冲击压缩下金属高压熔化规律相关问题的理论及实验研究
|
摘要
本文对当前金属高压熔化规律研究中所涉及的物态方程、熔化判据、熔化区内材料的强度、熔化机制和实验数据分析处理等问题进行了相对系统的研究:
1、Anderson所提出的等效Grüneisen系数在地球物理学和铁的高压熔化线的相关计算上得到了应用,并取得了良好的效果。根据Anderson所提出的等效Grüneisen系数的概念,本文在三项式物态方程基础上,对等效Grüneisen方程进行了推导。以等效Grüneisen方程为基础,对多种金属的冲击温度进行了计算,研究表明,该方法使用简便,计算结果与实验数据符合得很好。
2、对现有熔化判据进行了分析和比较,在此基础上采用由材料零温物态方程约束的熔化判据对金属熔化线进行了计算和对比分析。研究表明,在一定条件下,该熔化判据与Lindemann熔化判据和平均场理论所给出的熔化判据具有相同的物理内涵。计算表明,该熔化判据能够较好的描述金属的高压熔化曲线。在理论分析及比照分子动力学模拟的基础上,给出了该熔化判据的物理机制。
3、在SCG模型和修正的SCG模型基础上,通过引入能量权重,对材料剪切模量在固液混合相区内的变化行为进行了描述,在此基础上,对金属铝沿Hugoniot线的剪切模量进行了分析,得到的结果与实验数据基本相符。
4、利用逾渗理论和重整化群方法分析计算了各向同性材料剪切模量在固液混合相区内的临界变化行为。采用Huygens原理对材料在固液混合相区内声波的传播过程进行了分析,在此基础上,通过逾渗理论给出了剪切模量在固液混合相区内随熔化质量分数变化的临界点。当熔化质量分数达到0.313左右时,材料内部出现液相贯通区,假设材料此时开始表现出熔化性质,从而可将该点与光分析法中的纵波声速向体波声速的拐点相对应;当熔化质量分数大于0.687左右时,材料内部将不再存在一个可以贯通相对表面的固相区,因而此时材料的整体剪切模量消失。通过分析材料内部沿剪切作用面上液相区和固相区的组成,给出了九种承剪能力变化较小的简立方格子,在此基础了进行了重整化群变换,计算得到了临界的熔化质量分数,与逾渗理论的计算结果相吻合。
5、以铁冲击熔化结束点为参考点,黄海军等解决了长期以来令人困扰的铁动静态测量熔化温度存在差异的问题,但在冲击熔化初始压力点处,如何将Fe的冲击温度修正到平衡熔化温度的问题并没有得到解决。本文对此问题进行了研究,利用计算得到的临界熔化质量分数,在Luo等提出的过热模型的基础上,对Fe在冲击熔化初始压力点处的冲击温度进行了修正,修正得到的平衡熔化温度与黄海军等的计算结果以及Ma和Shen的实验结果能够落在同一条Lindemann熔化线上。
6、采用动高压手段和光分析方法对Ly12Al高压熔化温度进行了实验研究和理论分析。Ly12Al的阻抗较低,对其高压熔化规律进行实验测量存在较大的难度,通过实验测量了Ly12Al在100Gpa附近的辐射光谱,拟合所得温度结果经理论分析初步认定为熔化温度。
This thesis gives a more systematical study to the correlative problems in the melting law of metal at high pressure, such as equation of state, melting criterion, the material strength in melting region, melting mechanism and the analyse and process of experimental data:
(1) The effective Grüneisen coefficient proposed by Anderson has been applied in geophysics and in the calculation of the iron’s meling curve and the results shows that it is a good method. According to the effective Grüneisen coefficient conception and basing on the three term equation of state, we derived the effective Grüneisen equation of state. As an evolution, a new method to calculate shock temperature was proposed, the calculated results with some metals agree with experimental data well.
(2) Proposing a melting criterion constraint with 0K equation of state. This melting criterion can picture the high pressure melting curve of metal. Its physical mechanism was givn in the thesis by theoretical analysis and comparing molecular dynamics simulation. It has the same physical meaning as Lindemann melting criterion and the melting criterion given by mean field approach in some conditions.
(3) All the proposed high pressure and high temperature constitutive equations have a same limitation, i.e. they can not give the correct behavior of shear modulus in the solid-liquid mixing phase. By introducing the internal energy as power weight, we built a constitutive equation up to liquidus and which has no such a limition. With it, the shear modulus of aluminum along Hugoniot path was calculated, the results agreed experimental data and showed that the chang of shear modulus can be divided into three stages, that is, work hardening, temperature softening and melting.
(4) Discussing and analyzing the behavior of shear modulus in solid liquid mixing phase region with Percolation and Renormalized Group. The propagating process of sound in the melting material was analysed with Huygens principle. Then the critical melting mass function was calculated by using percolation and the results were that, at the critical melting mass function 0.313, a percolating liquid region appeared in the melting material, which was just corresponding to the turning point of longitudinal to bulk sound velocity; when melting mass fuction was larger than 0.687, there would be no percolation solid region in the material and this meaned that the shear modulus equaled zero. The analyzing results with percolation also indicated that the method, which was used to determine the shock induced melting region with sound velocities in shock compression experiment, had errors. By analyzing the constitution of liquid and solid of material in melting region along shearing plane, the behavior of shear modulus in melting region is predicted by renormalization group theory and is coincidence with that given by percolation theory.
(5) Taking the completing point of shock induced melting region as referring point, the problem, which has been puzzling for a long time, was solved by Huang Haijun. But at the initial point of shock induced melting region, how to modify the shock temperature to the equilibrium melting temperature still is not solved. Using the calculated critical melting mass function and basing the superheating model proposed by Luo et al, we amend the shock temperatue of iron at the initial point of shock induced melting region. The amended equilibrium melting temperature, together with the calculated result by Huang Haijun, the Ma’s and Shen’s static experimental data, is on the same Lindemann melting curve.
(6) With the SC experimental means and optical analyzing method, we measured the interfacial temperatures of Ly12Al/LiF around the pressure 100GPa. These interfacial temperature can thought as melting temperature by considering the gap effection.
1、Anderson所提出的等效Grüneisen系数在地球物理学和铁的高压熔化线的相关计算上得到了应用,并取得了良好的效果。根据Anderson所提出的等效Grüneisen系数的概念,本文在三项式物态方程基础上,对等效Grüneisen方程进行了推导。以等效Grüneisen方程为基础,对多种金属的冲击温度进行了计算,研究表明,该方法使用简便,计算结果与实验数据符合得很好。
2、对现有熔化判据进行了分析和比较,在此基础上采用由材料零温物态方程约束的熔化判据对金属熔化线进行了计算和对比分析。研究表明,在一定条件下,该熔化判据与Lindemann熔化判据和平均场理论所给出的熔化判据具有相同的物理内涵。计算表明,该熔化判据能够较好的描述金属的高压熔化曲线。在理论分析及比照分子动力学模拟的基础上,给出了该熔化判据的物理机制。
3、在SCG模型和修正的SCG模型基础上,通过引入能量权重,对材料剪切模量在固液混合相区内的变化行为进行了描述,在此基础上,对金属铝沿Hugoniot线的剪切模量进行了分析,得到的结果与实验数据基本相符。
4、利用逾渗理论和重整化群方法分析计算了各向同性材料剪切模量在固液混合相区内的临界变化行为。采用Huygens原理对材料在固液混合相区内声波的传播过程进行了分析,在此基础上,通过逾渗理论给出了剪切模量在固液混合相区内随熔化质量分数变化的临界点。当熔化质量分数达到0.313左右时,材料内部出现液相贯通区,假设材料此时开始表现出熔化性质,从而可将该点与光分析法中的纵波声速向体波声速的拐点相对应;当熔化质量分数大于0.687左右时,材料内部将不再存在一个可以贯通相对表面的固相区,因而此时材料的整体剪切模量消失。通过分析材料内部沿剪切作用面上液相区和固相区的组成,给出了九种承剪能力变化较小的简立方格子,在此基础了进行了重整化群变换,计算得到了临界的熔化质量分数,与逾渗理论的计算结果相吻合。
5、以铁冲击熔化结束点为参考点,黄海军等解决了长期以来令人困扰的铁动静态测量熔化温度存在差异的问题,但在冲击熔化初始压力点处,如何将Fe的冲击温度修正到平衡熔化温度的问题并没有得到解决。本文对此问题进行了研究,利用计算得到的临界熔化质量分数,在Luo等提出的过热模型的基础上,对Fe在冲击熔化初始压力点处的冲击温度进行了修正,修正得到的平衡熔化温度与黄海军等的计算结果以及Ma和Shen的实验结果能够落在同一条Lindemann熔化线上。
6、采用动高压手段和光分析方法对Ly12Al高压熔化温度进行了实验研究和理论分析。Ly12Al的阻抗较低,对其高压熔化规律进行实验测量存在较大的难度,通过实验测量了Ly12Al在100Gpa附近的辐射光谱,拟合所得温度结果经理论分析初步认定为熔化温度。
This thesis gives a more systematical study to the correlative problems in the melting law of metal at high pressure, such as equation of state, melting criterion, the material strength in melting region, melting mechanism and the analyse and process of experimental data:
(1) The effective Grüneisen coefficient proposed by Anderson has been applied in geophysics and in the calculation of the iron’s meling curve and the results shows that it is a good method. According to the effective Grüneisen coefficient conception and basing on the three term equation of state, we derived the effective Grüneisen equation of state. As an evolution, a new method to calculate shock temperature was proposed, the calculated results with some metals agree with experimental data well.
(2) Proposing a melting criterion constraint with 0K equation of state. This melting criterion can picture the high pressure melting curve of metal. Its physical mechanism was givn in the thesis by theoretical analysis and comparing molecular dynamics simulation. It has the same physical meaning as Lindemann melting criterion and the melting criterion given by mean field approach in some conditions.
(3) All the proposed high pressure and high temperature constitutive equations have a same limitation, i.e. they can not give the correct behavior of shear modulus in the solid-liquid mixing phase. By introducing the internal energy as power weight, we built a constitutive equation up to liquidus and which has no such a limition. With it, the shear modulus of aluminum along Hugoniot path was calculated, the results agreed experimental data and showed that the chang of shear modulus can be divided into three stages, that is, work hardening, temperature softening and melting.
(4) Discussing and analyzing the behavior of shear modulus in solid liquid mixing phase region with Percolation and Renormalized Group. The propagating process of sound in the melting material was analysed with Huygens principle. Then the critical melting mass function was calculated by using percolation and the results were that, at the critical melting mass function 0.313, a percolating liquid region appeared in the melting material, which was just corresponding to the turning point of longitudinal to bulk sound velocity; when melting mass fuction was larger than 0.687, there would be no percolation solid region in the material and this meaned that the shear modulus equaled zero. The analyzing results with percolation also indicated that the method, which was used to determine the shock induced melting region with sound velocities in shock compression experiment, had errors. By analyzing the constitution of liquid and solid of material in melting region along shearing plane, the behavior of shear modulus in melting region is predicted by renormalization group theory and is coincidence with that given by percolation theory.
(5) Taking the completing point of shock induced melting region as referring point, the problem, which has been puzzling for a long time, was solved by Huang Haijun. But at the initial point of shock induced melting region, how to modify the shock temperature to the equilibrium melting temperature still is not solved. Using the calculated critical melting mass function and basing the superheating model proposed by Luo et al, we amend the shock temperatue of iron at the initial point of shock induced melting region. The amended equilibrium melting temperature, together with the calculated result by Huang Haijun, the Ma’s and Shen’s static experimental data, is on the same Lindemann melting curve.
(6) With the SC experimental means and optical analyzing method, we measured the interfacial temperatures of Ly12Al/LiF around the pressure 100GPa. These interfacial temperature can thought as melting temperature by considering the gap effection.
