铜缺陷熔化及其冲击力学行为的分子动力学模拟
|
摘要
分子动力学模拟是人类认识物质世界的一种崭新的实验方式,人类可从原子、分子尺度上去研究和理解材料宏观的性质。近年来,随着分子动力学势函数的发展和计算机计算能力的大幅度提高,分子动力学模拟逐渐成熟,分子动力学模拟技术广泛应用到地球科学领域特别是应用于地球物理学研究中。分子动力学数值模拟实验有助于我们研究、理解在地球深内部环境中物质的状态和性质,特别是在研究地幔底部、外核直至内核的物质结构、组成、各向异性、状态方程等一系列重要的基础问题。物质熔化是地球内部一类重要的基本物理过程。为了分析和理解这一类过程,本文将采用分子动力学数值模拟的方式对物质熔化相关的过程进行研究。
本文综述了纳米尺度下材料的热力学行为,对如何采用分子动力学这一原子模拟技术分析材料热力学性能的数值方法进行了深入系统的阐述。我们采用分子动力学方法模拟了单晶铜的缺陷熔化过程,铜在静高压和冲击高压下的熔化过程,以及铜的冲击断裂过程,探讨了铜在冲击断裂中的一些力学行为。同时,还利用分子动力学模拟了纳米铜球粒子在撞击刚壁过程中的弹塑性行为。
从固体材料熔化及力学行为原子尺度模拟这一角度系统阐述了分子动力学数值模拟技术,讨论了分子动力学模拟中一些关键问题,如温度控制、压力控制、原子势函数等。
缺陷结构普遍存在于真实晶体中,特别是在地球内部。我们采用分子动力学方法模拟了有缺陷结构的单晶铜熔化行为。本文重点研究了层错缺陷和晶界缺陷。无论插入型层错还是抽出型层错,对熔化温度的影响基本可以忽略。层错缺陷的存在使得可以同时观察到均匀成核和非均匀成核,但只是稍微增加了成核速率和非均匀成核的概率。对于晶界缺陷本文研究了两种有代表性的对称(110)倾斜晶界,一种是低能量的∑=11/(113)／50.48°,另外一种是高能量的∑=27/(552)／148.41°。结果表明,在晶界区域内连续局部熔化会出现在不连续的整体熔化前,而连续的固态无序化会出现在局部熔化前。对前一种晶界缺陷,晶界区域的预熔化可以忽略不计,局部熔化发生在热动力学熔点附近。整个系统存在约13%的过热。对于后一种晶界缺陷,局部熔化存在着相当可观的预熔化,而整个系统体熔化过热程度已经可以忽略。
本文研究了金属铜在静高压下和冲击高压下的熔化行为。对于静高压条件下金属铜的熔化,本文分别利用两相法和过热-过冷回滞曲线法获得了铜在高压下的平衡熔化曲线,两种方法结果非常接近。最大过热和过冷程度独立于压力,近似保持常数。对于冲击熔化行为,我们研究了沿三个主要晶向(100),(110)和(111)冲击加载铜的熔化。沿(100)和沿(110)、(111)晶向冲击的熔化行为截然不同。对于<100>晶向,固体承受了最大约20%的过热,熔化时有明显的温度降。对于其它两个晶向,其熔化过程为准连续过程,并且存在着大约7%的预熔化。
本文借助分子动力学模拟研究了极高应变率下固体铜和液体铜由平面冲击导致的断裂。从自由表面速度历史推断断裂强度σsp和应变率是合理的一阶近似。对弱冲击强度来说断裂强度各向异性较为显著,并随着冲击强度增大逐渐递减。固体中空洞在缺陷位置成核。固体经受弱冲击时,断裂发生时没有伴随着拉伸熔化出现,而对于更强冲击或者当断裂温度Tsp足够高时,部分熔化可能出现在断裂之前或者伴随着断裂出现。断裂温度Tsp在研究的应变率范围内对断裂起着决定性作用。无论是固体铜还是液体铜,断裂强度σsp都随着断裂温度Tsp的增加而降低,并且对液体铜来说其σsp-Tsp成反幂指数关系。
本文研究了纳米铜球粒子撞击刚壁的弹塑性行为。铜球粒子在撞击过程中表现出了了高度弹性行为。对较小的粒子(半径小于1 nm),热涨落导致速度恢复系数波动很大,从而使得粒子表现出超弹性行为。对于较大的粒子(半径在2-15 nm范围内),铜球粒子仍然表现出了高度弹性,减小的速度恢复系数是由于碰撞过程中出现了塑性,这将导致不可逆的生热现象发生。
Molecular Dynamics(MD) is a brand new method to explore real world. Ma-croscopic properties of materials can be studied and understood at the atomic and molecular scale. Recently along the development of molecular dynamics potential functions and advance of computation speed, MD becomes more and more mature. MD simulations have been applied in many earth science fields, e.g. geophysics. MD simulations are very helpful to study and understand the state and properties of materials in the Earth interior, especially to study the structures, compositions, anisotropies and equations of state(EOS) of the materials in the lower mantle and outer core, even in the inner core. Melting is one of the most important processes for materials in the Earth interior. To understand this process, we conduct MD simulations to study the melting behaviors.
Thermodynamic behaviors of nano-scale materials are explained in this the-sis.Numerical method of simulating thermodynamics behaviors of materials by MD is elucidated in detail. Melting behaviors of single crystal copper with defective structures, melting behaviors of copper under hydrostatic and shock wave loading to high pressures and spallation of copper under shock wave loading are simula-ted with MD.The mechanical behaviors of copper during spallation are analyzed. Moreover, elastic and plastic behaviors of copper nanoparticles impact on a rigid wall are also simulated.
The methodology of simulating the thermodynamic behaviors of solid ma-terials by molecular dynamics method is elucidated indetail.Some key techniques ,such as the control of temperature and stress, potential functions are emphasized.
Defective structures are omnipresent in real solids, especially in the interior of the Earth. MD simulations are performed to investigate melting behaviors of cop-per with defective structures. This thesis focuses on stacking faults(SF) and grain boundary(GB).Both intrinsic and extrinsic SF induce negligible reduction in the temperature at melting. The existence of SF makes it is impossile to observe homo-geneous and heterogeneous nucleations simultaneously, but only slightly increases the nucleation rate and probability of nucleation at heterogeneous nucleations sites. Two representative types of symmetric (110) tilt GBs are explored, one isΣ=11/(113)/50.48°with low GB energy and the other isΣ= 27/(552)/148.41°with high GB energy. The results show within the GB region, continuous local melting precedes discontinuous bulk melting, while continuous solid state disor- dering may precede local melting. ForΣ= 11/(113)/50.48°with low GB energy, premelting of the GB region is negligible and local melting occurs near the ther-modynamic melting temperature. The GB region as a whole is superheated by about 13%before its bulk melting. The the case ofΣ= 27/(552)/148.41°with high GB energy, considerable premelting is observed for local melting, while the bulk melting occurs with negligible superheating.
Melting behaviors of copper under hydrostatic and shock wave loading to high pressures are studied. In the case of hydrostaic melting of copper, equilibrium mel-ting curve are obtained by both two-phase method and superheating-supercooling hysteresis method. They show very similar results. The amount of superheating or supercooling is independent of pressure and keep a constant nearly. For shock-induced melting of copper, we investigate melting under shock wave loading along three main crystallographic directions:(100). (110) and (111). Melting behaviors under shock wave loading along (100) and (110), (111) are very different. Fr the former, solid undergoes about 20%superheating before it melts with a pronoun-ced temperature drop. For the latter, melting is quasi-continuous and premelting about 7%is observed.
MD simulations are carried out to study spallation in solid and liquid copper incuded by planar shock loading at exteme strain rates. It is a reasonable firs-order approximation deducing spall strengthσsp and strain ratesεfrom free surface velocity history. The anisotroy inσsp is pronounced for weak shocks and decreases for stronger shocks. Voids are nucleated at a defective site in a solid. For weak solid shocks, spallation occurs without tensile melting, for stronger shocks or if the temperature right before spallation Tsp is sufficiently high, spallation may be accompanied or preceded by partial melting. Tsp appears to have a dominant effect on spallation for the narrow range ofεstudied here.σsp decreases with increasing Tsp for both solid and liquid copper andσsp-Tsp follows an inverse power law for liquids.
Elastic and plastic behaviors of copper nanoparticles impacting on a rigid wall are studied. The copper nanoparticles can be highly elastic during impact. Thermal fluctuations induce large fluctuations in the velocity restitution coefficient for small particles, and thus cause superelastic. Copper nanoparticles are still highly elastic for larger particles. The reduced restitution coefficient is due to plasticity during impact, which gives rise to irreversible heating.
