interatomic interactions in solids. Phys. Rev. B,1986, 34(12): 8486-8495
[96] Zhang B W, Ouyang Y F, Liao S Z, et al. An anslytic MEAM mode for all BCC transition metals. Physica B, 1999, 262(3-4): 218-225
[97] Hu W Y, Zhang B W, Huang B Y, et al. Analytic modified embedded atom potentials for HCP metlas. J. Phys.: Conden. Mater, 2001, 13(6): 1193-1213
[98] 王丽, 边秀房, 李辉. 金属 Cu 液固转变及晶体生长的分子动力学模拟. 化学物理学报,2000, 16(9): 852-829
[99] 陈魁英, 刘洪波, 金朝晖, 胡壮麒. 过冷液态Mg 70 Zn30合金微观结构的分子动力学研究. 自然科学进展-国家重点实验室通讯,1996, 6(1): 98-104
[100] Xiao S F, Hu W Y. Comparative study of microstructural evolution during melting and crystallization. J. Chem. Phys. 2006, 125(1): 014503-7
[101] Sheng H W, He J H, Ma E. Molecular dynamics simulation studies of atomic-level structures in rapidly quenched Ag-Cu nonequilibrium alloys. Phys. Rev. B, 65(18): 184203-10
[102] Finnis M W, Sinclair J E. A simple empirical n-body potential for transition-metals. Philos. Mag. A, 1984, 50(1): 45-55
[103] Yamamoto R, Doyama M. The polyhedron anc cavity analyses of a structural model of amorphous iron. J. Phys. F: Metal Phys., 1979, 9(4): 617-627
[104] Hsu C S, Rahman A. Interaction potentials and their effect on crystal nucleation and symmetry. J. Chem. Phys., 1979, 71(12): 4974-4986
[105] Watanabe M S, Tsumuraya K. Crystallization and glass formation processes in liquid sodium: a molecular dynamics study. J. Chem. Phys., 1987, 87(8): 4891-4900
[106] Srolovitz D, Maeda K Takeuch S, et al. Local structure and topology of model amorphous metal. J. Phys. F: Metal Phys., 1981, 11(11): 2209-2219
[107] Takagi T, Ohkubo T, Hirotsu Y, et al. Local structure of amorphous Zr 70 Pd30 alloy studied by electron diffraction. Appl. Phys. Lett., 2001, 79(4): 485-487
[108] Boudreaux D S, Frost H J. Short-range order in theoretical models of binary metallic glass alloys. Phys. Rev. B, 1981, 23(4): 1506-1516
[109] Ten Wolde P R, Ruiz-Montero M J, Frenkel D. Numerical calculation of the rate of crystal nucleation in a Lennard-Jones system at moderate unercooling. J. Chem. Phys. 1996, 104(24): 9932-9947
[110] Liu H R, Liu R S, Zhang A L, et al. A simulation study of microstructure evolution during solidification process of liquid metal Ni. Chin. Phys., 2007, 16(12): 3747-3753
[111] 郑采星, 刘让苏, 彭平. 二元液态金属 Cu-Ni 和 Ag-Cu 凝固过程的分子动力学模拟研究. 原子与分子物理学报. 2003, 20(2): 163-168
[112] 郑采星, 刘让苏, 田泽安 等. 二元液态金属Ag x Cu1-x快速凝固过程的分子动力学模拟研究. 稀有金属材料与工程, 2005, 34(3): 350-354
[113] Liu J, Zhao J Z, Hu Z Q. MD study of the glass transition in binary liquid metals: Ni 6 Cu 4 and Ag 6 Cu 4. Intermetallics, 2007, 15(10): 1361-1366
[114] Liu J, Zhao J Z, Hu Z Q. The development of microstructure in a rapidly solidified Cu. Mater. Sci. Eng. A, 2007, 452 (1): 103-109
[115] 孙民华, 边秀房, 王艳 等. Al 80 Cu20合金液态原子微观结构及其与非晶形成能力的关系. 金属功能材料, 2001, 8(4): 33-37
[116] 李辉, 边秀房, 李玉忱 等. 铁磁性物质 Co 的液态结构分子动力学模拟. 化学学报, 1999, 57(1): 47-52
[117] 王丽, 衣粟, 边秀房. Ni3Al合金液态与非晶中的原子团簇. 物理化学学报. 2002, 18(4): 297-301
[118] Bai X M, Li Mo. Test of classical nucleation theory via molecular-dynamics simulation. J. Chem. Phys., 2005, 122(22): 224510-8
[119] Liu J, Zhao J Z, Hu Z Q. Kinetic details of the nucleation in supercooled liquid metals. Appl. Phys. Lett., 2006, 89(3): 031903-4
[120] Honeycutt J D, Anderson H C. Small system size artifacts in the molecular dynamics simulation of homogeneous crystal nucleation in supercooled atomic liquids. J. Phys. Chem., 1986, 90(8): 1585-1589
[121] Gasser U, Weeks E R, Schofield A, et al. Real-space imaging of nucleation and growth in colloidal crystallization. Science, 2001, 292(13): 258-262
[122] Moroni D, ten Wolde P R, Bolhuis P G. Interplay between structure and size in a critical crystal nucleus. Phys. Rev. Lett., 2005, 94(17): 235703-4
[123] Palle N, Dantzig J A. An adaptive mesh refinement scheme for sodification problems. Metall. Mater. Trans. A, 1996, 27(3): 695-705
[124] Curreri P A, Kaukler W F. Real-time X-ray transmission microscopy of solidifying Al-In alloy. Metall. Mater. Trans. A, 1996, 27(3): 801-808
[125] Wang L, Cong H R, Zhang Y N, Bian X F. Medium-range order of liquid metal in the quenched state. Physica B, 2005, 355(1-4): 140-146
[126] 李基永, 刘让苏, 周征 等. 液态金属的初始状态对凝固微结构影响的模拟研究. 原子与分子物理学报, 1998, 15(2): 193-197
[127] 刘让苏, 刘凤翔, 李基永 等. 液态金属 Al 的热历史对凝固微结构的影响. 物理化学学报, 2003, 19(9): 791-794
[128] Liu C S, Xia J C, Zhu Z G, et al. The cooling rate dependence of crystallization of liq uid copper: A molecular dynamics study. 2001, 114(17): 7506-7512
[129] Johnson M D, Hutchinson P, March N H. Ion-Ion oscillatory potentials in liquid metals. Proc. R. Soc. A, 1964, 282(3): 283-302
[130] Lai S K, Chen H S. The structural and dynamical liquid-glass transition for metallic sodium. J. Phys.: Condens. Matter, 1993, 5(26): 4325-4332
[131] Qi D W, Lu J, Wang S. Crystallization properties of a supercooled metallic liquid. J. Chem. Phys., 1992, 96(1): 513-516
[132] Verlet L. Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev., 1967, 159(1): 98-103
[133] Rahman A, Stillinger F H. Molecular dynamics study of liquid water. J. Chem. Phys., 1971, 55(7): 3336-3359