引文
[1] 霍裕平. 物理学学科发展战略.见:科学走向新世纪. 北京:科学出版社,2001.17
[2] Turnbull D,Research and Applications. In :Seitz F,and Turnbull D ed.Solid State Physics,v.2.:Academic, New York, 1956. 226
[3] Ubbelhode A R.Melting and Crystal Structure, Oxford: Clarendon, 1965.
[4] Lindemann F A.Uber die Berechnumg molekularer.Physikalisches Zeitsch, 1910, 11: 609~612
[5] Gilvarry J J.The Lindemann and Grüneisen laws.Phys Rev, 1956, 102: 308~316
[6] Gilvarry J J.Grüneisen’s laws and the fusion curve at high pressure.Phys Rev, 1956, 102: 317~325
[7] Gilvarry J J.Equation of the fusion curve.Phys Rev, 1956, 102: 325~331
[8] Ziman J M.Priciples of the Theory of Solids.Cambidge: Cambridge University Press, 1965.
[9] Gilvarry J J.Lindemann and Grüneisen laws and a melting law at high pressures.Phys Rev , 1966, 16: 1089~1091
[10] Vaidya S N,and Gopal E S R.Melting law at high pressures.Phys Rev Lett, 1966, 17: 635~636
[11] Ross M.Generalized Lindemann melting law.Phys Rev, 1969, 184: 233~242
[12] Stacey F D,and Irvine R D.Theory of melting: Thermodynamics basis of Lindemann law.Aust J Phys, 1977, 30: 631~640
[13] Martin C J,O’Connor D A.An experimental test of Lindemann law. J Phys C, 1977, 10: 3521~3526
[14] Wolf G H, Jeanloz R.Lindemann melting law: Anharmonic correction and test of its validity for minerals.J Geophys Res, 1984, 89: 7821~7835
[15] Mulargia F,Quareni F.Validity of the Sutherland-Lindemann law and melting temperatures in the Earth’s interior.Geophys J,1988, 92: 269~282
[16] Stern E A,Zhang K.Local premelting about impurities.Phys Rev Lett, 1988, 60: 1872~1875
[17] Poirier J P.Lindemann law and the melting temperature of perovskites.Phys. Earth Planet Interiors, 1989, 54: 364~369
[18] Fang Z H.Pressure dependence of the melting temperature of rare-gas solids.J Phys Condens Matter, 1996, 8: 7067~7071
[19] Liu P C,Okamoto P R,Zaluzec N J, Meshii M.Boron-implantation-induced crystalline-to-amprphous transition in nickel: An experimental assessment of the generalized Lindemann melting criterion.Phys Rev B, 1999, 60(2): 800~814
[20] Luo S N, Strachan A, Swift D C.Vibrational density of states and Lindemannmelting law.J. Chem. Phys., 2005, 122: 194709
[21] Kechin V V.Melting curve equations at high pressure. Phys Rev B, 2001, 65: 052102
[22] Wang Y, Ahuja R, Johansson B.Melting of iron and other metals at earth’s core conditions A simplified computational approach.Phys Rev B, 2001, 65: 014104
[23] Born M,Huang K.Dynamical Theory of Crystal Lattice.Clarendon: Oxford, 1954.
[24] Jin Z H, Gumbsch P, Lu K, et al.Melting mechanisms at the limit of superheating.Phys Rev Lett, 2001, 87(5): 055703
[25] Cotterill R M J.Dislocation like Structures in a Simulated Liquid.Phys Rev Lett, 1979, 42:1541
[26] Janke W. Models of defect-mediated melting.Int J Theor Phys, 1990, 29: 1251
[27] Crawford R K.Neutron scattering from solid-rubidium near the solid-liquid transition.Bull Am Phys Soc, 1979, 24: 385; Cotterill R M J, Kristensen J K.A transmission electron microscopy investigation of the melting transition.Philos Mag, 1977, 36: 453
[28] Mizushima S.Dislocation model of liquid structure.J Phys Soc Jpn, 1960, 15: 70
[29] Ookawa A.A model theory of liquid.J Phys Soc Jpn, 1960, 15: 2191
[30] Poirier J P.Dislocation-mediated melting of iron and the temperature of the Earth’s core.Geophys J R Astr Soc,1986, 85: 315~328
[31] Ninomiya T. Theory of melting: Dislocation model.J Phys Soc Jpn, 1978, 44: 263~271
[32] Burakovsky L, Preston D L, Silbar R R.Melting as a dislocation-mediated phase transition. Phys Rev B, 2000, 61: 15011
[33] Jayaraman A.Diamond anvil cell and high-pressure physical investigations.Rev Mod Phys, 1983, 55: 65~110
[34] Mao H K, Bell P M, Shaner J W, et al. Specific volume measurements of Cu, Mo, Pd, and Ag and calibration of the ruby R1 fluorescence pressure gauge from 0.06 to 1 Mbar.J Appl Phys, 1978, 49: 3276~3283
[35] Chijikoe A D, Nellis W J, Soldatov A, et al.The ruby pressure standard to 150 GPa.J Appl Phys, 2005, 98: 114905
[36] Heinz D L, Jeanoz R.Temperature measurements in the laser-heated diamond anvil cell.In: Manghnani M H, Syono Y, ed. High-Pressure Research in Mineral Physics: TERAPUB, Tokyo/American Geophysical Union, Washington,D. C., 1971.113~127
[37] Shen G, Rivers M L, Wang Y,et al.Laser heated diamond cell system at the advanced photon source for in situ x-ray measurements at high pressure and temperature.Rev Sci Instrum, 2001, 72: 1273~1282
[38] Boehler R.Temperature in the earth’s score from melting-point measurements of iron at high static pressures.Nature, 1993, 363: 534
[39] Saxena S K, Shen G, Lazor P.Experimental evidence for a new iron phase and implications for earth’s core.Science, 1993, 260: 1312
[40] Boehler R, Ross M.Melting curve of aluminum in a diamond cell to 0.8 Mbar implications for iron.Earth Planet Sci Lett, 1997, 153: 223
[41] Errandonea D, Somayazulu M, Hausermann D, et al.Melting of tantalum at high pressure determined by angle dispersive x-ray diffraction in a double-sided laser-heated diamond-anvil cell.J Phys: Condens Matter, 2003, 15: 7635~7649
[42] Errandonea D, Schwager B, et al.Systematics of transition-metal melting.Phys Rev B, 2001, 63: 132104
[43] Errandonea D, Boehler R, Ross M.Melting of the alkaline-earth metals to 80 GPa.Phys Rev B, 2001, 65: 012108
[44] Shen G, Lazor P, Saxena S K.Melting of wustite and iron up to pressures of 600kbar.Phys Chem Minerals, 1993, 20: 91
[45] Shen G, Mao H K, Hemley R J, et al. Melting and crystal structure of iron at high pressures and temperatures.Geophys Res Lett, 1998, 25: 373
[46] 经福谦.实验物态方程导引.第二版. 北京:科学出版社, 1999.
[47] 王礼立.应力波基础.北京:国防工业出版社, 1985.
[48] Johnson J N, Cheret R . Shock waves in solids an evolutionary perspective.Shock Waves, 1999, 9: 193-200
[49] Huser G, Koenig M, et al. Temperature and melting of laser-shocked iron releasing into an LiF window.Physics of plasmas, 2005, 12: 060701
[50] Baumung K, Kanel G I, et al.Shock-melting pressures from no-planar impacts.Int J Impact Engng, 1997, 20: 101-110
[51] Duvall G E, Graham R A.Phase transitions under shock-wave loading. Rev Mod Phys, 1977, 49(3): 523
[52] 唐志平.冲击相变基础.合肥:中国科学技术大学,1992.
[53] Fritz J N, Morgan J A.An Electromagnetic Technique for Measuring Material Velocity.Rev Sci Instrum, 1973, 44: 215~221
[54] Rosenberg Z, Brar N S.Measuring sound velocities along release adiabats with Manganin stress gauges.Rev Sci Instrum, 1988, 59: 991-993
[55] McQueen R G, Hopson J W, Fritz J N.Optical technique for determing rarefaction wave velocities at very high pressure.Rev Sci Instrum, 1982, 53: 245~250
[56] Duffy T S, Ahrens T J.Sound velocity at high pressure and their geophysical implication.J Geophys Res, 1992, 97: 4503~4520
[57] Tan H, Dai C D, Zhang L Y, et al.Method to determine the melting temperatures of metals under megabar shock pressures.Appl Phys Lett, 2005, 87: 221905
[58] Tan H, Ahrens T J.Shock temperature measurements for metals.High Press Res, 1990, 2: 159
[59] 谭华.金属冲击温度测量(II).高压物理学报,1996, 10:161
[60] Tang W H, Jing F Q, Zhang R Q, et al.Thermal relaxation phenomena across the metalwindow interface and its significance to shock temperature measurements of metals.J Appl Phys, 1996, 80: 3248
[61] Tang W H, Zhang R Q, Jing F Q, et al.Theoretical investigation of the apparent spectral radiancwindow interface in shock temperature experiments.J Appl Phys, 1998, 83: 2469
[62] 汤文辉.金属冲击温度测量的理论和实验研究:博士学位论文.长沙:国防科技大学,1995.
[63] Allen M P, Tildesley D J.Computer simulation of liquids.Oxford: Clarendon, 1987.
[64] Frenkel D, Smit B.Understanding Molecular Simulation-From Algorithms to Applications.San Diego, CA: Academic, 1996.
[65] Alder B J, Wainwright T E.Phase Transition for a Hard Sphere System.J Chem Phys, 1957, 27: 1208
[66] Belongoshko A B, Ahuja R, Johansson B.Quasi–Ab Initio Molecular Dynamic Study of Fe Melting.Phys Rev Lett, 2000, 84: 3638
[67] Morris J R, Wang C Z, Ho K M.Melting line of aluminum from simulations of coexisting phases.Phys Rev B, 1994, 49: 3109
[68] Moriarty J A, Young D A, Ross M.Theoretical study of the aluminum melting curve to very high pressure.Phys Rev B, 1984, 30: 578
[69] Mei J,Davenport J W.Free-energy calculations and the melting point of Al.Phys Rev B, 1992, 46: 21
[70] Straub G K, Aidun J B, Willis J M, et al. Ab initio calculation of melting andthermodynamic properties of crystal and liquid aluminum.Phys Rev B, 1994, 50: 5055
[71] Belonoshko A B, Ahuja R.Embedded-atom molecular dynamic study of iron melting.Phys Earth Planet Inter, 1997, 102: 171~184
[72] Belonoshko A B, Ahuja R et al.Quasi ab initio molecular dynamic study of Cu melting.Phys Rev B, 2000, 61: 3838
[73] Moriarty J A, Belak J F, et al. Quantum-based atomisticsimulation of materials properties in transition metals.J Phys Condens Matter, 2002, 14: 2825
[74] Alfe D, Gillan M J, Price G D.The melting curve of iron at the pressures of the Earth’s core from ab initio calculation.Nature, 1999, 401: 462
[75] Fan W, Gong X G.Superheated melting of grain boundaries.Phys Rev B, 2005, 72: 064121
[1] 汪志诚.热力学统计物理.第二版.北京:高等教育出版社,1993.
[2] Grüneisen E. Theorie des festen Zustandes einatomiger Element.Ann Physik, 1992, 12: 257
[3] Knopoff L, Shapiro J N.Comments on the interrelationships between Grüneisen’s parameter and shock and isothermal equations of state.J Geophys Res.1969, 74: 1439
[4] Poirier J P.Introduction to the Physics of the Earth’s Interior.secondedition.New York: Cambridge University Press, 2000.
