纳米晶体材料中晶粒生长及变形机理的研究
|
摘要
近年来,纳米材料在越来越多的领域得到应用。因此对纳米材料的制备工艺、变形及破坏机理的研究受到了广泛的关注。大多固体材料都是由晶粒构成的,其或为单晶体或为多晶体。晶粒边界上原子的不规则排列使得材料内部储存的能量很高,因此晶界易成为缺陷的源头。一方面在能量驱动下,晶粒会逐渐长大以减小晶界的面积;另一方面,晶粒的尺寸、分布情况和变形方式与材料性能及其使用寿命密切相关,不同尺寸的晶粒在外载作用下其变形机理不尽相同。因此,深刻地了解和剖析晶粒生长的基本特征和变形机理对于材料设计具有重要的指导意义。
针对单相多晶材料中的晶粒生长情况,本文提出了一个理论的生长模型,其中考虑晶粒的生长来自于两方面的作用:系统的平均场效应和邻域的局部效应,即将传统的扩散控制机制和曲率引导机制相结合,并对此模型的求解给出了相应的有限差分格式。计算结果表明,晶粒在生长过程中具有一个尺寸效应,当晶粒尺寸很小时,如纳米级别,生长主要是由扩散作用引起的。当尺寸增大,晶粒生长逐渐变为一个由曲率控制的过程,这与实验观测一致。这两个阶段的生长分别具有自相似的特征。与其它模型的结果相比,基于此模型所预测的晶粒尺寸分布函数与实验结果吻合的更好。
在多相材料中(通常以两相为原型),针对其晶粒生长机理和特征的认识尚不完整,且很难导出相应的理论模型,因此晶粒生长过程主要采用模特卡罗方法进行模拟研究。本文通过扩展传统的Q态Potts模型,将其运用到两相不相溶固体材料晶粒生长的研究中。主要考虑了具有不同晶格方向的相同组分的晶格重定向和不同组分之间的扩散作用。蒙特卡罗模拟结果表明两相材料中晶粒尺寸与生长时间满足一个幂指数关系。由于附加相的存在,晶粒生长受到了很大程度的抑制。这时候生长指数为0.16,即为单相生长情况的1/3,这与实验结果相一致。同时研究发现为了控制单相材料生长而添加另一相物质时,附加相的最佳体积百分比约为7%～11%,实验中常用的比例为5%～10%,两者吻合很好。两相材料中晶粒尺寸基本上满足对数正态分布,表明所研究系统中的晶粒属于正常形态的生长模式,且此分布与时间无关。分析结果还显示了晶界能与表面能之比存在一个临界值(～2.6),当实际比值大于临界值时,其中一相材料更趋于形成网状结构附着在另一相的边界上,否则其将更容易以颗粒形式散布在系统中。
在对材料微结构的变化,即晶粒生长,有了一定的认识的基础上,本文展开了对具有特定微结构的纳米晶体材料的变形机理研究。基于分子动力学方法,研究了单相单晶铜纳米线的变形机理。对纳米线的弯曲加载模拟结果表明,纳米单晶铜材料的塑性变形主要是由原子在密排面内的滑移所引导。塑性变形过程中所形成的形变孪晶将相互作用和影响,导致原子局部微结构的转化,从而形成两个相连的五折孪晶,这一过程是第一次从计算机模拟的角度观测到。而相连五折孪晶的出现对铜纳米线有很好的增强作用,从而使得供给纳米线塑性变形的位错运动受到抑制。
对纳米单相多晶铜材料,同样采用分子动力学方法模拟了其在拉伸载荷作用下的变形机理。数值实验的试件首先用前面所建立的扩展Potts模型结合蒙特卡罗方法模拟获得,这样的系统满足尺寸的对数正态分布,与实验更相符。然后采用单轴拉伸加载,同时控制其它两个垂直方向的应力。模拟结果表明,纳米多晶铜的变形主要存在两种方式,即小晶粒的变形主要是通过晶界滑移和晶粒旋转引导的,而大晶粒的变形则主要是由位错运动控制。此外,研究还发现这两种机理控制着不同的变形阶段,如晶粒旋转主要发生在塑性变形的初期,而塑性变形中后期则主要由位错运动引导。随着系统晶粒平均尺寸的改变,这两种机理所占的比重不尽相同,从而导致了纳米材料与传统粗晶材料的物理力学性能具有较大的差别。此外,研究结果还表明由于外载的作用,系统内部所出现的高应力将导致晶粒的快速生长。
本文的研究工作是国家自然科学基金项目(10721062,10640420176,50679013)、长江学者和创新团队发展计划以及国家基础发展规划项目(2005CB321704)资助的一部分。
In the past few decades,nanocrystalline materials have attracted much attention because of their superior physico-mechanical properties.It is well known that the properties of a material are closely tied to its microstructure.Until now,a lot of research work has been conducted to investigate the microstructure evolution and the related deformation mechanisms, and significant successes have been achieved.Our knowledge on grain growth and deformation mechanisms of nanostructure,however,is still far from complete.Thus,a better understanding toward grain growth processes and deformation details is needed,which is the main goal of this work and will provide an effective way to tailor and optimize the fabrication of nanostructured materials.The research work is arranged as follows:
In chapter 1,some backgrounds of nanocrystalline materials are introduced and the related research work that has been done before is surveyed,which include the experimental observations,theoretical studies and numerical simulations of grain growth and deformation in nanocrytalline materials.In the last section,a brief description of this work is presented.
In chapter 2,a combined stochastic diffusion and mean-field model is developed for a systematic study of the grain growth in a pure single-phase polycrystalline material.A corresponding Fokker-Planck continuity equation is formulated,and the interplay/competition of stochastic and curvature-driven mechanisms is investigated.Numerical results show that when the grains are smaller than several tens of nanometres the dominating mechanism is stochastic diffusion-controlled of boundaries.As the grains grow the influence of the deterministic curvature-driven mechanism increases and finally controls the process.The transition ranges between these two mechanisms are about 2-26 and 2-15 nm with boundary energy of 0.01-1 J m~(-2) in two- and three-dimensional systems,respectively.The grain size distribution of a three-dimensional system changes dramatically with time,while it changes a little in a two-dimensional system.The grain size distribution from the combined model is in good agreement with experimental observations.
In chapter 3,a modified Potts model is proposed to systematically study normal grain growth in a single- or two-phase volume-conserved system.In this model,the driving forces for grain boundary migration are the interfacial energy between two phases and the boundary energy inside each phase.Simulation results show that the grain growth kinetics follows a power law with a temperature-independent exponent and the normalized grain size distribution is lognormal and time-invariant.The optimal volume fraction for the second-phase is found to be 7-11%for a well control of the primary grain growth,which is consistent with experimental data.Also a simple theoretical model is used to predict the potential microstructure in a two-phase system due to competition between interfacial and grain boundary energies.A critical energy ratio(～2.6) of grain boundary and interfacial energies is found for a common two-phase system and is supported by Monte Carlo simulations.
In chapter 4,the basic theories of the molecular dynamics method are introduced, including the motion equations,integration scheme,temperature/pressure control algorithm, empirical potential functions.In addition,some practical methods,such as periodic boundary condition,time step selection and neighboring list method,are also addressed.
In chapter 5,the deformation of single-crystalline copper nanowires under bending is studied using molecular dynamics simulations.The length and thickness effects on the stability and deformation of wires are also discussed.The results suggest that the plastic deformation is dominated by atomic slip on close-packed planes,and the twinning deformation is a primary mode in copper nanowires with sizes of～10 nm.It is found that an intermediate icosahedral phase is formed to facilitate the transformation from a low dense (010) plane in a face-centered-cubic lattice to a {111} close-packed fashion,forming tri-junctions composed of three deformation twins.These tri-junctions can easily interact with other deformation twins,forming two conjoint fivefold deformation twins.
In chapter 6,a combined Monte Carlo and molecular dynamics scheme is established to investigate the deformation mechanisms of polycrystalline nanostructured copper with grain size in the range of 6-18 nm.The results show that grain boundary mediated plastic deformation,such as grain boundary sliding and grain rotation,mainly occurs in small grains; while large grain deformation is dislocation-accommodated through nucleation,propagation and absorption of partial/extended dislocations.It is also found that these two mechanisms operate in the different stages.With the evolution of deformation,stress-assisted grain growth could also occur due to atomic diffusion and grain boundary migration.
Finally,the main contributions of this work are summarized and the further work is suggested.
This research work is supported by the National Natural Science Foundation of China under Project Nos.10721062,10640420176 and 50679013,the Program for Changjiang Scholars and Innovative Research Teams in Universities of China,and the National Key Basic Research Special Foundation of China(2005CB321704).
针对单相多晶材料中的晶粒生长情况,本文提出了一个理论的生长模型,其中考虑晶粒的生长来自于两方面的作用:系统的平均场效应和邻域的局部效应,即将传统的扩散控制机制和曲率引导机制相结合,并对此模型的求解给出了相应的有限差分格式。计算结果表明,晶粒在生长过程中具有一个尺寸效应,当晶粒尺寸很小时,如纳米级别,生长主要是由扩散作用引起的。当尺寸增大,晶粒生长逐渐变为一个由曲率控制的过程,这与实验观测一致。这两个阶段的生长分别具有自相似的特征。与其它模型的结果相比,基于此模型所预测的晶粒尺寸分布函数与实验结果吻合的更好。
在多相材料中(通常以两相为原型),针对其晶粒生长机理和特征的认识尚不完整,且很难导出相应的理论模型,因此晶粒生长过程主要采用模特卡罗方法进行模拟研究。本文通过扩展传统的Q态Potts模型,将其运用到两相不相溶固体材料晶粒生长的研究中。主要考虑了具有不同晶格方向的相同组分的晶格重定向和不同组分之间的扩散作用。蒙特卡罗模拟结果表明两相材料中晶粒尺寸与生长时间满足一个幂指数关系。由于附加相的存在,晶粒生长受到了很大程度的抑制。这时候生长指数为0.16,即为单相生长情况的1/3,这与实验结果相一致。同时研究发现为了控制单相材料生长而添加另一相物质时,附加相的最佳体积百分比约为7%～11%,实验中常用的比例为5%～10%,两者吻合很好。两相材料中晶粒尺寸基本上满足对数正态分布,表明所研究系统中的晶粒属于正常形态的生长模式,且此分布与时间无关。分析结果还显示了晶界能与表面能之比存在一个临界值(～2.6),当实际比值大于临界值时,其中一相材料更趋于形成网状结构附着在另一相的边界上,否则其将更容易以颗粒形式散布在系统中。
在对材料微结构的变化,即晶粒生长,有了一定的认识的基础上,本文展开了对具有特定微结构的纳米晶体材料的变形机理研究。基于分子动力学方法,研究了单相单晶铜纳米线的变形机理。对纳米线的弯曲加载模拟结果表明,纳米单晶铜材料的塑性变形主要是由原子在密排面内的滑移所引导。塑性变形过程中所形成的形变孪晶将相互作用和影响,导致原子局部微结构的转化,从而形成两个相连的五折孪晶,这一过程是第一次从计算机模拟的角度观测到。而相连五折孪晶的出现对铜纳米线有很好的增强作用,从而使得供给纳米线塑性变形的位错运动受到抑制。
对纳米单相多晶铜材料,同样采用分子动力学方法模拟了其在拉伸载荷作用下的变形机理。数值实验的试件首先用前面所建立的扩展Potts模型结合蒙特卡罗方法模拟获得,这样的系统满足尺寸的对数正态分布,与实验更相符。然后采用单轴拉伸加载,同时控制其它两个垂直方向的应力。模拟结果表明,纳米多晶铜的变形主要存在两种方式,即小晶粒的变形主要是通过晶界滑移和晶粒旋转引导的,而大晶粒的变形则主要是由位错运动控制。此外,研究还发现这两种机理控制着不同的变形阶段,如晶粒旋转主要发生在塑性变形的初期,而塑性变形中后期则主要由位错运动引导。随着系统晶粒平均尺寸的改变,这两种机理所占的比重不尽相同,从而导致了纳米材料与传统粗晶材料的物理力学性能具有较大的差别。此外,研究结果还表明由于外载的作用,系统内部所出现的高应力将导致晶粒的快速生长。
本文的研究工作是国家自然科学基金项目(10721062,10640420176,50679013)、长江学者和创新团队发展计划以及国家基础发展规划项目(2005CB321704)资助的一部分。
In the past few decades,nanocrystalline materials have attracted much attention because of their superior physico-mechanical properties.It is well known that the properties of a material are closely tied to its microstructure.Until now,a lot of research work has been conducted to investigate the microstructure evolution and the related deformation mechanisms, and significant successes have been achieved.Our knowledge on grain growth and deformation mechanisms of nanostructure,however,is still far from complete.Thus,a better understanding toward grain growth processes and deformation details is needed,which is the main goal of this work and will provide an effective way to tailor and optimize the fabrication of nanostructured materials.The research work is arranged as follows:
In chapter 1,some backgrounds of nanocrystalline materials are introduced and the related research work that has been done before is surveyed,which include the experimental observations,theoretical studies and numerical simulations of grain growth and deformation in nanocrytalline materials.In the last section,a brief description of this work is presented.
In chapter 2,a combined stochastic diffusion and mean-field model is developed for a systematic study of the grain growth in a pure single-phase polycrystalline material.A corresponding Fokker-Planck continuity equation is formulated,and the interplay/competition of stochastic and curvature-driven mechanisms is investigated.Numerical results show that when the grains are smaller than several tens of nanometres the dominating mechanism is stochastic diffusion-controlled of boundaries.As the grains grow the influence of the deterministic curvature-driven mechanism increases and finally controls the process.The transition ranges between these two mechanisms are about 2-26 and 2-15 nm with boundary energy of 0.01-1 J m~(-2) in two- and three-dimensional systems,respectively.The grain size distribution of a three-dimensional system changes dramatically with time,while it changes a little in a two-dimensional system.The grain size distribution from the combined model is in good agreement with experimental observations.
In chapter 3,a modified Potts model is proposed to systematically study normal grain growth in a single- or two-phase volume-conserved system.In this model,the driving forces for grain boundary migration are the interfacial energy between two phases and the boundary energy inside each phase.Simulation results show that the grain growth kinetics follows a power law with a temperature-independent exponent and the normalized grain size distribution is lognormal and time-invariant.The optimal volume fraction for the second-phase is found to be 7-11%for a well control of the primary grain growth,which is consistent with experimental data.Also a simple theoretical model is used to predict the potential microstructure in a two-phase system due to competition between interfacial and grain boundary energies.A critical energy ratio(～2.6) of grain boundary and interfacial energies is found for a common two-phase system and is supported by Monte Carlo simulations.
In chapter 4,the basic theories of the molecular dynamics method are introduced, including the motion equations,integration scheme,temperature/pressure control algorithm, empirical potential functions.In addition,some practical methods,such as periodic boundary condition,time step selection and neighboring list method,are also addressed.
In chapter 5,the deformation of single-crystalline copper nanowires under bending is studied using molecular dynamics simulations.The length and thickness effects on the stability and deformation of wires are also discussed.The results suggest that the plastic deformation is dominated by atomic slip on close-packed planes,and the twinning deformation is a primary mode in copper nanowires with sizes of～10 nm.It is found that an intermediate icosahedral phase is formed to facilitate the transformation from a low dense (010) plane in a face-centered-cubic lattice to a {111} close-packed fashion,forming tri-junctions composed of three deformation twins.These tri-junctions can easily interact with other deformation twins,forming two conjoint fivefold deformation twins.
In chapter 6,a combined Monte Carlo and molecular dynamics scheme is established to investigate the deformation mechanisms of polycrystalline nanostructured copper with grain size in the range of 6-18 nm.The results show that grain boundary mediated plastic deformation,such as grain boundary sliding and grain rotation,mainly occurs in small grains; while large grain deformation is dislocation-accommodated through nucleation,propagation and absorption of partial/extended dislocations.It is also found that these two mechanisms operate in the different stages.With the evolution of deformation,stress-assisted grain growth could also occur due to atomic diffusion and grain boundary migration.
Finally,the main contributions of this work are summarized and the further work is suggested.
This research work is supported by the National Natural Science Foundation of China under Project Nos.10721062,10640420176 and 50679013,the Program for Changjiang Scholars and Innovative Research Teams in Universities of China,and the National Key Basic Research Special Foundation of China(2005CB321704).
引文
[1]Gleiter H.Nanocrystalline materials.Progress in Materials Science.1989,33(4):223-315.
[2]Gleiter H.Nanostructured materials:basic concepts and microstructure.Acta Materialia.2000,48(1):1-29.
[3]Meyers M A,Mishra A,Benson D J.Mechanical properties of nanocrystalline materials.Progress in Materials Science.2006,51(4):427-556.