[134] Anderson H C. Molecular dynamics simulations at contant pressure and/or temperature. J. Chem. Phys., 1980, 72(4): 2384-2393
[135] Hoover W G, Evans D J. Lennard-Lones triple-point bulk and shear viscosities. Green-Kubo theory, Hamiltonian mechanics, and nonequilibrium molecular dynamics. Phys. Rev. A, 1980, 22(4): 1960-1697
[136] Parrinello M, Rahman A. Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys., 1981, 52(12): 7182-7190
[137] Hoover W G, Ladd A J, Moran B. High-strain-rate plastic flow studied via nonequilibrium molecular dynamics. Phys. Rev. Lett., 1982, 48(26): 1818-1820
[138] Evans D J. Computer “experiment” for nonlinear thermodynamics of Couette flow. J. Chem. Phys., 1983,78(6): 3297-3302
[139] Brown D, Clarke J H R. A comparison of constant energy, constant temperature and constant pressure ensembles in molecular dynamics simulations of atomic liquids. Mol. Phys., 1984, 51(5): 1243-1252
[140] Nose S. A molecular dynamics method for simulations in canonical ensemble. Mol. Phys. 1984, 52(2): 255-268
[141] Car R, Parrinello M. Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett., 1985, 55(22): 2571-2474
[142] 张跃, 谷景华, 尚家香, 马岳. 计算材料科学基础. 北京: 北京航空航天大 学 出版社, 2006, 82-84
[143] 冯端. 金属物理学:第一卷 结构与缺陷. 北京:科学出版社,1998,55-58
[144] Harrison W A. Electronic structure and the properties of metals. I. Formation.Phys. Rev. 1963, 129(6): 2503-2511
[145] Harrison W A. Electronic structure and the properties of metals. II. Application to Zinc. Phys. Rev. 1963, 129(6): 2512-2524
[146] 文玉华, 朱如曾, 周富信, 王崇愚. 分子动力学模拟的主要技术. 力学进展. 2003, 33(1): 65-73
[147] 陈正隆, 徐为人, 汤立达. 分子模拟的理论与实践. 北京:化学工业出版社, 2007, 84-85
[148] Masayuki Hasagawa, Mitsuo Watabe. Theory of compressibility of simple liquid metals. J. Phys. Soc. Jpn., 1972, 32(1): 14-28
[149] Leung C H, Stott M J, Young W H. Thermodynamic properties of solid alloy: application for Mg x Cd 1-x. J. Phys. F: Metal Phys., 1976, 6(6): 1039-1051
[150] Waseda Y. The structure of non-crystalline materials. New York: McGraw-Hill, 1980, 268-269
[151] 下地光雄. 液态金属. 北京:科学出版社, 1987, 218-219
[152] Guimbard J, Gobin P. The influence of quenching temperature on the hardening of pure alumimium quenched to -720 C. Brit. J. Appl. Phys., 1967, 18(4):1641-1644
[153] Manov V P, Popel S I, Buler P I, et al. The influence of quenching temperature on the structure and properties of amorphous. Mater. Sci. Eng. A, 1991, 133(15): 535-540
[154] 关绍康, 汤亚力, 沈福宁, 胡汉起. 熔体热历史对快凝铝铁基显微组织不均匀性的影响. 航空学报, 1994,15(11): 1395-1397
[155] 魏朋义, 傅恒志. 熔体温度对快凝 Al-Si 过共晶合金条带微观组织及性能的影响. 金属学报, 1996, 32(8): 817-822
[156] Wen Y H, Li N, Tu M J. Effect of quenching temperature on recovery stress of Fe-18Mn-5Si-8Cr-4Ni alloy. Scripta Mater., 2001, 44(7): 1113-1116
[157] Chi G C, Chen H S, Miller C E. The influence of quenching procedures on the kinetics of embrittlement in a Fe 40 Ni 40 B20 metallic glass. J. Appl. Phys., 49(3): 1715-1717
[158] 关绍康, 沈福宁, 胡汉起. 熔体热经历对快凝铝铁基合金中相形成的影响机制. 铸造, 1997, 46(11): 20-23
[159] 周晓明, 任英磊, 姜文辉 等. 铸造凝固冷速对原位自生(TiW)C/Fe 复合材料组织的影响. 航空材料学报, 2004, 24(6): 25-28
[160] 曾卫东, 周义刚. 冷速对 TC11 合金 β 加工显微组织和力学性能的影响. 金属学报, 2002, 38(12): 1273-1276
[161] 胡广勇,左良,程力智,梁志德. 快凝速度对淬态 Fe-6.5%Si 薄带织构的影响. 金属功能材料, 1998, 5(5): 207-209
[162] Yang C Y, Sayers D E, Paesler M A. X-ray-absorption spectroscopy studies of glassy As 2 S3: The role of rapid quenching. Phys. Rev. B, 1987, 36(15): 8122-8128
[163] Yue Y Z, von der Ohe R, Jensen S L. Fictive temperature, cooling rate, and viscosity of glasses. J. Chem. Phys., 2004, 20(17): 8053-8059
[164] Wendt H R, Abraham F F. Empirical criterion for the glass transition region based on Monte Carlo simulations. Phys. Rev. Lett. 1978, 41(18): 1244-1246
[165] Abraham F F. An isothermal-isobaric computer simulation of the supercooled-liquid/glass transition region: Is the short-range order in the amorphous solid fcc? J. Chem. Phys., 1980, 72(1): 359-365
[166] Lai S K, Chen H C. The structural and dynamical liquid-glass transition for metallic sodium. J. Phys. F: Met. Phys., 1993, 5(26): 4325-4342
[167] 黄卫东, 丁国陆, 周尧和. 非稳态过程与凝固界面形态选择. 1995, 9(3): 193-207
[168] 丁国陆, 林鑫, 黄卫东, 周尧和. 定向凝固一次枝晶间距的历史相关性. 金属学报. 1995, 31(10): A469-A474
[169] 湛垦华, 沈小峰. 普利高津与耗散结构理论. 西安: 陕西科技出版社, 1982: 60-61
[170] Heer W A. The physics of simple metal clusters experimental aspects and simple models. Rev. Mod. Phys. 1993, 65(3): 611-676
[171] Jensen P. Growth of nanostructures by cluster deposition experiments and simple models. Rev. Mod. Phys. 1999, 71(5): 1695-1735
[172] Diederich T, Doppner T, Fennel T, et al. Shell structure of magnesium and other divalent metal clusters. Phys. Rev. A, 2005, 72(2): 023203-4
[173] Diederich T, Doppner T, Braune J, et al. Electron delocalization in magnesium clusters grown in supercold helium droplets. Phys. Rev. Lett., 2001, 86(21): 4807-4810
[174] Gervais B, Giglio E, Jacquet E. Spectroscopic properties of Na clusters embedded in a rare-gas matrix. Phys. Rev. A, 2005, 71(1): 015201-4
[175] Martins J L, Buttet J, Car R. Electronic and structural properties of sodium clusters. Rhys. Rev. B. 1985, 31(4): 1804-1816