[5] Porter L J, Justo J F, Yip S.The importance of Grüneisen parameters in developing interatomic potentials.J Appl Phys,1997, 82: 5378
[6] Anderson O L.The Grüneisen ratio for the last 30 years.Geophys. J Int,2000, 143: 279
[7] Stacey F D.A thermal model of the earth.Phys Earth Planet Inter.1977, 15: 341
[8] Stacey F D.Applications of thermodynamics to fundamental Earth physics.J Geophys Surveys,1977, 3: 175
[9] Vaschenko V Y, Zubarev V N.Concerning the Grüneisen constant.Soviet Phys. Solid State.1963, 5: 653～655
[10] Knopoff L, Shapiro J N.Comments on the interrelationships between Grüneisen’s parameter and shock and isothermal equations of state.J Geophys. Res,1969, 74: 1439～1450
[11] Quareni F, Mulargia F.The validity of the common approximate expressions for Grüneisen parameter.Geophys J.1988, 93: 505～519
[12] Irvine R D, Stacey F D.Pressure dependence of the thermal Grüneisen parameter, with application to the Earth’s lower mantle and outer core.Phys Earth Planet Inte..1975, 11:157～165
[13] Dugdale J S, Macdonald D K C.Thermal expansion of solids.Phys Rev,1953, 89: 832～834
[14] Gilvarry J J.Grüneisen parameter for a solid under finite strain.Phys Rev.1956, 102: 331～340
[15] Migault A.Le Journal de Physique.1971, 32: 437; ibid..1972, 33: 707
[16] 张万箱.固体的特征频率及 Grüneisen 系数的普遍表达式. 物理学报,1984, 33: 1120～1128
[17] Barton M A, Stacey F D.The Grüneisen parameter at high pressure: a molecular dynamical study.Phys Earth Planet Inter.1985, 39: 167～177
[18] Stacey F D.Theory of thermal and elastic properties of the lower mantle and core.Phys Earth Plane. Inte..1995, 89: 219～245
[19] Stacey F D.Thermoelasticity of (Mg, Fe)SiO3 perovskite and a comparison with the lower mantle.Phys Earth Planet Inter.1996, 98: 65～77
[20] Stacey F D.Equation-of-state for close-packed materials at high pressures: geophysical evidence.J Phys Condens Matter,1999, 11: 575～582
[21] Anderson O L.Equation for thermal expansivity in planetary interiors.J Geophys Res,1967, 72: 3661～3668
[22] Anderson O L.Evidence supporting the approximation γρ=const for Grüneisen parameter of the Earth’s lower mantle.J Geophys Res,1979, 84: 3537～3542
[23] Birch F.Thermal expansion at high pressure.J Geophys Res.1968, 73: 817～819
[24] Brennan B J, Stacey F D.A thermodynamically based equation of state for the lower mantle.J Geophys Res,1979, 84: 5535～5539
[25] Steinberg D J.The temperature independence of Grüneisen’s gamma at high temperature.J Appl Phys,1981, 52: 6415～6417
[26] Anderson O L.The power balance at the core-mantle boundary.Phys Earth Planet Inter.2002, 131: 1～17
[27] Huang H J, Jing F Q, Cai L C, et al.Grüneisen parameter along Hugoniot and melting temperature of ε -iron: a thermodynamic computational method.Chin Phys Let, 2005, 22: 836
[28] 谭华.金属的冲击温度测量(Ⅰ)—高温计的标定和界面温度的确定.高压物理学报, 1994,8(4):254～263
[29] 谭华.金属的冲击温度测量 ( Ⅱ ) —界面卸载近似.高压物理学报,1996,10(3):161～169
[30] 谭华.金属的冲击温度测量(Ⅲ)—“基板/样品”界面间隙对辐射法测量冲击波温度的影响.高压物理学报,1999,13(3):161～168
[31] 谭华, 戴诚达.金属的冲击温度测量(Ⅳ)—“三层介质模型”及其应用.高压物理学报.2000, 14 (2):81～91
[32] 汤文辉.金属冲击温度测量的理论和实验研究:博士学位论文.长沙: 国防科技大学,1995.
[33] 汤文辉,张若棋,胡金彪,经福谦.冲击温度的近似计算方法.力学进展.1998,27(4):479～487.
[34] Walsh J M, Rice M H, McQueen R G, and Yarger F L.Shock-Wave Compressions of Twenty-Seven Metals.Equations of State of Metals.Phys Rev .1957, 108: 196
[35] Tang W H, Jing F Q, Hu J B, et al.New method for determining the shock temperature of metals.Chin. Phys. Lett.1994, 11(9): 569～572
[36] 经福谦.实验物态方程导引.第二版.北京:科学出版社, 1999.
[37] 特鲁宁等.高温高压下凝聚物质的性质.韩钧万译.绵阳: 流体物理研究所, 1996, 40～52
[38] Nellis W J, Mitchell A C, Young D A.Equation-of-state measurements for aluminum, copper, and tantalum in the pressure range 80-440GPa (0.8-4.4Mbar).J Appl Phys, 2003, 93(1): 304～310
[39] Brown J M, McQueen R G.Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa.J. Geophys. Res, 1986,91: 7485～7494
[40] McQueen R G, Marsh S P, eds: et al.In:Kinslow R, ed.High velocity impact phenomena.New York and London: Academic Press, 1970.
[41] Yoo C S, Holmes N. C., and Ross M, et al.Shock temperature and melting of iron at earth core conditions.Phys Rev Lett, 1993, 70: 3931～3934
[42] Williams Q, Jeanloz R, and Bass J. et al.The melting curve of iron to 250 GPa: a constraint on temperature at earth’s center.Science, 1987, 236: 181～183
[43] Hixson R. S., Fritz J. N.Shock compression of tunsten and molybdenum.J Appl Phys, 1991, 71:1721
[44] Marsh S. P.Los Alamos Shock Hugoniot Data.Berkerley: University of California Press,1979.
[45] Gschneidner K A.Physical Properties and Interrelationships of Metallic and Semimetallic Elements.In: Seitz F, and Turnbull D, ed.Solid State Physics, V.16.:New York&London: Academic Press, 1965: 275～426
[46] Brown J M, McQueen R G.Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa.J Geophys Res, 1986,91: 7485～7494
[47] 徐锡申, 张万箱等.实用物态方程理论导引.北京: 科学出版社, 1986.
[1] Glazov V M, Chizhevskaya S N, Glagoleva N N, Liquid semiconductors, ch. 3., New York: Plenum Press, 1969.
[2] Faber T E.Theory of liquid metals. Cambridege:Cambridge University Press.1972.81
[3] Martin C J, and O’Connor D. A.An experimental test of Lindemann law.J Phys C, 1977, 10: 3521~3526
[4] Wallace D C.Melting of elements.Proc R Soc Lond A, 1991,433: 631~661
[5] 杜宜瑾.凝聚态物理研究.合肥:安徽大学出版社.1998.
[6] Thiel M V, Ree F H.In: Schmidt S C, Dick R D, Forbes J W, et al, ed. shock compression of condensed matter-1991,New York: Elsevier Science Publishers B V,1992.165
[7] Wang Y, Ahuja R, Johansson B.Melting of iron and other metals at earth’s core conditions:A simplified computational approach.Phys Rev B, 2001,65: 014104
[8] Asay J R, Chhabildas L C, Dandekar D P.Shear strength of shock-loadedpolycrystalline tungsten.J Appl Phys, 1980, 51: 4774
[9] Vogler T J, Reinhart W D, Chhabildas L C.Dynamic behavior of boron carbide.J Appl Phys, 2004, 95: 4173
[10] Huang H, Asay J R.Compressive strength measurements in aluminum for shock compression over the stress range of 4-22 GPa.J Appl Phys, 2005, 98: 033524
[11] Rose J H, Smith J R, Guinea F, et al.Universal features of the equation of state of metals.Phys Rev B,1984, 29: 2963
[12] Vinet P, Ferrante J, Smith J R, Rose J H.A universal equation of state for solids.J Phys C: Solid State Phys, 1986, 19: L467
[13] Bose R S, Bose R P.An equation of state applied to solid up to 1 TPa.JPhys: Condens Matter, 1999, 11: 10375
[14] Bose R P, Bose R S.Applicability of three-parameter equation of state of solids: compatibility withfirst principles approaches and application to solids.J Phys: Condens Matter, 2003, 15: 1643
[15] 冉宪文, 汤文辉.一种计算固体冷能冷压和结合能的新方法.高压物理学报, 2003, 17(1): 50～55
[16] Sun J X, Wu Q, Cai L C, et al.Two universal equations of state for solids satisfying the limiting condition at high pressure.J Phys Chem Solids, 2005, 66: 773
[17] Sun J X.A modified Lennard-Jones-type equation of state for solids strictly satisfying the spinodal condition.J Phys: Condens Matter, 2005, 17: L103
[18] Renero C, Prieto F E, Icaza M.Comparison of two universal equation of state for solids.J Phys: Condens Matter,1990, 2: 295～300
[19] Bose R P, Bose R S.Applicability of isothermal three-parameter equations of state of solids—a reappraisal.J Phys: Condens Matter, 2005, 17: 6193
[20] 吴强.金属材料高压物态方程及 Grüneisen 系数的研究:博士学位论文.四川绵阳:中国工程物理研究院,2004.
[21] 胡金彪, 经福谦.利用冲击压缩数据计算材料物态方程的一个简便解析方法.高压物理学报, 1990, 4(3): 175～180
[22] Wang Y, Chen D Q, Zhang X W.Calculated Equation of State of Al, Cu, Ta, Mo, and W to 1000 GPa.Phys Rev Lett, 2000, 84: 3220
[23] Cynn H, Yoo C S.Equation of state of tantalum to 174 GPa.Phys Rev B, 1999, 59: 8526
[24] Hanstrom A, Lazor P . High pressure melting and equation of state ofaluminum.Journal of Alloys and Compounds, 2000, 305:209～215
[25] Boehler R, Ross M.Melting curve of aluminum in a diamond cell to 0.8 Mbar: implications for iron.Earth and Planetary Science Letters, 1997, 153:223～227
[26] Shaner J W, Brown J M, McQueen R G.Melting of Metals above 100GPa.In:MacCrone R K, Whalley E, ed.High Pressure in Science and Technology:North Holland, 1984.137
[27] Belonoshho A B, Ahuja R, Eriksson O, et al.Quasi ab initio molecular dynamics study of Cu melting.Phys Rev B, 2000, 61: 3838~3844
[28] Moriarty J A.High-Pressure ion-thermal properties of metals from ab initio interatomic potentials . In: Gupta Y M, ed . shock waves in condensed matter-1985, New York: Plenum Publishing Company, 1986.101-106
[29] 张凌云.无氧铜冲击熔化特性实验研究:硕士学位论文.四川绵阳:中国工程物理研究院,2004.