[4]张中太,林元华,唐子龙等.纳米材料及其技术的应用前景.材料工程.2000,3:42-48.
[5]Chikara H.Ultrafine particles.Physics Today.1987,11:44-51.
[6]Gleiter H.Nanostructured Materials:State-of-the-Art and Perspectives.Nanostructured Materials 1995,6(1-4):3-14.
[7]张立德,牟季美.纳米材料和纳米结构.北京:科学出版社,2001.
[8]文玉华,周富信,刘曰武.纳米材料的研究进展.力学进展.2001,31(1):47-61.
[9]Andres R P,Averback R S,Brown W L,et al.Research opportunities on clusters and cluster-assembled materials - A Department of Energy,Council on Materials Science Panel Report.Journal of Materials Research.1989,4(3):704-736.
[10]Dao M,Lu L,Asaro R J,et al.Toward a quantitative understanding of mechanical behavior of nanocrystalline metals.Acta Materialia.2007,55(12):4041-4065.
[11]Lu C S,Mai Y W,Shen Y G.Recent advances on understanding the origin of superhardness in nanocomposite coatings:A critical review.Journal of Materials Science.2006,41(3):937-950.
[12]Veprek S,Reiprich S,Shizhi L.Superhard nanocrystalline composite materials:The TiN/Si_3N_4 system.Applied Physics Letters.1995,66(20):2640-2642.
[13]王中林.纳米材料和纳米技术.科学中国人.2001,4:4-9.
[14]Gleiter H,Weissmüller J,Wollersheim O,et al.Nanocrystalline materials:a way to solids with tunable electronic structures and properties? Acta Materialia.2001,49(4):737-745.
[15]Mehl R E,Cahn R W,Historical development,in:Calm R W,Hansen P,ed.Physical Metallurgy.North Holland:Elsevier Science Publishers,1983:1-35.
[16]Langford G,Cohen M.Strain hardening of iron by severe plastic deformation.Transactions of the ASM.1969,62:623-638.
[17]Beck F.Cathodic dimerization.Angewandte Chemie International Edition in English.2003,11(9):760-781.
[18]Gleiter H,Materials with ultrafine grain size.in:Hansen N,ed.Deformation of polycrystals:mechanisms and microstructures.Roskilde:Riso National Laboratory,1981:15-21.
[19]Lu K.Nanocrystalline materials crystallized from amorphous solids:Nanocrystallization,structure,and properties.Materials Science and Engineering R:Reports.1996,16(4):161-221.
[20]Frost H J.Microstructural Evolution in Thin Films.Materials Characterization.1994,32:257-273.
[21]Thompson C V.Grain growth in thin film.Annual Reviews of Materials Science.1990,20:245-268.
[22]Thompson C V.Grain growth and evolution of other cellular structures.Solid State Physics.2001,55:269-314.
[23] Veprek S, Veprek-Heijman M G J, Karvankova P, et al. Different approaches to superhard coatings and nanocomposites. Thin Solid Films. 2005, 476(1): 1-29.
[24] Anderson M P, Srolovitz D J, Grest G S, et al. Computer simulation of grain growth -I. Kinetics. Acta Metallurgica 1984,32(5): 783-791.
[25] Atkinson H V. Theories of normal grain growth in pure single phase systems. Acta Metallurgica. 1988, 36(3): 469-491.
[26]Marlow T R, Koch C C, Grain Growth of Nanocrystalline Materials - A Review. in: Bourell D L, ed. Synthesis and Processing of Nanocrystalline Powder. Warrendale PA: TMS, 1996: 33-46.
[27] Hu H. Grain-growth in zone-refined iron. Canadian Metallurgical Quarterly. 1974, 13: 275-286.
[28] Zhang C, Suzuki A, Ishimaru T, et al. Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning. Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science. 2004,35(7): 1927-1933.
[29] Hillert M. On theory of normal and abnormal grain growth. Acta metallurgies 1965, 13(3): 227-238.
[30]Lifshitz I M, Slyozov V V. The kinetics of precipitation from supersaturated solid solutions. Journal of Physics and Chemistry of Solids. 1961, 19(1-2): 35-50.
[31] Louat N P. On the theory of normal grain growth. Acta Metallurgies 1974, 22(6): 721 -724.
[32]Hunderi O, Ryum N. The kinetics of normal grain growth. Journal of Materials Science. 1980, 15(5): 1104-1108.
[33]Abbruzzese G, Liicke K. A theory of texture controlled grain growth - I. Derivation and general discussion of the model. Acta Metallurgies 1986, 34(5): 905-914.
[34] Eichelkraut H, Abbruzzese G, Lucke K. A theory of texture controlled grain growth - II. Numerical and analytical treatment of grain growth in the presence of two texture components. Acta Metallurgica. 1988, 36(1): 55-68.
[35] Fischer F D, Svoboda J, Fratzl P. A thermodynamic approach to grain growth and coarsening. Philosophic Magazine. 2003, 83(9): 1075-1093.
[36] Gusak A M, Tu K N. Theory of normal grain growth in normalized size space. Acta Materialia. 2003, 51(13): 3895-3904.
[37] Saetre T O. On the theory of normal grain growth in two dimensions. Acta Materialia. 2002, 50(6): 1539-1546.
[38] Saetre T O. A mean field theory of grain growth: I. Modelling and Simulation in Materials Science and Engineering. 2004, 12(6): 1267-1277.
[39] Saetre T O. A mean field theory of grain growth: II. Modelling and Simulation in Materials Science and Engineering. 2004, 12(6): 1279-1292.
[40]Mullins W W. Grain growth of uniform boundaries with scaling. Acta Materialia. 1998, 46(17): 6219-6226.
[41]Pande C S, Rajagopal A K. Uniqueness and self similarity of size distributions in grain growth and coarsening. Acta Materialia. 2001, 49(10): 1805-1811.
[42] Mulheran P A, Harding J H. A statistical theory of normal grain growth. Material Science Forum 1992, 94-96: 367-372.
[43] Pande C S. On a stochastic theory of grain growth. Acta Metallurgica. 1987, 35(11): 2671-2678.
[44]Pande C S, Dantsker E. On a stochastic theory of grain growth - II. Acta Metallurgica et Materialia. 1990, 38(6): 945-951.
[45]Pande C S, Dantsker E. On a stochastic theory of grain growth - III. Acta Metallurgica et Materialia. 1991,39(6): 1359-1365.
[46] Pande C S, Dantsker E. On a stochastic theory of grain growth - IV. Acta Metallurgica et Materialia. 1994, 42(8): 2899-2903.
[47] Pande C S, Rajagopal A K. Modeling of grain growth in two dimensions. Acta Materialia. 2002, 50(11): 3013-3021.
[48] Helfen L, Wu D T, Birringer R, et al. The impact of stochastic atomic jumps on the kinetics of curvature-driven grain growth. Acta Materialia. 2003, 51(10): 2743-2754.
[49] Di Nunzio P E. A discrete approach to grain growth based on pair interactions. Acta Materialia. 2001, 49(15): 3635-3643.
[50]Lou C, Player M A. Advection-diffusion model for normal grain growth. Journal of Physics D: Applied Physics. 2001, 34: 1286-1292.
[51]Rios P R. A theory for grain boundary pining by particles. Acta Metallurgica. 1987, 35(12): 2805-2815.
[52]Hillert M. Inhibition of grain growth by second-phase particles. Acta Metallurgica. 1988, 36(12): 3177-3181.
[53] Miodownik M A. A review of microstructural computer models used to simulate grain growth and recrystallisation in aluminium alloys. Journal of Light Metals. 2002, 2(1): 125-135.
[54] Demirel M C, Kuprat A P, George D C, et al. Experimental verification of finite element simulation of curvature-driven grain growth in al-foil. Proceeding of the First Joiint International Conference on Recrystallisation and Grain Growth, Beilin, 2001: 297-302.
[55]Janssens K G F, Vanini F, Reissner J N. Thermodynamic and kinetic coupling of a random grid cellular automaton for the simulation of grain growth. Advanced Engineering Materials. 2002, 4(4): 200-202.
[56] Maurice C, Humphries J, 2- and 3-d curvature driven vertex simulations of grain growth, in Grain Growth in Polycrystalline Materials III, Weiland H, Adams B L, Rollett A D, Editors. 1998, TMS: Pittsburgh, Pennsylvania. 81-90.
[57]Brakke K. The Motion of a Surface by its Mean Curvature. New Jersey:Princeton University Press, 1978.
[58] Weygand D, Brechet Y, Lepinoux J. A vertex simulation of grain growth in 2d and 3d. Advanced Engineering Materials. 2001, 3(1-2): 67-71.
[59] Fan D N, Chen L Q. Diffusion-controlled grain growth in two-phase solids. Acta Materialia. 1997, 45(8): 3297-3310.
[60] Fan D N, Chen L Q. Computer simulation of grain growth using a continuum field model. Acta Materialia. 1997, 45(2): 611-622.
[61] Chen L Q. Phase-field models for microstructure evolution. Annual Reviews of Materials Research. 2002,32: 113-140.
[62]Lusk M T. A phase-field paradigm for grain growth and recrystallization. Proceedings: Mathematical, Physical and Engineering Sciences. 1999, 455(1982): 677-700.
[63]Warren J A,Kobayashi R,Carter W C.Modeling grain boundaries using a phase-field technique.Journal of Crystal Growth.2000,211(1-4):18-20.
[64]Krill Ⅲ C E,Chen L Q.Computer simulation of 3-D grain growth using a phase-field model.Acta Materialia.2002,50(12):3059-3075.
[65]Tikare V,Holm E A,Fan D N,et al.Comparsion of phase-field and Potts models for coarsening processes.Acta Materialia.1998.47:363-371.
[66]王永欣,陈铮,刘兵等.外场下失稳区合金沉淀机制的计算机研究.稀有金属材料与工程.2005,34(1):46-50.
[67]梁敏洁,陈铮,王永欣等.合金微结构的微观相场法模拟.热加工工艺.2006,35(16):63-66.
[68]魏齐龙,王永欣,陈铮.Al-Li合金相变的热分析动力学表征.稀有金属材料与工程.2006,35(6):941-944.
[69]朱耀产,杨根仓,王锦程等.多相场法数值模拟共晶凝固研究进展.特种铸造及有色合金.2004(3):45-47.
[70]朱耀产,杨根仓,王锦程等.二元共晶定向凝固的多相场法数值模拟.中国有色金属学报.2005,15(7):1026-1032.
[71]Fan D N,Chen S P,Chen L Q.Computer simulation of grain growth kinetics with solute drag.Journal of Materials Research.1999,14(3):1113-1123.
[72]Kazaryan A,Wang Y,Dregia S A,et al.Grain growth in systems with anisotropic boundary mobility:analytical model and computer simulation.Physical Review B.2001,63(18):184102.
[73]Srolovitz D J,Anderson M P,Sahni P S,et al.Computer simulation of grain growth - Ⅱ.Grain size distribution,topology,and local dynamics.Acta Metallurgica.1984,32(5):793-802.
[74]Srolovitz D J,Anderson M P,Grest G S,et al.Computer simulation of grain growth - Ⅲ.Influence of a particle dispersion.Acta Metallurgica.1984,32(9):1429-1438.
[75]Grest G S,Srolovitz D J,Anderson M P.Computer simulation of grain growth - Ⅳ.Anisotropic grain boundary energies.Acta Metallurgica.1985,33(3):509-520.
[76]Srolovitz D J,Grest G S,Anderson M P.Computer simulation of grain growth - Ⅴ.Abnormal grain growth.Acta Metallurgica.1985,33(12):2233-2247.
[77]Yu Q,Esche S K.A Monte Carlo algorithm for single phase normal grain growth with improved accuracy and efficiency.Computational Materials Science.2003,27(3):259-270.
[78]王海东,张海.晶粒生长的蒙特卡罗模拟研究进展.材料导报.2007,21(2):72-74.
[79]Holm E A,Sroiovitz D J,Cahn J W.Microstructural evolution in two-dimensional two-phase polycrystals.Acta Metallurgica et Materialia.1993,41(4):1119-1136.
[80]Liu Z J,Zhang C H,Shen Y G,et al.Monte Carlo simulation of nanocrystalline TiN/amorphous SiNx composite films.Journal of Applied Physics.2004,95(2):758-760.
[81]Holm E A,Hassold G N,Miodownik M A.On misorientation distribution evolution during anisotropic grain growth.Acta Materialia.2001,49(15):2981-2991.
[82]Moldovan D,Wolf D,Phillpot S R,et al.Mesoscopic simulation of two-dimensional grain growth with anisotropic grain-boundary properties.Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties.2002,82(7):1271-1297.
[83]Yang Z,Sista S,Elmer J W,et al.Three dimensional monte carlo simulation of grain growth,during GTA welding of titanium.Acta Materialia.2000,48(20):4813-4825.
[84]Rollett A D,Srolovitz D J,Anderson M P.Simulation and theory of abnormal grain growth - anisotropic grain boundary energies and mobilities.Acta Metallurgica.1988,37(4):1227-1240.
[85]Hinz D C,Szpunar J A.Modelling the effect of coinsidence site lattice boundaries on grain growth textures.Physical Review B.1995,52(14):9900-9909.
[86]张海.基于蒙特卡罗方法的晶粒生长模拟系统研究:(硕士学位论文).长沙:中南大学,2007.
[87]陈伟元,钟晓征,谭锐等.多晶材料晶粒生长的计算机模拟研究.原子与分子物理学报.2000,17(2):297-302.
[88]张继祥,关小军,孙胜.一种改进的晶粒长大Monte Carlo模拟方法.金属学报.2004,40(5):457-461.
[89]刘国权,宋晓艳,于海波等.一种Monte Carlo仿真新算法及其对三维个体晶粒长大速率拓扑依赖性理论方程的验证.金属学报.1999,35(3):245-248.
[90]秦湘阁,刘国权.基于Monte Carlo Potts方法的三维大尺度晶粒组织仿真模型及定量表征.北京科技大学学报.2004,26(1):49-52.
[9]]刘祖耀,李世晨,郑子樵等.正常晶粒长大的计算机模拟(Ⅰ)-晶粒长大动力学跃迁概率的改进.中国有色金属学报.2003,13(6):1357-1360.
[92]刘祖耀,郑子樵,陈大钦等.正常晶粒长大的计算机模拟(Ⅱ)-第二相粒子形状及取向的影响.中国有色金属学报.2004,14(1):122-126.
[93]郭靖原,洪泽恺,陈民.金属凝固与晶体生长过程的蒙特卡罗模拟.工程热物理学报.2001,22(6):725-728.
[94]Wolf D,Yamakov V,Phillpot S R,et al.Deformation of nanocrystalline materials by molecular-dynamics simulation:relationship to experiments? Acta Materialia.2005,53(1):1-40.
[95]Zhu X,Birringer R,Herr U,et al.X-ray diffraction studies of the structure of nanometer-sized crystalline materials.Physical Review B.1987,35(17):9085-9090.
[96]Fitzsimmons M R,Eastman J A,Müller-Stach M,et al.Structural characterization of nanometer-sized crystalline Pd by x-ray-diffraction techniques.Physical Review B.1991,44(6):2452-2460.
[97]Loffler J,Weissmüller J.Grain-boundary atomic structure in nanocrystalline palladium from x-ray atomic distribution functions.Physical Review B.1995,52(10):7076-7093.
[98]Thomas G J,Siegel R W,Eastman J A.Grain boundary in nanophase palladium:high resolution electronmicroscope and image simulation.Scripta Metallurgica et Materialia.1990,24(1):201-206.
[99]Haubold T,Birringer R.Lengeler B,et al.EXAFS studies of nanocrystalline materials exhibiting a new solid state structure.Physical Letters A.1989,135(8-9):461-466.
[100]Ke M,Hackney S A,Milligan W W,et al.Observation and measurement of grain rotation and plastic strain in nanostructured metal thin films.Nanostructured Materials.1995,5(6):689-697.
[101]Milligan W W,Hackney S A,Ke M,et al.In situ studies of deformation and fracture in nanophase materials.Nanostructured Materials.1993,2(3):267-276.
[102]Ichikawa S,Miyazawa K i,Ichinose H,et al.The microstructure of deformed nanocrystalline Ag and Ag/Fe alloy.Nanostructured Materials.1999,11(8):1301-1311.
[103] Zupan M, Legros, Marc, et al., Microsample Tensile Testing of Nanocrystalline Metals and Single-crystalline Alloys. in: Chung, Dunand, Liaw, et al., ed. Advanced Materials for the 21st Century: The 1999 Julia R. Weeterman Symposium. Warrendale: TMS Publications, 1999: 525-536.
[104] Youngdahl C J, Weertman J R, Hugo R C, et al. Deformation behavior in nanocrystalline copper. Scripta Materialia. 2001, 44(8-9): 1475-1478.