[176] Bonai?-Koutecky V, Fantucci P, Koutecky J. Systematic ab initio configuration-interaction of alkali-metal clusters. II. Relation betweenelecteronic structure and geometry of small sodium clusters. Phys. Rev. B, 1988, 37(9): 4369-4374
[177] Bj?rnholm S, Borggreen J, Echt O, et al. Mean-field quantization of several hundred electrons in sodium metal clusters. Phys. Rev. Lett., 1990, 65(13): 1627-1630
[178] Haberland H, Hippler T, Donges J, et al. Melting of sodium clusters: Where do the magic numbers come from? Phys. Rev. Lett., 2005, 94(28): 035701-4
[179] Oviedo J, Palmer R E. Amorphous structures of Cu, Ag, and Au nanoclusters from first principles calculations. J. Chem. Phys., 2002, 117(21): 9548-9551
[180] Solov’yov I A, Solov’yov A V, Greiner W. Cluster growing process and a sequence of magic numbers. Phys. Rev. Lett., 2003, 90(5): 053401-4
[181] Zhang Z, Hu W Y, Xiao S F. Shell and subshell periodic structures of icosahedral nickel nanoclusters. J. Chem. Phys., 2005, 122(21): 214501-5
[182] 陈玉红,张材荣,马军. Mg m Bn(m=1,2; n=1-4)团簇结构与性质的密度泛函理论研究. 物理学报,2006, 55(1): 171-178
[183] 王广厚. 原子团簇的稳定结构和幻数. 物理学进展, 2000, 20(1): 52-92
[184] Wang L, Bian X F, Zhang Y N. Structural simulation of clusters in liquid Ni 50 Al 50 alloys. Modelling Simul. Mater. Sci. Eng., 2002, 10(2): 331-339
[185] 刘俊, 赵九洲, 胡壮麒. Cu-50%Ni 合金快速凝固过程中原子团簇演变的分子动力学模拟. 金属学报, 2005, 41(2): 219-224
[186] 徐延祎, 王丽, 边秀房. 液态 Ni 原子团簇演变的计算机模拟. 原子与分子物理学报. 2002, 19(1): 65-74
[187] Kramer M J, Sordelet D J. Polymorphism in the short-range order of Zr 70 Pd 30 metallic glasses. J. Non-Cryst. Solids. 2005, 351(19-20): 1586-1593
[188] Doye J P K, Wales D J, Zetterling F H M, Dzugutov M. The favored cluster structures of model glass formers. J. Chem. Phys., 2003, 118(6): 2792-2799
[189] Martin T P. Shells of atoms. Phys. Rep., 1996, 273:199-241
[190] Flemings M C. Solidification processing. New York: McGraw-Hill. 1974, 290-319
[191] Doye J P K, Wales D J. Polytetrahedral clusters. Phys. Rev. Lett., 2001, 86(25): 5719-5722
[192] 卢博斯基. 非晶态金属合金. 北京:冶金工业出版社. 1989, 192-221
[193] Kulik T. Nanocrystallization of metallic glasses. J. Non-Cryst. Solids, 2001, 287(1): 145-161
[194] Li J M. Self-organized nanocrystalline stripe patterns generated during earlycrystallization of a nonequilibrium metallic glass. Appl. Phys. Lett., 2002, 90(4): 041913-3
[195] Li J M, Quan M X, Hu Z Q. Preferential precipitation sequence of metastable phase during crystallization of (Fe 0.99 Mo 0.01 ) 78 Si 9 B13 metallic glass. Appl. Phys. Lett. 1996, 69(16): 2356-2358
[196] Lu K. Nanocrystalline metals crystallized from amorphous solids: nonocrystallization, structure, and properties. Mater. Sci. Pep. 1996, R16(1): 161-221
[197] 苏勇, 陈翌庆,丁厚福,郑玉春. Al 9 1Ni 7 Y2纳米非晶复合材料晶化的研究. 兵器材料科学与工程, 2000, 23(4): 12-24
[198] 赵文君,徐晖,王智平 等. Fe 68 Nd 5 Zr 2 Y 4 B21大块非晶合金磁性能的研究. 稀有金属材料与工程, 2008, 37(1): 139-142
[199] 唐建成,吴爱华,张萌,刘文胜. 预退火对纳米晶Fe 86 Zr 7 B6Cu合金显微组织和软磁性能的影响. 中国有色金属学报, 2007, 17(10): 1593-1596
[200] 孙国元 陈光 陈国良. 非晶合金的晶化理论及几种 Mg 基非晶合金的晶化行为. 有色金属, 2004, 56(4): 1-7
[201] Lu K, Zhang X H. Identification of crystal nucleation and growth in an amorphous FeZr2 alloy by means of electrical resistance measurements. Phil. Mag. Lett., 2000, 80(12): 797-805
[202] Greer A L. Crystallization kinetics of iron-boron (Fe 80 B20) glass. Acta Metall., 1982, 30(1): 171-192
[203] 王亚平,卢柯. 非晶态合金晶化过程的高精度电阻监测研究. 中国科学, 2000, 30(3): 193-199
[204] Chen F F, Zhang H F, Qin F X, et al. Molecular dynamics study of atomic transport properties in rapidly cooling liquid copper. J. Chem. Phys. 2004, 120(4): 1826-1831
[205] Pei Q X, Lu C, Lee H P. Crystallization of amorphous alloy during isothermal annealing: a molecular dynamics study. J. Phys.: Condens. Matter, 2005, 17(10): 1493-1504
[206] Kelton K F, Lee G W, Gangopadhyay A K, et al. First X-ray scattering studies on electrostatically levitated metallic liquids: Demonstrated influence of local icosahedral order on the nucleation barrier. Phys. Rev. Lett. 2003, 90(19): 195504-4
[207] Lu K, Lück R, and Predel B. The temperature vs time transformation (T-T-T) diagram for a transition from the amorphous to the nanocrystalline state. Acta. Metall. Mater., 1994, 42(7): 2303-2311
[2] 傅 恒 志 ,柳 百 成 ,魏 炳 波 . 凝 固 科 学 技 术 与 发 展 . 北 京 :国 防 工 业出 版 社 , 2005, 2-69
[3] Alder B J, Wainwright T E. Phase transition for a hard sphere system. J. Chem. Phys., 1957, 27(5): 1208-1209
[4] Finney J L. Random Packing and the structure of simple liquids. Proc. R. Soc. A, 1970, 319(10): 479-493
[5] Steinhardt P J, Nelson D R, and Ronchetti M. Bond-orientational order in liquids and glasses. Rhys. Rev. B, 1983, 28(2): 784-805
[6] Honeycutt J D, Andersen H C. Molecular-dynamics study of melting and freezing of small Lennard-Jones clusters. J. Phys. Chem., 1987, 91(19), 4950-4963
[7] Chen H S. Glassy metals. Rep. Prog. Phys., 1980, 43(4): 353-432
[8] 惠希东, 陈国良. 块体非晶合金. 北京:化学工业出版社. 2007,75-87
[9] Bernal J. A geometrical approach to the structure of liquid. Nature, 1959, 183(17): 141-147