[30] Alfe D, Gillan M J, Price G D.The melting curve of iron at the pressures of the earth’s core from ab initio calculations.Nature, 1999, 401: 462
[31] Ma Y Z, Maddury S M, Shen G, et al.In situ X-ray diffraction studies of iron to earth-core conditions.Phys Earth Planet Inter, 2004, 143: 455~467
[32] Shen G, Mao H K, Hemley R J.Melting and crystal structure of iron at high pressures and temperatures.Geophys Res Lett, 1998, 25: 373~376
[33] Errandonea D, Schwager B, et al. Systematics of transition-metal melting.Phys Rev B, 2001, 63: 132104
[34] Moriarty J A.Angular forces and melting in bcc transition metals: A case study of molybdenum.Phys Rev B, 1994, 49:12413
[35] Belonoshko A B, Simak S I, Kochetov A E.High Pressure Melting of Molybdenum.Phys Rev Lett, 2004, 92:195701
[36] Hixson R S, Boness D A, Shaner J W.Acoustic Velocities and Phase Transitions in Molybdenum under Strong Shock Compression.Phys Rev Lett,1989, 62: 637
[37] Errandonea D, Somayazulu M, Hausermann D, et al.Melting of tantalum at high pressure determined by angle dispersive x-ray diffraction in a double-sided laser-heated diamond-anvil cell.J Phys: Condens Matter, 2003, 15: 7635～7649
[38] Fateeva N S, Vereshchagin L F.Sov Phys, 1971, 16: 322
[39] Moriarty J A, Belak J F, Rudd R E, et al.Quantum-based atomistic simulation of materials properties in transition metals.J Phys:Condens Matter, 2002, 14: 2825
[40] McQueen R G, Fritz J N, and Morris C E.the Velocity of Sound Behind StrongShock Waves in 2024 Al.In: Asay J R, Graham R A, Straub G K, ed.Shock Waves in Condensed Matter-1983, Amsterdam: North Holland Physics Publishing, 1984.95～98
[41] Hayes D, Hixson R S, McQueen R G.High Pressure Elastic Properties, Solid-Liquid Phase Boundary and Liquid Equation of State from Release Wave Measurements in Shock-Loaded Copper.In: Furnish M D, Chhabildas L C, Hixson R S, ed.Shock Compression of Condensed Matter-1999, NewYork: American Institute of Physics.2000.483～488
[42] Nguyen J H, Holmes N C.Melting of iron at the physical conditions of the Earth’s core.Nature, 2004, 427: 339～342
[43] Brown J M, Shaner J W.Rarefaction Velocities in Shocked Tantalum and The High Pressure Melting Point.In: Asay J R, Graham R A, Straub G K,ed.Shock Waves in Condensed Matter-1983, Amsterdam: North Holland Physics Publishing, 1984.91～94,
[44] Marsh S P.Los Alamos Shock Hugoniot Data.Berkerley: University of California Press.1979.
[45] Gschneidner K A.Physical Properties and Interrelationships of Metallic and Semimetallic Elements.In:Seitz F, Turnbull D, ed.Solid State Physics, Vol 16, New York&London: Academic Press, 1965.275～426
[46] Brown J M, McQueen R G.Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa.J Geophys Res, 1986, 91: 7485～7494
[47] 徐锡申, 张万箱等.实用物态方程理论导引.北京: 科学出版社, 1986.
[48] Burakovsky L, and Preston D L.Analytic model of the Grüneisen parameter all densities.J Phys Chem Solids, 2004, 65: 1581～1587
[1] Asay J R, and Chhabildas L C.Shear strength of shock-loaded polycrystalline tungsten.J Appl Phys,1980,51:4774
[2] Ross W C.The effect of material strength on determining pressures “on” and “off” the Hugoniot.J Appl Phys,1984,55:2741
[3] Johnson J N, Hixson R S, Gray G T.Quasielastic release in shock-compressed solids.J Appl Phys,1992,72: 429
[4] 华劲松. 高温高压下钨合金的本构方程研究:博士学位论文.四川绵阳: 中国工程物理研究院, 1999.
[5] 彭建祥, 经福谦, 王礼立等.冲击压缩下铝、铜、钨的剪切模量和屈服强度与压力和温度的相关性.物理学报,2005,54(5): 2194～2197
[6] Peng J. X., Jing F. Q., Wang L. L., et al.Pressure and temperature dependence of shear modulus and yield strength for aluminum, copper, and tungsten under shock compression.J Appl Phys, 2005, 98: 013508
[7] Birch F . Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressure and 300K.J Geophys Res, 1978, 83: 1257
[8] Duffy T S, Ahrens T J.Sound velocities at high pressure and temperature and their geophysical implications.J Geophys Res, 1992, 97(B4): 4503～4520
[9] Steinberg D J, Cochran S G, Guinan M W.A constitutive model for metals applicable for high-strain rate.J Appl Phys, 1980, 51(3): 1498
[10] Guinan M.Steinberg D.A simple approach to extrapolating measured polycrystalline shear moduli to very high pressure.J Phys Chem Solids, 1975, 36: 829
[11] 李茂生, 陈栋泉.高温高压下材料的本构模型.高压物理学报, 2001, 15(1): 24～31
[12] Burakovsky L, Preston D L, Silbar R R.Melting as a dislocation-mediated phase transition.Phys Rev B, 2000, 61: 15011
[13] Burakovsky L, Preston D L.Analytic model of the Grüneisen parameter all densities.J Phys Chem Solids, 2004, 65: 1581～1587
[14] Burakovsky L.Preston D L, Wang Y.Cold shear modulus and Grüneisen parameter at all densities.Solid State Commun, 2004, 132: 151
[15] Burakovsky L, Greeff C W, Preston D L.Analytic model of the shear modulus at all temperatures and densities.Phys Rev B, 2003, 67: 094107
[16] Burakovsky L, Preston D L.Generalized Guinan-Steinberg formula for the shear modulus at all pressures.Phys Rev B, 2005, 71:184118
[17] Asay J R, Chhabildas L C.Determination of the shear strength of shockcompressed 6061-T6 aluminum.In:Meyers M. A., and Murr L. E., ed.shock waves and high-strain-rate phenomena in metals:Plenum Press, 1981.417
[18] Asay J R, Chhabildas L C, et al. High pressure strength of shocked aluminum. In: Shock waves in condensed matter-1985 : Plenum press, 1986.145
[19] McQueen R G, Fritz J N, Morris C E. The velocity of sound behind strong shock waves in 2024 Al.In:Asay J R, Graham R A and Straub G K,ed.Shock Waves in Condensed Matter-1983. New York & Amsterdam: Elsevier, 1984.95～98
[20] Yu Y Y, Tan H, Dai C D, et al.Sound velocity and release behavior of shock-compressed Ly12Al.Chin Phys Lett, 2005, 22(7): 1742
[21] Duffy T S, Ahrens T J.Hugoniot sound velocities in metals with applications to the earth’s inner core.In:Syono Y., and Manghnani M. H., ed.High-Pressure Research: Application to Earth and Planetary Sciences, Tokyo: Terra Scientific Publication Company, 1992.353
[22] McQueen R G, Marsh S P, Fritz J. N.Hugoniot equation of state of twelve rocks.J Geophys Res, 1967, 72: 4999～5035
[23] 谭华.实验冲击波物理导引.四川绵阳: 中国工程物理研究院研究生部, 2006.
[24] 王贵朝.高压下一种弹性声速的经验表达式.高压物理学报, 1988, 2(1): 92～95
[25] Brown J M, Shaner J W.Rarefaction Velocities in Shocked Tantalum and The High Pressure Melting Point.In:Asay J R, Graham R A and Straub G K.,ed. Shock Waves in Condensed Matter-1983, Amsterdam: North Holland Physics Publishing, 1984. 91～94
[26] Hayes D, Hixson R S, McQueen R G.High Pressure Elastic Properties, Solid-Liquid Phase Boundary and Liquid Equation of State from Release Wave Measurements in Shock-Loaded Copper.In:Furnish M D, Chhabildas L C, and Hixson R S, ed.Shock Compression of Condensed Matter-1999, NewYork: American Institute of Physics, 2000.483～488
[27] McQueen R G, Hopson J W, Fritz J N.Optical technique for determing rarefaction wave velocities at very high pressure.Rev Sci Instrum, 1982, 53: 245～250
[28] Marsh S P.Los Alamos Shock Hugoniot Data.Berkerley: University ofCalifornia Press, 1979.
[29] Gschneidner K A.Physical Properties and Interrelationships of Metallic and Semimetallic Elements.In:Seitz F., and Turnbull D.,ed. Solid State Physics, v.16, New York&London: Academic Press, 1965.275～426
[30] 徐锡申, 张万箱等.实用物态方程理论导引.北京: 科学出版社, 1986.
[1] Dietrich Stauffer.Introduction of Percolation Theory.Taylor & Francis, London and Philadelphis, 1985;Geoffrey R. Grimmett.Percolation and Disordered Systems . Cambridge : Statistical Laboratory University of Cambridge, 1996.
[2] 李茂生, 陈栋泉.高温高压下材料的本构模型.高压物理学报.2001, 15(1): 24～31
[3] Hayes D, Hixson R S, McQueen R G.High Pressure Elastic Properties, Solid-Liquid Phase Boundary and Liquid Equation of State from Release Wave Measurements in Shock-Loaded Copper.In: Furnish M D, Chhabildas L C, Hixson R S, ed.Shock Compression of Condensed Matter-1999, NewYork: American Institute of Physics, 2000.483～488
[4] McQueen R G, Fritz J N, Morris C E.The velocity of sound behind strong shock waves in 2024 Al.In: Asay J R, Graham R A and Straub G K, ed.Shock Waves in Condensed Matter-1983 , New York: Amsterdam: Elsevier, 1984.95～98
[5] Brown J M, Shaner J W.Rarefaction Velocities in Shocked Tantalum and The High Pressure Melting Point.In: Asay J R, Graham R A and Straub G K, ed.Shock Waves in Condensed Matter-1983, Amsterdam: North Holland Physics Publishing, 1984.91～94
[6] McQueen R G, Hopson J W, Fritz J N.Optical technique for determing rarefaction wave velocities at very high pressure.Rev Sci Instrum.1982.53: 245～250
[7] Duffy T S, Ahrens T J.Sound velocity at high pressure and their geophysical implication.J Geophys Res.1992.97: 4503～4520
[8] 冉宪文 , 汤文辉.描述混合物固液相变的两个模型.高压物理学报.2003.17(3): 220～225
[9] Shaner J W, Brown J M, McQueen R G.Melting of Metals above 100GPa.In: MacCrone R K, Whalley E, ed.High Pressure in Science and Technology,North Holland, 1984.137
[10] Hanstrom A, Lazor P.High pressure melting and equation of state of aluminum.Journal of Alloys and Compounds.2000.305:209～215
[11] Boehler R, Ross M.Melting curve of aluminum in a diamond cell to 0.8 Mbar: implications for iron.Earth and Planetary Science Letters.1997.153:223~227
[12] Kanel G I, Baumung K, Singer J, et al.Dynamic strength of aluminum single crystals at melting. Appl Phys Lett, 2000, 72(22):3230
[13] Kanel G I, Razorenov S V, et al. Spall fracture properties of aluminum and magnesium at high temperatures. J Appl Phys, 1996, 79(11):8310
[14] Razorenov S V, Savinykh A S, Kanel G I, et al.Sub-microsecond yield and tensile strengths of metals and alloys at elevated temperatures.In: Furnish M D, Gupta Y M, Forbes J W, ed.NewYorK: American institute of physics, Shock Compression of Condensed Matter-2003, 2004.491
[15] Kanel G I, Razorenov S V, Fortov V E.Shock-wave compression and tension of solids at elevated temperatures: superheated crystal status, pre-melting, and anomalous growth of the yield strength. J Phys Condens Matter, 2004, 16: s1007～s1016
[16] Wilson K G.The renormalization group and critical phenomena.Rev Mod Phys, 1983, 55(3): 583～600
[17] 冯端.金属物理学(第二卷 相变).北京:科学出版社,1990.360
[18] 孙霞, 吴自勤, 黄畇.分形原理及其应用.合肥: 中国科技大学出版社, 2003.156
[19] Cardy J.Scaling and Renormalization in Statistical Physics.Cambridge: Cambridge University Press, 1996.
[20] Chowdhury D, Stauffer D . Principles of Equilibrium Statistical Mechanics.Weiheim: Wiley-VCH, 2000.
[21] Kadanoff L . Statistical Physics, Statics, Dynamics and Renormalization.Singapore: World Scientific, 2000.