本文综述了纳米尺度下材料的热力学行为,对如何采用分子动力学这一原子模拟技术分析材料热力学性能的数值方法进行了深入系统的阐述。我们采用分子动力学方法模拟了单晶铜的缺陷熔化过程,铜在静高压和冲击高压下的熔化过程,以及铜的冲击断裂过程,探讨了铜在冲击断裂中的一些力学行为。同时,还利用分子动力学模拟了纳米铜球粒子在撞击刚壁过程中的弹塑性行为。
从固体材料熔化及力学行为原子尺度模拟这一角度系统阐述了分子动力学数值模拟技术,讨论了分子动力学模拟中一些关键问题,如温度控制、压力控制、原子势函数等。
缺陷结构普遍存在于真实晶体中,特别是在地球内部。我们采用分子动力学方法模拟了有缺陷结构的单晶铜熔化行为。本文重点研究了层错缺陷和晶界缺陷。无论插入型层错还是抽出型层错,对熔化温度的影响基本可以忽略。层错缺陷的存在使得可以同时观察到均匀成核和非均匀成核,但只是稍微增加了成核速率和非均匀成核的概率。对于晶界缺陷本文研究了两种有代表性的对称(110)倾斜晶界,一种是低能量的∑=11/(113)／50.48°,另外一种是高能量的∑=27/(552)／148.41°。结果表明,在晶界区域内连续局部熔化会出现在不连续的整体熔化前,而连续的固态无序化会出现在局部熔化前。对前一种晶界缺陷,晶界区域的预熔化可以忽略不计,局部熔化发生在热动力学熔点附近。整个系统存在约13%的过热。对于后一种晶界缺陷,局部熔化存在着相当可观的预熔化,而整个系统体熔化过热程度已经可以忽略。
本文研究了金属铜在静高压下和冲击高压下的熔化行为。对于静高压条件下金属铜的熔化,本文分别利用两相法和过热-过冷回滞曲线法获得了铜在高压下的平衡熔化曲线,两种方法结果非常接近。最大过热和过冷程度独立于压力,近似保持常数。对于冲击熔化行为,我们研究了沿三个主要晶向(100),(110)和(111)冲击加载铜的熔化。沿(100)和沿(110)、(111)晶向冲击的熔化行为截然不同。对于<100>晶向,固体承受了最大约20%的过热,熔化时有明显的温度降。对于其它两个晶向,其熔化过程为准连续过程,并且存在着大约7%的预熔化。
本文借助分子动力学模拟研究了极高应变率下固体铜和液体铜由平面冲击导致的断裂。从自由表面速度历史推断断裂强度σsp和应变率是合理的一阶近似。对弱冲击强度来说断裂强度各向异性较为显著,并随着冲击强度增大逐渐递减。固体中空洞在缺陷位置成核。固体经受弱冲击时,断裂发生时没有伴随着拉伸熔化出现,而对于更强冲击或者当断裂温度Tsp足够高时,部分熔化可能出现在断裂之前或者伴随着断裂出现。断裂温度Tsp在研究的应变率范围内对断裂起着决定性作用。无论是固体铜还是液体铜,断裂强度σsp都随着断裂温度Tsp的增加而降低,并且对液体铜来说其σsp-Tsp成反幂指数关系。
本文研究了纳米铜球粒子撞击刚壁的弹塑性行为。铜球粒子在撞击过程中表现出了了高度弹性行为。对较小的粒子(半径小于1 nm),热涨落导致速度恢复系数波动很大,从而使得粒子表现出超弹性行为。对于较大的粒子(半径在2-15 nm范围内),铜球粒子仍然表现出了高度弹性,减小的速度恢复系数是由于碰撞过程中出现了塑性,这将导致不可逆的生热现象发生。
Molecular Dynamics(MD) is a brand new method to explore real world. Ma-croscopic properties of materials can be studied and understood at the atomic and molecular scale. Recently along the development of molecular dynamics potential functions and advance of computation speed, MD becomes more and more mature. MD simulations have been applied in many earth science fields, e.g. geophysics. MD simulations are very helpful to study and understand the state and properties of materials in the Earth interior, especially to study the structures, compositions, anisotropies and equations of state(EOS) of the materials in the lower mantle and outer core, even in the inner core. Melting is one of the most important processes for materials in the Earth interior. To understand this process, we conduct MD simulations to study the melting behaviors.
Thermodynamic behaviors of nano-scale materials are explained in this the-sis.Numerical method of simulating thermodynamics behaviors of materials by MD is elucidated in detail. Melting behaviors of single crystal copper with defective structures, melting behaviors of copper under hydrostatic and shock wave loading to high pressures and spallation of copper under shock wave loading are simula-ted with MD.The mechanical behaviors of copper during spallation are analyzed. Moreover, elastic and plastic behaviors of copper nanoparticles impact on a rigid wall are also simulated.
The methodology of simulating the thermodynamic behaviors of solid ma-terials by molecular dynamics method is elucidated indetail.Some key techniques ,such as the control of temperature and stress, potential functions are emphasized.
Defective structures are omnipresent in real solids, especially in the interior of the Earth. MD simulations are performed to investigate melting behaviors of cop-per with defective structures. This thesis focuses on stacking faults(SF) and grain boundary(GB).Both intrinsic and extrinsic SF induce negligible reduction in the temperature at melting. The existence of SF makes it is impossile to observe homo-geneous and heterogeneous nucleations simultaneously, but only slightly increases the nucleation rate and probability of nucleation at heterogeneous nucleations sites. Two representative types of symmetric (110) tilt GBs are explored, one isΣ=11/(113)/50.48°with low GB energy and the other isΣ= 27/(552)/148.41°with high GB energy. The results show within the GB region, continuous local melting precedes discontinuous bulk melting, while continuous solid state disor- dering may precede local melting. ForΣ= 11/(113)/50.48°with low GB energy, premelting of the GB region is negligible and local melting occurs near the ther-modynamic melting temperature. The GB region as a whole is superheated by about 13%before its bulk melting. The the case ofΣ= 27/(552)/148.41°with high GB energy, considerable premelting is observed for local melting, while the bulk melting occurs with negligible superheating.
Melting behaviors of copper under hydrostatic and shock wave loading to high pressures are studied. In the case of hydrostaic melting of copper, equilibrium mel-ting curve are obtained by both two-phase method and superheating-supercooling hysteresis method. They show very similar results. The amount of superheating or supercooling is independent of pressure and keep a constant nearly. For shock-induced melting of copper, we investigate melting under shock wave loading along three main crystallographic directions:(100). (110) and (111). Melting behaviors under shock wave loading along (100) and (110), (111) are very different. Fr the former, solid undergoes about 20%superheating before it melts with a pronoun-ced temperature drop. For the latter, melting is quasi-continuous and premelting about 7%is observed.
MD simulations are carried out to study spallation in solid and liquid copper incuded by planar shock loading at exteme strain rates. It is a reasonable firs-order approximation deducing spall strengthσsp and strain ratesεfrom free surface velocity history. The anisotroy inσsp is pronounced for weak shocks and decreases for stronger shocks. Voids are nucleated at a defective site in a solid. For weak solid shocks, spallation occurs without tensile melting, for stronger shocks or if the temperature right before spallation Tsp is sufficiently high, spallation may be accompanied or preceded by partial melting. Tsp appears to have a dominant effect on spallation for the narrow range ofεstudied here.σsp decreases with increasing Tsp for both solid and liquid copper andσsp-Tsp follows an inverse power law for liquids.
Elastic and plastic behaviors of copper nanoparticles impacting on a rigid wall are studied. The copper nanoparticles can be highly elastic during impact. Thermal fluctuations induce large fluctuations in the velocity restitution coefficient for small particles, and thus cause superelastic. Copper nanoparticles are still highly elastic for larger particles. The reduced restitution coefficient is due to plasticity during impact, which gives rise to irreversible heating.
引文
[1]Agrawal P M, Rice B M and Thompson D L,2003. Molecular dynamics study of the melting of nitromethane. J. Chem. Phys.,119(18):9617.
[2]Akella J and Kennedy G C,1971. Melting of Gold, Silver, and Copper-Proposal for a New High-Pressure Calibration Scale. Journal of Geophysical Research,76(20):4969-4977.
[3]Alder B J and Wainwright T E,1957. Phase Transition for a Hard Sphere System. J. Chem. Phys.,27:1208-1209.
[4]Alder B J and Wainwright T E,1958. Molecuar dynamics by electronic computers. International Symposium on Statistical Mechanical Theory of Transport Processed, Brussels.
[5]Alfe D, Gillan M J and Price G D,2002. Composition and temperature of the Earth's core constrained by combining ab initio calculations and seismic data. Earth and Planetary Science Letters,195(1-2):91-98.
[6]An Q, Luo S N, Han L B et al.,2008. Melting of Cu under hydrostatic and shock wave loading to high pressures. Journal of Physics:Condensed Matter,20:095220.
[7]An Q, Zheng L Q, Fu R S et al.,2006. Solid-liquid transitions of sodium chloride at high pressures. J. Chem. Phys.,125(15):154510.
[8]Ananin A V, Breusov O N, Dremin A N et al.,1974. Shock wave effect on refractory compounds. Porosh. Met. Akad. Nauk Ukr. SSR.,8:74-79.
[9]Andersen H C,1980. Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys.,72(4):2384-2393.
[10]Andersen T B and Austrheim H,2006. Fossil earthquakes recorded by pseu-dotachylytes in mantle peridotite from the Alpine subduction complex of Corsica. Earth and Planetary Science Letters,242:58-72.
[11]Andersen T B, Mair K, Austrheim H et al.,2008. Stress release in exhumed intermediate and deep earthquakes determined from ultramafic pseudota-chylyte. Geology,36(12):995-998.
[12]Anderson O L and Duba A,1997. Experimental Melting Curve of Iron Revisited. Journal of Geophysical Research.102-22695.
[13]Antoun T, Seaman L, Curran D R et al.,2003. Spall Fracture. New York: Springer.
[14]Avrami M,1940. Kinetics of phase change-II. Transformation-time relations for random distribution of nuclei. J. Chem. Phys.,8:212.
[15]Bancroft D, Peterson E L and Minshall S,1956. Polymorphism of Iron at High Pressure. J. Appl. Phys.,27(3):291-298.
[16]Baskes M I,1992. Modified embedded-atom potentials for cubic materials and impurities. Physical Review B,46(5):2727-2742.
[17]Beghein C and Trampert J,2003. Robust Normal Mode Constraints on Inner-Core Anisotropy from Model Space Search. Science,299(5606):552-555.
[18]Belak J,1998. On the nucleation and growth of voids at high strain-rates. Journal of Computer-Aided Materials Design,5:193-206.
[19]Belonoshko A B, Ahuja R, Eriksson O et al.,2000. Quasi ab initio molecular dynamic study of Cu melting. Physical Review B,61(6):3838-3844.
[20]Belonoshko A B, Ahuja R and Johansson B,2003. Stability of the body-centred-cubic phase of iron in the Earth's inner core. Nature,424:1032-1034.
[21]Belonoshko A B and Dubrovinsky L S,1997. A simulation study of induced failure and recrystallization of a perfect MgO crystal under non-hydrostatic compression:Application to melting in the diamond-anvil cell. American Mineralogist,82:441-451.
[22]Belonoshko A B, Skorodumova N V, Davis S et al.,2007. Origin of the Low Rigidity of the Earth's Inner Core. Science,316:1603-1605.
[23]Belonoshko A B, Skorodumova N V, Rosengren A et al.,2008. Elastic Ani-sotropy of Earth's Inner Core. Science,319:797-800.
[24]Berendsen H J C, Postma J P M, van Gunsteren W F et al.,1984. Molecular dynamics with coupling to an external bath. J. Chem. Phys.,81(8):3684-3690.
[25]Binder K,1992. The Monte Carlo Method in Condensed Matter Physics. Springer.
[26]Boehler R, Ross M, Soderlind P et al.,2001. High-Pressure Melting Curves of Argon. Krypton, and Xenon:Deviation from Corresponding States Theory. Physical Review Letters,86(25):5731-5734.