[10] Scott G D. Radial distribution of the random close packing of equal spheres. 1962, 194(9): 956-957
[11] Cohen M H, Turnbull D. Metastability of amorphous structures. 1964, 203(29): 964-964
[12] Sadoc J L, Dixmier J, Ginier A. Theoretical calculation of dense random packings of equal and non-equal sized hard spheres applications to amorphous metallic alloys. J. Non-Cryst. Solids, 1973, 12(1): 46-60
[13] Connel G A N. Dense random packing of hard and compressible spheres. Solid State Commun., 1975, 16(1): 109-112
[14] Barker J A, Hoare M R. Relaxation of the Bernal model. Nature, 1975, 257(11): 120-122
[15] Gaskill G S. A new structural model for transition metal? Metalloid glasses. Nature, 1978, 276(30): 484-485
[16] Miracle D B. A structure model for metallic glass. Nature, 2004, 3(19):697-702
[17] Sheng H W, Luo W K, Alamgir F M, et al. Atomic packing and short-to-medium-range order in metallic glasses. Nature, 2006, 439(26):419-425
[18] 王 广 厚 . 团 簇 物 理 学 . 上 海 : 上 海 科 学 技 术 出 版 社 , 2003, 1-9
[19] 李先芬. 共晶与匀晶系二元合金熔体结构转变及其对凝固的影响: [博士学位论文]. 合肥: 合肥工业大学, 2006, 18-19
[20] 边秀房,王伟民,李辉,马家骥. 金属熔体结构. 上海:上海交通大学出版社,2003, 66-79
[21] Reichert H, Klein O, Dosch H, et al. Observation of five-fold local symmetry in liquid lead. Nature, 2000, 408(14): 839-841
[22] Spaepen F. Condensed-matter science: Five-fold symmetry in liquid. Nature, 2000, 408(14): 781-782
[23] Schenk T, Moritz D H, Simonet V, et al. Icosahedral short-range order in deeply undercooled metallic melts. Phys. Rev. Lett., 2002, 89(7): 075507-4
[24] Steeb S, Entress H. Atom distribution and eleetrical resistivity of molten magnesium-tin alloys. Z. Metallkunde, 1966, 57(11): 803-807
[25] Alblas B P, van der Marel C, Geertsma W, et al. Experimental results for liquid Alkali-group IV alloys. J. Non-Cryst. Solids, 1984, 61(1): 201-206
[26] 潘学民, 边秀房, 秦敬玉, 王伟民. Cu-12%Al 合金熔体内中程有序原子团簇. 物理化学学报, 2001, 17(8): 707-712
[27] 丛红日, 边秀房, 李辉. Al 5 Fe2合金熔体中程有序结构的研究. 化学学报, 2002, 60(2): 287-292
[28] 边秀房,王伟明,潘学民 等. Al-TM 合金熔体的中程有序结构及其演化规律. 化学学报, 2002, 60(7): 1215-1219
[29] 边秀房,潘学民, 秦绪波 等. 金属熔体中程有序结构. 中国科学 E,2002, 32(2): 145-151
[30] Zhou J K, Bian X F, Wang W M, et al. Medium-range order and crystallization in amorphous Al–Ni–Pr alloys. Mater. Lett., 2004, 58(27): 2559-2563
[31] Zhang L, Wu Y S, Bian X F, et al. Short-range and medium-range order in liquid and amorphous Al90Fe5Ce5 alloys. J. Non-Cryst. Solids, 2000, 262(1-3): 169-176
[32] 秦敬玉. 液体 Al-Fe 合金的微观不均匀结构研究: [博士学位论文]. 济南: 山东工业大学, 1998, 70-83
[33] Jónsson H and Andersen H C. Icosahedral ordering in the Lennard-Jones liquid and glass. Phys. Rev. Lett., 1988, 60(22): 2295-2298
[34] Jakse N, Lebacq O, Pasturel A. Ab initio molecular-dynamics simulations of short-range order in liquid Al 80 Mn 20 and Al 80 Ni20 alloys. Phys. Rev. Lett., 2004, 93(20): 207801-4
[35] Jakse N, Pasturel. Local order of liquid and supercooled zirconium by ab initio molecular dynamics. Phys. Rev. Lett., 2003, 91(19): 195501-4
[36] Tomida T, Egami T. Molecular-dynamics study of orientational order in liquids and glasses and its relation to the glass transition. Phys. Rev. B, 1995, 52(5): 3290-3308
[37] Luo W K, Sheng H W, Alamgir F M, et al. Icosahedral short-range order in amorphous alloys. Phys. Rev. Lett., 2004, 92(14): 145502-4
[38] Cozzini S, Ronchetti M. Local icosahedral structures in binary-alloy clusters from molecular-dynamics simulation. Phys. Rev. B, 1996, 53(18): 12040-12049
[39] de la Fuente R O, Soler J M. Structure and stability of an amorphous metal. Phys. Rev. Lett., 1998, 81(15): 3159-3162
[40] Qi D W, Wang S. Icosahedral order and defects in metallic liquids and glasses. Phys. Rev. B, 1991, 44(2): 884-887
[41] Liu R S, Li J Y, Dong K J, et al. Formation and evolution properties of clusters in larger liquid metal system during rapid cooling processes. Mater. Sci. Eng. B, 2002, 94(2-3): 141-148
[42] Liu R S, Dong K J, Tian Z A, et al. Formation and magic number characteristics of clusters formed during solidification processes. J. Phys.: Condens. Matter, 2007, 19(19): 196103-17
[43] Liu R S, Dong K J, Li J Y, at al. Formation and description of nano-clusters formed during rapid solidification processes in liquid metals. J. Non-Cryst. Solids, 2005, 351(6-7): 612-617
[44] Dong K J, Liu R S, Yu A B, et al. Simulation study of the evolution mechanisms of clusters in a large-scale liquid Al system during rapid cooling processes. J. Phys.: Condens. Matter, 2003, 15(6): 743-753
[45] Zheng C X, Liu R S, Dong K J, et al. Simulation study on transition mechanisms of microstructures during forming processes of amorphous metals. Trans. Nonferrous Met. Soc. China, 2001, 11(1): 35-39
[46] Dong K J, Liu R S, Zheng C X, et al. Parallel algorithm of solidification process simulation for large-sized system of liquid metal atoms. Trans.Nonferrous Met. Soc. China, 2003, 13(4): 824-829
[47] 张爱龙,刘让苏,梁佳,郑采星. 冷却速率对液态 Ni 凝固过程中微观结构演变影响的模拟研究. 物理化学学报, 2005,21(4): 347-353
[48] 林艳,刘让苏,田泽安 等. 冷却速率对液态金属 Zn 快速凝固过程中微观结构的影响. 物理化学学报, 2008,24(2): 250-256
[49] Volmer M, Weber A. Nucleus formation in supersaturated systems. Z. Phys. Chem., 1926, 119(1): 277-301