[22] Brown J M, McQueen R G. Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77GPa and 400GPa.J Geophys Res, 1986.91:7485～7494
[23] Williams Q, Jeanloz R, Bass J, et al.The melting curve of iron to 250 GPa: a constraint on temperature at earth’s center.Science,1987, 236:181～183
[24] Boehler R.Temperature in the earth’s core from melting point measurements ofiron at high static pressures.Nature, 1993, 363: 534～536
[25] Yoo C S, Akella J, Campbell A J,et al.The phase diagram of iron by in situ x-ray diffraction: Implications for Earth’s core.Science, 1995, 270: 1473～1475
[26] Shen G, Hu J, Hemley R J, et al.High P-T phase diagram and equation of state of iron.Eos Trans.AGU, 77(46), Fall Meet. Suppl., 1996.F696,
[27] Bass J D, Svendson B, Ahrens T.The temperature of shock compressed iron.In: Manghnani M H, Syono Y,eds, High Pressure Reseach in Mineral Physics, v. 39. Geophysical Monograph Ser. 39, Washington, D. C: 1987. American Geophysical Union, 393~492.
[28] Yoo C S, Holmes N C, Ross M, et al. Shock temperatures and melting of iron at Earth core conditions. Phys Rev Lett, 1993. 70:3931-3934
[29] Anderson O L, Duba A. Experimental melting curve of iron revised, J Geophys Res 1997, 102: 22659-22669
[30] Laio A, Bernard S, Chiarotti G L, et al. Physics of iron at earth’s core conditions. Science, 2000, 287: 1027~1030
[31] Belonoshko A B, Ahujia R.Embedded-atom molecular dynamic study of iron melting.Phys Earth Plnaet Inter, 1997, 84: 171-184
[32] Neumann G S, Stixrude L, Cohen R E et al. Elasticity of iron at the temperature of the earth’s inner core, Nature, 2001.413: 57-60
[33] Stixrude L, Wasserman E, Composition and temperature of the earth’s inner core. J Geophys Res, 1997, 102: 24729-24739
[34] Alfe D, Gillan M J, Price G D.Composition and temperature of the earth’s inner core constrained by combining ab initio calculation and seismic data.Earth Planet Sci Lett, 2002, 195: 91-98
[35] Shen G, Mao H K, Hemley R J, et al. Melting and crystal structure of iron at high pressures and temperatures. Geophys Res Lett,1998, 25: 373-376
[36] Ma Y Z, Somayazulu M, Shen G, et al, In situ X-ray diffraction studies of iron to earth-core conditions, Phys Earth Planet Inter, 2004, 143: 455-467
[37] Luo S N, Ahrens T J. Shock-induced superheating and melting curves of geophysically important mineral, Phys Earth Planet Inter, 2004, 143: 369-386
[38] Luo S N, Ahrens T J. Superheating systematics of crystalline solids, Appl Phys Lett, 2003, 82(12): 1836-1838
[39] Lu K, and Li Y. Homogeneous Nucleation Catastrophe as a Kinetic Stability Limit for Superheated Crystal. Phys Rev Lett, 1998, 80: 4474-4477
[40] Nguyen J H, Holmes N C. Melting of iron at the physical conditions of the Earth’s core. Nature, 2004, 427:339-342
[41] Huang H J, Jing F Q, Cai L C, et al. Grüneisen parameter along Hugoniot and Melting Temperature of ε-iron: A thermodynamic computational method. Chin. Phys. Lett, 2005, 22: 836
[42] 李西军. 铁的高压熔化线研究:博士学位论文. 绵阳: 中国工程物理研究院.
[43] Boehler R, Ross M. Melting curve of aluminum in a diamond cell to 0.8 Mbar: implications for iron. Earth and Planetary Science Letters, 1997, 153:223-227
[1] 谭华.金属的冲击温度测量(I)-高温计的标定和界面温度的确定.高压物理学报,1994,8(4): 254-263
[2] Grover R, Urtiew P A.Thermal Relaxation at interfaces following shock compression. J Appl Phys,1974,45: 146
[3] 汤文辉.金属冲击温度测量的理论和实验研究:博士学位论文.长沙: 国防科技大学研究生院, 1995.
[4] McQueen R G, Hopson J W, Fritz J N.Optical technique for determing rarefaction wave velocities at very high pressure.Rev Sci Instrum,1982,53:245-250
[5] Duffy T S, Ahrens T J.Sound velocity at high pressure and their geophysical implication.J Geophys Res,1992,97: 4503～4520
[6] McQueen R G, Fritz J N, Morris C E.The velocity of sound behind strong shock waves in 2024 Al.In:Asay J R, Graham R A and Straub G K,ed. Shock Waves in Condensed Matter-1983 , New York & Amsterdam: Elsevier, 1984.95～98
[7] Urtiew P A, Grover R.Temperature deposition caused by shock interactions with material interfaces. J Appl Phys,1974,45:140
[8] 许灿华.铁在冲击压缩下熔化温度的直接测量:硕士学位论文.四川绵阳: 中国工程物理研究院, 2004.
[9] Tan H, Dai C D, Zhang L Y, et al.Method to determine the melting temperatures of metals under megabar shock pressures.Appl Phys Lett,2005,87: 221905
[10] 俞宇寅.强冲击载荷作用下 Ly12 铝合金的准弹性卸载特性及层裂研究:博士学位论文.四川绵阳: 中国工程物理研究院, 2006.
[11] 冉宪文, 汤文辉.描述混合物固-液相变的两个模型.高压物理学报,2003,17(3):220~225
[12] Hanstrom A, Lazor P.High pressure melting and equation of state of aluminum.Journal of Alloys and Compounds,2000,305:209～215
[13] Boehler R, Ross M.Melting curve of aluminum in a diamond cell to 0.8 Mbar: implications for iron.Earth and Planetary Science Letters,1997,153:223～227
[14] Shaner J W, Brown J M,McQueen R G. Melting of Metals above 100GPa.In: MacCrone R K, Whalley E, ed.High Pressure in Science and Technology:North Holland, 1984.137
[15] Urtiew P A, Grover R. The melting temperature of magnesium under shock loading. J Appl Phys, 1977, 48(3): 1122-1126.
[2] Turnbull D,Research and Applications. In :Seitz F,and Turnbull D ed.Solid State Physics,v.2.:Academic, New York, 1956. 226
[3] Ubbelhode A R.Melting and Crystal Structure, Oxford: Clarendon, 1965.
[4] Lindemann F A.Uber die Berechnumg molekularer.Physikalisches Zeitsch, 1910, 11: 609~612
[5] Gilvarry J J.The Lindemann and Grüneisen laws.Phys Rev, 1956, 102: 308~316
[6] Gilvarry J J.Grüneisen’s laws and the fusion curve at high pressure.Phys Rev, 1956, 102: 317~325
[7] Gilvarry J J.Equation of the fusion curve.Phys Rev, 1956, 102: 325~331
[8] Ziman J M.Priciples of the Theory of Solids.Cambidge: Cambridge University Press, 1965.
[9] Gilvarry J J.Lindemann and Grüneisen laws and a melting law at high pressures.Phys Rev , 1966, 16: 1089~1091
[10] Vaidya S N,and Gopal E S R.Melting law at high pressures.Phys Rev Lett, 1966, 17: 635~636
[11] Ross M.Generalized Lindemann melting law.Phys Rev, 1969, 184: 233~242
[12] Stacey F D,and Irvine R D.Theory of melting: Thermodynamics basis of Lindemann law.Aust J Phys, 1977, 30: 631~640
[13] Martin C J,O’Connor D A.An experimental test of Lindemann law. J Phys C, 1977, 10: 3521~3526
[14] Wolf G H, Jeanloz R.Lindemann melting law: Anharmonic correction and test of its validity for minerals.J Geophys Res, 1984, 89: 7821~7835
[15] Mulargia F,Quareni F.Validity of the Sutherland-Lindemann law and melting temperatures in the Earth’s interior.Geophys J,1988, 92: 269~282
[16] Stern E A,Zhang K.Local premelting about impurities.Phys Rev Lett, 1988, 60: 1872~1875
[17] Poirier J P.Lindemann law and the melting temperature of perovskites.Phys. Earth Planet Interiors, 1989, 54: 364~369
[18] Fang Z H.Pressure dependence of the melting temperature of rare-gas solids.J Phys Condens Matter, 1996, 8: 7067~7071
[19] Liu P C,Okamoto P R,Zaluzec N J, Meshii M.Boron-implantation-induced crystalline-to-amprphous transition in nickel: An experimental assessment of the generalized Lindemann melting criterion.Phys Rev B, 1999, 60(2): 800~814
[20] Luo S N, Strachan A, Swift D C.Vibrational density of states and Lindemannmelting law.J. Chem. Phys., 2005, 122: 194709
[21] Kechin V V.Melting curve equations at high pressure. Phys Rev B, 2001, 65: 052102
[22] Wang Y, Ahuja R, Johansson B.Melting of iron and other metals at earth’s core conditions A simplified computational approach.Phys Rev B, 2001, 65: 014104
[23] Born M,Huang K.Dynamical Theory of Crystal Lattice.Clarendon: Oxford, 1954.
[24] Jin Z H, Gumbsch P, Lu K, et al.Melting mechanisms at the limit of superheating.Phys Rev Lett, 2001, 87(5): 055703
[25] Cotterill R M J.Dislocation like Structures in a Simulated Liquid.Phys Rev Lett, 1979, 42:1541
[26] Janke W. Models of defect-mediated melting.Int J Theor Phys, 1990, 29: 1251
[27] Crawford R K.Neutron scattering from solid-rubidium near the solid-liquid transition.Bull Am Phys Soc, 1979, 24: 385; Cotterill R M J, Kristensen J K.A transmission electron microscopy investigation of the melting transition.Philos Mag, 1977, 36: 453
[28] Mizushima S.Dislocation model of liquid structure.J Phys Soc Jpn, 1960, 15: 70
[29] Ookawa A.A model theory of liquid.J Phys Soc Jpn, 1960, 15: 2191
[30] Poirier J P.Dislocation-mediated melting of iron and the temperature of the Earth’s core.Geophys J R Astr Soc,1986, 85: 315~328
[31] Ninomiya T. Theory of melting: Dislocation model.J Phys Soc Jpn, 1978, 44: 263~271
[32] Burakovsky L, Preston D L, Silbar R R.Melting as a dislocation-mediated phase transition. Phys Rev B, 2000, 61: 15011
[33] Jayaraman A.Diamond anvil cell and high-pressure physical investigations.Rev Mod Phys, 1983, 55: 65~110
[34] Mao H K, Bell P M, Shaner J W, et al. Specific volume measurements of Cu, Mo, Pd, and Ag and calibration of the ruby R1 fluorescence pressure gauge from 0.06 to 1 Mbar.J Appl Phys, 1978, 49: 3276~3283
[35] Chijikoe A D, Nellis W J, Soldatov A, et al.The ruby pressure standard to 150 GPa.J Appl Phys, 2005, 98: 114905
[36] Heinz D L, Jeanoz R.Temperature measurements in the laser-heated diamond anvil cell.In: Manghnani M H, Syono Y, ed. High-Pressure Research in Mineral Physics: TERAPUB, Tokyo/American Geophysical Union, Washington,D. C., 1971.113~127
[37] Shen G, Rivers M L, Wang Y,et al.Laser heated diamond cell system at the advanced photon source for in situ x-ray measurements at high pressure and temperature.Rev Sci Instrum, 2001, 72: 1273~1282
[38] Boehler R.Temperature in the earth’s score from melting-point measurements of iron at high static pressures.Nature, 1993, 363: 534
[39] Saxena S K, Shen G, Lazor P.Experimental evidence for a new iron phase and implications for earth’s core.Science, 1993, 260: 1312
[40] Boehler R, Ross M.Melting curve of aluminum in a diamond cell to 0.8 Mbar implications for iron.Earth Planet Sci Lett, 1997, 153: 223
[41] Errandonea D, Somayazulu M, Hausermann D, et al.Melting of tantalum at high pressure determined by angle dispersive x-ray diffraction in a double-sided laser-heated diamond-anvil cell.J Phys: Condens Matter, 2003, 15: 7635~7649
[42] Errandonea D, Schwager B, et al.Systematics of transition-metal melting.Phys Rev B, 2001, 63: 132104
[43] Errandonea D, Boehler R, Ross M.Melting of the alkaline-earth metals to 80 GPa.Phys Rev B, 2001, 65: 012108
[44] Shen G, Lazor P, Saxena S K.Melting of wustite and iron up to pressures of 600kbar.Phys Chem Minerals, 1993, 20: 91
[45] Shen G, Mao H K, Hemley R J, et al. Melting and crystal structure of iron at high pressures and temperatures.Geophys Res Lett, 1998, 25: 373
[46] 经福谦.实验物态方程导引.第二版. 北京:科学出版社, 1999.