[105] Cheng S, Spencer J A, Milligan W W. Strength and tension/compression asymmetry in nanostructured and ultrafine-grain metals. Acta Materialia. 2003, 51(15): 4505-4518.
[106] Legros M, Elliott B R, Rittner M N, et al. Microsample tensile testing of nanocrystalline metals. Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties. 2000, 80(4): 1017-1026.
[107] Markmann J, Bunzel P, Rosner H, et al. Microstructure evolution during rolling of inert-gas condensed palladium. Scripta Materialia. 2003, 49(7): 637-644.
[108] Chen M W, Ma E, Hemker K J, et al. Deformation twinning in nanocrystalline aluminum. Science. 2003, 300(5623): 1275-1277.
[109] Hemker K J. Understanding how nanocrystalline metals deform. Science. 2004, 304(5668): 221-222.
[110] He J, Li Y, Li B, et al. Relay protection for UHV transmission lines. Part Two: Disposition of relay protection. Dianli Xitong Zidonghua/Automation of Electric Power Systems. 2002, 26(24): 1-6.
[111] He J, Lavernia E J. Development of nanocrystalline structure during cryomilling of Inconel 625. Journal of Materials Research. 2001, 16(9): 2724-2732.
[112] Wang Y, Chen M, Zhou F, et al. High tensile ductility in a nanostructured metal. Nature. 2002, 419(6910): 912-915.
[113] Liao X Z, Zhao Y H, Srinivasan S G, et al. Deformation twinning in nanocrystalline copper at room temperature and low strain rate. Applied Physics Letters. 2004, 84(4): 592-594.
[114] Kumar K S, Suresh S, Chisholm M F, et al. Deformation of electrodeposited nanocrystalline nickel. Acta Materialia. 2003, 51(2): 387-405.
[115] 5osner H, Markmann J, Weissmu?ller J. Deformation twinning in nanocrystalline Pd. Philosophical Magazine Letters. 2004, 84(5): 321-334.
[116] Liao X Z, Kilmametov A R, Valiev R Z, et al. High-pressure torsion-induced grain growth in electrodeposited nanocrystalline Ni. Applied Physics Letters. 2006, 88(2): 021909.
[117] Liao X Z, Zhou F, Lavernia E J, et al. Deformation twins in nanocrystalline Al. Applied Physics Letters. 2003, 83(24): 5062-5064.
[118] Liao X Z, Zhou F, Lavernia E J, et al. Deformation mechanism in nanocrystalline Al: Partial dislocation slip. Applied Physics Letters. 2003, 83(4): 632-634.
[119] Lu L, Sui M L, Lu K. Superplastic extensibility of nanocrystalline copper at room temperature. Science. 2000,287(5457): 1463-1466.
[120] Champion Y, Langlois C, Guerin-Mailly S, et al. Near-Perfect Elastoplasticity in Pure Nanocrystalline Copper. Science. 2003, 300(5617): 310-311.
[121] McFadden S X, Mishra R S, Vallev R Z, et al. Low-temperature superplasticity in nanostructured nickel and metal alloys. Nature. 1999,398(6729): 684-686.
[122] Karch J, Birringer R, Gleiter H. Ceramics ductile at low temperature. Nature. 1987, 330(6148): 556-558.
[123] Mukherjee A K. An examination of the constitutive equation for elevated temperature plasticity. Materials Science and Engineering A - Structural Materials Properties Microstructure and Processing. 2002,322(1-2): 1-22.
[124] Shan Z W, Stach E A, Wiezorek J M K, et al. Grain boundary-mediated plasticity in nanocrystalline nickel. Science. 2004, 305(5684): 654-657.
[125] Hall E O. The Deformation and Ageing of Mild Steel: III Discussion of Results. Proceedings of the Physical Society B. 1951, 64(9): 747-753.
[126] Petch N J. The cleavage strength of polycrystals. Journal of Iron and Steel Institute. 1953, 174(1): 25-28.
[127] Shen T D, Schwarz R B, Feng S, et al. Effect of solute segregation on the strength of nanocrystalline alloys: Inverse Hall-Petch relation. Acta Materialia. 2007, 55(15): 5007-5013.
[128] Carlton C E, Ferreira P J. What is behind the inverse Hall-Petch effect in nanocrystalline materials? Acta Materialia. 2007, 55(11): 3749-3756.
[129] Giga A, Kimoto Y, Takigawa Y, et al. Demonstration of an inverse Hall-Petch relationship in electrodeposited nanocrystalline Ni-W alloys through tensile testing. Scripta Materialia. 2006, 55(2): 143-146.
[130] 王晋宝.碳纳米管的相关力学问题的研究:(博士学位论文)).大连:大连理工大学,2007.
[131] Allen M P, Tildesley D J. Computer Simulation of Liquids. Oxford:Clarendon Press, 1986.
[132] Rapaport D C. The Art of Molecular Dynamics Simulation. 2nd ed. New York:Cambridge University Press, 2004.
[133] Liu W K, Karpov E G, Park H S. Nano Mechanics and Materials: Theory, Multiscale Methods and Applications. Chichester: John Wiley & Sons Ltd, 2006.
[134] Philips R. Crystals, Defects and Microstructures: Modeling Across Scales. Cambridge:Cambridge University Press, 2001.
[135] Phillpot S R, Wolf D, Gleiter H. Molecular-dynamics study of the synthesis and characterization of a fully dense, three-dimensional nanocrystalline material. Journal of Applied Physics. 1995, 78(2): 847-861.
[136] Phillpot S R, Wolf D, Gleiter H. A structural model for grain boundaries in nanocrystalline materials. Scripta Metallurgica et Materialia. 1995,33(8): 1245-1251.
[137] Yamakov V, Wolf D, Salazar M, et al. Length-scale effects in the nucleation of extended dislocations in nanocrystalline Al by molecular-dynamics simulation. Acta Materialia. 2001, 49(14): 2713-2722.
[138] Yamakov V, Wolf D, Phillpot S R, et al. Deformation twinning in nanocrystalline Al by molecular-dynamics simulation. Acta Materialia. 2002, 50(20): 5005-5020.
[139] Yamakov V, Wolf D, Phillpot S R, et al. Deformation-mechanism map for nanocrystalline metals by molecular-dynamics simulation. Nature Materials. 2004, 3(1): 43-47.
[140] Yamakov V, Wolf D, Phillpot S R, et al. Dislocation-dislocation and dislocation-twin reactions in nanocrystalline Al by molecular dynamics simulation. Acta Materialia. 2003, 51(14): 4135-4147.
[141] Yamakov V, Wolf D, Phillpot S R. et al. Grain-boundary diffusion creep in nanocrystalline palladium by molecular-dynamics simulation. Acta Materialia. 2002, 50(1): 61-73.
[142] Yamakov V, Moldovan D, Rastogi K, et al. Relation between grain growth and grain-boundary diffusion in a pure material by molecular dynamics simulations. Acta Materialia. 2006, 54(15): 4053-4061.
[143] Van Swygenhoven H, Caro A. Plactic behavior of nanophase Ni: A molecular dynamics computer simulation. Applied Physics Letters. 1997, 71(22): 1652-1654.
[144] Van Swygenhoven H, Spaczer M, Caro A, et al. Competing plastic deformation mechanisms in nanophase metals. Physical Review B. 1999, 60(1): 22-25.
[145] Van Swygenhoven H, Derlet P M. Grain-boundary sliding in nanocrystalline fcc metals. Physical Review B. 2001, 64(22): 224105.
[146] Van Swygenhoven H, Derlet P M, Hasnaoui A. Atomic mechanism for dislocation emission from nanosized grain boundaries. Physical Review B. 2002, 66(2): 024101.
[147] Froseth A G, Derlet P M, Van Swygenhoven H. Dislocations emitted from nanocrystalline grain boundaries: nucleation and splitting distance. Acta Materialia. 2004, 52: 5863-5870.
[148] Schiotz J, Di Tolla F D, Jacobsen K W. Softening of nanocrystalline metals at very small grain sizes. Nature. 1998, 391(6667): 561-563.
[149] Schiotz J, Vegge T, Di Tolla F D, et al. Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Physical.Review B. 1999, 60(17): 11971-11983.
[150] Schiotz J, Jacobsen K W. A Maximum in the Strength of Nanocrystalline Copper. Science. 2003, 301(5638): 1357-1359.
[151] Schiotz J. Strain-induced coarsening in nanocrystalline metals under cyclic deformation. Materials Science and Engineering A - Structural Materials Properties Microstructure and Processing. 2004, 375-77: 975-979.
[152] Yang W, Wang H T, Hong W. Deformation of Nano-grained Metals. Proceedings of International Symposium of Young Scholars on Mechanics and Material Engineering for Science and Experiments, Changsha,2001: 1-12.
[153] Yang W, Tang J-C, Ing Y-S. et al. Transient dislocation emission from a crack tip. Journal of the Mechanics and Physics of Solids. 2001,49(10): 2431-2453.
[154] Cao A J, Wei Y G. Formation of fivefold deformation twins in nanocrystalline face-centered-cubic copper based on molecular dynamics simulations. Applied Physics Letters. 2006, 89(4): 041919.
[155] Cao A J, Wei Y G. Atomistic simulations of the mechanical behavior of fivefold twinned nanowires. Physical Review B. 2006,74(21): 214108.
[156] Wang J, Duan H L, Huang Z P, et al. A scaling law for properties of nano-structured materials. Proceedings of the Royal Society A. 2006,462(2069): 1355-1363.
[157] Duan H L, Wang J, Huang Z P, et al. Eshelby formalism for nano-inhomogeneities. Proceedings of the Royal Society A. 2005, 461(2062): 3335-3353.
[158] Yi X, Duan H L, Karihaloo B L, et al. Eshelby formalism for multi-shell nano-inhomogeneities. Archives of Mechanics. 2007, 59(3): 259-282.
[1] Tjong S C, Chen H. Nanocrystalline materials and coatings. Materials Science and Engineering R: Reports. 2004,45(1-2): 1-88.
[2] Lu C S, Mai Y W, Shen Y G. Recent advances on understanding the origin of superhardness in nanocomposite coatings: A critical review. Journal of Materials Science. 2006, 41(3): 937-950.
[3] Tjong S C, Chen H. Nanocrystalline materials and coatings. Materials Science & Engineering R-Reports. 2004,45(1-2): 1-88.
[4] Shen Y G, Liu Z J, Lu Y H, et al. Monte Carlo simulation of microstructure and grain growth in nc-Ti(N, B)/a-(TiB2, BN) nanocomposite films. Fracture of Materials: Moving Forwards. 2006, 312: 357-362.
[5] Hu H. Grain-growth in zone-refined iron. Canadian Metallurgical Quarterly. 1974, 13: 275-286.
[6] Zhang C, Suzuki A, Ishimaru T, et al. Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning. Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science. 2004, 35(7): 1927-1933.
[7] Anderson M P, Srolovitz D J, Grest G S, et al. Computer simulation of grain growth -I. Kinetics. Acta Metallurgica 1984, 32(5): 783-791.
[8] Zheng Y G, Lu C, Mai Y W, et al. Monte Carlo simulation of grain growth in two-phase nanocrystalline materials. Applied Physics Letters. 2006, 88(14): 144103.
[9] Lifshitz I M, Slyozov V V. The kinetics of precipitation from supersaturated solid solutions. Journal of Physics and Chemistry of Solids. 1961,19(1-2): 35-50.
[10] Thompson C V. Grain growth in thin film. Annual Reviews of Materials Science. 1990, 20: 245-268.
[11]Diao X X, Mai Y W. Self-similarity of crack propagation in inhomogeneous materials. Philosophical Magazine Letters. 1999, 79(4): 187-193.
[12] Atkinson H V. Theories of normal grain growth in pure single phase systems. Acta Metallurgica 1988, 36(3): 469-491.
[13]Pande C S, Masumura R A, Marsh S P. Stochastic analysis of two-dimensional grain growth. Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties. 2001, 81(5): 1229-1239.
[14]Pande C S, Rajagopal A K. Uniqueness and self similarity of size distributions in grain growth and coarsening. Acta Materialia. 2001, 49(10): 1805-1811.
[15]Helfen L, Wu D T, Birringer R, et al. The impact of stochastic atomic jumps on the kinetics of curvature-driven grain growth. Acta Materialia. 2003, 51(10): 2743-2754.
[16]Mullins W W. Grain growth of uniform boundaries with scaling. Acta Materialia. 1998, 46(17): 6219-6226.
[17] Hillert M. On theory of normal and abnormal grain growth. Acta metallurgica. 1965, 13(3): 227-238.
[18]Gusak A M, Tu K N. Theory of normal grain growth in normalized size space. Acta Materialia. 2003, 51(13): 3895-3904.
[19]Kadanoff L P. Statistical Physics: Statics, Dynamics and Renormalization. 北京:世界图书出版公司,2003.
[20] Saetre T O. A mean field theory of grain growth: I. Modelling and Simulation in Materials Science and Engineering. 2004, 12(6): 1267-1277.
[21] Mulheran P A, Harding J H. A statistical theory of normal grain growth. Material Science Forum 1992, 94-96: 367-372.
[22] Louat N P. On the theory of normal grain growth. Acta Metallurgica. 1974, 22(6): 721-724.
[23]Ryum N, Hunderi O. On the analytic description of normal grain growth. Acta Metallurgica. 1989, 37(5): 1375-1379.
[24] Press W H, Teukolsky S A, Vetterling W T, et al. Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. Cambridge:Cambridge University Press, 1992.
[25] Shan Z W, Stach E A, Wiezorek J M K, et al. Grain boundary-mediated plasticity in nanocrystalline nickel. Science. 2004, 305(5684): 654-657.
[26]Gleiter H. Nanostructured materials: basic concepts and microstructure. Acta Materialia. 2000, 48(1): 1-29.
[27]Maximenko A L, Olevsky E A. Effective diffusion coefficients in solid-state sintering. Acta Materialia. 2004, 52(10): 2953-2963.
[1]Tjong S C,Chen H.Nanocrystalline materials and coatings.Materials Science & Engineering R-Reports.2004,45(1-2):1-88.
[2]Liu Z J,Zhang C H,Shen Y G,et al.Monte Carlo simulation of nanocrystalline TiN/amorphous SiN_x composite films.Journal of Applied Physics.2004,95(2):758-760.
[3]Lu C S,Mai Y W,Shen Y G.Recent advances on understanding the origin of superhardness in nanocomposite coatings:A critical review.Journal of Materials Science.2006,41(3):937-950.
[4]Liu Z J,Shum P W,Shen Y G.Hardening mechanisms of nanocrystalline Ti-Al-N solid solution films.Thin Solid Films.2004,468(1-2):161-166
[5]Fan D N,Chen L Q.Diffusion-controlled grain growth in two-phase solids.Acta Materialia.1997,45(8):3297-3310.
[6]Lifshitz I M,Slyozov V V.The kinetics of precipitation from supersaturated solid solutions.Journal of Physics and Chemistry of Solids.1961,19(1-2):35-50.
[7]Hillert M.On theory of normal and abnormal grain growth.Acta metallurgica.1965,13(3):227-238.
[8]Maurice M,Humphries J,2- and 3-D Curvature Driven Vertex Simulations of Grain Growth,in Grain Growth in Polycrystalline Materials Ⅲ,Weiland H,Adams B L,Rollett A D,Editors.1998,The Minerals,Metals and Materials Society:Pittsburgh.81-90.
[9]Anderson M P,Srolovitz D J,Grest G S,et al.Computer simulation of grain growth-Ⅰ.Kinetics.Acta Metallurgica.1984,32(5):783-791.
[10]Potts R B.Some generalized order-disorder transformations.Proceedings of the Cambridge Philosophical Society.1952,48:106-109.
[11]Holm E A,Srolovitz D J,Cahn J W.Microstructural evolution in two-dimensional two-phase polycrystals.Acta Metallurgica et Materialia.1993,41(4):1119-1136.
[12]张海.基于蒙特卡罗方法的晶粒生长模拟系统研究:(硕士学位论文).长沙:中南大学,2007.
[13]陈伟元,钟晓征,谭锐等.多晶材料晶粒生长的计算机模拟研究.原子与分子物理学报.2000,17(2):297-302.
[14]张继祥,关小军,孙胜.一种改进的晶粒长大Monte Carlo模拟方法.金属学报.2004,40(5):457-461.
[15]刘国权,宋晓艳,于海波等.一种Monte Carlo仿真新算法及其对三维个体晶粒长大速率拓扑依赖性理论方程的验证.金属学报.1999,35(3):245-248.
[16]秦湘阁,刘国权.基于Monte Carlo Potts方法的三维大尺度晶粒组织仿真模型及定量表征.北京科技大学学报.2004,26(1):49-52.