[50] Becher R, D?ring W. The kinetic treatment of nuclear formation in supersatured vapors. Ann. Phys., 1935, 24(2): 719-771
[51] Turnbull D, Fisher J C. Rate of nucleation in condensed systems. J. Chem. Phys., 1949, 17(1): 71-73
[52] 李超. 金属学原理. 哈尔滨:哈尔滨工业大学出版社, 1996, 52-54
[53] 冯端. 金属物理学: 第二卷 相变. 北京:科学出版社, 2000, 111-114
[54] Johnson W A, Mehl R F. Reaction kinetics in processes of nucleation and growth. Trans. AIME, 1939, 135(2): 416-458
[55] Avrami M. Kinetics of phase change I. J. Chem. Phys. 1939, 7(12): 1103-1112
[56] Avrami M. Kinetics of phase change II. J. Chem. Phys. 1940, 8(2): 212-224
[57] Raabe D. 计算材料学. 北京:化学工业出版社. 2002, 3-10
[58] 陈舜麟. 计算材料科学. 北京:化学工业出版社. 2005, 1-9
[59] Mandell M J, McTague J P, Rahman. Crystal nucleation in a three-dimensional Lennard-Jones system. II. Nucleation kinetics for 256 and 500 pacticies. J. Chem. Phys., 1977, 66(7): 3070-3081
[60] Jund P, Caprion D, Jullien R. Is there an ideal quenching rate for an ideal glass? Phys. Rev. Lett., 1997, 79(1): 91-94
[61] Yu D Q, Chen M, Han X. Structure analysis methods for crystalline solids and supercooled liquids. Phys. Rev. E, 2005, 72(5): 051202
[62] O’Malley B, Snook I. Crystal nucleation in the hard sphere system. Phys. Rev. Lett., 2003, 90(8): 085702-4
[63] Kob W. Computer simulations of supercooled liquids and glasses. J. Phys.: Condens. Matter, 1999, 11(10): R85-R115
[64] Rahman A. Correlations in the motion of atoms in liquid argon. Phys. Rev., 1964, 136(2A): A405-A411
[65] Rahman A. Density fluctuations in liquid rubidium. II. Molecular-dynamics calculations. Phys. Rev. A, 1974, 9(4): 1667-1671
[66] Van Duijneveldt J S, Frenkel D. Computer simulation study of free energy barriers in crystal nucleation. J. Chem. Phys., 1992, 96(6): 4655-4668
[67] Halicio?lu T, Pound G M. Calculation of potential energy parameters form crystalline state properties. Phys. Stat. Sol. 1975, 30(2): 619-623
[68] Zhen S, Davies G J. Calculation of the Lennard-Jones n-m potential energy parameters for metals. Phys. Stat. Sol. A, 1983, 78(2): 595-605
[69] Ghatee M H, Sanchooli M. Structural properties of liquid cesium metal by application of cohesive energy density. Fluid Phase Equilib., 2006, 240(1): 22-28
[70] Heine V, Abarenkov V. A new method for the electronic structure of metals. Phil. Mag., 1964, 9(99): 451-465
[71] Shaw R. Optimum Form of a Modified Heine-Abarenkov Model Potential for the Theory of Simple Metals. Phys. Rev., 1968, 174(3): 173-781
[72] Appapillai M, Williams A R. The optimized model potential for thirty-three elements. J. Phys. F: Metal. Phys., 1973, 3(4): 759-770
[73] Harrison W A. Model pseudopotential and the Kohn effect in lead. Phys. Rev., 1965, 139(1A): A179-A185
[74] Jena P, Das T P, Mahanti S D. Pseudopotential calculation of the knight shift and relaxation time in magnesium. Phys. Rev. B, 1970, 2(6): 2264-2267
[75] Hausleitner C, Hafner. A novel hybridised nearly-free-electron tight-binding-bond approach to interatomic forces in disordered transition-metal alloys application to the modelling of metallic glasses. J. Phys.: Condens. Matter, 1990, 2(31): 6651-6657
[76] Woo C H, Wang S, Matsuura M. Electronic structure of metals. I. Energy independent model pseudopotential formalism. J. Phys. F: Metal Phys., 1975, 5(10): 1836-1848
[77] Woo C H, Wang S, Matsuura M. Electronic structure of metals. II. Phonon spectra and Fermi surface distortions. J. Phys. F: Metal Phys., 1975, 5(10): 1849-1859
[78] Wang S, Lai S K. Structure and electrical resistivities of liquid binary alloys. J. Phys. F: Metal. Phys., 1980, 10(12): 2717-2737
[79] Li D H, Li X R, Wang S. Variational calculation of Helmholtz free energies with applications to the sp-type liquid metals. J. Phys. F: Metal. Phys., 1986, 16(3): 309-321
[80] Lai S K, Wang S, Wang K P. A computer “experiment” on the microstructureof amorphous Cr. J. Chem. Phys., 1987, 87(1): 599-603
[81] Li D H, Moore, R A, Wang S. A computer and analytic study of the metallic liquid-glass transition. J. Chem. Phys., 1988, 88(4): 2700-2705
[82] Lu J, Szpunar J A. Glass formation and crystallization of liquid and glass rubidium: A constant-pressure molecular-dynamics study. J. Chem. Phys., 1992, 97(2): 1313-1319
[83] Qi D W, Lu J, Wang S. Crystallization properties of a supercooled metallic liquid. J. Chem. Phys., 1992, 96(1): 513-516
[84] Liu C F, Wang S. On the phase transitions of binary Al 0.86 V0.14 glass. J. Phys.: Condens. Matter, 1992, 4(32): 6729-6734
[85] Jin Z H, Lu K, Gong Y D, et al. Glass transition and atomic structures in supercooled Ga 0.15 Zn 0.15 Mg0.7 metallic liquids: A constant pressure molecular dynamics study. J. Chem. Phys., 1997, 106(21): 8830-8840
[86] Liu R S, Wang S. Anomalies in the structure factor for some rapidly quenched metals. Phys. Rev. B, 1992, 46(18): 12001-12003
[87] Liu R S, Qi D W,Wang S. Subpeaks of the structure factors for rapidly quenched metals. Phys. Rev. B, 1992, 45(1): 451-453
[88] 张海涛, 刘让苏, 侯兆阳 等. 冷速对液态金属 Ga 凝固过程中微观结构演变影响的模拟研究. 2006, 55(5): 2409-2417