[47] 王礼立.应力波基础.北京:国防工业出版社, 1985.
[48] Johnson J N, Cheret R . Shock waves in solids an evolutionary perspective.Shock Waves, 1999, 9: 193-200
[49] Huser G, Koenig M, et al. Temperature and melting of laser-shocked iron releasing into an LiF window.Physics of plasmas, 2005, 12: 060701
[50] Baumung K, Kanel G I, et al.Shock-melting pressures from no-planar impacts.Int J Impact Engng, 1997, 20: 101-110
[51] Duvall G E, Graham R A.Phase transitions under shock-wave loading. Rev Mod Phys, 1977, 49(3): 523
[52] 唐志平.冲击相变基础.合肥:中国科学技术大学,1992.
[53] Fritz J N, Morgan J A.An Electromagnetic Technique for Measuring Material Velocity.Rev Sci Instrum, 1973, 44: 215~221
[54] Rosenberg Z, Brar N S.Measuring sound velocities along release adiabats with Manganin stress gauges.Rev Sci Instrum, 1988, 59: 991-993
[55] McQueen R G, Hopson J W, Fritz J N.Optical technique for determing rarefaction wave velocities at very high pressure.Rev Sci Instrum, 1982, 53: 245~250
[56] Duffy T S, Ahrens T J.Sound velocity at high pressure and their geophysical implication.J Geophys Res, 1992, 97: 4503~4520
[57] Tan H, Dai C D, Zhang L Y, et al.Method to determine the melting temperatures of metals under megabar shock pressures.Appl Phys Lett, 2005, 87: 221905
[58] Tan H, Ahrens T J.Shock temperature measurements for metals.High Press Res, 1990, 2: 159
[59] 谭华.金属冲击温度测量(II).高压物理学报,1996, 10:161
[60] Tang W H, Jing F Q, Zhang R Q, et al.Thermal relaxation phenomena across the metalwindow interface and its significance to shock temperature measurements of metals.J Appl Phys, 1996, 80: 3248
[61] Tang W H, Zhang R Q, Jing F Q, et al.Theoretical investigation of the apparent spectral radiancwindow interface in shock temperature experiments.J Appl Phys, 1998, 83: 2469
[62] 汤文辉.金属冲击温度测量的理论和实验研究:博士学位论文.长沙:国防科技大学,1995.
[63] Allen M P, Tildesley D J.Computer simulation of liquids.Oxford: Clarendon, 1987.
[64] Frenkel D, Smit B.Understanding Molecular Simulation-From Algorithms to Applications.San Diego, CA: Academic, 1996.
[65] Alder B J, Wainwright T E.Phase Transition for a Hard Sphere System.J Chem Phys, 1957, 27: 1208
[66] Belongoshko A B, Ahuja R, Johansson B.Quasi–Ab Initio Molecular Dynamic Study of Fe Melting.Phys Rev Lett, 2000, 84: 3638
[67] Morris J R, Wang C Z, Ho K M.Melting line of aluminum from simulations of coexisting phases.Phys Rev B, 1994, 49: 3109
[68] Moriarty J A, Young D A, Ross M.Theoretical study of the aluminum melting curve to very high pressure.Phys Rev B, 1984, 30: 578
[69] Mei J,Davenport J W.Free-energy calculations and the melting point of Al.Phys Rev B, 1992, 46: 21
[70] Straub G K, Aidun J B, Willis J M, et al. Ab initio calculation of melting andthermodynamic properties of crystal and liquid aluminum.Phys Rev B, 1994, 50: 5055
[71] Belonoshko A B, Ahuja R.Embedded-atom molecular dynamic study of iron melting.Phys Earth Planet Inter, 1997, 102: 171~184
[72] Belonoshko A B, Ahuja R et al.Quasi ab initio molecular dynamic study of Cu melting.Phys Rev B, 2000, 61: 3838
[73] Moriarty J A, Belak J F, et al. Quantum-based atomisticsimulation of materials properties in transition metals.J Phys Condens Matter, 2002, 14: 2825
[74] Alfe D, Gillan M J, Price G D.The melting curve of iron at the pressures of the Earth’s core from ab initio calculation.Nature, 1999, 401: 462
[75] Fan W, Gong X G.Superheated melting of grain boundaries.Phys Rev B, 2005, 72: 064121
[1] 汪志诚.热力学统计物理.第二版.北京:高等教育出版社,1993.
[2] Grüneisen E. Theorie des festen Zustandes einatomiger Element.Ann Physik, 1992, 12: 257
[3] Knopoff L, Shapiro J N.Comments on the interrelationships between Grüneisen’s parameter and shock and isothermal equations of state.J Geophys Res.1969, 74: 1439
[4] Poirier J P.Introduction to the Physics of the Earth’s Interior.secondedition.New York: Cambridge University Press, 2000.
[5] Porter L J, Justo J F, Yip S.The importance of Grüneisen parameters in developing interatomic potentials.J Appl Phys,1997, 82: 5378
[6] Anderson O L.The Grüneisen ratio for the last 30 years.Geophys. J Int,2000, 143: 279
[7] Stacey F D.A thermal model of the earth.Phys Earth Planet Inter.1977, 15: 341
[8] Stacey F D.Applications of thermodynamics to fundamental Earth physics.J Geophys Surveys,1977, 3: 175
[9] Vaschenko V Y, Zubarev V N.Concerning the Grüneisen constant.Soviet Phys. Solid State.1963, 5: 653～655
[10] Knopoff L, Shapiro J N.Comments on the interrelationships between Grüneisen’s parameter and shock and isothermal equations of state.J Geophys. Res,1969, 74: 1439～1450
[11] Quareni F, Mulargia F.The validity of the common approximate expressions for Grüneisen parameter.Geophys J.1988, 93: 505～519
[12] Irvine R D, Stacey F D.Pressure dependence of the thermal Grüneisen parameter, with application to the Earth’s lower mantle and outer core.Phys Earth Planet Inte..1975, 11:157～165
[13] Dugdale J S, Macdonald D K C.Thermal expansion of solids.Phys Rev,1953, 89: 832～834
[14] Gilvarry J J.Grüneisen parameter for a solid under finite strain.Phys Rev.1956, 102: 331～340
[15] Migault A.Le Journal de Physique.1971, 32: 437; ibid..1972, 33: 707
[16] 张万箱.固体的特征频率及 Grüneisen 系数的普遍表达式. 物理学报,1984, 33: 1120～1128
[17] Barton M A, Stacey F D.The Grüneisen parameter at high pressure: a molecular dynamical study.Phys Earth Planet Inter.1985, 39: 167～177
[18] Stacey F D.Theory of thermal and elastic properties of the lower mantle and core.Phys Earth Plane. Inte..1995, 89: 219～245
[19] Stacey F D.Thermoelasticity of (Mg, Fe)SiO3 perovskite and a comparison with the lower mantle.Phys Earth Planet Inter.1996, 98: 65～77
[20] Stacey F D.Equation-of-state for close-packed materials at high pressures: geophysical evidence.J Phys Condens Matter,1999, 11: 575～582
[21] Anderson O L.Equation for thermal expansivity in planetary interiors.J Geophys Res,1967, 72: 3661～3668
[22] Anderson O L.Evidence supporting the approximation γρ=const for Grüneisen parameter of the Earth’s lower mantle.J Geophys Res,1979, 84: 3537～3542
[23] Birch F.Thermal expansion at high pressure.J Geophys Res.1968, 73: 817～819
[24] Brennan B J, Stacey F D.A thermodynamically based equation of state for the lower mantle.J Geophys Res,1979, 84: 5535～5539
[25] Steinberg D J.The temperature independence of Grüneisen’s gamma at high temperature.J Appl Phys,1981, 52: 6415～6417
[26] Anderson O L.The power balance at the core-mantle boundary.Phys Earth Planet Inter.2002, 131: 1～17
[27] Huang H J, Jing F Q, Cai L C, et al.Grüneisen parameter along Hugoniot and melting temperature of ε -iron: a thermodynamic computational method.Chin Phys Let, 2005, 22: 836
[28] 谭华.金属的冲击温度测量(Ⅰ)—高温计的标定和界面温度的确定.高压物理学报, 1994,8(4):254～263
[29] 谭华.金属的冲击温度测量 ( Ⅱ ) —界面卸载近似.高压物理学报,1996,10(3):161～169
[30] 谭华.金属的冲击温度测量(Ⅲ)—“基板/样品”界面间隙对辐射法测量冲击波温度的影响.高压物理学报,1999,13(3):161～168
[31] 谭华, 戴诚达.金属的冲击温度测量(Ⅳ)—“三层介质模型”及其应用.高压物理学报.2000, 14 (2):81～91
[32] 汤文辉.金属冲击温度测量的理论和实验研究:博士学位论文.长沙: 国防科技大学,1995.
[33] 汤文辉,张若棋,胡金彪,经福谦.冲击温度的近似计算方法.力学进展.1998,27(4):479～487.
[34] Walsh J M, Rice M H, McQueen R G, and Yarger F L.Shock-Wave Compressions of Twenty-Seven Metals.Equations of State of Metals.Phys Rev .1957, 108: 196
[35] Tang W H, Jing F Q, Hu J B, et al.New method for determining the shock temperature of metals.Chin. Phys. Lett.1994, 11(9): 569～572
[36] 经福谦.实验物态方程导引.第二版.北京:科学出版社, 1999.
[37] 特鲁宁等.高温高压下凝聚物质的性质.韩钧万译.绵阳: 流体物理研究所, 1996, 40～52
[38] Nellis W J, Mitchell A C, Young D A.Equation-of-state measurements for aluminum, copper, and tantalum in the pressure range 80-440GPa (0.8-4.4Mbar).J Appl Phys, 2003, 93(1): 304～310
[39] Brown J M, McQueen R G.Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa.J. Geophys. Res, 1986,91: 7485～7494
[40] McQueen R G, Marsh S P, eds: et al.In:Kinslow R, ed.High velocity impact phenomena.New York and London: Academic Press, 1970.
[41] Yoo C S, Holmes N. C., and Ross M, et al.Shock temperature and melting of iron at earth core conditions.Phys Rev Lett, 1993, 70: 3931～3934
[42] Williams Q, Jeanloz R, and Bass J. et al.The melting curve of iron to 250 GPa: a constraint on temperature at earth’s center.Science, 1987, 236: 181～183
[43] Hixson R. S., Fritz J. N.Shock compression of tunsten and molybdenum.J Appl Phys, 1991, 71:1721
[44] Marsh S. P.Los Alamos Shock Hugoniot Data.Berkerley: University of California Press,1979.