[27]Boness D A and Brown J M,1993. Bulk superheating of solid KBr and CsBr with shock waves. Physical Review Letters,71(18):2931-2934.
[28]Born M,1939. Thermodynamics of crystals and melting. J. Chem. Phys., 7(8):591-603.
[29]Bouchon M and Ihmle P,1999. Stress drop and frictional heating during the 1994 Deep Bolivia Earthquake. Geophysical Research Letters,26(23):3521-3524.
[30]Bouchon M and Vallee M,2003. Observation of Long Supershear Rupture During the Magnitude 8.1 Kunlunshan Earthquake. Science,301:824-826.
[31]Bowden F P and Hughes T P,1939. The mechanism of sliding on ice and snow. Proc.R.Soc.Lond.A,172:280-298.
[32]Bowden F P and Tabor D,1954. The Friction and Lubrication of Solids. Oxford, England:The Clarendon.
[33]Boyer L L,1985. Theory of melting based on lattice instability. Phase Transit,5:1-48.
[34]Brillouin L,1938. On thermal dependence of elasticity in solids. Proceedings Mathematical Sciences,8(5):251-254.
[35]Bringa E M, Cazamias J U, Erhart P et al.,2004. Atomistic shock Hugoniot simulation of single-crystal copper. J. Appl. Phys.,96(7):3793-3799.
[36]Broughton J Q and Gilmer G H,1986. Thermodynamic Criteria for Grain-Boundary Melting:A Molecular-Dynamics Study. Physical Review Letters, 56(25):2692-2695.
[37]Cahn R W,1978. Crystal Defects and Melting. Nature,273(5633):491-492.
[38]Cao A and Romanowicz B,2007. Test of the innermost inner core mo-dels using broadband PKIKP travel time residuals. Geophysical Research Letters,34:L08303.
[39]Car R and Parrinello M,1985. Unified Approach for Molecular Dynamics and Density-Functional Theory. Physical Review Letters,55(22):2471-2474.
[40]Carlson G A and Levine H S,1975. Dynamic tensile strength of glycerol. J. Appl. Phys.,46(4):1594-1601.
[41]Castle J C and van der Hilst R D,2000. The core-mantle boundary under the Gulf of Alaska:No ULVZ for shear waves. Earth and Planetary Science Letters,176:311-321.
[42]Chalmers B, Christian J W and Massalski T B,1972. Grain-Boundary Mi-gration. Progress in Material Science,16:13-42.
[43]Cho S A,1982. Role of lattice structure on the Lindemann fusion theory of metals. J. Phys. F Met. Phys.,12:1069-1083.
[44]Christian J W,1965. The Theory of Transformation in Metals and Alloys. New York:Pergaman.
[45]Ciccotti G, Guillope M and Pontikis V,1983. High-angle grain-boundary premelting transition:A molecular-dynamics study. Physical Review B, 27(9):5576-5585.
[46]Ciccotti G and Hoover W G,1986. Molecular-Dynamics Simulation of Statistical-Mechanical Systems. Elsevier Science.
[47]Cochran S and banner D,1977. Spall studies in uranium. J. Appl. Phys., 48(7):2729-2737.
[48]Creager K C,1992. Anisotropy of the inner core from differential travel times of the phases PKP and PKIKP. Nature,356:309-314.
[49]Curran D R, Seaman L and Shockley D A,1987. Dynamic failure of solids. Physics Reports,147:253-388.
[50]Dai C, Tan H and Geng H,2002. Model for assessing the melting on Hugo-niots of metals:Al, Pb, Cu, Mo, Fe, and U. J. Appl. Phys.,92(9):5019-5026.
[51]Dash J G,1975. Films of Solid Surface. London:Academic.
[52]Daw M S and Baskes M I,1983. Semiempirical, Quantum Mechanical Cal-culation of Hydrogen Embrittlement in Metals. Physical Review Letters, 50(17):1285-1288.
[53]Daw M S and Baskes M I,1984. Embedded-atom method:Derivation and application to impurities, surfaces, and other defects in metals. Physical Review B,29(12):6443-6453.
[54]Dekel E, Eliezer S, Henis Z et al.,1998. Spallation model for the high strain rates range. J. Appl. Phys.,84(9):4851-4858.
[55]Dremov V, Petrovtsev A, Sapozhnikov P et al.,2006. Molecular dynamics simulations of the initial stages of spall in nanocrystalline copper. Physical Review B,74(14):144110.
[56]Dubrovinsky L, Dubrovinskaia N, Narygina O et al.,2007. Body-Centered Cubic Iron-Nickel Alloy in Earth's Core. Science,316(5833):1880-1883.
[57]Duvall G E and Graham R A,1977. Phase transitions under shock-wave loading. Rev. Mod. Phys.,49(3):523-579.
[58]Ercolessi F, Parrinello M and Tosatti E,1988. Simulation of gold in the glue model. Philosophical magazine. A.,58(1):213-226.
[59]Eyring H and John M S,1969. Significant liquid structures. New York Wiley.
[60]Fan W and Gong X G,2005. Superheated melting of grain boundaries. Physical Review B,72(6):064121.
[61]Finnis M W and Sinclair J E,1984. A simple empirical N-body potential for transition metals. Philosophical magazine. A.,50(1):45-55.
[62]Forsblom M and Grimvall G,2005. How superheated crystals melt. Nature Mater.,4:388-390.
[63]Frenkel D and Smit B,2002. Understanding molecular simulation:from algorithms to applications. Academic.
[64]Frenkel J,1955. Introduction to the theory of metals. Warsaw:PWN.
[65]Fukushima E and Ookawa A,1955. Some Characters of the Soap Bubble Raft in a Vibrating State. Journal of the Physical Society of Japan,10:970-981.
[66]Garnero E J, Grand S P and Helmberger D V,1993. Low P-wave velocity at the base of the mantle. Geophysical Research Letters.20(17):1843-1846.
[67]Garnero E J and Helmberger D V,1996. Seismic detection of a thin laterally varying boundary layer at the base of the mantle beneath the central-Pacific. Geophysical Research Letters,23(9):977-980.
[68]Gaudio P D, Toro G D, Han R et al.,2009. Frictional melting of peridotite and seismic slip. Journal of Geophysical Research.114(B6):306-324.
[69]Germann T C, Holian B L, Lomdahl P S et al.,2000. Orientation Dependence in Molecular Dynamics Simulations of Shocked Single Crystals. Physical Review Letters,84(23):5351-5354.
[70]Gibson J B, Goland A N, Milgram M et al.,1960. Dynamics of Radiation Damage. Physical Review,120(4):1229-1253.
[71]Gilvarry J J,1956. The Lindemann and Gruneisen Laws. Physical Review, 102(2):308-316.
[72]Gomez L, Dobry A, Geuting C et al.,2003. Dislocation Lines as the Precursor of the Melting of Crystalline Solids Observed in Monte Carlo Simulations. Physical Review Letters,90(9).095701.
[73]Gorecki T,1974. Vacancies and changes of physical properties of metals at the melting point. Z Metallk,65(6):426-431.
[74]Gorecki T,1976. Vacancies of Changes of the First Coordination Sphere Radius of Metals at the Melting Point. Z Metallk,67(4):269-273.
[75]Graham R A,1974. Shock-wave compression of x-cut quartz as determined by electrical response measurements. Journal of Physics and Chemistry of Solids,35(3):355-372.
[76]Haile J M,1997. Molecular Dynamics Simulation-Elementary Methods. New York:Wiley InterScience.
[77]Hanggi P, Talkner P and Borkovec M,1990. Reaction-rate theory:fifty years after Kramers. Rev. Mod. Phys.,62(2):251-341.
[78]Harrison J A, White C T, Colton R J et al.,1995. Investigation of the atomic-scale friction and energy dissipation in diamond using molecular dynamics. Thin Solid Films,260:205-211.
[79]Harrison W A,1966. Pseudopotentials in Metals. New York:Benjamin.
[80]Herzfeld K F and Goeppert-Mayer M,1934. On the Theory of Fusion. Phy-sical Review,46(11):995-1001.
[81]Holian B L and Lomdahl P S,1998. Plasticity induced by shock waves in nonequilibrium molecular-dynamics simulations. Science,280(5372):2085-2088.
[82]Holian B L and Straub G K,1979. Molecular Dynamics of Shock Waves in Three-Dimensional Solids:Transition from Nonsteady to Steady Waves in Perfect Crystals and Implications for the Rankine-Hugoniot Conditions. Physical Review Letters,43(21):1598-1600.
[83]Honeycutt J D and Andersen H C.1987. Molecular dynamics study of melting and freezing of small Lennard-Jones clusters. J. Phys. Chem., 91(19):4950-4963.
[84]Hoover W G,1985. Canonical dynamics:Equilibrium phase-space distribu-tions. Physical Review A,31(3):1695-1697.
[85]Hunter L and Siegel S,1942. The Variation with Temperature of the Prin-cipal Elastic Moduli of NaCl near the Melting Point. Physical Review, 61(1-2):84-90.
[86]Ishii M and Dziewonski A M,2002. The innermost inner core of the earth: Evidence for a change in anisotropic behavior at the radius of about 300 km. Proceedings of the National Academy of Sciences of the United States of America,99:13966-13968.
[87]Japel S, Schwager B, Boehler R et al.,2005. Melting of Copper and Ni-ckel at High Pressure:The Role of d Electrons. Physical Review Letters, 95(16):167801.
[88]Jeffreys H.1942. On the mechanics of faulting. Geological Magazine.79:291-295.
[89]Jeong J W and Chang K J,1999. Molecular-dynamics simulations for the shock Hugoniot meltings of Cu, Pd and Pt. Journal of Physics:Condensed Matter,11:3799-3806.
[90]Jin Z H, Gumbsch P, Lu K et al.,2001. Melting Mechanisms at the Limit of Superheating. Physical Review Letters,87(5):055703.
[91]Johnson Q and Mitchell A C,1972. First X-Ray Diffraction Evidence for a Phase Transition during Shock-Wave Compression. Physical Review Letters, 29(20):1369-1371.
[92]Johnson W A and Mehl R F,1939. Reaction kinetics in processes of nuclea-tion and growth. Am. Inst. Min. Met. Engrs.-Trans.,135:416.
[93]Kadas K, Vitos L, Johansson B et al.,2009. Stability of body-centered cubic iron-magnesium alloys in the Earth's inner core. Proceedings of the National Academy of Sciences of the United States of America,106(37):15560-15562.