[89] 刘让苏, 覃树萍, 侯兆阳 等. 液态金属 In 凝固过程中微观结构转变的模拟研究. 2004, 53(9): 3119-3124
[90] Swope W C, Anderson H C. 10 6 particle molecular-dynamics study of homogeneous nucleation of crystals in supercooled atomic liquid. Phys. Rev. B., 1991, 41(10): 7042-7054
[91] Streitz F H, Glosli J N, Patel M V. Beyond finite-size scaling in solidification simulations. Phys. Rev. Lett., 2006, 96(22): 225701-4
[92] Daw M S, Baskes M I. Embedded atom method:Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B, 1983, 29(12): 6443-6453
[93] Johnson R A. Analytic nearest-neighbor model for FCC metals. Phys. Rev. B, 1989, 37(12): 3924-3931
[94] Foiles S M, Baskes M I, Daw M S. Embedded-atom-method function for the fcc metal Cu, Ag, Au, Ni, Pd, Pt and their alloys. Phys. Rev. B, 1986, 33(12): 7983-7991
[95] Manninen M, Johnson R A. Interatomic interactions in solids. Phys. Rev. B,1986, 34(12): 8486-8495
[96] Zhang B W, Ouyang Y F, Liao S Z, et al. An anslytic MEAM mode for all BCC transition metals. Physica B, 1999, 262(3-4): 218-225
[97] Hu W Y, Zhang B W, Huang B Y, et al. Analytic modified embedded atom potentials for HCP metlas. J. Phys.: Conden. Mater, 2001, 13(6): 1193-1213
[98] 王丽, 边秀房, 李辉. 金属 Cu 液固转变及晶体生长的分子动力学模拟. 化学物理学报,2000, 16(9): 852-829
[99] 陈魁英, 刘洪波, 金朝晖, 胡壮麒. 过冷液态Mg 70 Zn30合金微观结构的分子动力学研究. 自然科学进展-国家重点实验室通讯,1996, 6(1): 98-104
[100] Xiao S F, Hu W Y. Comparative study of microstructural evolution during melting and crystallization. J. Chem. Phys. 2006, 125(1): 014503-7
[101] Sheng H W, He J H, Ma E. Molecular dynamics simulation studies of atomic-level structures in rapidly quenched Ag-Cu nonequilibrium alloys. Phys. Rev. B, 65(18): 184203-10
[102] Finnis M W, Sinclair J E. A simple empirical n-body potential for transition-metals. Philos. Mag. A, 1984, 50(1): 45-55
[103] Yamamoto R, Doyama M. The polyhedron anc cavity analyses of a structural model of amorphous iron. J. Phys. F: Metal Phys., 1979, 9(4): 617-627
[104] Hsu C S, Rahman A. Interaction potentials and their effect on crystal nucleation and symmetry. J. Chem. Phys., 1979, 71(12): 4974-4986
[105] Watanabe M S, Tsumuraya K. Crystallization and glass formation processes in liquid sodium: a molecular dynamics study. J. Chem. Phys., 1987, 87(8): 4891-4900
[106] Srolovitz D, Maeda K Takeuch S, et al. Local structure and topology of model amorphous metal. J. Phys. F: Metal Phys., 1981, 11(11): 2209-2219
[107] Takagi T, Ohkubo T, Hirotsu Y, et al. Local structure of amorphous Zr 70 Pd30 alloy studied by electron diffraction. Appl. Phys. Lett., 2001, 79(4): 485-487
[108] Boudreaux D S, Frost H J. Short-range order in theoretical models of binary metallic glass alloys. Phys. Rev. B, 1981, 23(4): 1506-1516
[109] Ten Wolde P R, Ruiz-Montero M J, Frenkel D. Numerical calculation of the rate of crystal nucleation in a Lennard-Jones system at moderate unercooling. J. Chem. Phys. 1996, 104(24): 9932-9947
[110] Liu H R, Liu R S, Zhang A L, et al. A simulation study of microstructure evolution during solidification process of liquid metal Ni. Chin. Phys., 2007, 16(12): 3747-3753
[111] 郑采星, 刘让苏, 彭平. 二元液态金属 Cu-Ni 和 Ag-Cu 凝固过程的分子动力学模拟研究. 原子与分子物理学报. 2003, 20(2): 163-168
[112] 郑采星, 刘让苏, 田泽安 等. 二元液态金属Ag x Cu1-x快速凝固过程的分子动力学模拟研究. 稀有金属材料与工程, 2005, 34(3): 350-354
[113] Liu J, Zhao J Z, Hu Z Q. MD study of the glass transition in binary liquid metals: Ni 6 Cu 4 and Ag 6 Cu 4. Intermetallics, 2007, 15(10): 1361-1366
[114] Liu J, Zhao J Z, Hu Z Q. The development of microstructure in a rapidly solidified Cu. Mater. Sci. Eng. A, 2007, 452 (1): 103-109
[115] 孙民华, 边秀房, 王艳 等. Al 80 Cu20合金液态原子微观结构及其与非晶形成能力的关系. 金属功能材料, 2001, 8(4): 33-37
[116] 李辉, 边秀房, 李玉忱 等. 铁磁性物质 Co 的液态结构分子动力学模拟. 化学学报, 1999, 57(1): 47-52
[117] 王丽, 衣粟, 边秀房. Ni3Al合金液态与非晶中的原子团簇. 物理化学学报. 2002, 18(4): 297-301
[118] Bai X M, Li Mo. Test of classical nucleation theory via molecular-dynamics simulation. J. Chem. Phys., 2005, 122(22): 224510-8
[119] Liu J, Zhao J Z, Hu Z Q. Kinetic details of the nucleation in supercooled liquid metals. Appl. Phys. Lett., 2006, 89(3): 031903-4
[120] Honeycutt J D, Anderson H C. Small system size artifacts in the molecular dynamics simulation of homogeneous crystal nucleation in supercooled atomic liquids. J. Phys. Chem., 1986, 90(8): 1585-1589
[121] Gasser U, Weeks E R, Schofield A, et al. Real-space imaging of nucleation and growth in colloidal crystallization. Science, 2001, 292(13): 258-262
[122] Moroni D, ten Wolde P R, Bolhuis P G. Interplay between structure and size in a critical crystal nucleus. Phys. Rev. Lett., 2005, 94(17): 235703-4
[123] Palle N, Dantzig J A. An adaptive mesh refinement scheme for sodification problems. Metall. Mater. Trans. A, 1996, 27(3): 695-705
[124] Curreri P A, Kaukler W F. Real-time X-ray transmission microscopy of solidifying Al-In alloy. Metall. Mater. Trans. A, 1996, 27(3): 801-808
[125] Wang L, Cong H R, Zhang Y N, Bian X F. Medium-range order of liquid metal in the quenched state. Physica B, 2005, 355(1-4): 140-146
[126] 李基永, 刘让苏, 周征 等. 液态金属的初始状态对凝固微结构影响的模拟研究. 原子与分子物理学报, 1998, 15(2): 193-197