[45] Gschneidner K A.Physical Properties and Interrelationships of Metallic and Semimetallic Elements.In: Seitz F, and Turnbull D, ed.Solid State Physics, V.16.:New York&London: Academic Press, 1965: 275～426
[46] Brown J M, McQueen R G.Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa.J Geophys Res, 1986,91: 7485～7494
[47] 徐锡申, 张万箱等.实用物态方程理论导引.北京: 科学出版社, 1986.
[1] Glazov V M, Chizhevskaya S N, Glagoleva N N, Liquid semiconductors, ch. 3., New York: Plenum Press, 1969.
[2] Faber T E.Theory of liquid metals. Cambridege:Cambridge University Press.1972.81
[3] Martin C J, and O’Connor D. A.An experimental test of Lindemann law.J Phys C, 1977, 10: 3521~3526
[4] Wallace D C.Melting of elements.Proc R Soc Lond A, 1991,433: 631~661
[5] 杜宜瑾.凝聚态物理研究.合肥:安徽大学出版社.1998.
[6] Thiel M V, Ree F H.In: Schmidt S C, Dick R D, Forbes J W, et al, ed. shock compression of condensed matter-1991,New York: Elsevier Science Publishers B V,1992.165
[7] Wang Y, Ahuja R, Johansson B.Melting of iron and other metals at earth’s core conditions:A simplified computational approach.Phys Rev B, 2001,65: 014104
[8] Asay J R, Chhabildas L C, Dandekar D P.Shear strength of shock-loadedpolycrystalline tungsten.J Appl Phys, 1980, 51: 4774
[9] Vogler T J, Reinhart W D, Chhabildas L C.Dynamic behavior of boron carbide.J Appl Phys, 2004, 95: 4173
[10] Huang H, Asay J R.Compressive strength measurements in aluminum for shock compression over the stress range of 4-22 GPa.J Appl Phys, 2005, 98: 033524
[11] Rose J H, Smith J R, Guinea F, et al.Universal features of the equation of state of metals.Phys Rev B,1984, 29: 2963
[12] Vinet P, Ferrante J, Smith J R, Rose J H.A universal equation of state for solids.J Phys C: Solid State Phys, 1986, 19: L467
[13] Bose R S, Bose R P.An equation of state applied to solid up to 1 TPa.JPhys: Condens Matter, 1999, 11: 10375
[14] Bose R P, Bose R S.Applicability of three-parameter equation of state of solids: compatibility withfirst principles approaches and application to solids.J Phys: Condens Matter, 2003, 15: 1643
[15] 冉宪文, 汤文辉.一种计算固体冷能冷压和结合能的新方法.高压物理学报, 2003, 17(1): 50～55
[16] Sun J X, Wu Q, Cai L C, et al.Two universal equations of state for solids satisfying the limiting condition at high pressure.J Phys Chem Solids, 2005, 66: 773
[17] Sun J X.A modified Lennard-Jones-type equation of state for solids strictly satisfying the spinodal condition.J Phys: Condens Matter, 2005, 17: L103
[18] Renero C, Prieto F E, Icaza M.Comparison of two universal equation of state for solids.J Phys: Condens Matter,1990, 2: 295～300
[19] Bose R P, Bose R S.Applicability of isothermal three-parameter equations of state of solids—a reappraisal.J Phys: Condens Matter, 2005, 17: 6193
[20] 吴强.金属材料高压物态方程及 Grüneisen 系数的研究:博士学位论文.四川绵阳:中国工程物理研究院,2004.
[21] 胡金彪, 经福谦.利用冲击压缩数据计算材料物态方程的一个简便解析方法.高压物理学报, 1990, 4(3): 175～180
[22] Wang Y, Chen D Q, Zhang X W.Calculated Equation of State of Al, Cu, Ta, Mo, and W to 1000 GPa.Phys Rev Lett, 2000, 84: 3220
[23] Cynn H, Yoo C S.Equation of state of tantalum to 174 GPa.Phys Rev B, 1999, 59: 8526
[24] Hanstrom A, Lazor P . High pressure melting and equation of state ofaluminum.Journal of Alloys and Compounds, 2000, 305:209～215
[25] Boehler R, Ross M.Melting curve of aluminum in a diamond cell to 0.8 Mbar: implications for iron.Earth and Planetary Science Letters, 1997, 153:223～227
[26] Shaner J W, Brown J M, McQueen R G.Melting of Metals above 100GPa.In:MacCrone R K, Whalley E, ed.High Pressure in Science and Technology:North Holland, 1984.137
[27] Belonoshho A B, Ahuja R, Eriksson O, et al.Quasi ab initio molecular dynamics study of Cu melting.Phys Rev B, 2000, 61: 3838~3844
[28] Moriarty J A.High-Pressure ion-thermal properties of metals from ab initio interatomic potentials . In: Gupta Y M, ed . shock waves in condensed matter-1985, New York: Plenum Publishing Company, 1986.101-106
[29] 张凌云.无氧铜冲击熔化特性实验研究:硕士学位论文.四川绵阳:中国工程物理研究院,2004.
[30] Alfe D, Gillan M J, Price G D.The melting curve of iron at the pressures of the earth’s core from ab initio calculations.Nature, 1999, 401: 462
[31] Ma Y Z, Maddury S M, Shen G, et al.In situ X-ray diffraction studies of iron to earth-core conditions.Phys Earth Planet Inter, 2004, 143: 455~467
[32] Shen G, Mao H K, Hemley R J.Melting and crystal structure of iron at high pressures and temperatures.Geophys Res Lett, 1998, 25: 373~376
[33] Errandonea D, Schwager B, et al. Systematics of transition-metal melting.Phys Rev B, 2001, 63: 132104
[34] Moriarty J A.Angular forces and melting in bcc transition metals: A case study of molybdenum.Phys Rev B, 1994, 49:12413
[35] Belonoshko A B, Simak S I, Kochetov A E.High Pressure Melting of Molybdenum.Phys Rev Lett, 2004, 92:195701
[36] Hixson R S, Boness D A, Shaner J W.Acoustic Velocities and Phase Transitions in Molybdenum under Strong Shock Compression.Phys Rev Lett,1989, 62: 637
[37] Errandonea D, Somayazulu M, Hausermann D, et al.Melting of tantalum at high pressure determined by angle dispersive x-ray diffraction in a double-sided laser-heated diamond-anvil cell.J Phys: Condens Matter, 2003, 15: 7635～7649
[38] Fateeva N S, Vereshchagin L F.Sov Phys, 1971, 16: 322
[39] Moriarty J A, Belak J F, Rudd R E, et al.Quantum-based atomistic simulation of materials properties in transition metals.J Phys:Condens Matter, 2002, 14: 2825
[40] McQueen R G, Fritz J N, and Morris C E.the Velocity of Sound Behind StrongShock Waves in 2024 Al.In: Asay J R, Graham R A, Straub G K, ed.Shock Waves in Condensed Matter-1983, Amsterdam: North Holland Physics Publishing, 1984.95～98
[41] Hayes D, Hixson R S, McQueen R G.High Pressure Elastic Properties, Solid-Liquid Phase Boundary and Liquid Equation of State from Release Wave Measurements in Shock-Loaded Copper.In: Furnish M D, Chhabildas L C, Hixson R S, ed.Shock Compression of Condensed Matter-1999, NewYork: American Institute of Physics.2000.483～488
[42] Nguyen J H, Holmes N C.Melting of iron at the physical conditions of the Earth’s core.Nature, 2004, 427: 339～342
[43] Brown J M, Shaner J W.Rarefaction Velocities in Shocked Tantalum and The High Pressure Melting Point.In: Asay J R, Graham R A, Straub G K,ed.Shock Waves in Condensed Matter-1983, Amsterdam: North Holland Physics Publishing, 1984.91～94,
[44] Marsh S P.Los Alamos Shock Hugoniot Data.Berkerley: University of California Press.1979.
[45] Gschneidner K A.Physical Properties and Interrelationships of Metallic and Semimetallic Elements.In:Seitz F, Turnbull D, ed.Solid State Physics, Vol 16, New York&London: Academic Press, 1965.275～426
[46] Brown J M, McQueen R G.Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa.J Geophys Res, 1986, 91: 7485～7494
[47] 徐锡申, 张万箱等.实用物态方程理论导引.北京: 科学出版社, 1986.
[48] Burakovsky L, and Preston D L.Analytic model of the Grüneisen parameter all densities.J Phys Chem Solids, 2004, 65: 1581～1587
[1] Asay J R, and Chhabildas L C.Shear strength of shock-loaded polycrystalline tungsten.J Appl Phys,1980,51:4774
[2] Ross W C.The effect of material strength on determining pressures “on” and “off” the Hugoniot.J Appl Phys,1984,55:2741
[3] Johnson J N, Hixson R S, Gray G T.Quasielastic release in shock-compressed solids.J Appl Phys,1992,72: 429
[4] 华劲松. 高温高压下钨合金的本构方程研究:博士学位论文.四川绵阳: 中国工程物理研究院, 1999.
[5] 彭建祥, 经福谦, 王礼立等.冲击压缩下铝、铜、钨的剪切模量和屈服强度与压力和温度的相关性.物理学报,2005,54(5): 2194～2197
[6] Peng J. X., Jing F. Q., Wang L. L., et al.Pressure and temperature dependence of shear modulus and yield strength for aluminum, copper, and tungsten under shock compression.J Appl Phys, 2005, 98: 013508
[7] Birch F . Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressure and 300K.J Geophys Res, 1978, 83: 1257
[8] Duffy T S, Ahrens T J.Sound velocities at high pressure and temperature and their geophysical implications.J Geophys Res, 1992, 97(B4): 4503～4520
[9] Steinberg D J, Cochran S G, Guinan M W.A constitutive model for metals applicable for high-strain rate.J Appl Phys, 1980, 51(3): 1498
[10] Guinan M.Steinberg D.A simple approach to extrapolating measured polycrystalline shear moduli to very high pressure.J Phys Chem Solids, 1975, 36: 829
[11] 李茂生, 陈栋泉.高温高压下材料的本构模型.高压物理学报, 2001, 15(1): 24～31
[12] Burakovsky L, Preston D L, Silbar R R.Melting as a dislocation-mediated phase transition.Phys Rev B, 2000, 61: 15011
[13] Burakovsky L, Preston D L.Analytic model of the Grüneisen parameter all densities.J Phys Chem Solids, 2004, 65: 1581～1587
[14] Burakovsky L.Preston D L, Wang Y.Cold shear modulus and Grüneisen parameter at all densities.Solid State Commun, 2004, 132: 151
[15] Burakovsky L, Greeff C W, Preston D L.Analytic model of the shear modulus at all temperatures and densities.Phys Rev B, 2003, 67: 094107
[16] Burakovsky L, Preston D L.Generalized Guinan-Steinberg formula for the shear modulus at all pressures.Phys Rev B, 2005, 71:184118
[17] Asay J R, Chhabildas L C.Determination of the shear strength of shockcompressed 6061-T6 aluminum.In:Meyers M. A., and Murr L. E., ed.shock waves and high-strain-rate phenomena in metals:Plenum Press, 1981.417
[18] Asay J R, Chhabildas L C, et al. High pressure strength of shocked aluminum. In: Shock waves in condensed matter-1985 : Plenum press, 1986.145
[19] McQueen R G, Fritz J N, Morris C E. The velocity of sound behind strong shock waves in 2024 Al.In:Asay J R, Graham R A and Straub G K,ed.Shock Waves in Condensed Matter-1983. New York & Amsterdam: Elsevier, 1984.95～98
[20] Yu Y Y, Tan H, Dai C D, et al.Sound velocity and release behavior of shock-compressed Ly12Al.Chin Phys Lett, 2005, 22(7): 1742
[21] Duffy T S, Ahrens T J.Hugoniot sound velocities in metals with applications to the earth’s inner core.In:Syono Y., and Manghnani M. H., ed.High-Pressure Research: Application to Earth and Planetary Sciences, Tokyo: Terra Scientific Publication Company, 1992.353
[22] McQueen R G, Marsh S P, Fritz J. N.Hugoniot equation of state of twelve rocks.J Geophys Res, 1967, 72: 4999～5035
[23] 谭华.实验冲击波物理导引.四川绵阳: 中国工程物理研究院研究生部, 2006.