[94]Kadau K, Germann T C, Lomdahl P S et al.,2002. Microscopic View of Structural Phase Transitions Induced by Shock Waves. Science, 296(5573):1681-1684.
[95]Kanamori H, Anderson D L and Heaton T H.1994. Frictional Melting During the Rupture of the 1994 Bolivian Earthquake. Science,279:839-842.
[96]Kane G,1939. The Equation of State of Frozen Neon, Argon, Krypton and Xenon. J. Chem. Phys.,7:603-614.
[97]Kanel G I, Razorenov S V, Baumung K et al.,1996. Spall fracture pro-perties of aluminum and magnesium at high temperatures. J. Appl. Phys., 79(11):8310-8317.
[98]Kanel G I, Razorenov S V, Baumung K et al.,2001. Dynamic yield and tensile strength of aluminum single crystals at temperatures up to the melting point. J. Appl. Phys.,90(1):136-143.
[99]Kelton K F,1991. Crystal nucleation in liquids and glasses. Solid State Phys.,45:75.
[100]Kleinert H,1989. Gauge Fields in Condensed Matter. Singapore:World Scientific.
[101]Laio A, Bernard S, Chiarotti G L et al.,2000. Physics of Iron at Earth's Core Conditions. Science,287(5455):1027-1030.
[102]Lay T and Garnero E J,2004. Core-mantle boundary structures and pro-cesses. Geophysical Research Letters,28:387-390.
[103]Lebowitz J L, Percus J K and Verlet L,1967. Ensemble Dependence of Fluctuations with Application to Machine Computations. Physical Review, 153(1):250-254.
[104]Lees A W and Edwards S F,1972. The computer study of transport pro-cesses under extreme conditions. Journal of Physics C:Solid State Physics, 5:1921-1928.
[105]Lehmann I,1936. Publ. Bur.Cent.Assoc.Int.Seismol.A,14(3).
[106]Li B, Clapp P C, Rifkin J A et al.,2003. Molecular dynamics calculation of heat dissipation during sliding friction. International Journal of Heat and Mass Transfer,46:37-43.
[107]Li J,2003. AtomEye:An efficient atomistic configuration viewer. Modelling Simulation in Materials Science and Engineering.11:173-177.
[108]Lide D R,2006. CRC handbook of chemistry and physics 2005-2006:A Ready reference book of chemical and physical data.1.
[109]Lill J V,1994. The integration of molecular dynamics simulations with impo-sed temperature and stress. Computer Physics Communications,79(2):219-248.
[110]Lin J F, Heinz D L, Campbell A J et al..2002. Iron-Silicon Alloy in Earth's Core. Science,295(5553):313-315.
[111]Lin Z and Zhigilei L V,2007. Time-resolved diffraction profiles and structural dynamics of Ni film under short laser pulse irradiation. Journal of Physics: Conference Series,59:11-15.
[112]Lindemann F A,1910. The Calculation of Molecular Vibration Frequencies. Phys. Z.,11:609.
[113]Link S, Wang Z L and El-Sayed M A,2000. How Does a Gold Nanorod Melt. Journal of Physical Chemistry B,104(33):7867-7870.
[114]Luo S N and Ahrens T J,2004. Shock-induced superheating and melting curves of geophysically important minerals. Physics of The Earth and Pla-netary Interiors,143-144:369-386.
[115]Luo S N, Ahrens T J, Cag in T et al.,2003. Maximum superheating and undercooling:Systematics, molecular dynamics simulations, and dynamic experiments. Physical Review B,68(13):134206.
[116]Luo S N, Han L B, Xie Y et al.,2008. The relation between shock-state particle velocity and free surface velocity:A molecular dynamics study on single crystal Cu and silica glass. J. Appl. Phys.,103(9):093530.
[117]Luo S N, Strachan A and Swift D C,2004. Nonequilibrium melting and crys-tallization of a model Lennard-Jones system. J. Chem. Phys.,120(24):11640.
[118]Luo S N, Strachan A and Swift D C,2005a. Deducing solid-liquid interfa-cial energy from superheating or supercooling:application to H2O at high pressures. Modelling Simul. Mater. Sci. Eng.,13:321-328.
[119]Luo S N, Strachan A and Swift D C,2005b. Vibrational density of states and Lindemann melting law. J. Chem. Phys..122(19):194709.
[120]Luo S N and Swift D C,2007. On high-pressure melting of tantalum. Physica B:Condensed Matter,388:139-144.
[121]Luo S N, Zheng L Q, An Q et al.,2006a. Tensile Failure of Single-Crystal and Nanocrystalline Lennard-Jones Solids Under Uniaxial Strain. International Journal of Modern Physics C-Physics,17(11):1551-1561.
[122]Luo S N, Zheng L Q, Strachan A et al.,2007. Melting dynamics of super-heated argon:Nucleation and growth. J. Chem. Phys.,126(3):034505.
[123]Luo S N, Zheng L Q and Tschauner O,2006b. Solid-state disordering and melting of silica stishovite:the role of defects. Journal of Physics:Conden-sed Matter,18:659-668.
[124]Lutsko J F,1989. Generalized expressions for the calculation of elastic constants by computer simulation. J.Appl.Phys.,65(8):2991-2997.
[125]Lutsko J F, Wolf D, Phillpot S R et al.,1989. Molecular-dynamics study of lattice-defect-nucleated melting in metals using an embedded-atom-method potential. Physical Review B,40(5):2841-2855.
[126]Lyzenga G A, Ahrens T J and Mitchell A C,1983. Shock temperatures of SiO2 and their geophysical implications. Journal of Geophysical Research, 88(B3):2431-2444.
[127]Marsh S P,1980. LASL SHock HUgoniot Data. Berkeley, CA:University of California.
[128]Matsui M,1989. Molecular dynamics study of the structural and thermody-namic properties of MgO crystal with quantum correction. J. Chem. Phys., 91(1):489-494.
[129]McKenzie D and Brune J N,1972. Melting on fault planes during large ear-thquakes. Geophysical Journal of the Royal Astronomical Society,29(1):65-78.
[130]Melchionna S, Ciccotti G and Holian B L,1993. Hoover NPT dynamics for systems varying in shape and size. Molecular Physics,78(3):533-544.
[131]Meyers M A, Traiviratana S. Lubarda V A et al.,2009. The role of disloca-tions in the growth of nanosized voids in ductile failure of metals. Journal of the Minerals, Metals and Materials Society,61(2):35-41.
[132]Minich R W, Cazamias J U, Kumar M et al.,2004. Effect of microstructu-ral length scales on spall behavior of copper. Metallurgical and Materials Transactions A,35(9):2663-2673.
[133]Mirwald P W and Kennedy G C,1979. The melting curve of gold, silver and copper to 60-kbar pressure. Journal of Geophysical Research,84(B12):6750-6756.
[134]Mishin Y, Lozovoi A Y and Alavi A,2003. Evaluation of diffusion mecha-nisms in NiAl by embedded-atom and first-principles calculations. Physical Review B,67(1):014201.
[135]Mishin Y, Mehl M J, Papaconstantopoulos D A et al.,2001. Structural sta-bility and lattice defects in copper:Ab initio, tight-binding, and embedded-atom calculations. Physical Review B,63(22):224106.
[136]Mori J and Helmberger D V,1995. Localized boundary layer below the mid-Pacific velocity anomaly identified from a PcP precursor. Journal of Geophysical Research,100(B10):20359-20365.
[137]Morris J R and Song X,2002. The melting lines of model systems calculated from coexistence simulations. J. Chem. Phys.,116:9352.
[138]Morris J R and Song X,2003. The anisotropic free energy of the Lennard-Jones crystal-melt interface. J. Chem. Phys.,119(7):3920-3925.
[139]Morris J R, Wang C Z, Ho K M et al.,1994. Melting line of aluminum from simulations of coexisting phases. Physical Review B,49(5):3109-3115.
[140]Moshe E, Eliezer S, Henis Z et al.,2000. Experimental measurements of the strength of metals approaching the theoretical limit predicted by the equation of state. Applied Physics Letters,76(12):1555-1557.
[141]Nose S,1984. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys.,81(1):511-519.
[142]Nose S,2002. A molecular dynamics method for simulations in the canonical ensemble. Molecular Physics,100(1):191-198.
[143]Obata M and Karato S,1995. Ultramafic pseudotachylite from the Balmuc-cia peridotite. Ivrea-Verbano zone, northern Italy. Tectonophysics,242:313-328.
[144]Paisley D L, Luo S N, Greenfield S R et al.,2008. Laser-launched flyer plate and confined laser ablation for shock wave loading:Validation and applications. Review of Scientific Instruments.79(2):023902.
[145]Parrinello M and Rahman A,1981. Polymorphic transitions in single crys-tals:A new molecular dynamics method. J. Appl. Phys.,52:7182-7190.
[146]Paskin A and Dienes G J,1972. Molecular Dynamic Simulations of Shock Waves in a Three-Dimensional Solid. J. Appl. Phys.,43(4):1605.
[147]Persch S T, Vidale J E and Earle P S,2001. Absence of short-period ULVZ precursors to PcP and ScP from two regions of the CMB. Geophysical Research Letters,28:387-390.
[148]Piccardo B G, Ranalli G, Marasco M et al.,2008. Ultramafic pseudotachy-lytes in the Mt. Moncuni peridotite(lanzao Massif,western Alps):Tectonic evolution and upper mantle seismicity. Period Mineral,76:181-197.
[149]Porter D A and Easterling K E,2001. Phase Transformations in Metals and Alloys. Cheltenham:Nelson Thornes Ltd.
[150]Rahman A,1964. Correlations in the Motion of Atoms in Liquid Argon. Physical Review,136:A405-A411.
[151]Rapaport D C,1995. The art of molecular dynamics simulation. Cambridge, England:Cambridge University.
[152]Ravelo R, Holian B L, Germann T C et al.,2005. Shock Compression of Condensed Matter:270.
[153]Ray J R and Rahman A,1984. Statistical ensembles and molecular dynamics studies of anisotropic solids. J. Chem. Phys.,80(9):4423-4428.
[154]Remler D K and Madden P A,1990. Molecular dynamics without effective potentials via the car-parrinello approach. Molecular Physics,70:921-966.
[155]Revenaugh J and Meyer R,1997. Seismic Evidence of Partial Melt Within a Possibly Ubiquitous Low-Velocity Layer at the Base of the Mantle. Science, 277(5326):670-673.