[127] 刘让苏, 刘凤翔, 李基永 等. 液态金属 Al 的热历史对凝固微结构的影响. 物理化学学报, 2003, 19(9): 791-794
[128] Liu C S, Xia J C, Zhu Z G, et al. The cooling rate dependence of crystallization of liq uid copper: A molecular dynamics study. 2001, 114(17): 7506-7512
[129] Johnson M D, Hutchinson P, March N H. Ion-Ion oscillatory potentials in liquid metals. Proc. R. Soc. A, 1964, 282(3): 283-302
[130] Lai S K, Chen H S. The structural and dynamical liquid-glass transition for metallic sodium. J. Phys.: Condens. Matter, 1993, 5(26): 4325-4332
[131] Qi D W, Lu J, Wang S. Crystallization properties of a supercooled metallic liquid. J. Chem. Phys., 1992, 96(1): 513-516
[132] Verlet L. Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev., 1967, 159(1): 98-103
[133] Rahman A, Stillinger F H. Molecular dynamics study of liquid water. J. Chem. Phys., 1971, 55(7): 3336-3359
[134] Anderson H C. Molecular dynamics simulations at contant pressure and/or temperature. J. Chem. Phys., 1980, 72(4): 2384-2393
[135] Hoover W G, Evans D J. Lennard-Lones triple-point bulk and shear viscosities. Green-Kubo theory, Hamiltonian mechanics, and nonequilibrium molecular dynamics. Phys. Rev. A, 1980, 22(4): 1960-1697
[136] Parrinello M, Rahman A. Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys., 1981, 52(12): 7182-7190
[137] Hoover W G, Ladd A J, Moran B. High-strain-rate plastic flow studied via nonequilibrium molecular dynamics. Phys. Rev. Lett., 1982, 48(26): 1818-1820
[138] Evans D J. Computer “experiment” for nonlinear thermodynamics of Couette flow. J. Chem. Phys., 1983,78(6): 3297-3302
[139] Brown D, Clarke J H R. A comparison of constant energy, constant temperature and constant pressure ensembles in molecular dynamics simulations of atomic liquids. Mol. Phys., 1984, 51(5): 1243-1252
[140] Nose S. A molecular dynamics method for simulations in canonical ensemble. Mol. Phys. 1984, 52(2): 255-268
[141] Car R, Parrinello M. Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett., 1985, 55(22): 2571-2474
[142] 张跃, 谷景华, 尚家香, 马岳. 计算材料科学基础. 北京: 北京航空航天大 学 出版社, 2006, 82-84
[143] 冯端. 金属物理学:第一卷 结构与缺陷. 北京:科学出版社,1998,55-58
[144] Harrison W A. Electronic structure and the properties of metals. I. Formation.Phys. Rev. 1963, 129(6): 2503-2511
[145] Harrison W A. Electronic structure and the properties of metals. II. Application to Zinc. Phys. Rev. 1963, 129(6): 2512-2524
[146] 文玉华, 朱如曾, 周富信, 王崇愚. 分子动力学模拟的主要技术. 力学进展. 2003, 33(1): 65-73
[147] 陈正隆, 徐为人, 汤立达. 分子模拟的理论与实践. 北京:化学工业出版社, 2007, 84-85
[148] Masayuki Hasagawa, Mitsuo Watabe. Theory of compressibility of simple liquid metals. J. Phys. Soc. Jpn., 1972, 32(1): 14-28
[149] Leung C H, Stott M J, Young W H. Thermodynamic properties of solid alloy: application for Mg x Cd 1-x. J. Phys. F: Metal Phys., 1976, 6(6): 1039-1051
[150] Waseda Y. The structure of non-crystalline materials. New York: McGraw-Hill, 1980, 268-269
[151] 下地光雄. 液态金属. 北京:科学出版社, 1987, 218-219
[152] Guimbard J, Gobin P. The influence of quenching temperature on the hardening of pure alumimium quenched to -720 C. Brit. J. Appl. Phys., 1967, 18(4):1641-1644
[153] Manov V P, Popel S I, Buler P I, et al. The influence of quenching temperature on the structure and properties of amorphous. Mater. Sci. Eng. A, 1991, 133(15): 535-540
[154] 关绍康, 汤亚力, 沈福宁, 胡汉起. 熔体热历史对快凝铝铁基显微组织不均匀性的影响. 航空学报, 1994,15(11): 1395-1397
[155] 魏朋义, 傅恒志. 熔体温度对快凝 Al-Si 过共晶合金条带微观组织及性能的影响. 金属学报, 1996, 32(8): 817-822
[156] Wen Y H, Li N, Tu M J. Effect of quenching temperature on recovery stress of Fe-18Mn-5Si-8Cr-4Ni alloy. Scripta Mater., 2001, 44(7): 1113-1116
[157] Chi G C, Chen H S, Miller C E. The influence of quenching procedures on the kinetics of embrittlement in a Fe 40 Ni 40 B20 metallic glass. J. Appl. Phys., 49(3): 1715-1717
[158] 关绍康, 沈福宁, 胡汉起. 熔体热经历对快凝铝铁基合金中相形成的影响机制. 铸造, 1997, 46(11): 20-23
[159] 周晓明, 任英磊, 姜文辉 等. 铸造凝固冷速对原位自生(TiW)C/Fe 复合材料组织的影响. 航空材料学报, 2004, 24(6): 25-28
[160] 曾卫东, 周义刚. 冷速对 TC11 合金 β 加工显微组织和力学性能的影响. 金属学报, 2002, 38(12): 1273-1276
[161] 胡广勇,左良,程力智,梁志德. 快凝速度对淬态 Fe-6.5%Si 薄带织构的影响. 金属功能材料, 1998, 5(5): 207-209
[162] Yang C Y, Sayers D E, Paesler M A. X-ray-absorption spectroscopy studies of glassy As 2 S3: The role of rapid quenching. Phys. Rev. B, 1987, 36(15): 8122-8128
[163] Yue Y Z, von der Ohe R, Jensen S L. Fictive temperature, cooling rate, and viscosity of glasses. J. Chem. Phys., 2004, 20(17): 8053-8059
[164] Wendt H R, Abraham F F. Empirical criterion for the glass transition region based on Monte Carlo simulations. Phys. Rev. Lett. 1978, 41(18): 1244-1246
[165] Abraham F F. An isothermal-isobaric computer simulation of the supercooled-liquid/glass transition region: Is the short-range order in the amorphous solid fcc? J. Chem. Phys., 1980, 72(1): 359-365
[166] Lai S K, Chen H C. The structural and dynamical liquid-glass transition for metallic sodium. J. Phys. F: Met. Phys., 1993, 5(26): 4325-4342
[167] 黄卫东, 丁国陆, 周尧和. 非稳态过程与凝固界面形态选择. 1995, 9(3): 193-207
[168] 丁国陆, 林鑫, 黄卫东, 周尧和. 定向凝固一次枝晶间距的历史相关性. 金属学报. 1995, 31(10): A469-A474
[169] 湛垦华, 沈小峰. 普利高津与耗散结构理论. 西安: 陕西科技出版社, 1982: 60-61