[17]Raabe D.计算材料学.北京:化学工业出版社,2002.
[18]王海东,张海.晶粒生长的蒙特卡罗模拟研究进展.材料导报.2007,21(2):72-74.
[19]周燕.关于线性同余组合发生器的周期性和统计性质.重庆大学学报(自然科学版).2000,23(6):67-70.
[20]Metropolis N,Rosenbluth A W,Rosenbluth M N,et al.Equation of State Calculations by Fast Computing Machines.The Journal of Chemical Physics.1953,21(6):1087-1092.
[21]Radhakrishnan B, Zacharia T. Simulation of Curvature-Driven Grain-Growth by Using a Modified Monte-Carlo Algorithm. Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science. 1995, 26(1): 167-180.
[22] Yu Q, Esche S K. A Monte Carlo algorithm for single phase normal grain growth with improved accuracy and efficiency. Computational Materials Science. 2003, 27(3): 259-270.
[23] Atkinson H V. Theories of normal grain growth in pure single phase systems. Acta Metallurgica. 1988, 36(3): 469-491.
[24]Gusak A M, Tu K N. Theory of normal grain growth in normalized size space. Acta Materialia. 2003, 51(13): 3895-3904.
[25] Thompson C V. Grain growth in thin film. Annual Reviews of Materials Science. 1990, 20: 245-268.
[26] Veprek S, Reiprich S, Shizhi L. Superhard nanocrystalline composite materials: The TiN/Si_3N_4 system. Applied Physics Letters. 1995, 66(20): 2640-2642.
[27]Xun Y, Lavernia E J, Mohamed F A. Grain growth in nanocrystalline Zn-22% Al. Materials Science and Engineering A - Structural Materials Properties Microstructure and Processing. 2004, 371(1-2): 135-140.
[28]Yamazaki D, Kato T, Ohtani E, et al. Grain Growth Rates of MgSiO_3 Perovskite and Periclase Under Lower Mantle Conditions. Science. 1996, 274(5295): 2052-2054.
[29] Zheng Y G, Lu C, Mai Y W, et al. Monte Carlo simulation of grain growth in two-phase nanocrystalline materials. Applied Physics Letters. 2006, 88(14): 144103.
[30] Kurtz S K, Carpay F M A. Microstructure and normal grain growth in metals and ceramics. Part I. Theory. Journal of Applied Physics. 1980, 51(11): 5725-5744.
[31] Mas D L, Crowley P D. The effect of second-phase particles on stable grain size in regionally metamorphosed polyphase calcite marbles. Journal of Metamorphic Geology. 1996, 14(2): 155-162.
[32]Hillert M. Inhibition of grain growth by second-phase particles. Acta Metallurgica. 1988, 36(12): 3177-3181.
[33]Shen Y G, Liu Z J, Lu Y H, et al. Monte Carlo simulation of microstructure and grain growth in nc-Ti(N, B)/a-(TiB2, BN) nanocomposite films. Fracture of Materials: Moving Forwards. 2006, 312: 357-362.
[1]Raabe D.计算材料学.北京:化学工业出版社,2002.
[2]Liu W K,Karpov E G,Park H S.Nano Mechanics and Materials:Theory,Multiscale Methods and Applications.Chichester:John Wiley & Sons Ltd,2006.
[3]Phllips R.Crystals,Defects and Microstructures:Modeling Across Scales.Cambridge:Cambridge University Press,2001.
[4]文玉华,朱如曾,周富信等.分子动力学模拟的主要技术.力学进展.2003,33(1):65-73.
[5]Meyers M A,Mishra A,Benson D J.Mechanical properties of nanocrystalline materials.Progress in Materials Science.2006,51(4):427-556.
[6]Schiotz J,Di Tolla F D,Jacobsen K W.Softening of nanocrystalline metals at very small grain sizes.Nature.1998,391(6667):561-563.
[7]Van Swygenhoven H,Derlet P M.Grain-boundary sliding in nanocrystalline fcc metals.Physical Review B.2001,64(22):224105.
[8]Wolf D,Yamakov V,Phillpot S R,et al.Deformation of nanocrystalline materials by molecular-dynamics simulation:relationship to experiments? Acta Materialia.2005,53(1):1-40.
[9]Yamakov V,Wolf D,Phillpot S R,et al.Deformation-mechanism map for nanocrystalline metals by molecular-dynamics simulation.Nature Materials.2004,3(1):43-47.
[10]梁海弋.纳米铜力学行为的分子动力学模拟:(博士学位论文).合肥:中国科学技术大学,2001.
[11]Alder B J,Wainwright T E.Phase Transition for a Hard Sphere System.The Journal of Chemical Physics.1957,27(5):1208-1209.
[12]Rahman A.Correlations in the Motion of Atoms in Liquid Argon.Physical Review.1964,136(2):405-411.
[13]Rahman A,Stillinger F H.Molecular dynamics study of liquid water.The Journal of Chemical Physics.1971,55(7):3336-3359.
[14]Rychaert J P,Ciccotti G,Berendsen H J C.Numerical integration of the Cartesian equations of dynamics of n-alkanes.Journal of Computational Physics.1977,23(3):327-341.
[15]van Gunsteren W F,Berendsen H J C.Algorithms for macromolecular dynamics and constraint dynamics.Molecular Physics.1977,34(5):1311-1327
[16]Andersen H C.Molecular dynamics simulations at constant pressure and/or temperature.The Journal of Chemical Physics.1980,72(4):2384-2393.
[17]Parrinello M,Rahman A.Crystal Structure and Pair Potentials:A Molecular-Dynamics Study.Physical Review Letters.1980,45(14):1196-1199.
[18]Gillan M J,Dixon M.The calculation of thermal conductivities by perturbed molecular dynamics simulation.Journal of Physics C:Solid State Physics.1983,16(5):869-878.
[19]Berendsen H J C,Postma J P M,van Gunsteren W F,et al.Molecular dynamics with coupling to an external bath.The Journal of Chemical Physics.1984,81(8):3684-3690.
[20]Hoover W G.Canonical dynamics:Equilibrium phase-space distributions.Physical Review A.1985,31(3):1695-1697.
[21]Nosé S.A unified formulation of the constant temperature molecular dynamics methods.The Journal of Chemical Physics.1984,81(1):511-519.
[22]Rapaport D C.The Art of Molecular Dynamics Simulation.2nd ed.New York:Cambridge University Press,2004.
[23]Allen M P,Tildesley D J.Computer Simulation of Liquids.Oxford:Clarendon Press,1986.
[24]钟万勰,杨再石.连续时间LQ控制主要本征对算法.应用数学和力学.1991,12(1):45-50.
[25]Zhong W X,Williams F W.A Precise Time-Step Integration Method.Proceedings of the Institution of Mechanical Engineers Part C:Journal of Mechanical Engineering Science.1994,208(6):427-430.
[26]Lennard-Jones J E.On the Forces between Atoms and lons.Proceedings of the Royal Society A.1925,109(752):584-597.
[27]Lennard-Jones J E,Dent B M.The Forces between Atoms and Ions Ⅱ.Proceedings of the Royal Society A.1926,112(760):230-234.
[28]Girifalco L A,Weizer V G.Application of the Morse Potential Function to Cubic Metals.Physical Review.1959,114(3):687-690.
[29]Shen L M,Chen Z.An investigation of the effect of interfacial atomic potential on the stress transition in thin films.Modelling and Simulation in Materials Science and Engineering.2004,12(4):347-369.
[30]Tersoff J.Modeling solid-state chemistry:Interatomic potentials for multicomponent systems.Physical Review B.1989,39(8):5566-5568.
[31]Huang S P,Mainardi D S,Balbuena P B.Structure and dynamics of graphite-supported bimetallic nanoclusters.Surface Science.2003,545(3):163-179.
[32]Sutton A P,Chen J.Long-range Finnis-Sinclair potentials.Philosophical Magazine Letters.1990,61(3):139-146.
[33]Kart H H,Tomak M,Cagin T.Thermal and mechanical properties of Cu-Au intermetallic alloys.Modelling and Simulation in Materials Science and Engineering.2005,13(5):657-669.
[34]Wang L,Zhang H W,Zhang Z Q,et al.Buckling behaviors of single-walled carbon nanotubes filled with metal atoms.Applied Physics Letters.2007,91(5):051122.
[35]Daw M S,Baskes M I.Embedded-atom method:Derivation and application to impurities,surfaces,and other defects in metals.Physical Review B.1984,29(12):6443-6453.
[36]Foiles S M,Baskes M I,Daw M S.Embedded-atom-method functions for the fcc metals Cu,Ag,Au,Ni,Pd,Pt,and their alloys.Physical Review B.1986,33(12):7983-7991.
[37]冯端.金属物理学.北京:科学出版社,2000.
[38]Johnson R A,Wilson W D,Interatomic Potentials and Simulation of Lattice Defects.in:Gehlen P C,Beeler J R,Jaffee R I,ed.Interatomic Potentials and Simulation of Lattice Defects.New York:Plenum 1972.
[39]Finnis M W,Sinclair J E.A simple empirical N-body potential for transition metals.Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties.1984,50(1):45-55.
[40]Ackland G J,Vitek V.Many-body potentials and atomic-scale relaxations in noble-metal alloys.Physical Review B.1990,41(15):10324-10333.
[41]Jacobsen K W,Norskov J K,Puska M J.Interatomic interactions in the effective-medium theory.Physical Review B.1987,35(14):7423-7442.
[42] Born M, Huang K. Dynamical Theory of Crystal Lattices. New York:Oxford University Press, 1954.
[43] Zhou M. A new look at the atomic level virial stress: on continuum-molecular system equivalence. Proceedings of the Royal Society A. 2003,459(2037): 2347-2392.
[44] Cormier J, Rickman J M, Delph T J. Stress calculation in atomistic simulations of perfect and imperfect solids. Journal of Applied Physics. 2001, 89(1): 99-104.
[45]Todd B D, Evans D J, Daivis P J. Pressure Tensor for Inhomogeneous Fluids. Physical Review E. 1995, 52(2): 1627-1638.
[46]Chueng K S, Yip S. Atomic-level stress in an inhomogeneous system. Journal of Applied Physics. 1991, 70(10): 5688-5690.
[47] Jean J S. The Dynamical Theory of Gases. New York:Dover, 1960.
[48]Griebel M, Knapek S, Zumbusch G. Numerical Simulation in Molecular Dynamics: Numerics, Algorithms, Parallelization, Applications. Texts in Computational Science and Engineering, ed. Barth T J, Griebel M, Keyes D E, et al. Berlin Heidelberg:Springer-Verlag, 2007.
[1] Landman U, Luedtke W D, Burnham N A, et al. Atomistic mechanisms and dynamics of adhesion, nanoindentation, and fracture. Science. 1990, 248(4954): 454-461.
[2] Lieber C M. Nanoscale science and technology: Building a big future from small things. MRS Bulletin. 2003, 28(7): 486-491.
[3] Xia Y N, Yang P D, Sun Y G, et al. One-dimensional nanostructures: Synthesis, characterization, and applications. Advanced Materials. 2003, 15(5): 353-389.
[4] Yu M F, Lourie O, Dyer M J, et al. Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load. Science. 2000, 287(5453): 637-640.
[5] Wu Y, Xiang J, Yang C, et al. Single-crystal metallic nanowires and metal/semiconductor nanowire heterostructures. Nature. 2004, 430(7000): 61-65.
[6] Winn D, Doherty M F. Modeling crystal shapes of organic materials grown from solution. Aiche Journal. 2000, 46(7): 1348-1367.
[7] Mann S. The chemistry of form. Angewandte Chemie. 2000, 39(19): 3392-3406.
[8] Li J B, Wang L W. Shape effects on electronic states of nanocrystals. Nano Letters. 2003, 3(10): 1357-1363.
[9] Ohnishi H, Kondo Y, Takayanagi K. Quantized conductance through individual rows of suspended gold atoms. Nature. 1998, 395(6704): 780-783.
[10]Gulseren O, Ercolessi F, Tosatti E. Noncrystalline Structures of Ultrathin Unsupported Nanowires. Physical Review Letters. 1998, 80(17): 3775-3778.
[11]Rodrigues V, Fuhrer T, Ugarte D. Signature of Atomic Structure in the Quantum Conductance of Gold Nanowires. Physical Review Letters. 2000, 85(19): 4124-4127.
[12] Ji C J, Park H S. Geometric effects on the inelastic deformation of metal nanowires. Applied Physics Letters. 2006, 89(18): 181916.
[13] Park H S, Zimmerman J A. Modeling inelasticity and failure in gold nanowires. Physical Review B. 2005, 72(5): 054106.
[14] Liang H Y, Upmanyu M, Huang H C. Size-dependent elasticity of nanowires: Nonlinear effects. Physical Review B. 2005, 71(24): 241403.
[15]Cao A J, Wei Y G. Formation of fivefold deformation twins in nanocrystalline face-centered-cubic copper based on molecular dynamics simulations. Applied Physics Letters. 2006, 89(4): 041919.
[16]Shankar M R, King A H. How surface stresses lead to size-dependent mechanics of tensile deformation in nanowires. Applied Physics Letters. 2007, 90(14): 141907.
[17]Branicio P S, Rino J-P. Large deformation and amorphization of Ni nanowires under uniaxial strain: A molecular dynamics study. Physical Review B. 2000, 62(24): 16950-16955.
[18] da Silva E Z, da Silva A J R, Fazzio A. How Do Gold Nanowires Break? Physical Review Letters. 2001, 87(25): 256102.
[19]Coura P Z, Legoas S B, Moreira A S, et al. On the Structural and Stability Features of Linear Atomic Suspended Chains Formed from Gold Nanowires Stretching. Nano Letters. 2004, 4(7): 1187-1191.
[20] Gall K, Diao J, Dunn M L, et al. Tetragonal Phase Transformation in Gold Nanowires. Journal of Engineering Materials and Technology. 2005, 127(4): 417-422.
[21] Diao J, Gall K, Dunn M L. Surface-stress-induced phase transformation in metal nanowires. Nature Materials. 2003, 2(10): 656-660.
[22] Liang W, Zhou M. Response of copper nanowires in dynamic tensile deformation. Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science. 2004, 218(6): 599-606.
[23]Liang W, Zhou M, Ke F. Shape Memory Effect in Cu Nanowires. Nano Letters. 2005, 5(10): 2039-2043.
[24]Mehrez H, Ciraci S. Yielding and fracture mechanisms of nanowires. Physical Review B. 1997, 56(19): 12632-12642.
[25] Park H S, Gall K, Zimmerman J A. Shape Memory and Pseudoelasticity in Metal Nanowires. Physical Review Letters. 2005, 95(25): 255504.
[26] Park H S, Gall K, Zimmerman J A. Deformation of FCC nanowires by twinning and slip. Journal of the Mechanics and Physics of Solids. 2006, 54(9): 1862-1881.
[27] Diao J, Gall K, Dunn M L. Yield Strength Asymmetry in Metal Nanowires. Nano Letters. 2004,4(10): 1863-1867.
[28] Sankaranarayanan S K R S, Bhethanabotla V R, Joseph B. Molecular dynamics simulation of temperature and strain rate effects on the elastic properties of bimetallic Pd-Pt nanowires. Physical Review B. 2007, 76(13): 134117.
[29] Cao A J, Wei Y G. Atomistic simulations of the mechanical behavior of fivefold twinned nanowires. Physical Review B. 2006, 74(21): 214108.
[30] Liao X Z, Zhao Y H, Srinivasan S G, et al. Deformation twinning in nanocrystalline copper at room temperature and low strain rate. Applied Physics Letters. 2004, 84(4): 592-594.
[31] Wu B, Heidelberg A, Boland J J, et al. Microstructure-hardened silver nanowires. Nano Letters. 2006, 6(3): 468-472.
[32] Daw M S, Baskes M I. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Physical Review B. 1984, 29(12): 6443-6453.
[33]Foiles S M, Baskes M I, Daw M S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Physical Review B. 1986, 33(12): 7983-7991.
[34] Hoover W G. Canonical dynamics: Equilibrium phase-space distributions. Physical Review A. 1985. 31(3): 1695-1697.
[35] Nose S. A unified formulation of the constant temperature molecular dynamics methods. The Journal of Chemical Physics. 1984, 81 (1): 511 -519.
[36] Plimpton S. Fast Parallel Algorithms for Short-Range Molecular-Dynamics. Journal of Computational Physics. 1995, 117(1): 1-19.
[37]Schiotz J. Strain-induced coarsening in nanocrystalline metals under cyclic deformation. Materials Science and Engineering A - Structural Materials Properties Microstructure and Processing. 2004, 375-77: 975-979.