[24] 王贵朝.高压下一种弹性声速的经验表达式.高压物理学报, 1988, 2(1): 92～95
[25] Brown J M, Shaner J W.Rarefaction Velocities in Shocked Tantalum and The High Pressure Melting Point.In:Asay J R, Graham R A and Straub G K.,ed. Shock Waves in Condensed Matter-1983, Amsterdam: North Holland Physics Publishing, 1984. 91～94
[26] Hayes D, Hixson R S, McQueen R G.High Pressure Elastic Properties, Solid-Liquid Phase Boundary and Liquid Equation of State from Release Wave Measurements in Shock-Loaded Copper.In:Furnish M D, Chhabildas L C, and Hixson R S, ed.Shock Compression of Condensed Matter-1999, NewYork: American Institute of Physics, 2000.483～488
[27] McQueen R G, Hopson J W, Fritz J N.Optical technique for determing rarefaction wave velocities at very high pressure.Rev Sci Instrum, 1982, 53: 245～250
[28] Marsh S P.Los Alamos Shock Hugoniot Data.Berkerley: University ofCalifornia Press, 1979.
[29] Gschneidner K A.Physical Properties and Interrelationships of Metallic and Semimetallic Elements.In:Seitz F., and Turnbull D.,ed. Solid State Physics, v.16, New York&London: Academic Press, 1965.275～426
[30] 徐锡申, 张万箱等.实用物态方程理论导引.北京: 科学出版社, 1986.
[1] Dietrich Stauffer.Introduction of Percolation Theory.Taylor & Francis, London and Philadelphis, 1985;Geoffrey R. Grimmett.Percolation and Disordered Systems . Cambridge : Statistical Laboratory University of Cambridge, 1996.
[2] 李茂生, 陈栋泉.高温高压下材料的本构模型.高压物理学报.2001, 15(1): 24～31
[3] Hayes D, Hixson R S, McQueen R G.High Pressure Elastic Properties, Solid-Liquid Phase Boundary and Liquid Equation of State from Release Wave Measurements in Shock-Loaded Copper.In: Furnish M D, Chhabildas L C, Hixson R S, ed.Shock Compression of Condensed Matter-1999, NewYork: American Institute of Physics, 2000.483～488
[4] McQueen R G, Fritz J N, Morris C E.The velocity of sound behind strong shock waves in 2024 Al.In: Asay J R, Graham R A and Straub G K, ed.Shock Waves in Condensed Matter-1983 , New York: Amsterdam: Elsevier, 1984.95～98
[5] Brown J M, Shaner J W.Rarefaction Velocities in Shocked Tantalum and The High Pressure Melting Point.In: Asay J R, Graham R A and Straub G K, ed.Shock Waves in Condensed Matter-1983, Amsterdam: North Holland Physics Publishing, 1984.91～94
[6] McQueen R G, Hopson J W, Fritz J N.Optical technique for determing rarefaction wave velocities at very high pressure.Rev Sci Instrum.1982.53: 245～250
[7] Duffy T S, Ahrens T J.Sound velocity at high pressure and their geophysical implication.J Geophys Res.1992.97: 4503～4520
[8] 冉宪文 , 汤文辉.描述混合物固液相变的两个模型.高压物理学报.2003.17(3): 220～225
[9] Shaner J W, Brown J M, McQueen R G.Melting of Metals above 100GPa.In: MacCrone R K, Whalley E, ed.High Pressure in Science and Technology,North Holland, 1984.137
[10] Hanstrom A, Lazor P.High pressure melting and equation of state of aluminum.Journal of Alloys and Compounds.2000.305:209～215
[11] Boehler R, Ross M.Melting curve of aluminum in a diamond cell to 0.8 Mbar: implications for iron.Earth and Planetary Science Letters.1997.153:223~227
[12] Kanel G I, Baumung K, Singer J, et al.Dynamic strength of aluminum single crystals at melting. Appl Phys Lett, 2000, 72(22):3230
[13] Kanel G I, Razorenov S V, et al. Spall fracture properties of aluminum and magnesium at high temperatures. J Appl Phys, 1996, 79(11):8310
[14] Razorenov S V, Savinykh A S, Kanel G I, et al.Sub-microsecond yield and tensile strengths of metals and alloys at elevated temperatures.In: Furnish M D, Gupta Y M, Forbes J W, ed.NewYorK: American institute of physics, Shock Compression of Condensed Matter-2003, 2004.491
[15] Kanel G I, Razorenov S V, Fortov V E.Shock-wave compression and tension of solids at elevated temperatures: superheated crystal status, pre-melting, and anomalous growth of the yield strength. J Phys Condens Matter, 2004, 16: s1007～s1016
[16] Wilson K G.The renormalization group and critical phenomena.Rev Mod Phys, 1983, 55(3): 583～600
[17] 冯端.金属物理学(第二卷 相变).北京:科学出版社,1990.360
[18] 孙霞, 吴自勤, 黄畇.分形原理及其应用.合肥: 中国科技大学出版社, 2003.156
[19] Cardy J.Scaling and Renormalization in Statistical Physics.Cambridge: Cambridge University Press, 1996.
[20] Chowdhury D, Stauffer D . Principles of Equilibrium Statistical Mechanics.Weiheim: Wiley-VCH, 2000.
[21] Kadanoff L . Statistical Physics, Statics, Dynamics and Renormalization.Singapore: World Scientific, 2000.
[22] Brown J M, McQueen R G. Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77GPa and 400GPa.J Geophys Res, 1986.91:7485～7494
[23] Williams Q, Jeanloz R, Bass J, et al.The melting curve of iron to 250 GPa: a constraint on temperature at earth’s center.Science,1987, 236:181～183
[24] Boehler R.Temperature in the earth’s core from melting point measurements ofiron at high static pressures.Nature, 1993, 363: 534～536
[25] Yoo C S, Akella J, Campbell A J,et al.The phase diagram of iron by in situ x-ray diffraction: Implications for Earth’s core.Science, 1995, 270: 1473～1475
[26] Shen G, Hu J, Hemley R J, et al.High P-T phase diagram and equation of state of iron.Eos Trans.AGU, 77(46), Fall Meet. Suppl., 1996.F696,
[27] Bass J D, Svendson B, Ahrens T.The temperature of shock compressed iron.In: Manghnani M H, Syono Y,eds, High Pressure Reseach in Mineral Physics, v. 39. Geophysical Monograph Ser. 39, Washington, D. C: 1987. American Geophysical Union, 393~492.
[28] Yoo C S, Holmes N C, Ross M, et al. Shock temperatures and melting of iron at Earth core conditions. Phys Rev Lett, 1993. 70:3931-3934
[29] Anderson O L, Duba A. Experimental melting curve of iron revised, J Geophys Res 1997, 102: 22659-22669
[30] Laio A, Bernard S, Chiarotti G L, et al. Physics of iron at earth’s core conditions. Science, 2000, 287: 1027~1030
[31] Belonoshko A B, Ahujia R.Embedded-atom molecular dynamic study of iron melting.Phys Earth Plnaet Inter, 1997, 84: 171-184
[32] Neumann G S, Stixrude L, Cohen R E et al. Elasticity of iron at the temperature of the earth’s inner core, Nature, 2001.413: 57-60
[33] Stixrude L, Wasserman E, Composition and temperature of the earth’s inner core. J Geophys Res, 1997, 102: 24729-24739
[34] Alfe D, Gillan M J, Price G D.Composition and temperature of the earth’s inner core constrained by combining ab initio calculation and seismic data.Earth Planet Sci Lett, 2002, 195: 91-98
[35] Shen G, Mao H K, Hemley R J, et al. Melting and crystal structure of iron at high pressures and temperatures. Geophys Res Lett,1998, 25: 373-376
[36] Ma Y Z, Somayazulu M, Shen G, et al, In situ X-ray diffraction studies of iron to earth-core conditions, Phys Earth Planet Inter, 2004, 143: 455-467
[37] Luo S N, Ahrens T J. Shock-induced superheating and melting curves of geophysically important mineral, Phys Earth Planet Inter, 2004, 143: 369-386
[38] Luo S N, Ahrens T J. Superheating systematics of crystalline solids, Appl Phys Lett, 2003, 82(12): 1836-1838
[39] Lu K, and Li Y. Homogeneous Nucleation Catastrophe as a Kinetic Stability Limit for Superheated Crystal. Phys Rev Lett, 1998, 80: 4474-4477
[40] Nguyen J H, Holmes N C. Melting of iron at the physical conditions of the Earth’s core. Nature, 2004, 427:339-342
[41] Huang H J, Jing F Q, Cai L C, et al. Grüneisen parameter along Hugoniot and Melting Temperature of ε-iron: A thermodynamic computational method. Chin. Phys. Lett, 2005, 22: 836
[42] 李西军. 铁的高压熔化线研究:博士学位论文. 绵阳: 中国工程物理研究院.
[43] Boehler R, Ross M. Melting curve of aluminum in a diamond cell to 0.8 Mbar: implications for iron. Earth and Planetary Science Letters, 1997, 153:223-227
[1] 谭华.金属的冲击温度测量(I)-高温计的标定和界面温度的确定.高压物理学报,1994,8(4): 254-263
[2] Grover R, Urtiew P A.Thermal Relaxation at interfaces following shock compression. J Appl Phys,1974,45: 146
[3] 汤文辉.金属冲击温度测量的理论和实验研究:博士学位论文.长沙: 国防科技大学研究生院, 1995.
[4] McQueen R G, Hopson J W, Fritz J N.Optical technique for determing rarefaction wave velocities at very high pressure.Rev Sci Instrum,1982,53:245-250
[5] Duffy T S, Ahrens T J.Sound velocity at high pressure and their geophysical implication.J Geophys Res,1992,97: 4503～4520
[6] McQueen R G, Fritz J N, Morris C E.The velocity of sound behind strong shock waves in 2024 Al.In:Asay J R, Graham R A and Straub G K,ed. Shock Waves in Condensed Matter-1983 , New York & Amsterdam: Elsevier, 1984.95～98
[7] Urtiew P A, Grover R.Temperature deposition caused by shock interactions with material interfaces. J Appl Phys,1974,45:140
[8] 许灿华.铁在冲击压缩下熔化温度的直接测量:硕士学位论文.四川绵阳: 中国工程物理研究院, 2004.
[9] Tan H, Dai C D, Zhang L Y, et al.Method to determine the melting temperatures of metals under megabar shock pressures.Appl Phys Lett,2005,87: 221905
[10] 俞宇寅.强冲击载荷作用下 Ly12 铝合金的准弹性卸载特性及层裂研究:博士学位论文.四川绵阳: 中国工程物理研究院, 2006.
[11] 冉宪文, 汤文辉.描述混合物固-液相变的两个模型.高压物理学报,2003,17(3):220~225
[12] Hanstrom A, Lazor P.High pressure melting and equation of state of aluminum.Journal of Alloys and Compounds,2000,305:209～215
[13] Boehler R, Ross M.Melting curve of aluminum in a diamond cell to 0.8 Mbar: implications for iron.Earth and Planetary Science Letters,1997,153:223～227
[14] Shaner J W, Brown J M,McQueen R G. Melting of Metals above 100GPa.In: MacCrone R K, Whalley E, ed.High Pressure in Science and Technology:North Holland, 1984.137
[15] Urtiew P A, Grover R. The melting temperature of magnesium under shock loading. J Appl Phys, 1977, 48(3): 1122-1126.