[156]Richards P G,1976. Dynamic motions near an earthquake fault a three-dimensional solution. Bulletin of the Seismological Society of America, 66(1):1-32.
[157]Rittner J D and Seidman D N,1996.<110> symmetric tilt grain-boundary structures in fcc metals with low stacking-fault energies. Physical Review B,54(10):6999-7015.
[158]Romanowicz B, Li X D and Durek J,1996. Anisotropy in the Inner Core: Could It Be Due To Low-Order Convection? Science,274(5289):963-966.
[159]Schardin H,1941. Die Schlierenverfahren und ihre Anwendung. Ergeh. Exakten Naturwiss.,10:303-439.
[160]Schmid M, Hofer W, Varga P et al.,1995. Surface stress, surface elasticity, and the size effect in surface segregation. Physical Review B,51(16):10937-10946.
[161]Slagle O D and Mckinstry H A,1967. Temperature Dependence of the Elastic Constants of the Alkali Halides. I. NaCl, KCl, and KBr. J. Appl. Phys., 38:437-446.
[162]Solca J, Dyson A J, steinebrunner G et al.,1997. Melting curve for argon calculated from pure theory. Chemical Physics,224:253-261.
[163]Song X and Helmberger D V,1995. Depth dependence of anisotropy of Earth's inner core. J. Geophys. Res.,100(B6):9805-9816.
[164]Srinivasan S G, Baskes M I and Wagner G J,2007. Atomistic simulations of shock induced microstructural evolution and spallation in single crystal nickel. J. Appl. Phys.,101(4):043504.
[165]Stadler J, Mikulla R and Trebin H R,1997. IMD:A software package for molecular dynamics studies on parallel computers. International Journal of Modern Physics C-Physics,8(5):1131-1140.
[166]Stixrude L and Cohen R E,1995. High-Pressure Elasticity of Iron and Anisotropy of Earth's Inner Core. Science,267(5206):1972-1975.
[167]Strachan A, Qag in T and Goddard W A,2001. Critical behavior in spallation failure of metals. Physical Review B,63(6):060103.
[168]Straub G K, Holian B L and Swanson R E,1980. Bull. Am. Phys. Soc., 25:549.
[169]Sun Z H, Wang X X, Soh A K et al.,2006. On stress calculations in atomistic simulations. Modelling and Simulation in Materials Science and Engineering, 14(3):423-431.
[170]Sutherland W,1891. A kinetic theory of solids, with an Experimental In-troduction. Philosophical Magazine,32:42.
[171]Sutmann G,2002. Classical molecular dynamics. Quantum Simulations of Complex Many-Body Systems:From Theory to Algorithms,10:211-254.
[172]Sutton A P and Chen J,1990. Long-range Finnis-Sinclair potentials. Philo-sophical magazine letters,61(3):139-146.
[173]Swegle J W,1990. Irreversible phase transition and wave propagation in silicate geologic materials. J. Appl. Phys.,68:1563-1579.
[174]Tallon J L,1989. A hierarchy of catastrophes as a succession of stability limits for the crystalline state. Nature,342:658-660.
[175]Tallon J L, Robinson W H and Smedley S I,1977. A melting criterion based on the dilatation dependence of shear moduli. Nature,266:337-338.
[176]Tang Z P,2008. Shock-Induced Phase Transitions. Beijing:Science.
[177]Tolman R C,1949. The Effect of Droplet Size on Surface Tension. J. Chem. Phys.,17(3):333.
[178]Tonks D L, Alexander D J, Sheffield S A et al.,2000. Spallation strength of single crystal and polycrystalline copper. Journal de Physique IV,10:787-792.
[179]Tonks D L, Zurek A K and Thissell W R,2003. Coalescence rate model for ductile damage in metals. Journal de Physique IV,110:893.
[180]Tsai D H and Beckett C W,1966. Shock wave propagation in cubic lattices. Journal of Geophysical Research,71(10):2601.
[181]Tuckerman M E and Parrinello M,1994. Integrating the Car-Parrinello equations. I. Basic integration techniques. J. Chem. Phys.,101:1302-1315.
[182]Ubbelhode A R,1979. The molten state of matter:Melting and crystal structure. New York:Wiley.
[183]Verlet L,1967. Computer "Experiments" on Classical Fluids. I. Thermody-namical Properties of Lennard-Jones Molecules. Physical Review,159(1):98.
[184]Vidale J E and Hedlin M A H,1998. Evidence for partial melt at the core-mantle boundary north of Tonga from the strong scattering of seismic waves. Nature,391:682-685.
[185]Vitek V,1968. Intrinsic stacking faults in body-centred cubic crystals. Phi-losophical Magazine,18(154):773-786.
[186]Vocadlo L,2007. Ab initio calculations of the elasticity of iron and iron alloys at inner core conditions:Evidence for a partially molten inner core? Earth and Planetary Science Letters,254(1-2):227-232.
[187]Vocadlo L, Alfe D, Gillman M J et al.,2003. Possible thermal and chemical stabilization of body-centred-cubic iron in the Earth's core. nature,424:536-539.
[188]Vocadlo L, Alfe D, Price G D et al.,2004. Ab initio melting curve of copper by the phase coexistence approach. J. Chem. Phys.,120(6):2072.
[189]Wang J, Li J, Yip S et al.,1995. Mechanical instabilities of homogeneous crystals. Physical Review B,52(17):12627-12635.
[190]Wang J, Li J, Yip S et al.,1997. Unifying two criteria of Born:Elastic instability and melting of homogeneous crystals. Physica A,240:396-403.
[191]Wang J, Yip S, Phillpo S R et al.,1993. Crystal instabilities at finite strain. Physical Review Letters,71(25):4182-4185.
[192]Wang L W, Zhang L and Lu K,2005. Vacancy-decomposition-induced lattice instability and its correlation with the kinetic stability limit of crystals. Philosophical Magazine Letters,85(5):213-219.
[193]Wedekind J, Strey R and Reguera D,2007. New method to analyze simula-tions of activated processes. J. Chem. Phys.,126(13):134103.
[194]Wen L and Helmberger D V,1998. Ultra-Low Velocity Zones Near the Core-Mantle Boundary from Broadband PKP Precursors. Science, 279(5357):1701-1703.
[195]Williams Q, Jeanloz R, Bass J et al.,1987. The Melting Curve of Iron to 250 Gigapascals:A Constraint on the Temperature at Earth's Center. Science, 236(4798):181-182.
[196]Xie Y, Han L B, An Q et al.,2009. Release melting of shock-loaded single crystal Cu. J. Appl. Phys.,105(6):066103.
[197]Yip S, Li J, Tang M et al.,2001. Mechanistic aspects and atomic-level conse-quences of elastic instabilities in homogeneous crystals. Materials Science and Engineering A,317:236-240.
[198]Yoo C S, Holmes N C, Ross M et al.,1993. Shock temperatures and melting of iron at Earth core conditions. Physical Review Letters,70(25):3931-3934.
[199]Young C J and Lay T,1987. Evidence for a shear velocity discontinuity in the lower mantle beneath India and the Indian Ocean. Phys.Earth Planet.Inter, 49:37-53.
[200]Zhao S J,Wang S Q, Zhang T G et al.,2000. A cluster-induced structu-ral disorder and melting transition in the grain boundary of B2 NiAl:a molecular-dynamics simulation on parallel computers. Journal of Physics Condensed Matter,12:L549-L555.
[201]Zheng L Q, An Q, Xie Y et al.,2007. Homogeneous nucleation and growth of melt in copper. J. Chem. Phys.,127(16):164503.
[202]Zope R R and Mishin Y,2003. Interatomic potentials for atomistic simula-tions of the Ti-Al system. Physical Review B,68(2):024102.
[203]周蕙兰,1990.地球内部物理.北京：地震出版社.
[204]张弢,张晓茹,吴爱玲等,2003.金属铜升温熔化过程的分子动力学模拟.物理化学学报,19(8)：709-713.
[205]李西军,龚自正,刘福生等,2000.铁高压熔化线的测量—熔化机理的影响.高压物理学报,15(3)：221-225.
[206]王丽,边秀房,2000.金属Cu熔化结晶过程的分子动力学模拟.化学物理学报,13(5)：544-550.
[207]王海龙,王秀喜,梁海弋,2005.金属Cu体熔化与表面熔化行为的分子动力学模拟与分析.金属学报,41(6)：568-572.
[2]Akella J and Kennedy G C,1971. Melting of Gold, Silver, and Copper-Proposal for a New High-Pressure Calibration Scale. Journal of Geophysical Research,76(20):4969-4977.
[3]Alder B J and Wainwright T E,1957. Phase Transition for a Hard Sphere System. J. Chem. Phys.,27:1208-1209.
[4]Alder B J and Wainwright T E,1958. Molecuar dynamics by electronic computers. International Symposium on Statistical Mechanical Theory of Transport Processed, Brussels.
[5]Alfe D, Gillan M J and Price G D,2002. Composition and temperature of the Earth's core constrained by combining ab initio calculations and seismic data. Earth and Planetary Science Letters,195(1-2):91-98.
[6]An Q, Luo S N, Han L B et al.,2008. Melting of Cu under hydrostatic and shock wave loading to high pressures. Journal of Physics:Condensed Matter,20:095220.
[7]An Q, Zheng L Q, Fu R S et al.,2006. Solid-liquid transitions of sodium chloride at high pressures. J. Chem. Phys.,125(15):154510.
[8]Ananin A V, Breusov O N, Dremin A N et al.,1974. Shock wave effect on refractory compounds. Porosh. Met. Akad. Nauk Ukr. SSR.,8:74-79.
[9]Andersen H C,1980. Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys.,72(4):2384-2393.
[10]Andersen T B and Austrheim H,2006. Fossil earthquakes recorded by pseu-dotachylytes in mantle peridotite from the Alpine subduction complex of Corsica. Earth and Planetary Science Letters,242:58-72.
[11]Andersen T B, Mair K, Austrheim H et al.,2008. Stress release in exhumed intermediate and deep earthquakes determined from ultramafic pseudota-chylyte. Geology,36(12):995-998.
[12]Anderson O L and Duba A,1997. Experimental Melting Curve of Iron Revisited. Journal of Geophysical Research.102-22695.
[13]Antoun T, Seaman L, Curran D R et al.,2003. Spall Fracture. New York: Springer.
[14]Avrami M,1940. Kinetics of phase change-II. Transformation-time relations for random distribution of nuclei. J. Chem. Phys.,8:212.
[15]Bancroft D, Peterson E L and Minshall S,1956. Polymorphism of Iron at High Pressure. J. Appl. Phys.,27(3):291-298.
[16]Baskes M I,1992. Modified embedded-atom potentials for cubic materials and impurities. Physical Review B,46(5):2727-2742.
[17]Beghein C and Trampert J,2003. Robust Normal Mode Constraints on Inner-Core Anisotropy from Model Space Search. Science,299(5606):552-555.
[18]Belak J,1998. On the nucleation and growth of voids at high strain-rates. Journal of Computer-Aided Materials Design,5:193-206.
[19]Belonoshko A B, Ahuja R, Eriksson O et al.,2000. Quasi ab initio molecular dynamic study of Cu melting. Physical Review B,61(6):3838-3844.
[20]Belonoshko A B, Ahuja R and Johansson B,2003. Stability of the body-centred-cubic phase of iron in the Earth's inner core. Nature,424:1032-1034.
[21]Belonoshko A B and Dubrovinsky L S,1997. A simulation study of induced failure and recrystallization of a perfect MgO crystal under non-hydrostatic compression:Application to melting in the diamond-anvil cell. American Mineralogist,82:441-451.
[22]Belonoshko A B, Skorodumova N V, Davis S et al.,2007. Origin of the Low Rigidity of the Earth's Inner Core. Science,316:1603-1605.
[23]Belonoshko A B, Skorodumova N V, Rosengren A et al.,2008. Elastic Ani-sotropy of Earth's Inner Core. Science,319:797-800.
[24]Berendsen H J C, Postma J P M, van Gunsteren W F et al.,1984. Molecular dynamics with coupling to an external bath. J. Chem. Phys.,81(8):3684-3690.
[25]Binder K,1992. The Monte Carlo Method in Condensed Matter Physics. Springer.
[26]Boehler R, Ross M, Soderlind P et al.,2001. High-Pressure Melting Curves of Argon. Krypton, and Xenon:Deviation from Corresponding States Theory. Physical Review Letters,86(25):5731-5734.
[27]Boness D A and Brown J M,1993. Bulk superheating of solid KBr and CsBr with shock waves. Physical Review Letters,71(18):2931-2934.
[28]Born M,1939. Thermodynamics of crystals and melting. J. Chem. Phys., 7(8):591-603.
[29]Bouchon M and Ihmle P,1999. Stress drop and frictional heating during the 1994 Deep Bolivia Earthquake. Geophysical Research Letters,26(23):3521-3524.
[30]Bouchon M and Vallee M,2003. Observation of Long Supershear Rupture During the Magnitude 8.1 Kunlunshan Earthquake. Science,301:824-826.
[31]Bowden F P and Hughes T P,1939. The mechanism of sliding on ice and snow. Proc.R.Soc.Lond.A,172:280-298.
[32]Bowden F P and Tabor D,1954. The Friction and Lubrication of Solids. Oxford, England:The Clarendon.
[33]Boyer L L,1985. Theory of melting based on lattice instability. Phase Transit,5:1-48.
[34]Brillouin L,1938. On thermal dependence of elasticity in solids. Proceedings Mathematical Sciences,8(5):251-254.
[35]Bringa E M, Cazamias J U, Erhart P et al.,2004. Atomistic shock Hugoniot simulation of single-crystal copper. J. Appl. Phys.,96(7):3793-3799.
[36]Broughton J Q and Gilmer G H,1986. Thermodynamic Criteria for Grain-Boundary Melting:A Molecular-Dynamics Study. Physical Review Letters, 56(25):2692-2695.
[37]Cahn R W,1978. Crystal Defects and Melting. Nature,273(5633):491-492.
[38]Cao A and Romanowicz B,2007. Test of the innermost inner core mo-dels using broadband PKIKP travel time residuals. Geophysical Research Letters,34:L08303.
[39]Car R and Parrinello M,1985. Unified Approach for Molecular Dynamics and Density-Functional Theory. Physical Review Letters,55(22):2471-2474.
[40]Carlson G A and Levine H S,1975. Dynamic tensile strength of glycerol. J. Appl. Phys.,46(4):1594-1601.
[41]Castle J C and van der Hilst R D,2000. The core-mantle boundary under the Gulf of Alaska:No ULVZ for shear waves. Earth and Planetary Science Letters,176:311-321.
[42]Chalmers B, Christian J W and Massalski T B,1972. Grain-Boundary Mi-gration. Progress in Material Science,16:13-42.
[43]Cho S A,1982. Role of lattice structure on the Lindemann fusion theory of metals. J. Phys. F Met. Phys.,12:1069-1083.
[44]Christian J W,1965. The Theory of Transformation in Metals and Alloys. New York:Pergaman.
[45]Ciccotti G, Guillope M and Pontikis V,1983. High-angle grain-boundary premelting transition:A molecular-dynamics study. Physical Review B, 27(9):5576-5585.
[46]Ciccotti G and Hoover W G,1986. Molecular-Dynamics Simulation of Statistical-Mechanical Systems. Elsevier Science.
[47]Cochran S and banner D,1977. Spall studies in uranium. J. Appl. Phys., 48(7):2729-2737.
[48]Creager K C,1992. Anisotropy of the inner core from differential travel times of the phases PKP and PKIKP. Nature,356:309-314.
[49]Curran D R, Seaman L and Shockley D A,1987. Dynamic failure of solids. Physics Reports,147:253-388.
[50]Dai C, Tan H and Geng H,2002. Model for assessing the melting on Hugo-niots of metals:Al, Pb, Cu, Mo, Fe, and U. J. Appl. Phys.,92(9):5019-5026.
[51]Dash J G,1975. Films of Solid Surface. London:Academic.
[52]Daw M S and Baskes M I,1983. Semiempirical, Quantum Mechanical Cal-culation of Hydrogen Embrittlement in Metals. Physical Review Letters, 50(17):1285-1288.
[53]Daw M S and Baskes M I,1984. Embedded-atom method:Derivation and application to impurities, surfaces, and other defects in metals. Physical Review B,29(12):6443-6453.
[54]Dekel E, Eliezer S, Henis Z et al.,1998. Spallation model for the high strain rates range. J. Appl. Phys.,84(9):4851-4858.
[55]Dremov V, Petrovtsev A, Sapozhnikov P et al.,2006. Molecular dynamics simulations of the initial stages of spall in nanocrystalline copper. Physical Review B,74(14):144110.
[56]Dubrovinsky L, Dubrovinskaia N, Narygina O et al.,2007. Body-Centered Cubic Iron-Nickel Alloy in Earth's Core. Science,316(5833):1880-1883.
[57]Duvall G E and Graham R A,1977. Phase transitions under shock-wave loading. Rev. Mod. Phys.,49(3):523-579.
[58]Ercolessi F, Parrinello M and Tosatti E,1988. Simulation of gold in the glue model. Philosophical magazine. A.,58(1):213-226.
[59]Eyring H and John M S,1969. Significant liquid structures. New York Wiley.
[60]Fan W and Gong X G,2005. Superheated melting of grain boundaries. Physical Review B,72(6):064121.
[61]Finnis M W and Sinclair J E,1984. A simple empirical N-body potential for transition metals. Philosophical magazine. A.,50(1):45-55.
[62]Forsblom M and Grimvall G,2005. How superheated crystals melt. Nature Mater.,4:388-390.
[63]Frenkel D and Smit B,2002. Understanding molecular simulation:from algorithms to applications. Academic.
[64]Frenkel J,1955. Introduction to the theory of metals. Warsaw:PWN.
[65]Fukushima E and Ookawa A,1955. Some Characters of the Soap Bubble Raft in a Vibrating State. Journal of the Physical Society of Japan,10:970-981.
[66]Garnero E J, Grand S P and Helmberger D V,1993. Low P-wave velocity at the base of the mantle. Geophysical Research Letters.20(17):1843-1846.
[67]Garnero E J and Helmberger D V,1996. Seismic detection of a thin laterally varying boundary layer at the base of the mantle beneath the central-Pacific. Geophysical Research Letters,23(9):977-980.
[68]Gaudio P D, Toro G D, Han R et al.,2009. Frictional melting of peridotite and seismic slip. Journal of Geophysical Research.114(B6):306-324.
[69]Germann T C, Holian B L, Lomdahl P S et al.,2000. Orientation Dependence in Molecular Dynamics Simulations of Shocked Single Crystals. Physical Review Letters,84(23):5351-5354.
[70]Gibson J B, Goland A N, Milgram M et al.,1960. Dynamics of Radiation Damage. Physical Review,120(4):1229-1253.
[71]Gilvarry J J,1956. The Lindemann and Gruneisen Laws. Physical Review, 102(2):308-316.
[72]Gomez L, Dobry A, Geuting C et al.,2003. Dislocation Lines as the Precursor of the Melting of Crystalline Solids Observed in Monte Carlo Simulations. Physical Review Letters,90(9).095701.
[73]Gorecki T,1974. Vacancies and changes of physical properties of metals at the melting point. Z Metallk,65(6):426-431.
[74]Gorecki T,1976. Vacancies of Changes of the First Coordination Sphere Radius of Metals at the Melting Point. Z Metallk,67(4):269-273.
[75]Graham R A,1974. Shock-wave compression of x-cut quartz as determined by electrical response measurements. Journal of Physics and Chemistry of Solids,35(3):355-372.
[76]Haile J M,1997. Molecular Dynamics Simulation-Elementary Methods. New York:Wiley InterScience.
[77]Hanggi P, Talkner P and Borkovec M,1990. Reaction-rate theory:fifty years after Kramers. Rev. Mod. Phys.,62(2):251-341.
[78]Harrison J A, White C T, Colton R J et al.,1995. Investigation of the atomic-scale friction and energy dissipation in diamond using molecular dynamics. Thin Solid Films,260:205-211.
[79]Harrison W A,1966. Pseudopotentials in Metals. New York:Benjamin.
[80]Herzfeld K F and Goeppert-Mayer M,1934. On the Theory of Fusion. Phy-sical Review,46(11):995-1001.
[81]Holian B L and Lomdahl P S,1998. Plasticity induced by shock waves in nonequilibrium molecular-dynamics simulations. Science,280(5372):2085-2088.
[82]Holian B L and Straub G K,1979. Molecular Dynamics of Shock Waves in Three-Dimensional Solids:Transition from Nonsteady to Steady Waves in Perfect Crystals and Implications for the Rankine-Hugoniot Conditions. Physical Review Letters,43(21):1598-1600.
[83]Honeycutt J D and Andersen H C.1987. Molecular dynamics study of melting and freezing of small Lennard-Jones clusters. J. Phys. Chem., 91(19):4950-4963.
[84]Hoover W G,1985. Canonical dynamics:Equilibrium phase-space distribu-tions. Physical Review A,31(3):1695-1697.
[85]Hunter L and Siegel S,1942. The Variation with Temperature of the Prin-cipal Elastic Moduli of NaCl near the Melting Point. Physical Review, 61(1-2):84-90.
[86]Ishii M and Dziewonski A M,2002. The innermost inner core of the earth: Evidence for a change in anisotropic behavior at the radius of about 300 km. Proceedings of the National Academy of Sciences of the United States of America,99:13966-13968.
[87]Japel S, Schwager B, Boehler R et al.,2005. Melting of Copper and Ni-ckel at High Pressure:The Role of d Electrons. Physical Review Letters, 95(16):167801.
[88]Jeffreys H.1942. On the mechanics of faulting. Geological Magazine.79:291-295.
[89]Jeong J W and Chang K J,1999. Molecular-dynamics simulations for the shock Hugoniot meltings of Cu, Pd and Pt. Journal of Physics:Condensed Matter,11:3799-3806.
[90]Jin Z H, Gumbsch P, Lu K et al.,2001. Melting Mechanisms at the Limit of Superheating. Physical Review Letters,87(5):055703.
[91]Johnson Q and Mitchell A C,1972. First X-Ray Diffraction Evidence for a Phase Transition during Shock-Wave Compression. Physical Review Letters, 29(20):1369-1371.
[92]Johnson W A and Mehl R F,1939. Reaction kinetics in processes of nuclea-tion and growth. Am. Inst. Min. Met. Engrs.-Trans.,135:416.
[93]Kadas K, Vitos L, Johansson B et al.,2009. Stability of body-centered cubic iron-magnesium alloys in the Earth's inner core. Proceedings of the National Academy of Sciences of the United States of America,106(37):15560-15562.
[94]Kadau K, Germann T C, Lomdahl P S et al.,2002. Microscopic View of Structural Phase Transitions Induced by Shock Waves. Science, 296(5573):1681-1684.
[95]Kanamori H, Anderson D L and Heaton T H.1994. Frictional Melting During the Rupture of the 1994 Bolivian Earthquake. Science,279:839-842.
[96]Kane G,1939. The Equation of State of Frozen Neon, Argon, Krypton and Xenon. J. Chem. Phys.,7:603-614.
[97]Kanel G I, Razorenov S V, Baumung K et al.,1996. Spall fracture pro-perties of aluminum and magnesium at high temperatures. J. Appl. Phys., 79(11):8310-8317.
[98]Kanel G I, Razorenov S V, Baumung K et al.,2001. Dynamic yield and tensile strength of aluminum single crystals at temperatures up to the melting point. J. Appl. Phys.,90(1):136-143.
[99]Kelton K F,1991. Crystal nucleation in liquids and glasses. Solid State Phys.,45:75.
[100]Kleinert H,1989. Gauge Fields in Condensed Matter. Singapore:World Scientific.
[101]Laio A, Bernard S, Chiarotti G L et al.,2000. Physics of Iron at Earth's Core Conditions. Science,287(5455):1027-1030.
[102]Lay T and Garnero E J,2004. Core-mantle boundary structures and pro-cesses. Geophysical Research Letters,28:387-390.
[103]Lebowitz J L, Percus J K and Verlet L,1967. Ensemble Dependence of Fluctuations with Application to Machine Computations. Physical Review, 153(1):250-254.
[104]Lees A W and Edwards S F,1972. The computer study of transport pro-cesses under extreme conditions. Journal of Physics C:Solid State Physics, 5:1921-1928.
[105]Lehmann I,1936. Publ. Bur.Cent.Assoc.Int.Seismol.A,14(3).
[106]Li B, Clapp P C, Rifkin J A et al.,2003. Molecular dynamics calculation of heat dissipation during sliding friction. International Journal of Heat and Mass Transfer,46:37-43.
[107]Li J,2003. AtomEye:An efficient atomistic configuration viewer. Modelling Simulation in Materials Science and Engineering.11:173-177.
[108]Lide D R,2006. CRC handbook of chemistry and physics 2005-2006:A Ready reference book of chemical and physical data.1.
[109]Lill J V,1994. The integration of molecular dynamics simulations with impo-sed temperature and stress. Computer Physics Communications,79(2):219-248.
[110]Lin J F, Heinz D L, Campbell A J et al..2002. Iron-Silicon Alloy in Earth's Core. Science,295(5553):313-315.
[111]Lin Z and Zhigilei L V,2007. Time-resolved diffraction profiles and structural dynamics of Ni film under short laser pulse irradiation. Journal of Physics: Conference Series,59:11-15.
[112]Lindemann F A,1910. The Calculation of Molecular Vibration Frequencies. Phys. Z.,11:609.
[113]Link S, Wang Z L and El-Sayed M A,2000. How Does a Gold Nanorod Melt. Journal of Physical Chemistry B,104(33):7867-7870.
[114]Luo S N and Ahrens T J,2004. Shock-induced superheating and melting curves of geophysically important minerals. Physics of The Earth and Pla-netary Interiors,143-144:369-386.
[115]Luo S N, Ahrens T J, Cag in T et al.,2003. Maximum superheating and undercooling:Systematics, molecular dynamics simulations, and dynamic experiments. Physical Review B,68(13):134206.
[116]Luo S N, Han L B, Xie Y et al.,2008. The relation between shock-state particle velocity and free surface velocity:A molecular dynamics study on single crystal Cu and silica glass. J. Appl. Phys.,103(9):093530.
[117]Luo S N, Strachan A and Swift D C,2004. Nonequilibrium melting and crys-tallization of a model Lennard-Jones system. J. Chem. Phys.,120(24):11640.
[118]Luo S N, Strachan A and Swift D C,2005a. Deducing solid-liquid interfa-cial energy from superheating or supercooling:application to H2O at high pressures. Modelling Simul. Mater. Sci. Eng.,13:321-328.
[119]Luo S N, Strachan A and Swift D C,2005b. Vibrational density of states and Lindemann melting law. J. Chem. Phys..122(19):194709.
[120]Luo S N and Swift D C,2007. On high-pressure melting of tantalum. Physica B:Condensed Matter,388:139-144.
[121]Luo S N, Zheng L Q, An Q et al.,2006a. Tensile Failure of Single-Crystal and Nanocrystalline Lennard-Jones Solids Under Uniaxial Strain. International Journal of Modern Physics C-Physics,17(11):1551-1561.
[122]Luo S N, Zheng L Q, Strachan A et al.,2007. Melting dynamics of super-heated argon:Nucleation and growth. J. Chem. Phys.,126(3):034505.
[123]Luo S N, Zheng L Q and Tschauner O,2006b. Solid-state disordering and melting of silica stishovite:the role of defects. Journal of Physics:Conden-sed Matter,18:659-668.
[124]Lutsko J F,1989. Generalized expressions for the calculation of elastic constants by computer simulation. J.Appl.Phys.,65(8):2991-2997.
[125]Lutsko J F, Wolf D, Phillpot S R et al.,1989. Molecular-dynamics study of lattice-defect-nucleated melting in metals using an embedded-atom-method potential. Physical Review B,40(5):2841-2855.
[126]Lyzenga G A, Ahrens T J and Mitchell A C,1983. Shock temperatures of SiO2 and their geophysical implications. Journal of Geophysical Research, 88(B3):2431-2444.
[127]Marsh S P,1980. LASL SHock HUgoniot Data. Berkeley, CA:University of California.
[128]Matsui M,1989. Molecular dynamics study of the structural and thermody-namic properties of MgO crystal with quantum correction. J. Chem. Phys., 91(1):489-494.
[129]McKenzie D and Brune J N,1972. Melting on fault planes during large ear-thquakes. Geophysical Journal of the Royal Astronomical Society,29(1):65-78.
[130]Melchionna S, Ciccotti G and Holian B L,1993. Hoover NPT dynamics for systems varying in shape and size. Molecular Physics,78(3):533-544.
[131]Meyers M A, Traiviratana S. Lubarda V A et al.,2009. The role of disloca-tions in the growth of nanosized voids in ductile failure of metals. Journal of the Minerals, Metals and Materials Society,61(2):35-41.
[132]Minich R W, Cazamias J U, Kumar M et al.,2004. Effect of microstructu-ral length scales on spall behavior of copper. Metallurgical and Materials Transactions A,35(9):2663-2673.
[133]Mirwald P W and Kennedy G C,1979. The melting curve of gold, silver and copper to 60-kbar pressure. Journal of Geophysical Research,84(B12):6750-6756.
[134]Mishin Y, Lozovoi A Y and Alavi A,2003. Evaluation of diffusion mecha-nisms in NiAl by embedded-atom and first-principles calculations. Physical Review B,67(1):014201.
[135]Mishin Y, Mehl M J, Papaconstantopoulos D A et al.,2001. Structural sta-bility and lattice defects in copper:Ab initio, tight-binding, and embedded-atom calculations. Physical Review B,63(22):224106.
[136]Mori J and Helmberger D V,1995. Localized boundary layer below the mid-Pacific velocity anomaly identified from a PcP precursor. Journal of Geophysical Research,100(B10):20359-20365.
[137]Morris J R and Song X,2002. The melting lines of model systems calculated from coexistence simulations. J. Chem. Phys.,116:9352.
[138]Morris J R and Song X,2003. The anisotropic free energy of the Lennard-Jones crystal-melt interface. J. Chem. Phys.,119(7):3920-3925.
[139]Morris J R, Wang C Z, Ho K M et al.,1994. Melting line of aluminum from simulations of coexisting phases. Physical Review B,49(5):3109-3115.
[140]Moshe E, Eliezer S, Henis Z et al.,2000. Experimental measurements of the strength of metals approaching the theoretical limit predicted by the equation of state. Applied Physics Letters,76(12):1555-1557.
[141]Nose S,1984. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys.,81(1):511-519.
[142]Nose S,2002. A molecular dynamics method for simulations in the canonical ensemble. Molecular Physics,100(1):191-198.
[143]Obata M and Karato S,1995. Ultramafic pseudotachylite from the Balmuc-cia peridotite. Ivrea-Verbano zone, northern Italy. Tectonophysics,242:313-328.
[144]Paisley D L, Luo S N, Greenfield S R et al.,2008. Laser-launched flyer plate and confined laser ablation for shock wave loading:Validation and applications. Review of Scientific Instruments.79(2):023902.
[145]Parrinello M and Rahman A,1981. Polymorphic transitions in single crys-tals:A new molecular dynamics method. J. Appl. Phys.,52:7182-7190.
[146]Paskin A and Dienes G J,1972. Molecular Dynamic Simulations of Shock Waves in a Three-Dimensional Solid. J. Appl. Phys.,43(4):1605.
[147]Persch S T, Vidale J E and Earle P S,2001. Absence of short-period ULVZ precursors to PcP and ScP from two regions of the CMB. Geophysical Research Letters,28:387-390.
[148]Piccardo B G, Ranalli G, Marasco M et al.,2008. Ultramafic pseudotachy-lytes in the Mt. Moncuni peridotite(lanzao Massif,western Alps):Tectonic evolution and upper mantle seismicity. Period Mineral,76:181-197.
[149]Porter D A and Easterling K E,2001. Phase Transformations in Metals and Alloys. Cheltenham:Nelson Thornes Ltd.
[150]Rahman A,1964. Correlations in the Motion of Atoms in Liquid Argon. Physical Review,136:A405-A411.
[151]Rapaport D C,1995. The art of molecular dynamics simulation. Cambridge, England:Cambridge University.
[152]Ravelo R, Holian B L, Germann T C et al.,2005. Shock Compression of Condensed Matter:270.
[153]Ray J R and Rahman A,1984. Statistical ensembles and molecular dynamics studies of anisotropic solids. J. Chem. Phys.,80(9):4423-4428.
[154]Remler D K and Madden P A,1990. Molecular dynamics without effective potentials via the car-parrinello approach. Molecular Physics,70:921-966.
[155]Revenaugh J and Meyer R,1997. Seismic Evidence of Partial Melt Within a Possibly Ubiquitous Low-Velocity Layer at the Base of the Mantle. Science, 277(5326):670-673.
[156]Richards P G,1976. Dynamic motions near an earthquake fault a three-dimensional solution. Bulletin of the Seismological Society of America, 66(1):1-32.
[157]Rittner J D and Seidman D N,1996.<110> symmetric tilt grain-boundary structures in fcc metals with low stacking-fault energies. Physical Review B,54(10):6999-7015.
[158]Romanowicz B, Li X D and Durek J,1996. Anisotropy in the Inner Core: Could It Be Due To Low-Order Convection? Science,274(5289):963-966.
[159]Schardin H,1941. Die Schlierenverfahren und ihre Anwendung. Ergeh. Exakten Naturwiss.,10:303-439.
[160]Schmid M, Hofer W, Varga P et al.,1995. Surface stress, surface elasticity, and the size effect in surface segregation. Physical Review B,51(16):10937-10946.
[161]Slagle O D and Mckinstry H A,1967. Temperature Dependence of the Elastic Constants of the Alkali Halides. I. NaCl, KCl, and KBr. J. Appl. Phys., 38:437-446.
[162]Solca J, Dyson A J, steinebrunner G et al.,1997. Melting curve for argon calculated from pure theory. Chemical Physics,224:253-261.
[163]Song X and Helmberger D V,1995. Depth dependence of anisotropy of Earth's inner core. J. Geophys. Res.,100(B6):9805-9816.
[164]Srinivasan S G, Baskes M I and Wagner G J,2007. Atomistic simulations of shock induced microstructural evolution and spallation in single crystal nickel. J. Appl. Phys.,101(4):043504.
[165]Stadler J, Mikulla R and Trebin H R,1997. IMD:A software package for molecular dynamics studies on parallel computers. International Journal of Modern Physics C-Physics,8(5):1131-1140.
[166]Stixrude L and Cohen R E,1995. High-Pressure Elasticity of Iron and Anisotropy of Earth's Inner Core. Science,267(5206):1972-1975.
[167]Strachan A, Qag in T and Goddard W A,2001. Critical behavior in spallation failure of metals. Physical Review B,63(6):060103.
[168]Straub G K, Holian B L and Swanson R E,1980. Bull. Am. Phys. Soc., 25:549.
[169]Sun Z H, Wang X X, Soh A K et al.,2006. On stress calculations in atomistic simulations. Modelling and Simulation in Materials Science and Engineering, 14(3):423-431.
[170]Sutherland W,1891. A kinetic theory of solids, with an Experimental In-troduction. Philosophical Magazine,32:42.
[171]Sutmann G,2002. Classical molecular dynamics. Quantum Simulations of Complex Many-Body Systems:From Theory to Algorithms,10:211-254.
[172]Sutton A P and Chen J,1990. Long-range Finnis-Sinclair potentials. Philo-sophical magazine letters,61(3):139-146.
[173]Swegle J W,1990. Irreversible phase transition and wave propagation in silicate geologic materials. J. Appl. Phys.,68:1563-1579.
[174]Tallon J L,1989. A hierarchy of catastrophes as a succession of stability limits for the crystalline state. Nature,342:658-660.
[175]Tallon J L, Robinson W H and Smedley S I,1977. A melting criterion based on the dilatation dependence of shear moduli. Nature,266:337-338.
[176]Tang Z P,2008. Shock-Induced Phase Transitions. Beijing:Science.
[177]Tolman R C,1949. The Effect of Droplet Size on Surface Tension. J. Chem. Phys.,17(3):333.
[178]Tonks D L, Alexander D J, Sheffield S A et al.,2000. Spallation strength of single crystal and polycrystalline copper. Journal de Physique IV,10:787-792.
[179]Tonks D L, Zurek A K and Thissell W R,2003. Coalescence rate model for ductile damage in metals. Journal de Physique IV,110:893.
[180]Tsai D H and Beckett C W,1966. Shock wave propagation in cubic lattices. Journal of Geophysical Research,71(10):2601.
[181]Tuckerman M E and Parrinello M,1994. Integrating the Car-Parrinello equations. I. Basic integration techniques. J. Chem. Phys.,101:1302-1315.
[182]Ubbelhode A R,1979. The molten state of matter:Melting and crystal structure. New York:Wiley.
[183]Verlet L,1967. Computer "Experiments" on Classical Fluids. I. Thermody-namical Properties of Lennard-Jones Molecules. Physical Review,159(1):98.
[184]Vidale J E and Hedlin M A H,1998. Evidence for partial melt at the core-mantle boundary north of Tonga from the strong scattering of seismic waves. Nature,391:682-685.
[185]Vitek V,1968. Intrinsic stacking faults in body-centred cubic crystals. Phi-losophical Magazine,18(154):773-786.
[186]Vocadlo L,2007. Ab initio calculations of the elasticity of iron and iron alloys at inner core conditions:Evidence for a partially molten inner core? Earth and Planetary Science Letters,254(1-2):227-232.
[187]Vocadlo L, Alfe D, Gillman M J et al.,2003. Possible thermal and chemical stabilization of body-centred-cubic iron in the Earth's core. nature,424:536-539.
[188]Vocadlo L, Alfe D, Price G D et al.,2004. Ab initio melting curve of copper by the phase coexistence approach. J. Chem. Phys.,120(6):2072.
[189]Wang J, Li J, Yip S et al.,1995. Mechanical instabilities of homogeneous crystals. Physical Review B,52(17):12627-12635.
[190]Wang J, Li J, Yip S et al.,1997. Unifying two criteria of Born:Elastic instability and melting of homogeneous crystals. Physica A,240:396-403.
[191]Wang J, Yip S, Phillpo S R et al.,1993. Crystal instabilities at finite strain. Physical Review Letters,71(25):4182-4185.
[192]Wang L W, Zhang L and Lu K,2005. Vacancy-decomposition-induced lattice instability and its correlation with the kinetic stability limit of crystals. Philosophical Magazine Letters,85(5):213-219.
[193]Wedekind J, Strey R and Reguera D,2007. New method to analyze simula-tions of activated processes. J. Chem. Phys.,126(13):134103.
[194]Wen L and Helmberger D V,1998. Ultra-Low Velocity Zones Near the Core-Mantle Boundary from Broadband PKP Precursors. Science, 279(5357):1701-1703.
[195]Williams Q, Jeanloz R, Bass J et al.,1987. The Melting Curve of Iron to 250 Gigapascals:A Constraint on the Temperature at Earth's Center. Science, 236(4798):181-182.
[196]Xie Y, Han L B, An Q et al.,2009. Release melting of shock-loaded single crystal Cu. J. Appl. Phys.,105(6):066103.
[197]Yip S, Li J, Tang M et al.,2001. Mechanistic aspects and atomic-level conse-quences of elastic instabilities in homogeneous crystals. Materials Science and Engineering A,317:236-240.
[198]Yoo C S, Holmes N C, Ross M et al.,1993. Shock temperatures and melting of iron at Earth core conditions. Physical Review Letters,70(25):3931-3934.
[199]Young C J and Lay T,1987. Evidence for a shear velocity discontinuity in the lower mantle beneath India and the Indian Ocean. Phys.Earth Planet.Inter, 49:37-53.
[200]Zhao S J,Wang S Q, Zhang T G et al.,2000. A cluster-induced structu-ral disorder and melting transition in the grain boundary of B2 NiAl:a molecular-dynamics simulation on parallel computers. Journal of Physics Condensed Matter,12:L549-L555.
[201]Zheng L Q, An Q, Xie Y et al.,2007. Homogeneous nucleation and growth of melt in copper. J. Chem. Phys.,127(16):164503.
[202]Zope R R and Mishin Y,2003. Interatomic potentials for atomistic simula-tions of the Ti-Al system. Physical Review B,68(2):024102.
[203]周蕙兰,1990.地球内部物理.北京：地震出版社.
[204]张弢,张晓茹,吴爱玲等,2003.金属铜升温熔化过程的分子动力学模拟.物理化学学报,19(8)：709-713.
[205]李西军,龚自正,刘福生等,2000.铁高压熔化线的测量—熔化机理的影响.高压物理学报,15(3)：221-225.
[206]王丽,边秀房,2000.金属Cu熔化结晶过程的分子动力学模拟.化学物理学报,13(5)：544-550.
[207]王海龙,王秀喜,梁海弋,2005.金属Cu体熔化与表面熔化行为的分子动力学模拟与分析.金属学报,41(6)：568-572.