[38] Stankovic I, Kroger M, Hess S. Recognition and analysis of local structure in polycrystalline configurations. Computer Physics Communications. 2002, 145(3): 371-384.
[39] Rapaport D C. The Art of Molecular Dynamics Simulation. 2nd ed. New York:Cambridge University Press, 2004.
[40] Allen M P, Tildesley D J. Computer Simulation of Liquids. Oxford:Clarendon Press, 1987.
[41] Zimmerman J A, Kelchner C L, Klein P A, et al. Surface Step Effects on Nanoindentation. Physical Review Letters. 2001, 87(16): 165507.
[42] Kittel C. Introduction to Solid State Physics. 7 ed. New York:John Wiley and Sons, Inc., 1996.
[43]Ehrhart P. The configuration of atomic defects as determined from scattering studies. Journal of Nuclear Materials. 1978, 69-70: 200-214.
[44] Siegel R W. Vacancy concentrations in metals. Journal of Nuclear Materials. 1978, 69-70: 117-146.
[45] Balluffi R W. Vacancy defect mobilities and binding energies obtained from annealing studies. Journal of Nuclear Materials. 1978, 69-70: 240-263.
[46] Tyson W R, Miller W A. Surface free energies of solid metals: Estimation from liquid surface tension measurements. Surface Science. 1977, 62(1): 267-276.
[47] Mishin Y, Mehl M J, Papaconstantopoulos D A, et al. Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations. Physical Review B. 2001, 63(22): 224106.
[48]Frank F C. Supercooling of Liquids. Proceedings of the Royal Society A. 1952, 215(1120): 43-46.
[49] Barker J A, Hoare M R, Finney J L. Relaxation of the Bernal model. Nature. 1975, 257(5522): 120-122.
[1] Gleiter H. Nanocrystalline materials. Progress in Materials Science. 1989, 33(4): 223-315.
[2] Gleiter H. Nanostructured Materials: State-of-the-Art and Perspectives. Nanostructured Materials 1995, 6(1-4): 3-14.
[3] Gleiter H. Nanostructured materials: basic concepts and microstructure. Acta Materialia. 2000, 48(1): 1-29.
[4] Meyers M A, Mishra A, Benson D J. Mechanical properties of nanocrystalline materials. Progress in Materials Science. 2006, 51(4): 427-556.
[5] Lu C S, Mai Y W, Shen Y G. Recent advances on understanding the origin of superhardness in nanocomposite coatings: A critical review. Journal of Materials Science. 2006, 41(3): 937-950.
[6] Murayama M, Howe J M, Hidaka H, et al. Atomic-level observation of disclination dipoles in mechanically milled, nanocrystalline Fe. Science. 2002, 295(5564): 2433-2435.
[7] Chen M W, Livi K J T. Wright P K, et al. Microstructural characterization of a platinum-modified diffusion aluminide bond coat for thermal barrier coatings. Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science. 2003, 34(10): 2289-2299.
[8] Chen M W, Ma E, Hemker K J, et al. Deformation twinning in nanocrystalline aluminum. Science. 2003,300(5623): 1275-1277.
[9] Liao X Z, Zhao Y H, Srinivasan S G, et al. Deformation twinning in nanocrystalline copper at room temperature and low strain rate. Applied Physics Letters. 2004, 84(4): 592-594.
[10] Shan Z W, Stach E A, Wiezorek J M K, et al. Grain boundary-mediated plasticity in nanocrystalline nickel. Science. 2004, 305(5684): 654-657.
[11] Gutkin M Y, Ovid'ko I A. Grain boundary migration as rotational deformation mode in nanocrystalline materials. Applied Physics Letters. 2005, 87(25): 251916.
[12]Gutkin M Y, Ovid'ko I A. Special mechanism for dislocation nucleation in nanomaterials. Applied Physics Letters. 2006, 88(21): 211901.
[13] Wolf D, Yamakov V, Phillpot S R, et al. Deformation of nanocrystalline materials by molecular-dynamics simulation: relationship to experiments? Acta Materialia. 2005, 53(1): 1-40.
[14]Schiotz J, Di Tolla F D, Jacobsen K W. Softening of nanocrystalline metals at very small grain sizes. Nature. 1998, 391(6667): 561-563.
[15]Schiotz J. Strain-induced coarsening in nanocrystalline metals under cyclic deformation. Materials Science and Engineering A - Structural Materials Properties Microstructure and Processing. 2004, 375-377: 975-979.
[16] Van Swygenhoven H, Spaczer M, Caro A, et al. Competing plastic deformation mechanisms in nanophase metals. Physical Review B. 1999, 60(1): 22.
[17] Van Swygenhoven H, Derlet P M. Grain-boundary sliding in nanocrystalline fcc metals. Physical Review B. 2001, 64(22): 224105.
[18] Van Swygenhoven H, Derlet P M, Fr(?)seth A G. Nucleation and propagation of dislocations in nanocrystalline fcc metals. Acta Materialia. 2006, 54(7): 1975-1983.
[19] Van Swygenhoven H, Derlet P M, Hasnaoui A. Atomic mechanism for dislocation emission from nanosized grain boundaries. Physical Review B. 2002, 66(2): 024101.
[20] Yamakov V, Wolf D, Phillpot S R, et al. Dislocation-dislocation and dislocation-twin reactions in nanocrystalline Al by molecular dynamics simulation. Acta Materialia. 2003, 51(14): 4135-4147.
[21] Yamakov V, Wolf D, Salazar M. et al. Length-scale effects in the nucleation of extended dislocations in nanocrystalline Al by molecular-dynamics simulation. Acta Materialia. 2001, 49(14): 2713-2722.
[22] Sansoz F, Molinari J F. Mechanical behavior of Sigma tilt grain boundaries in nanoscale Cu and Al: A quasicontinuum study. Acta Materialia. 2005, 53(7): 1931-1944.
[23] Atkinson H V. Theories of normal grain growth in pure single phase systems. Acta Metallurgica. 1988, 36(3): 469-491.
[24] Zheng Y G, Lu C, Mai Y W, et al. Monte Carlo simulation of grain growth in two-phase nanocrystalline materials. Applied Physics Letters. 2006, 88(14): 144103.
[25] Zheng Y G, Lu C, Mai Y W, et al. Model-based simulation of normal grain growth in a two-phase nanostructured system. Science and Technology of Advanced Materials. 2006, 7(8): 812-818.
[26] Hoover W G. Canonical dynamics: Equilibrium phase-space distributions. Physical Review A. 1985, 31(3): 1695-1697.
[27]Nose S. A unified formulation of the constant temperature molecular dynamics methods. The Journal of Chemical Physics. 1984, 81(1): 511-519.
[28] Daw M S, Baskes M I. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Physical Review B. 1984, 29(12): 6443-6453.
[29]Foiles S M, Baskes M I, Daw M S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Physical Review B. 1986, 33(12): 7983-7991.
[30] Balluffi R W. Vacancy defect mobilities and binding energies obtained from annealing studies. Journal of Nuclear Materials. 1978,69-70: 240-263.
[31]Ehrhart P. The configuration of atomic defects as determined from scattering studies. Journal of Nuclear Materials. 1978, 69-70: 200-214.
[32] Plimpton S. Fast Parallel Algorithms for Short-Range Molecular-Dynamics. Journal of Computational Physics. 1995, 117(1): 1-19.
[33] Stankovic I, Kroger M, Hess S. Recognition and analysis of local structure in polycrystalline configurations. Computer Physics Communications. 2002, 145(3): 371-384.
[34] Allen M P, Tildesley D J. Computer Simulation of Liquids. Oxford:Clarendon Press, 1986.
[35]Rapaport D C. The Art of Molecular Dynamics Simulation. 2nd ed. New York:Cambridge University Press, 2004.
[36] Lu L, Sui M L, Lu K. Superplastic extensibility of nanocrystalline copper at room temperature. Science. 2000,287(5457): 1463-1466.
[37]Lu L, Shen Y F, Chen X H, et al. Ultrahigh strength and high electrical conductivity in copper. Science. 2004, 304(5669): 422-426.
[38] Sansoz F, Dupont V. Grain growth behavior at absolute zero during nanocrystalline metal indentation. Applied Physics Letters. 2006, 89(11): 111901.
[39]Humphrey W, Dalke A, Schulten K. VMD: Visual molecular dynamics. Journal of Molecular Graphics. 1996, 14(1): 33-38.
[2]Gleiter H.Nanostructured materials:basic concepts and microstructure.Acta Materialia.2000,48(1):1-29.
[3]Meyers M A,Mishra A,Benson D J.Mechanical properties of nanocrystalline materials.Progress in Materials Science.2006,51(4):427-556.
[4]张中太,林元华,唐子龙等.纳米材料及其技术的应用前景.材料工程.2000,3:42-48.
[5]Chikara H.Ultrafine particles.Physics Today.1987,11:44-51.
[6]Gleiter H.Nanostructured Materials:State-of-the-Art and Perspectives.Nanostructured Materials 1995,6(1-4):3-14.
[7]张立德,牟季美.纳米材料和纳米结构.北京:科学出版社,2001.
[8]文玉华,周富信,刘曰武.纳米材料的研究进展.力学进展.2001,31(1):47-61.
[9]Andres R P,Averback R S,Brown W L,et al.Research opportunities on clusters and cluster-assembled materials - A Department of Energy,Council on Materials Science Panel Report.Journal of Materials Research.1989,4(3):704-736.
[10]Dao M,Lu L,Asaro R J,et al.Toward a quantitative understanding of mechanical behavior of nanocrystalline metals.Acta Materialia.2007,55(12):4041-4065.
[11]Lu C S,Mai Y W,Shen Y G.Recent advances on understanding the origin of superhardness in nanocomposite coatings:A critical review.Journal of Materials Science.2006,41(3):937-950.
[12]Veprek S,Reiprich S,Shizhi L.Superhard nanocrystalline composite materials:The TiN/Si_3N_4 system.Applied Physics Letters.1995,66(20):2640-2642.
[13]王中林.纳米材料和纳米技术.科学中国人.2001,4:4-9.
[14]Gleiter H,Weissmüller J,Wollersheim O,et al.Nanocrystalline materials:a way to solids with tunable electronic structures and properties? Acta Materialia.2001,49(4):737-745.
[15]Mehl R E,Cahn R W,Historical development,in:Calm R W,Hansen P,ed.Physical Metallurgy.North Holland:Elsevier Science Publishers,1983:1-35.
[16]Langford G,Cohen M.Strain hardening of iron by severe plastic deformation.Transactions of the ASM.1969,62:623-638.
[17]Beck F.Cathodic dimerization.Angewandte Chemie International Edition in English.2003,11(9):760-781.
[18]Gleiter H,Materials with ultrafine grain size.in:Hansen N,ed.Deformation of polycrystals:mechanisms and microstructures.Roskilde:Riso National Laboratory,1981:15-21.
[19]Lu K.Nanocrystalline materials crystallized from amorphous solids:Nanocrystallization,structure,and properties.Materials Science and Engineering R:Reports.1996,16(4):161-221.
[20]Frost H J.Microstructural Evolution in Thin Films.Materials Characterization.1994,32:257-273.
[21]Thompson C V.Grain growth in thin film.Annual Reviews of Materials Science.1990,20:245-268.
[22]Thompson C V.Grain growth and evolution of other cellular structures.Solid State Physics.2001,55:269-314.
[23] Veprek S, Veprek-Heijman M G J, Karvankova P, et al. Different approaches to superhard coatings and nanocomposites. Thin Solid Films. 2005, 476(1): 1-29.
[24] Anderson M P, Srolovitz D J, Grest G S, et al. Computer simulation of grain growth -I. Kinetics. Acta Metallurgica 1984,32(5): 783-791.
[25] Atkinson H V. Theories of normal grain growth in pure single phase systems. Acta Metallurgica. 1988, 36(3): 469-491.
[26]Marlow T R, Koch C C, Grain Growth of Nanocrystalline Materials - A Review. in: Bourell D L, ed. Synthesis and Processing of Nanocrystalline Powder. Warrendale PA: TMS, 1996: 33-46.
[27] Hu H. Grain-growth in zone-refined iron. Canadian Metallurgical Quarterly. 1974, 13: 275-286.
[28] Zhang C, Suzuki A, Ishimaru T, et al. Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning. Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science. 2004,35(7): 1927-1933.
[29] Hillert M. On theory of normal and abnormal grain growth. Acta metallurgies 1965, 13(3): 227-238.
[30]Lifshitz I M, Slyozov V V. The kinetics of precipitation from supersaturated solid solutions. Journal of Physics and Chemistry of Solids. 1961, 19(1-2): 35-50.
[31] Louat N P. On the theory of normal grain growth. Acta Metallurgies 1974, 22(6): 721 -724.
[32]Hunderi O, Ryum N. The kinetics of normal grain growth. Journal of Materials Science. 1980, 15(5): 1104-1108.
[33]Abbruzzese G, Liicke K. A theory of texture controlled grain growth - I. Derivation and general discussion of the model. Acta Metallurgies 1986, 34(5): 905-914.
[34] Eichelkraut H, Abbruzzese G, Lucke K. A theory of texture controlled grain growth - II. Numerical and analytical treatment of grain growth in the presence of two texture components. Acta Metallurgica. 1988, 36(1): 55-68.
[35] Fischer F D, Svoboda J, Fratzl P. A thermodynamic approach to grain growth and coarsening. Philosophic Magazine. 2003, 83(9): 1075-1093.
[36] Gusak A M, Tu K N. Theory of normal grain growth in normalized size space. Acta Materialia. 2003, 51(13): 3895-3904.
[37] Saetre T O. On the theory of normal grain growth in two dimensions. Acta Materialia. 2002, 50(6): 1539-1546.
[38] Saetre T O. A mean field theory of grain growth: I. Modelling and Simulation in Materials Science and Engineering. 2004, 12(6): 1267-1277.
[39] Saetre T O. A mean field theory of grain growth: II. Modelling and Simulation in Materials Science and Engineering. 2004, 12(6): 1279-1292.
[40]Mullins W W. Grain growth of uniform boundaries with scaling. Acta Materialia. 1998, 46(17): 6219-6226.
[41]Pande C S, Rajagopal A K. Uniqueness and self similarity of size distributions in grain growth and coarsening. Acta Materialia. 2001, 49(10): 1805-1811.
[42] Mulheran P A, Harding J H. A statistical theory of normal grain growth. Material Science Forum 1992, 94-96: 367-372.
[43] Pande C S. On a stochastic theory of grain growth. Acta Metallurgica. 1987, 35(11): 2671-2678.
[44]Pande C S, Dantsker E. On a stochastic theory of grain growth - II. Acta Metallurgica et Materialia. 1990, 38(6): 945-951.
[45]Pande C S, Dantsker E. On a stochastic theory of grain growth - III. Acta Metallurgica et Materialia. 1991,39(6): 1359-1365.
[46] Pande C S, Dantsker E. On a stochastic theory of grain growth - IV. Acta Metallurgica et Materialia. 1994, 42(8): 2899-2903.
[47] Pande C S, Rajagopal A K. Modeling of grain growth in two dimensions. Acta Materialia. 2002, 50(11): 3013-3021.
[48] Helfen L, Wu D T, Birringer R, et al. The impact of stochastic atomic jumps on the kinetics of curvature-driven grain growth. Acta Materialia. 2003, 51(10): 2743-2754.
[49] Di Nunzio P E. A discrete approach to grain growth based on pair interactions. Acta Materialia. 2001, 49(15): 3635-3643.
[50]Lou C, Player M A. Advection-diffusion model for normal grain growth. Journal of Physics D: Applied Physics. 2001, 34: 1286-1292.
[51]Rios P R. A theory for grain boundary pining by particles. Acta Metallurgica. 1987, 35(12): 2805-2815.
[52]Hillert M. Inhibition of grain growth by second-phase particles. Acta Metallurgica. 1988, 36(12): 3177-3181.
[53] Miodownik M A. A review of microstructural computer models used to simulate grain growth and recrystallisation in aluminium alloys. Journal of Light Metals. 2002, 2(1): 125-135.
[54] Demirel M C, Kuprat A P, George D C, et al. Experimental verification of finite element simulation of curvature-driven grain growth in al-foil. Proceeding of the First Joiint International Conference on Recrystallisation and Grain Growth, Beilin, 2001: 297-302.
[55]Janssens K G F, Vanini F, Reissner J N. Thermodynamic and kinetic coupling of a random grid cellular automaton for the simulation of grain growth. Advanced Engineering Materials. 2002, 4(4): 200-202.
[56] Maurice C, Humphries J, 2- and 3-d curvature driven vertex simulations of grain growth, in Grain Growth in Polycrystalline Materials III, Weiland H, Adams B L, Rollett A D, Editors. 1998, TMS: Pittsburgh, Pennsylvania. 81-90.