[170] Heer W A. The physics of simple metal clusters experimental aspects and simple models. Rev. Mod. Phys. 1993, 65(3): 611-676
[171] Jensen P. Growth of nanostructures by cluster deposition experiments and simple models. Rev. Mod. Phys. 1999, 71(5): 1695-1735
[172] Diederich T, Doppner T, Fennel T, et al. Shell structure of magnesium and other divalent metal clusters. Phys. Rev. A, 2005, 72(2): 023203-4
[173] Diederich T, Doppner T, Braune J, et al. Electron delocalization in magnesium clusters grown in supercold helium droplets. Phys. Rev. Lett., 2001, 86(21): 4807-4810
[174] Gervais B, Giglio E, Jacquet E. Spectroscopic properties of Na clusters embedded in a rare-gas matrix. Phys. Rev. A, 2005, 71(1): 015201-4
[175] Martins J L, Buttet J, Car R. Electronic and structural properties of sodium clusters. Rhys. Rev. B. 1985, 31(4): 1804-1816
[176] Bonai?-Koutecky V, Fantucci P, Koutecky J. Systematic ab initio configuration-interaction of alkali-metal clusters. II. Relation betweenelecteronic structure and geometry of small sodium clusters. Phys. Rev. B, 1988, 37(9): 4369-4374
[177] Bj?rnholm S, Borggreen J, Echt O, et al. Mean-field quantization of several hundred electrons in sodium metal clusters. Phys. Rev. Lett., 1990, 65(13): 1627-1630
[178] Haberland H, Hippler T, Donges J, et al. Melting of sodium clusters: Where do the magic numbers come from? Phys. Rev. Lett., 2005, 94(28): 035701-4
[179] Oviedo J, Palmer R E. Amorphous structures of Cu, Ag, and Au nanoclusters from first principles calculations. J. Chem. Phys., 2002, 117(21): 9548-9551
[180] Solov’yov I A, Solov’yov A V, Greiner W. Cluster growing process and a sequence of magic numbers. Phys. Rev. Lett., 2003, 90(5): 053401-4
[181] Zhang Z, Hu W Y, Xiao S F. Shell and subshell periodic structures of icosahedral nickel nanoclusters. J. Chem. Phys., 2005, 122(21): 214501-5
[182] 陈玉红,张材荣,马军. Mg m Bn(m=1,2; n=1-4)团簇结构与性质的密度泛函理论研究. 物理学报,2006, 55(1): 171-178
[183] 王广厚. 原子团簇的稳定结构和幻数. 物理学进展, 2000, 20(1): 52-92
[184] Wang L, Bian X F, Zhang Y N. Structural simulation of clusters in liquid Ni 50 Al 50 alloys. Modelling Simul. Mater. Sci. Eng., 2002, 10(2): 331-339
[185] 刘俊, 赵九洲, 胡壮麒. Cu-50%Ni 合金快速凝固过程中原子团簇演变的分子动力学模拟. 金属学报, 2005, 41(2): 219-224
[186] 徐延祎, 王丽, 边秀房. 液态 Ni 原子团簇演变的计算机模拟. 原子与分子物理学报. 2002, 19(1): 65-74
[187] Kramer M J, Sordelet D J. Polymorphism in the short-range order of Zr 70 Pd 30 metallic glasses. J. Non-Cryst. Solids. 2005, 351(19-20): 1586-1593
[188] Doye J P K, Wales D J, Zetterling F H M, Dzugutov M. The favored cluster structures of model glass formers. J. Chem. Phys., 2003, 118(6): 2792-2799
[189] Martin T P. Shells of atoms. Phys. Rep., 1996, 273:199-241
[190] Flemings M C. Solidification processing. New York: McGraw-Hill. 1974, 290-319
[191] Doye J P K, Wales D J. Polytetrahedral clusters. Phys. Rev. Lett., 2001, 86(25): 5719-5722
[192] 卢博斯基. 非晶态金属合金. 北京:冶金工业出版社. 1989, 192-221
[193] Kulik T. Nanocrystallization of metallic glasses. J. Non-Cryst. Solids, 2001, 287(1): 145-161
[194] Li J M. Self-organized nanocrystalline stripe patterns generated during earlycrystallization of a nonequilibrium metallic glass. Appl. Phys. Lett., 2002, 90(4): 041913-3
[195] Li J M, Quan M X, Hu Z Q. Preferential precipitation sequence of metastable phase during crystallization of (Fe 0.99 Mo 0.01 ) 78 Si 9 B13 metallic glass. Appl. Phys. Lett. 1996, 69(16): 2356-2358
[196] Lu K. Nanocrystalline metals crystallized from amorphous solids: nonocrystallization, structure, and properties. Mater. Sci. Pep. 1996, R16(1): 161-221
[197] 苏勇, 陈翌庆,丁厚福,郑玉春. Al 9 1Ni 7 Y2纳米非晶复合材料晶化的研究. 兵器材料科学与工程, 2000, 23(4): 12-24
[198] 赵文君,徐晖,王智平 等. Fe 68 Nd 5 Zr 2 Y 4 B21大块非晶合金磁性能的研究. 稀有金属材料与工程, 2008, 37(1): 139-142
[199] 唐建成,吴爱华,张萌,刘文胜. 预退火对纳米晶Fe 86 Zr 7 B6Cu合金显微组织和软磁性能的影响. 中国有色金属学报, 2007, 17(10): 1593-1596
[200] 孙国元 陈光 陈国良. 非晶合金的晶化理论及几种 Mg 基非晶合金的晶化行为. 有色金属, 2004, 56(4): 1-7
[201] Lu K, Zhang X H. Identification of crystal nucleation and growth in an amorphous FeZr2 alloy by means of electrical resistance measurements. Phil. Mag. Lett., 2000, 80(12): 797-805
[202] Greer A L. Crystallization kinetics of iron-boron (Fe 80 B20) glass. Acta Metall., 1982, 30(1): 171-192
[203] 王亚平,卢柯. 非晶态合金晶化过程的高精度电阻监测研究. 中国科学, 2000, 30(3): 193-199
[204] Chen F F, Zhang H F, Qin F X, et al. Molecular dynamics study of atomic transport properties in rapidly cooling liquid copper. J. Chem. Phys. 2004, 120(4): 1826-1831
[205] Pei Q X, Lu C, Lee H P. Crystallization of amorphous alloy during isothermal annealing: a molecular dynamics study. J. Phys.: Condens. Matter, 2005, 17(10): 1493-1504
[206] Kelton K F, Lee G W, Gangopadhyay A K, et al. First X-ray scattering studies on electrostatically levitated metallic liquids: Demonstrated influence of local icosahedral order on the nucleation barrier. Phys. Rev. Lett. 2003, 90(19): 195504-4
[207] Lu K, Lück R, and Predel B. The temperature vs time transformation (T-T-T) diagram for a transition from the amorphous to the nanocrystalline state. Acta. Metall. Mater., 1994, 42(7): 2303-2311