[57]Brakke K. The Motion of a Surface by its Mean Curvature. New Jersey:Princeton University Press, 1978.
[58] Weygand D, Brechet Y, Lepinoux J. A vertex simulation of grain growth in 2d and 3d. Advanced Engineering Materials. 2001, 3(1-2): 67-71.
[59] Fan D N, Chen L Q. Diffusion-controlled grain growth in two-phase solids. Acta Materialia. 1997, 45(8): 3297-3310.
[60] Fan D N, Chen L Q. Computer simulation of grain growth using a continuum field model. Acta Materialia. 1997, 45(2): 611-622.
[61] Chen L Q. Phase-field models for microstructure evolution. Annual Reviews of Materials Research. 2002,32: 113-140.
[62]Lusk M T. A phase-field paradigm for grain growth and recrystallization. Proceedings: Mathematical, Physical and Engineering Sciences. 1999, 455(1982): 677-700.
[63]Warren J A,Kobayashi R,Carter W C.Modeling grain boundaries using a phase-field technique.Journal of Crystal Growth.2000,211(1-4):18-20.
[64]Krill Ⅲ C E,Chen L Q.Computer simulation of 3-D grain growth using a phase-field model.Acta Materialia.2002,50(12):3059-3075.
[65]Tikare V,Holm E A,Fan D N,et al.Comparsion of phase-field and Potts models for coarsening processes.Acta Materialia.1998.47:363-371.
[66]王永欣,陈铮,刘兵等.外场下失稳区合金沉淀机制的计算机研究.稀有金属材料与工程.2005,34(1):46-50.
[67]梁敏洁,陈铮,王永欣等.合金微结构的微观相场法模拟.热加工工艺.2006,35(16):63-66.
[68]魏齐龙,王永欣,陈铮.Al-Li合金相变的热分析动力学表征.稀有金属材料与工程.2006,35(6):941-944.
[69]朱耀产,杨根仓,王锦程等.多相场法数值模拟共晶凝固研究进展.特种铸造及有色合金.2004(3):45-47.
[70]朱耀产,杨根仓,王锦程等.二元共晶定向凝固的多相场法数值模拟.中国有色金属学报.2005,15(7):1026-1032.
[71]Fan D N,Chen S P,Chen L Q.Computer simulation of grain growth kinetics with solute drag.Journal of Materials Research.1999,14(3):1113-1123.
[72]Kazaryan A,Wang Y,Dregia S A,et al.Grain growth in systems with anisotropic boundary mobility:analytical model and computer simulation.Physical Review B.2001,63(18):184102.
[73]Srolovitz D J,Anderson M P,Sahni P S,et al.Computer simulation of grain growth - Ⅱ.Grain size distribution,topology,and local dynamics.Acta Metallurgica.1984,32(5):793-802.
[74]Srolovitz D J,Anderson M P,Grest G S,et al.Computer simulation of grain growth - Ⅲ.Influence of a particle dispersion.Acta Metallurgica.1984,32(9):1429-1438.
[75]Grest G S,Srolovitz D J,Anderson M P.Computer simulation of grain growth - Ⅳ.Anisotropic grain boundary energies.Acta Metallurgica.1985,33(3):509-520.
[76]Srolovitz D J,Grest G S,Anderson M P.Computer simulation of grain growth - Ⅴ.Abnormal grain growth.Acta Metallurgica.1985,33(12):2233-2247.
[77]Yu Q,Esche S K.A Monte Carlo algorithm for single phase normal grain growth with improved accuracy and efficiency.Computational Materials Science.2003,27(3):259-270.
[78]王海东,张海.晶粒生长的蒙特卡罗模拟研究进展.材料导报.2007,21(2):72-74.
[79]Holm E A,Sroiovitz D J,Cahn J W.Microstructural evolution in two-dimensional two-phase polycrystals.Acta Metallurgica et Materialia.1993,41(4):1119-1136.
[80]Liu Z J,Zhang C H,Shen Y G,et al.Monte Carlo simulation of nanocrystalline TiN/amorphous SiNx composite films.Journal of Applied Physics.2004,95(2):758-760.
[81]Holm E A,Hassold G N,Miodownik M A.On misorientation distribution evolution during anisotropic grain growth.Acta Materialia.2001,49(15):2981-2991.
[82]Moldovan D,Wolf D,Phillpot S R,et al.Mesoscopic simulation of two-dimensional grain growth with anisotropic grain-boundary properties.Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties.2002,82(7):1271-1297.
[83]Yang Z,Sista S,Elmer J W,et al.Three dimensional monte carlo simulation of grain growth,during GTA welding of titanium.Acta Materialia.2000,48(20):4813-4825.
[84]Rollett A D,Srolovitz D J,Anderson M P.Simulation and theory of abnormal grain growth - anisotropic grain boundary energies and mobilities.Acta Metallurgica.1988,37(4):1227-1240.
[85]Hinz D C,Szpunar J A.Modelling the effect of coinsidence site lattice boundaries on grain growth textures.Physical Review B.1995,52(14):9900-9909.
[86]张海.基于蒙特卡罗方法的晶粒生长模拟系统研究:(硕士学位论文).长沙:中南大学,2007.
[87]陈伟元,钟晓征,谭锐等.多晶材料晶粒生长的计算机模拟研究.原子与分子物理学报.2000,17(2):297-302.
[88]张继祥,关小军,孙胜.一种改进的晶粒长大Monte Carlo模拟方法.金属学报.2004,40(5):457-461.
[89]刘国权,宋晓艳,于海波等.一种Monte Carlo仿真新算法及其对三维个体晶粒长大速率拓扑依赖性理论方程的验证.金属学报.1999,35(3):245-248.
[90]秦湘阁,刘国权.基于Monte Carlo Potts方法的三维大尺度晶粒组织仿真模型及定量表征.北京科技大学学报.2004,26(1):49-52.
[9]]刘祖耀,李世晨,郑子樵等.正常晶粒长大的计算机模拟(Ⅰ)-晶粒长大动力学跃迁概率的改进.中国有色金属学报.2003,13(6):1357-1360.
[92]刘祖耀,郑子樵,陈大钦等.正常晶粒长大的计算机模拟(Ⅱ)-第二相粒子形状及取向的影响.中国有色金属学报.2004,14(1):122-126.
[93]郭靖原,洪泽恺,陈民.金属凝固与晶体生长过程的蒙特卡罗模拟.工程热物理学报.2001,22(6):725-728.
[94]Wolf D,Yamakov V,Phillpot S R,et al.Deformation of nanocrystalline materials by molecular-dynamics simulation:relationship to experiments? Acta Materialia.2005,53(1):1-40.
[95]Zhu X,Birringer R,Herr U,et al.X-ray diffraction studies of the structure of nanometer-sized crystalline materials.Physical Review B.1987,35(17):9085-9090.
[96]Fitzsimmons M R,Eastman J A,Müller-Stach M,et al.Structural characterization of nanometer-sized crystalline Pd by x-ray-diffraction techniques.Physical Review B.1991,44(6):2452-2460.
[97]Loffler J,Weissmüller J.Grain-boundary atomic structure in nanocrystalline palladium from x-ray atomic distribution functions.Physical Review B.1995,52(10):7076-7093.
[98]Thomas G J,Siegel R W,Eastman J A.Grain boundary in nanophase palladium:high resolution electronmicroscope and image simulation.Scripta Metallurgica et Materialia.1990,24(1):201-206.
[99]Haubold T,Birringer R.Lengeler B,et al.EXAFS studies of nanocrystalline materials exhibiting a new solid state structure.Physical Letters A.1989,135(8-9):461-466.
[100]Ke M,Hackney S A,Milligan W W,et al.Observation and measurement of grain rotation and plastic strain in nanostructured metal thin films.Nanostructured Materials.1995,5(6):689-697.
[101]Milligan W W,Hackney S A,Ke M,et al.In situ studies of deformation and fracture in nanophase materials.Nanostructured Materials.1993,2(3):267-276.
[102]Ichikawa S,Miyazawa K i,Ichinose H,et al.The microstructure of deformed nanocrystalline Ag and Ag/Fe alloy.Nanostructured Materials.1999,11(8):1301-1311.
[103] Zupan M, Legros, Marc, et al., Microsample Tensile Testing of Nanocrystalline Metals and Single-crystalline Alloys. in: Chung, Dunand, Liaw, et al., ed. Advanced Materials for the 21st Century: The 1999 Julia R. Weeterman Symposium. Warrendale: TMS Publications, 1999: 525-536.
[104] Youngdahl C J, Weertman J R, Hugo R C, et al. Deformation behavior in nanocrystalline copper. Scripta Materialia. 2001, 44(8-9): 1475-1478.
[105] Cheng S, Spencer J A, Milligan W W. Strength and tension/compression asymmetry in nanostructured and ultrafine-grain metals. Acta Materialia. 2003, 51(15): 4505-4518.
[106] Legros M, Elliott B R, Rittner M N, et al. Microsample tensile testing of nanocrystalline metals. Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties. 2000, 80(4): 1017-1026.
[107] Markmann J, Bunzel P, Rosner H, et al. Microstructure evolution during rolling of inert-gas condensed palladium. Scripta Materialia. 2003, 49(7): 637-644.
[108] Chen M W, Ma E, Hemker K J, et al. Deformation twinning in nanocrystalline aluminum. Science. 2003, 300(5623): 1275-1277.
[109] Hemker K J. Understanding how nanocrystalline metals deform. Science. 2004, 304(5668): 221-222.
[110] He J, Li Y, Li B, et al. Relay protection for UHV transmission lines. Part Two: Disposition of relay protection. Dianli Xitong Zidonghua/Automation of Electric Power Systems. 2002, 26(24): 1-6.
[111] He J, Lavernia E J. Development of nanocrystalline structure during cryomilling of Inconel 625. Journal of Materials Research. 2001, 16(9): 2724-2732.
[112] Wang Y, Chen M, Zhou F, et al. High tensile ductility in a nanostructured metal. Nature. 2002, 419(6910): 912-915.
[113] Liao X Z, Zhao Y H, Srinivasan S G, et al. Deformation twinning in nanocrystalline copper at room temperature and low strain rate. Applied Physics Letters. 2004, 84(4): 592-594.
[114] Kumar K S, Suresh S, Chisholm M F, et al. Deformation of electrodeposited nanocrystalline nickel. Acta Materialia. 2003, 51(2): 387-405.
[115] 5osner H, Markmann J, Weissmu?ller J. Deformation twinning in nanocrystalline Pd. Philosophical Magazine Letters. 2004, 84(5): 321-334.
[116] Liao X Z, Kilmametov A R, Valiev R Z, et al. High-pressure torsion-induced grain growth in electrodeposited nanocrystalline Ni. Applied Physics Letters. 2006, 88(2): 021909.
[117] Liao X Z, Zhou F, Lavernia E J, et al. Deformation twins in nanocrystalline Al. Applied Physics Letters. 2003, 83(24): 5062-5064.
[118] Liao X Z, Zhou F, Lavernia E J, et al. Deformation mechanism in nanocrystalline Al: Partial dislocation slip. Applied Physics Letters. 2003, 83(4): 632-634.
[119] Lu L, Sui M L, Lu K. Superplastic extensibility of nanocrystalline copper at room temperature. Science. 2000,287(5457): 1463-1466.
[120] Champion Y, Langlois C, Guerin-Mailly S, et al. Near-Perfect Elastoplasticity in Pure Nanocrystalline Copper. Science. 2003, 300(5617): 310-311.
[121] McFadden S X, Mishra R S, Vallev R Z, et al. Low-temperature superplasticity in nanostructured nickel and metal alloys. Nature. 1999,398(6729): 684-686.
[122] Karch J, Birringer R, Gleiter H. Ceramics ductile at low temperature. Nature. 1987, 330(6148): 556-558.
[123] Mukherjee A K. An examination of the constitutive equation for elevated temperature plasticity. Materials Science and Engineering A - Structural Materials Properties Microstructure and Processing. 2002,322(1-2): 1-22.
[124] Shan Z W, Stach E A, Wiezorek J M K, et al. Grain boundary-mediated plasticity in nanocrystalline nickel. Science. 2004, 305(5684): 654-657.
[125] Hall E O. The Deformation and Ageing of Mild Steel: III Discussion of Results. Proceedings of the Physical Society B. 1951, 64(9): 747-753.
[126] Petch N J. The cleavage strength of polycrystals. Journal of Iron and Steel Institute. 1953, 174(1): 25-28.
[127] Shen T D, Schwarz R B, Feng S, et al. Effect of solute segregation on the strength of nanocrystalline alloys: Inverse Hall-Petch relation. Acta Materialia. 2007, 55(15): 5007-5013.
[128] Carlton C E, Ferreira P J. What is behind the inverse Hall-Petch effect in nanocrystalline materials? Acta Materialia. 2007, 55(11): 3749-3756.
[129] Giga A, Kimoto Y, Takigawa Y, et al. Demonstration of an inverse Hall-Petch relationship in electrodeposited nanocrystalline Ni-W alloys through tensile testing. Scripta Materialia. 2006, 55(2): 143-146.
[130] 王晋宝.碳纳米管的相关力学问题的研究:(博士学位论文)).大连:大连理工大学,2007.
[131] Allen M P, Tildesley D J. Computer Simulation of Liquids. Oxford:Clarendon Press, 1986.
[132] Rapaport D C. The Art of Molecular Dynamics Simulation. 2nd ed. New York:Cambridge University Press, 2004.
[133] Liu W K, Karpov E G, Park H S. Nano Mechanics and Materials: Theory, Multiscale Methods and Applications. Chichester: John Wiley & Sons Ltd, 2006.
[134] Philips R. Crystals, Defects and Microstructures: Modeling Across Scales. Cambridge:Cambridge University Press, 2001.
[135] Phillpot S R, Wolf D, Gleiter H. Molecular-dynamics study of the synthesis and characterization of a fully dense, three-dimensional nanocrystalline material. Journal of Applied Physics. 1995, 78(2): 847-861.
[136] Phillpot S R, Wolf D, Gleiter H. A structural model for grain boundaries in nanocrystalline materials. Scripta Metallurgica et Materialia. 1995,33(8): 1245-1251.
[137] Yamakov V, Wolf D, Salazar M, et al. Length-scale effects in the nucleation of extended dislocations in nanocrystalline Al by molecular-dynamics simulation. Acta Materialia. 2001, 49(14): 2713-2722.
[138] Yamakov V, Wolf D, Phillpot S R, et al. Deformation twinning in nanocrystalline Al by molecular-dynamics simulation. Acta Materialia. 2002, 50(20): 5005-5020.
[139] Yamakov V, Wolf D, Phillpot S R, et al. Deformation-mechanism map for nanocrystalline metals by molecular-dynamics simulation. Nature Materials. 2004, 3(1): 43-47.
[140] Yamakov V, Wolf D, Phillpot S R, et al. Dislocation-dislocation and dislocation-twin reactions in nanocrystalline Al by molecular dynamics simulation. Acta Materialia. 2003, 51(14): 4135-4147.
[141] Yamakov V, Wolf D, Phillpot S R. et al. Grain-boundary diffusion creep in nanocrystalline palladium by molecular-dynamics simulation. Acta Materialia. 2002, 50(1): 61-73.
[142] Yamakov V, Moldovan D, Rastogi K, et al. Relation between grain growth and grain-boundary diffusion in a pure material by molecular dynamics simulations. Acta Materialia. 2006, 54(15): 4053-4061.
[143] Van Swygenhoven H, Caro A. Plactic behavior of nanophase Ni: A molecular dynamics computer simulation. Applied Physics Letters. 1997, 71(22): 1652-1654.
[144] Van Swygenhoven H, Spaczer M, Caro A, et al. Competing plastic deformation mechanisms in nanophase metals. Physical Review B. 1999, 60(1): 22-25.
[145] Van Swygenhoven H, Derlet P M. Grain-boundary sliding in nanocrystalline fcc metals. Physical Review B. 2001, 64(22): 224105.
[146] Van Swygenhoven H, Derlet P M, Hasnaoui A. Atomic mechanism for dislocation emission from nanosized grain boundaries. Physical Review B. 2002, 66(2): 024101.
[147] Froseth A G, Derlet P M, Van Swygenhoven H. Dislocations emitted from nanocrystalline grain boundaries: nucleation and splitting distance. Acta Materialia. 2004, 52: 5863-5870.
[148] Schiotz J, Di Tolla F D, Jacobsen K W. Softening of nanocrystalline metals at very small grain sizes. Nature. 1998, 391(6667): 561-563.
[149] Schiotz J, Vegge T, Di Tolla F D, et al. Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Physical.Review B. 1999, 60(17): 11971-11983.
[150] Schiotz J, Jacobsen K W. A Maximum in the Strength of Nanocrystalline Copper. Science. 2003, 301(5638): 1357-1359.
[151] Schiotz J. Strain-induced coarsening in nanocrystalline metals under cyclic deformation. Materials Science and Engineering A - Structural Materials Properties Microstructure and Processing. 2004, 375-77: 975-979.
[152] Yang W, Wang H T, Hong W. Deformation of Nano-grained Metals. Proceedings of International Symposium of Young Scholars on Mechanics and Material Engineering for Science and Experiments, Changsha,2001: 1-12.
[153] Yang W, Tang J-C, Ing Y-S. et al. Transient dislocation emission from a crack tip. Journal of the Mechanics and Physics of Solids. 2001,49(10): 2431-2453.
[154] Cao A J, Wei Y G. Formation of fivefold deformation twins in nanocrystalline face-centered-cubic copper based on molecular dynamics simulations. Applied Physics Letters. 2006, 89(4): 041919.
[155] Cao A J, Wei Y G. Atomistic simulations of the mechanical behavior of fivefold twinned nanowires. Physical Review B. 2006,74(21): 214108.
[156] Wang J, Duan H L, Huang Z P, et al. A scaling law for properties of nano-structured materials. Proceedings of the Royal Society A. 2006,462(2069): 1355-1363.
[157] Duan H L, Wang J, Huang Z P, et al. Eshelby formalism for nano-inhomogeneities. Proceedings of the Royal Society A. 2005, 461(2062): 3335-3353.
[158] Yi X, Duan H L, Karihaloo B L, et al. Eshelby formalism for multi-shell nano-inhomogeneities. Archives of Mechanics. 2007, 59(3): 259-282.
[1] Tjong S C, Chen H. Nanocrystalline materials and coatings. Materials Science and Engineering R: Reports. 2004,45(1-2): 1-88.
[2] Lu C S, Mai Y W, Shen Y G. Recent advances on understanding the origin of superhardness in nanocomposite coatings: A critical review. Journal of Materials Science. 2006, 41(3): 937-950.
[3] Tjong S C, Chen H. Nanocrystalline materials and coatings. Materials Science & Engineering R-Reports. 2004,45(1-2): 1-88.
[4] Shen Y G, Liu Z J, Lu Y H, et al. Monte Carlo simulation of microstructure and grain growth in nc-Ti(N, B)/a-(TiB2, BN) nanocomposite films. Fracture of Materials: Moving Forwards. 2006, 312: 357-362.
[5] Hu H. Grain-growth in zone-refined iron. Canadian Metallurgical Quarterly. 1974, 13: 275-286.
[6] Zhang C, Suzuki A, Ishimaru T, et al. Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning. Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science. 2004, 35(7): 1927-1933.
[7] Anderson M P, Srolovitz D J, Grest G S, et al. Computer simulation of grain growth -I. Kinetics. Acta Metallurgica 1984, 32(5): 783-791.
[8] Zheng Y G, Lu C, Mai Y W, et al. Monte Carlo simulation of grain growth in two-phase nanocrystalline materials. Applied Physics Letters. 2006, 88(14): 144103.
[9] Lifshitz I M, Slyozov V V. The kinetics of precipitation from supersaturated solid solutions. Journal of Physics and Chemistry of Solids. 1961,19(1-2): 35-50.
[10] Thompson C V. Grain growth in thin film. Annual Reviews of Materials Science. 1990, 20: 245-268.
[11]Diao X X, Mai Y W. Self-similarity of crack propagation in inhomogeneous materials. Philosophical Magazine Letters. 1999, 79(4): 187-193.
[12] Atkinson H V. Theories of normal grain growth in pure single phase systems. Acta Metallurgica 1988, 36(3): 469-491.
[13]Pande C S, Masumura R A, Marsh S P. Stochastic analysis of two-dimensional grain growth. Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties. 2001, 81(5): 1229-1239.
[14]Pande C S, Rajagopal A K. Uniqueness and self similarity of size distributions in grain growth and coarsening. Acta Materialia. 2001, 49(10): 1805-1811.
[15]Helfen L, Wu D T, Birringer R, et al. The impact of stochastic atomic jumps on the kinetics of curvature-driven grain growth. Acta Materialia. 2003, 51(10): 2743-2754.
[16]Mullins W W. Grain growth of uniform boundaries with scaling. Acta Materialia. 1998, 46(17): 6219-6226.
[17] Hillert M. On theory of normal and abnormal grain growth. Acta metallurgica. 1965, 13(3): 227-238.
[18]Gusak A M, Tu K N. Theory of normal grain growth in normalized size space. Acta Materialia. 2003, 51(13): 3895-3904.
[19]Kadanoff L P. Statistical Physics: Statics, Dynamics and Renormalization. 北京:世界图书出版公司,2003.
[20] Saetre T O. A mean field theory of grain growth: I. Modelling and Simulation in Materials Science and Engineering. 2004, 12(6): 1267-1277.
[21] Mulheran P A, Harding J H. A statistical theory of normal grain growth. Material Science Forum 1992, 94-96: 367-372.
[22] Louat N P. On the theory of normal grain growth. Acta Metallurgica. 1974, 22(6): 721-724.
[23]Ryum N, Hunderi O. On the analytic description of normal grain growth. Acta Metallurgica. 1989, 37(5): 1375-1379.
[24] Press W H, Teukolsky S A, Vetterling W T, et al. Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. Cambridge:Cambridge University Press, 1992.
[25] Shan Z W, Stach E A, Wiezorek J M K, et al. Grain boundary-mediated plasticity in nanocrystalline nickel. Science. 2004, 305(5684): 654-657.
[26]Gleiter H. Nanostructured materials: basic concepts and microstructure. Acta Materialia. 2000, 48(1): 1-29.
[27]Maximenko A L, Olevsky E A. Effective diffusion coefficients in solid-state sintering. Acta Materialia. 2004, 52(10): 2953-2963.
[1]Tjong S C,Chen H.Nanocrystalline materials and coatings.Materials Science & Engineering R-Reports.2004,45(1-2):1-88.
[2]Liu Z J,Zhang C H,Shen Y G,et al.Monte Carlo simulation of nanocrystalline TiN/amorphous SiN_x composite films.Journal of Applied Physics.2004,95(2):758-760.
[3]Lu C S,Mai Y W,Shen Y G.Recent advances on understanding the origin of superhardness in nanocomposite coatings:A critical review.Journal of Materials Science.2006,41(3):937-950.
[4]Liu Z J,Shum P W,Shen Y G.Hardening mechanisms of nanocrystalline Ti-Al-N solid solution films.Thin Solid Films.2004,468(1-2):161-166
[5]Fan D N,Chen L Q.Diffusion-controlled grain growth in two-phase solids.Acta Materialia.1997,45(8):3297-3310.
[6]Lifshitz I M,Slyozov V V.The kinetics of precipitation from supersaturated solid solutions.Journal of Physics and Chemistry of Solids.1961,19(1-2):35-50.
[7]Hillert M.On theory of normal and abnormal grain growth.Acta metallurgica.1965,13(3):227-238.
[8]Maurice M,Humphries J,2- and 3-D Curvature Driven Vertex Simulations of Grain Growth,in Grain Growth in Polycrystalline Materials Ⅲ,Weiland H,Adams B L,Rollett A D,Editors.1998,The Minerals,Metals and Materials Society:Pittsburgh.81-90.
[9]Anderson M P,Srolovitz D J,Grest G S,et al.Computer simulation of grain growth-Ⅰ.Kinetics.Acta Metallurgica.1984,32(5):783-791.
[10]Potts R B.Some generalized order-disorder transformations.Proceedings of the Cambridge Philosophical Society.1952,48:106-109.
[11]Holm E A,Srolovitz D J,Cahn J W.Microstructural evolution in two-dimensional two-phase polycrystals.Acta Metallurgica et Materialia.1993,41(4):1119-1136.
[12]张海.基于蒙特卡罗方法的晶粒生长模拟系统研究:(硕士学位论文).长沙:中南大学,2007.
[13]陈伟元,钟晓征,谭锐等.多晶材料晶粒生长的计算机模拟研究.原子与分子物理学报.2000,17(2):297-302.
[14]张继祥,关小军,孙胜.一种改进的晶粒长大Monte Carlo模拟方法.金属学报.2004,40(5):457-461.
[15]刘国权,宋晓艳,于海波等.一种Monte Carlo仿真新算法及其对三维个体晶粒长大速率拓扑依赖性理论方程的验证.金属学报.1999,35(3):245-248.
[16]秦湘阁,刘国权.基于Monte Carlo Potts方法的三维大尺度晶粒组织仿真模型及定量表征.北京科技大学学报.2004,26(1):49-52.
[17]Raabe D.计算材料学.北京:化学工业出版社,2002.
[18]王海东,张海.晶粒生长的蒙特卡罗模拟研究进展.材料导报.2007,21(2):72-74.
[19]周燕.关于线性同余组合发生器的周期性和统计性质.重庆大学学报(自然科学版).2000,23(6):67-70.
[20]Metropolis N,Rosenbluth A W,Rosenbluth M N,et al.Equation of State Calculations by Fast Computing Machines.The Journal of Chemical Physics.1953,21(6):1087-1092.
[21]Radhakrishnan B, Zacharia T. Simulation of Curvature-Driven Grain-Growth by Using a Modified Monte-Carlo Algorithm. Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science. 1995, 26(1): 167-180.
[22] Yu Q, Esche S K. A Monte Carlo algorithm for single phase normal grain growth with improved accuracy and efficiency. Computational Materials Science. 2003, 27(3): 259-270.
[23] Atkinson H V. Theories of normal grain growth in pure single phase systems. Acta Metallurgica. 1988, 36(3): 469-491.
[24]Gusak A M, Tu K N. Theory of normal grain growth in normalized size space. Acta Materialia. 2003, 51(13): 3895-3904.
[25] Thompson C V. Grain growth in thin film. Annual Reviews of Materials Science. 1990, 20: 245-268.
[26] Veprek S, Reiprich S, Shizhi L. Superhard nanocrystalline composite materials: The TiN/Si_3N_4 system. Applied Physics Letters. 1995, 66(20): 2640-2642.
[27]Xun Y, Lavernia E J, Mohamed F A. Grain growth in nanocrystalline Zn-22% Al. Materials Science and Engineering A - Structural Materials Properties Microstructure and Processing. 2004, 371(1-2): 135-140.
[28]Yamazaki D, Kato T, Ohtani E, et al. Grain Growth Rates of MgSiO_3 Perovskite and Periclase Under Lower Mantle Conditions. Science. 1996, 274(5295): 2052-2054.
[29] Zheng Y G, Lu C, Mai Y W, et al. Monte Carlo simulation of grain growth in two-phase nanocrystalline materials. Applied Physics Letters. 2006, 88(14): 144103.
[30] Kurtz S K, Carpay F M A. Microstructure and normal grain growth in metals and ceramics. Part I. Theory. Journal of Applied Physics. 1980, 51(11): 5725-5744.
[31] Mas D L, Crowley P D. The effect of second-phase particles on stable grain size in regionally metamorphosed polyphase calcite marbles. Journal of Metamorphic Geology. 1996, 14(2): 155-162.
[32]Hillert M. Inhibition of grain growth by second-phase particles. Acta Metallurgica. 1988, 36(12): 3177-3181.
[33]Shen Y G, Liu Z J, Lu Y H, et al. Monte Carlo simulation of microstructure and grain growth in nc-Ti(N, B)/a-(TiB2, BN) nanocomposite films. Fracture of Materials: Moving Forwards. 2006, 312: 357-362.
[1]Raabe D.计算材料学.北京:化学工业出版社,2002.
[2]Liu W K,Karpov E G,Park H S.Nano Mechanics and Materials:Theory,Multiscale Methods and Applications.Chichester:John Wiley & Sons Ltd,2006.
[3]Phllips R.Crystals,Defects and Microstructures:Modeling Across Scales.Cambridge:Cambridge University Press,2001.
[4]文玉华,朱如曾,周富信等.分子动力学模拟的主要技术.力学进展.2003,33(1):65-73.
[5]Meyers M A,Mishra A,Benson D J.Mechanical properties of nanocrystalline materials.Progress in Materials Science.2006,51(4):427-556.
[6]Schiotz J,Di Tolla F D,Jacobsen K W.Softening of nanocrystalline metals at very small grain sizes.Nature.1998,391(6667):561-563.
[7]Van Swygenhoven H,Derlet P M.Grain-boundary sliding in nanocrystalline fcc metals.Physical Review B.2001,64(22):224105.
[8]Wolf D,Yamakov V,Phillpot S R,et al.Deformation of nanocrystalline materials by molecular-dynamics simulation:relationship to experiments? Acta Materialia.2005,53(1):1-40.
[9]Yamakov V,Wolf D,Phillpot S R,et al.Deformation-mechanism map for nanocrystalline metals by molecular-dynamics simulation.Nature Materials.2004,3(1):43-47.
[10]梁海弋.纳米铜力学行为的分子动力学模拟:(博士学位论文).合肥:中国科学技术大学,2001.
[11]Alder B J,Wainwright T E.Phase Transition for a Hard Sphere System.The Journal of Chemical Physics.1957,27(5):1208-1209.
[12]Rahman A.Correlations in the Motion of Atoms in Liquid Argon.Physical Review.1964,136(2):405-411.
[13]Rahman A,Stillinger F H.Molecular dynamics study of liquid water.The Journal of Chemical Physics.1971,55(7):3336-3359.
[14]Rychaert J P,Ciccotti G,Berendsen H J C.Numerical integration of the Cartesian equations of dynamics of n-alkanes.Journal of Computational Physics.1977,23(3):327-341.
[15]van Gunsteren W F,Berendsen H J C.Algorithms for macromolecular dynamics and constraint dynamics.Molecular Physics.1977,34(5):1311-1327
[16]Andersen H C.Molecular dynamics simulations at constant pressure and/or temperature.The Journal of Chemical Physics.1980,72(4):2384-2393.
[17]Parrinello M,Rahman A.Crystal Structure and Pair Potentials:A Molecular-Dynamics Study.Physical Review Letters.1980,45(14):1196-1199.
[18]Gillan M J,Dixon M.The calculation of thermal conductivities by perturbed molecular dynamics simulation.Journal of Physics C:Solid State Physics.1983,16(5):869-878.
[19]Berendsen H J C,Postma J P M,van Gunsteren W F,et al.Molecular dynamics with coupling to an external bath.The Journal of Chemical Physics.1984,81(8):3684-3690.
[20]Hoover W G.Canonical dynamics:Equilibrium phase-space distributions.Physical Review A.1985,31(3):1695-1697.
[21]Nosé S.A unified formulation of the constant temperature molecular dynamics methods.The Journal of Chemical Physics.1984,81(1):511-519.
[22]Rapaport D C.The Art of Molecular Dynamics Simulation.2nd ed.New York:Cambridge University Press,2004.
[23]Allen M P,Tildesley D J.Computer Simulation of Liquids.Oxford:Clarendon Press,1986.
[24]钟万勰,杨再石.连续时间LQ控制主要本征对算法.应用数学和力学.1991,12(1):45-50.
[25]Zhong W X,Williams F W.A Precise Time-Step Integration Method.Proceedings of the Institution of Mechanical Engineers Part C:Journal of Mechanical Engineering Science.1994,208(6):427-430.
[26]Lennard-Jones J E.On the Forces between Atoms and lons.Proceedings of the Royal Society A.1925,109(752):584-597.
[27]Lennard-Jones J E,Dent B M.The Forces between Atoms and Ions Ⅱ.Proceedings of the Royal Society A.1926,112(760):230-234.
[28]Girifalco L A,Weizer V G.Application of the Morse Potential Function to Cubic Metals.Physical Review.1959,114(3):687-690.
[29]Shen L M,Chen Z.An investigation of the effect of interfacial atomic potential on the stress transition in thin films.Modelling and Simulation in Materials Science and Engineering.2004,12(4):347-369.
[30]Tersoff J.Modeling solid-state chemistry:Interatomic potentials for multicomponent systems.Physical Review B.1989,39(8):5566-5568.
[31]Huang S P,Mainardi D S,Balbuena P B.Structure and dynamics of graphite-supported bimetallic nanoclusters.Surface Science.2003,545(3):163-179.
[32]Sutton A P,Chen J.Long-range Finnis-Sinclair potentials.Philosophical Magazine Letters.1990,61(3):139-146.
[33]Kart H H,Tomak M,Cagin T.Thermal and mechanical properties of Cu-Au intermetallic alloys.Modelling and Simulation in Materials Science and Engineering.2005,13(5):657-669.
[34]Wang L,Zhang H W,Zhang Z Q,et al.Buckling behaviors of single-walled carbon nanotubes filled with metal atoms.Applied Physics Letters.2007,91(5):051122.
[35]Daw M S,Baskes M I.Embedded-atom method:Derivation and application to impurities,surfaces,and other defects in metals.Physical Review B.1984,29(12):6443-6453.
[36]Foiles S M,Baskes M I,Daw M S.Embedded-atom-method functions for the fcc metals Cu,Ag,Au,Ni,Pd,Pt,and their alloys.Physical Review B.1986,33(12):7983-7991.
[37]冯端.金属物理学.北京:科学出版社,2000.
[38]Johnson R A,Wilson W D,Interatomic Potentials and Simulation of Lattice Defects.in:Gehlen P C,Beeler J R,Jaffee R I,ed.Interatomic Potentials and Simulation of Lattice Defects.New York:Plenum 1972.
[39]Finnis M W,Sinclair J E.A simple empirical N-body potential for transition metals.Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties.1984,50(1):45-55.
[40]Ackland G J,Vitek V.Many-body potentials and atomic-scale relaxations in noble-metal alloys.Physical Review B.1990,41(15):10324-10333.
[41]Jacobsen K W,Norskov J K,Puska M J.Interatomic interactions in the effective-medium theory.Physical Review B.1987,35(14):7423-7442.
[42] Born M, Huang K. Dynamical Theory of Crystal Lattices. New York:Oxford University Press, 1954.
[43] Zhou M. A new look at the atomic level virial stress: on continuum-molecular system equivalence. Proceedings of the Royal Society A. 2003,459(2037): 2347-2392.
[44] Cormier J, Rickman J M, Delph T J. Stress calculation in atomistic simulations of perfect and imperfect solids. Journal of Applied Physics. 2001, 89(1): 99-104.
[45]Todd B D, Evans D J, Daivis P J. Pressure Tensor for Inhomogeneous Fluids. Physical Review E. 1995, 52(2): 1627-1638.
[46]Chueng K S, Yip S. Atomic-level stress in an inhomogeneous system. Journal of Applied Physics. 1991, 70(10): 5688-5690.
[47] Jean J S. The Dynamical Theory of Gases. New York:Dover, 1960.
[48]Griebel M, Knapek S, Zumbusch G. Numerical Simulation in Molecular Dynamics: Numerics, Algorithms, Parallelization, Applications. Texts in Computational Science and Engineering, ed. Barth T J, Griebel M, Keyes D E, et al. Berlin Heidelberg:Springer-Verlag, 2007.
[1] Landman U, Luedtke W D, Burnham N A, et al. Atomistic mechanisms and dynamics of adhesion, nanoindentation, and fracture. Science. 1990, 248(4954): 454-461.
[2] Lieber C M. Nanoscale science and technology: Building a big future from small things. MRS Bulletin. 2003, 28(7): 486-491.
[3] Xia Y N, Yang P D, Sun Y G, et al. One-dimensional nanostructures: Synthesis, characterization, and applications. Advanced Materials. 2003, 15(5): 353-389.
[4] Yu M F, Lourie O, Dyer M J, et al. Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load. Science. 2000, 287(5453): 637-640.
[5] Wu Y, Xiang J, Yang C, et al. Single-crystal metallic nanowires and metal/semiconductor nanowire heterostructures. Nature. 2004, 430(7000): 61-65.
[6] Winn D, Doherty M F. Modeling crystal shapes of organic materials grown from solution. Aiche Journal. 2000, 46(7): 1348-1367.
[7] Mann S. The chemistry of form. Angewandte Chemie. 2000, 39(19): 3392-3406.
[8] Li J B, Wang L W. Shape effects on electronic states of nanocrystals. Nano Letters. 2003, 3(10): 1357-1363.
[9] Ohnishi H, Kondo Y, Takayanagi K. Quantized conductance through individual rows of suspended gold atoms. Nature. 1998, 395(6704): 780-783.
[10]Gulseren O, Ercolessi F, Tosatti E. Noncrystalline Structures of Ultrathin Unsupported Nanowires. Physical Review Letters. 1998, 80(17): 3775-3778.
[11]Rodrigues V, Fuhrer T, Ugarte D. Signature of Atomic Structure in the Quantum Conductance of Gold Nanowires. Physical Review Letters. 2000, 85(19): 4124-4127.
[12] Ji C J, Park H S. Geometric effects on the inelastic deformation of metal nanowires. Applied Physics Letters. 2006, 89(18): 181916.
[13] Park H S, Zimmerman J A. Modeling inelasticity and failure in gold nanowires. Physical Review B. 2005, 72(5): 054106.
[14] Liang H Y, Upmanyu M, Huang H C. Size-dependent elasticity of nanowires: Nonlinear effects. Physical Review B. 2005, 71(24): 241403.
[15]Cao A J, Wei Y G. Formation of fivefold deformation twins in nanocrystalline face-centered-cubic copper based on molecular dynamics simulations. Applied Physics Letters. 2006, 89(4): 041919.
[16]Shankar M R, King A H. How surface stresses lead to size-dependent mechanics of tensile deformation in nanowires. Applied Physics Letters. 2007, 90(14): 141907.
[17]Branicio P S, Rino J-P. Large deformation and amorphization of Ni nanowires under uniaxial strain: A molecular dynamics study. Physical Review B. 2000, 62(24): 16950-16955.
[18] da Silva E Z, da Silva A J R, Fazzio A. How Do Gold Nanowires Break? Physical Review Letters. 2001, 87(25): 256102.
[19]Coura P Z, Legoas S B, Moreira A S, et al. On the Structural and Stability Features of Linear Atomic Suspended Chains Formed from Gold Nanowires Stretching. Nano Letters. 2004, 4(7): 1187-1191.
[20] Gall K, Diao J, Dunn M L, et al. Tetragonal Phase Transformation in Gold Nanowires. Journal of Engineering Materials and Technology. 2005, 127(4): 417-422.
[21] Diao J, Gall K, Dunn M L. Surface-stress-induced phase transformation in metal nanowires. Nature Materials. 2003, 2(10): 656-660.
[22] Liang W, Zhou M. Response of copper nanowires in dynamic tensile deformation. Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science. 2004, 218(6): 599-606.
[23]Liang W, Zhou M, Ke F. Shape Memory Effect in Cu Nanowires. Nano Letters. 2005, 5(10): 2039-2043.
[24]Mehrez H, Ciraci S. Yielding and fracture mechanisms of nanowires. Physical Review B. 1997, 56(19): 12632-12642.
[25] Park H S, Gall K, Zimmerman J A. Shape Memory and Pseudoelasticity in Metal Nanowires. Physical Review Letters. 2005, 95(25): 255504.
[26] Park H S, Gall K, Zimmerman J A. Deformation of FCC nanowires by twinning and slip. Journal of the Mechanics and Physics of Solids. 2006, 54(9): 1862-1881.
[27] Diao J, Gall K, Dunn M L. Yield Strength Asymmetry in Metal Nanowires. Nano Letters. 2004,4(10): 1863-1867.
[28] Sankaranarayanan S K R S, Bhethanabotla V R, Joseph B. Molecular dynamics simulation of temperature and strain rate effects on the elastic properties of bimetallic Pd-Pt nanowires. Physical Review B. 2007, 76(13): 134117.
[29] Cao A J, Wei Y G. Atomistic simulations of the mechanical behavior of fivefold twinned nanowires. Physical Review B. 2006, 74(21): 214108.
[30] Liao X Z, Zhao Y H, Srinivasan S G, et al. Deformation twinning in nanocrystalline copper at room temperature and low strain rate. Applied Physics Letters. 2004, 84(4): 592-594.
[31] Wu B, Heidelberg A, Boland J J, et al. Microstructure-hardened silver nanowires. Nano Letters. 2006, 6(3): 468-472.
[32] Daw M S, Baskes M I. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Physical Review B. 1984, 29(12): 6443-6453.
[33]Foiles S M, Baskes M I, Daw M S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Physical Review B. 1986, 33(12): 7983-7991.
[34] Hoover W G. Canonical dynamics: Equilibrium phase-space distributions. Physical Review A. 1985. 31(3): 1695-1697.
[35] Nose S. A unified formulation of the constant temperature molecular dynamics methods. The Journal of Chemical Physics. 1984, 81 (1): 511 -519.
[36] Plimpton S. Fast Parallel Algorithms for Short-Range Molecular-Dynamics. Journal of Computational Physics. 1995, 117(1): 1-19.
[37]Schiotz J. Strain-induced coarsening in nanocrystalline metals under cyclic deformation. Materials Science and Engineering A - Structural Materials Properties Microstructure and Processing. 2004, 375-77: 975-979.
[38] Stankovic I, Kroger M, Hess S. Recognition and analysis of local structure in polycrystalline configurations. Computer Physics Communications. 2002, 145(3): 371-384.
[39] Rapaport D C. The Art of Molecular Dynamics Simulation. 2nd ed. New York:Cambridge University Press, 2004.
[40] Allen M P, Tildesley D J. Computer Simulation of Liquids. Oxford:Clarendon Press, 1987.
[41] Zimmerman J A, Kelchner C L, Klein P A, et al. Surface Step Effects on Nanoindentation. Physical Review Letters. 2001, 87(16): 165507.
[42] Kittel C. Introduction to Solid State Physics. 7 ed. New York:John Wiley and Sons, Inc., 1996.
[43]Ehrhart P. The configuration of atomic defects as determined from scattering studies. Journal of Nuclear Materials. 1978, 69-70: 200-214.
[44] Siegel R W. Vacancy concentrations in metals. Journal of Nuclear Materials. 1978, 69-70: 117-146.
[45] Balluffi R W. Vacancy defect mobilities and binding energies obtained from annealing studies. Journal of Nuclear Materials. 1978, 69-70: 240-263.
[46] Tyson W R, Miller W A. Surface free energies of solid metals: Estimation from liquid surface tension measurements. Surface Science. 1977, 62(1): 267-276.
[47] Mishin Y, Mehl M J, Papaconstantopoulos D A, et al. Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations. Physical Review B. 2001, 63(22): 224106.
[48]Frank F C. Supercooling of Liquids. Proceedings of the Royal Society A. 1952, 215(1120): 43-46.
[49] Barker J A, Hoare M R, Finney J L. Relaxation of the Bernal model. Nature. 1975, 257(5522): 120-122.
[1] Gleiter H. Nanocrystalline materials. Progress in Materials Science. 1989, 33(4): 223-315.
[2] Gleiter H. Nanostructured Materials: State-of-the-Art and Perspectives. Nanostructured Materials 1995, 6(1-4): 3-14.
[3] Gleiter H. Nanostructured materials: basic concepts and microstructure. Acta Materialia. 2000, 48(1): 1-29.
[4] Meyers M A, Mishra A, Benson D J. Mechanical properties of nanocrystalline materials. Progress in Materials Science. 2006, 51(4): 427-556.
[5] Lu C S, Mai Y W, Shen Y G. Recent advances on understanding the origin of superhardness in nanocomposite coatings: A critical review. Journal of Materials Science. 2006, 41(3): 937-950.
[6] Murayama M, Howe J M, Hidaka H, et al. Atomic-level observation of disclination dipoles in mechanically milled, nanocrystalline Fe. Science. 2002, 295(5564): 2433-2435.
[7] Chen M W, Livi K J T. Wright P K, et al. Microstructural characterization of a platinum-modified diffusion aluminide bond coat for thermal barrier coatings. Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science. 2003, 34(10): 2289-2299.
[8] Chen M W, Ma E, Hemker K J, et al. Deformation twinning in nanocrystalline aluminum. Science. 2003,300(5623): 1275-1277.
[9] Liao X Z, Zhao Y H, Srinivasan S G, et al. Deformation twinning in nanocrystalline copper at room temperature and low strain rate. Applied Physics Letters. 2004, 84(4): 592-594.
[10] Shan Z W, Stach E A, Wiezorek J M K, et al. Grain boundary-mediated plasticity in nanocrystalline nickel. Science. 2004, 305(5684): 654-657.
[11] Gutkin M Y, Ovid'ko I A. Grain boundary migration as rotational deformation mode in nanocrystalline materials. Applied Physics Letters. 2005, 87(25): 251916.
[12]Gutkin M Y, Ovid'ko I A. Special mechanism for dislocation nucleation in nanomaterials. Applied Physics Letters. 2006, 88(21): 211901.
[13] Wolf D, Yamakov V, Phillpot S R, et al. Deformation of nanocrystalline materials by molecular-dynamics simulation: relationship to experiments? Acta Materialia. 2005, 53(1): 1-40.
[14]Schiotz J, Di Tolla F D, Jacobsen K W. Softening of nanocrystalline metals at very small grain sizes. Nature. 1998, 391(6667): 561-563.
[15]Schiotz J. Strain-induced coarsening in nanocrystalline metals under cyclic deformation. Materials Science and Engineering A - Structural Materials Properties Microstructure and Processing. 2004, 375-377: 975-979.
[16] Van Swygenhoven H, Spaczer M, Caro A, et al. Competing plastic deformation mechanisms in nanophase metals. Physical Review B. 1999, 60(1): 22.
[17] Van Swygenhoven H, Derlet P M. Grain-boundary sliding in nanocrystalline fcc metals. Physical Review B. 2001, 64(22): 224105.
[18] Van Swygenhoven H, Derlet P M, Fr(?)seth A G. Nucleation and propagation of dislocations in nanocrystalline fcc metals. Acta Materialia. 2006, 54(7): 1975-1983.
[19] Van Swygenhoven H, Derlet P M, Hasnaoui A. Atomic mechanism for dislocation emission from nanosized grain boundaries. Physical Review B. 2002, 66(2): 024101.
[20] Yamakov V, Wolf D, Phillpot S R, et al. Dislocation-dislocation and dislocation-twin reactions in nanocrystalline Al by molecular dynamics simulation. Acta Materialia. 2003, 51(14): 4135-4147.
[21] Yamakov V, Wolf D, Salazar M. et al. Length-scale effects in the nucleation of extended dislocations in nanocrystalline Al by molecular-dynamics simulation. Acta Materialia. 2001, 49(14): 2713-2722.
[22] Sansoz F, Molinari J F. Mechanical behavior of Sigma tilt grain boundaries in nanoscale Cu and Al: A quasicontinuum study. Acta Materialia. 2005, 53(7): 1931-1944.
[23] Atkinson H V. Theories of normal grain growth in pure single phase systems. Acta Metallurgica. 1988, 36(3): 469-491.
[24] Zheng Y G, Lu C, Mai Y W, et al. Monte Carlo simulation of grain growth in two-phase nanocrystalline materials. Applied Physics Letters. 2006, 88(14): 144103.
[25] Zheng Y G, Lu C, Mai Y W, et al. Model-based simulation of normal grain growth in a two-phase nanostructured system. Science and Technology of Advanced Materials. 2006, 7(8): 812-818.
[26] Hoover W G. Canonical dynamics: Equilibrium phase-space distributions. Physical Review A. 1985, 31(3): 1695-1697.
[27]Nose S. A unified formulation of the constant temperature molecular dynamics methods. The Journal of Chemical Physics. 1984, 81(1): 511-519.
[28] Daw M S, Baskes M I. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Physical Review B. 1984, 29(12): 6443-6453.
[29]Foiles S M, Baskes M I, Daw M S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Physical Review B. 1986, 33(12): 7983-7991.
[30] Balluffi R W. Vacancy defect mobilities and binding energies obtained from annealing studies. Journal of Nuclear Materials. 1978,69-70: 240-263.
[31]Ehrhart P. The configuration of atomic defects as determined from scattering studies. Journal of Nuclear Materials. 1978, 69-70: 200-214.
[32] Plimpton S. Fast Parallel Algorithms for Short-Range Molecular-Dynamics. Journal of Computational Physics. 1995, 117(1): 1-19.
[33] Stankovic I, Kroger M, Hess S. Recognition and analysis of local structure in polycrystalline configurations. Computer Physics Communications. 2002, 145(3): 371-384.
[34] Allen M P, Tildesley D J. Computer Simulation of Liquids. Oxford:Clarendon Press, 1986.
[35]Rapaport D C. The Art of Molecular Dynamics Simulation. 2nd ed. New York:Cambridge University Press, 2004.
[36] Lu L, Sui M L, Lu K. Superplastic extensibility of nanocrystalline copper at room temperature. Science. 2000,287(5457): 1463-1466.
[37]Lu L, Shen Y F, Chen X H, et al. Ultrahigh strength and high electrical conductivity in copper. Science. 2004, 304(5669): 422-426.
[38] Sansoz F, Dupont V. Grain growth behavior at absolute zero during nanocrystalline metal indentation. Applied Physics Letters. 2006, 89(11): 111901.
[39]Humphrey W, Dalke A, Schulten K. VMD: Visual molecular dynamics. Journal of Molecular Graphics. 1996, 14(1): 33-38.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |