Citation: | Liu Haifeng, Song Haifeng, Zhang Qili, Zhang Gongmu, Zhao Yanhong. Validation for equation of state in wide regime: Copper as prototype[J]. Matter and Radiation at Extremes, 2016, 1(2). doi: 10.1016/j.mre.2016.03.002 |
[1] |
V. Bushman, G.I. Kanel, A.L. Ni, V.E. Fortov, Intense Dynamic Loading of Condensed Matter, Taylor&Francis, London, 1993.
|
[2] |
M.D. Knudson, M.P. Desjarlais, Adiabatic release measurements in aluminum between 400 and 1200 GPa: characterization of aluminum as a shock standard in the multimegabar regime, Phys. Rev. B 91 (2015) 224105.10.1103/physrevb.91.224105
|
[3] |
H.K. Mao, R.J. Hemley, Ultrahigh pressure transitions in solid hydrogen, Rev. Mod. Phys. 66 (1994) 671.10.1103/revmodphys.66.671
|
[4] |
T. Kimura, N. Ozaki, T. Okuchi, T. Mashimo, K. Miyanishi, et al., Static compression experiments for advanced coupling techniques of laser-driven dynamic compression and precompression target, J. Phys. Conf. Ser. 215 (2010) 012152.10.1088/1742-6596/215/1/012152
|
[5] |
R.P. Feymnan, N. Metropolis, E. Teller, Equations of state of elements based on the generalized Fermi-Thomas theory, Phys. Rev. 75 (10) (1949) 1561–1573.10.1103/physrev.75.1561
|
[6] |
S.L. McCarthy, The Kirzhnits Corrections to the Thomas-Fermi Equation of State, Lawrence Livermore Laboratory, 1965. Report UCRL-14364.
|
[7] |
D.A. Kirzhnits, Y.E. Lozovik, G.V. Shpatakovskaya, Statistical model of matter, Soviet Physics Uspekhi 18 (1975) 649.10.1070/pu1975v018n09abeh005199
|
[8] |
A.F. Nikiforov, V.G. Novikov, V.B. Uvarov, Quantum-statistical Models of Hot Dense Matter: Methods for Computation Opacity and Equation of State, vol. 37, Springer Science & Business Media, 2006.
|
[9] |
W. Ebeling, A. Forster, V.E. Fortov, V.K. Gryaznov, A.Y. Polishchuk, Thermophysical Properties of Hot Dense Plasmas, B. G. Teubner, Verlagsgesellschaft, Stuttgart Leipzig, 1991.
|
[10] |
D.C. Wallace, Statistical Physics of Crystals and Liquids, World Scientific, Singapore, 2003.
|
[11] |
W. Lorenzen, B. Holst, R. Redmer, Demixing of hydrogen and helium at megabar pressures, Phys. Rev. Lett. 102 (2009) 115701.10.1103/physrevlett.102.115701
|
[12] |
S.A. Bonev, B. Militzer, G. Galli, Ab initio simulations of dense liquid deuterium: comparison with gas-gun shock-wave experiments, Phys. Rev. B 69 (2004) 014101.10.1103/physrevb.69.014101
|
[13] |
L.A. Collins, S.R. Bickham, J.D. Kress, S. Mazevet, T.J. Lenosky, et al., Dynamical and optical properties of warm dense hydrogen, Phys. Rev. B 63 (2001) 184110.10.1103/physrevb.63.184110
|
[14] |
M.P. Desjarlais, Density-functional calculations of the liquid deuterium Hugoniot, reshock, and reverberation timing, Phys. Rev. B 68 (2003) 064204.10.1103/physrevb.68.064204
|
[15] |
K.T. Delaney, C. Pierleoni, D.M. Ceperley, Quantum Monte Carlo simulation of the high-pressure molecular-atomic crossover in fluid hydrogen, Phys. Rev. Lett. 97 (2006) 235702.10.1103/physrevlett.97.235702
|
[16] |
B. Militzer, D.M. Ceperley, J.D. Kress, J.D. Johnson, L.A. Collins, et al., Calculation of a deuterium double shock Hugoniot from Ab initio simulations, Phys. Rev. Lett. 87 (2001) 275502.10.1103/physrevlett.87.275502
|
[17] |
F. Lin, M.A. Morales, K.T. Delaney, C. Pierleoni, R.M. Martin, et al., Electrical conductivity of high-pressure liquid hydrogen by quantum Monte Carlo methods, Phys. Rev. Lett. 103 (2009) 256401.10.1103/physrevlett.103.256401
|
[18] |
S.P. Lyon, J.D. Johnson, SESAME: The Los Alamos National Laboratory Equation of State Database, Los Alamos National Laboratory, Los Alamos, NM, 1992. Technical report LA-UR-92-3407.
|
[19] |
R.M. More, K.H. Warren, D.A. Young, G.B. Zimmerman, A new quotidian equation of state (QEOS) for hot dense matter, Phys. Fluids 31 (10) (Oct. 1988) 3059–3078.10.1063/1.866963
|
[20] |
Xishen Xu, Wanxiang Zhang, Theoretical Introduction to Equation of State, Scientific Press, Beijing, 1986 (in Chinese).
|
[21] |
Haifeng Liu, Haifeng Song, Gongmu Zhang, The single phase and two-phase equations of state for aluminum, AIP Conf. Proc. 1426 (2012) 832–835.10.1063/1.3686407
|
[22] |
N.N. Kalitkin, L.V. Kuz'mina, Russ. J., Plasma Phys. 2 (5) (1976) 478.
|
[23] |
S.B. Kormer, A.I. Funtikov, V.D. Urlin, A.N. Kolesnikova, Dynamical compression of porous metals and the equation of state with variable specific heat at high temperatures, Zh. Eksp. Teor. Fiz. 42 (1962) 686–701 (in Russian)
|
[24] |
G.I. Kerley, Rational Function Method of Interpolation, LA-6903-MS, 1977.
|
[25] |
S.P. Marsh (Ed.), LASL Shock Hugoniot Data, Univ. California Press, Berkeley, 1980.
|
[26] |
A.C. Mitchell, W.J. Nellis, Shock compression of aluminum, copper and tantalum, J. Appl. Phys. 52 (1981) 3363–3374.10.1063/1.329160
|
[27] |
B.L. Glushak, A.P. Zharkov, M.V. Zhernokletov, V. Ya. Ternovoi, A.S. Filimonov, et al., Experimental investigation of the thermodynamics of dense plasmas formed from metals at high energy concentrations, Sov. Phys. JETP 69 (4) (1989) 739–749.
|
[28] |
Xiang Wang, Summary of Technique in measurement of Equation of State, Report in Institute of Fluid Physics, 2002 (unpublished).
|
[29] |
P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136 (1964) B864.10.1103/physrev.136.b864
|
[30] |
A. Khein, D.J. Umrigar, All-electron study of gradient corrections to the local-density functional in metallic systems, Phys. Rev. B 51 (1995) 4105.10.1103/physrevb.51.4105
|
[31] |
P.M. Bell, Ji-an Xu, H.K. Mao, Static compression of gold and copper and calibration of the ruby pressure scale to pressures to 1.8 megabars (static. RNO), Shock Waves Condens. Matter (1986) 125–130 Springer US.
|
[32] |
C.W. Greeff, J.C. Boettger, M.J. Graf, J.D. Johnson, Theoretical investigation of the Cu EOS standard, J. Phys. Chem. Sol. 67 (2006) 2033–2040.10.1016/j.jpcs.2006.05.055
|
[33] |
G. Kress, J. Hafner, Ab initio molecular dynamics for open-shell transition metals, Phys. Rev. B 48 (1993) 13115.10.1103/PhysRevB.48.13115 doi: 10.1103/PhysRevB.54.11169
|
[34] |
P. Blaha, K. Schwarz, P. Sorantin, S.B. Trickey, Full-potential, linearized augmented plane wave programs for crystalline systems, Comput. Phys. Commun. 59 (399) (1990).10.1016/0010-4655(90)90187-6
|
[35] |
K. Schwarz, P. Blaha, G. Madsen, Electronic Structure calculations of solids using Wien2k package for material sciences, Comput. Phys. Commun. 147 (2002) 71.10.1016/s0010-4655(02)00206-0
|
[36] |
J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865.10.1103/physrevlett.77.3865
|
[37] |
J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple [Phys. Rev. Lett. 77, 3865 (1996)10.1103/physrevlett.77.3865], doi: 10.1103/physrevlett.78.1396
|
[38] |
Y. Wang, D. Chen, X. Zhang, Calculated equation of state of Al, Cu, Ta, Mo, and W to 1000 GPa, Phys. Rev. Lett. 84 (2000) 3220.10.1103/physrevlett.84.3220
|
[39] |
N.N. Kalitkin, L.V. Kuzmina, in: V.E. Fortov, L.V. Al'tshuler, R.F. Trunin, A.I. Funtikov (Eds.), Wide-range Characteristic Thermodynamic Curves, in High Pressure Shock Compression of Solids VII., Springer, 2004.
|
[40] |
L.V. Al'tshuler, S.E. Brusnikin, High. Temp. 27 (1) (1989) 39–47.
|
[41] |
N.N. Kalitkin, I.A. Govorukhina, Sov. Phys. Solid State 7 (2) (1965) 287–292.
|
[42] |
E.A. Kuzmenkov, Izv. Sib. Div. Russ. Acad. Sci. 6 (1989) 106–112.
|
[43] |
P.W. Bridgman, Proc. Am. Acad. Sci. 76 (6) (1949) 189.
|
[44] |
H.K. Mao, P.M. Bell, J.W. Shaner, D.J. Steinberg, Specific volume measurements of Cu, Mo, Pd, and Ag and calibration of the ruby R 1fluorescence pressure gauge from 0.06 to 1 Mbar, J. Appl. Phys. 49 (6) (1978) 3276–3283.10.1063/1.325277
|
[45] |
A. Dewaele, P. Loubeyre, M. Mezouar, Equations of state of six metals above 94GPa, Phys. Rev. B 70 (2004) 094112.10.1103/physrevb.70.094112
|
[46] |
L.V. Al'tshuler, S.B. Kormer, A.A. Bakanova, R.F. Trunin, Equations of state for aluminum, copper and lead in the high pressure region, Sov. Phys. JETP 11 (1960) 573–579.
|
[47] |
W.J. Nellis, J.A. Moriarty, A.C. Mitchell, Metals physics at ultrahigh pressure: aluminum, copper, and lead as prototypes, Phys. Rev. Lett. 60 (1988) 1414.10.1103/physrevlett.60.1414
|
[48] |
L.V. Al'tshuler, S.E. Brusnikin, E.A. Kuzmenkov, J. Appl. Mech. Tech. Phys. 28 (1) (1987) 129–141.10.1007/bf00918785
|
[49] |
Song Haifeng, Haifeng Liu, Modified mean-field potential approach to the thermodynamic properties of a low-symmetry crystal: beryllium as a prototype, Phys. Rev. B 75 (2007) 245126.10.1103/physrevb.75.245126
|
[50] |
J.C. Boettger, Int. J. Quantum Chem. Sym 27 (1993) 147–154.10.1002/qua.560480817
|
[51] |
J.-P. Davis, J.L. Brown, M.D. Knudson, R.W. Lemke, Analysis of shockless dynamic compression data on solids to multi-megabar pressures: application to tantalum, J. Appl. Phys. 116 (2014) 204903.10.1063/1.4902863
|
[52] |
J.M. Walsh, M.H. Rice, R.G. Mcqueen, F.L. Yarger, Shock-wave compressions of twenty-seven metals equations of state of metals, Phys. Rev. 108 (1957) 196–216.10.1103/physrev.108.196
|
[53] |
R.G. McQueen, S.P. Marsh, Equation of state for nineteen metallic elements, J. Appl. Phys. 31 (1960) 1253–1269.10.1063/1.1735815
|
[54] |
W.J. Mitchell, J.A. Nellis, R.A. Moriarty, N.C. Heinle, R. E. Tipton Holmes, G.W. Repp, Equation of state of Al, Cu, Mo, and Pb at shock pressures up to 2.4 TPa (24 Mbar), J. Appl. Phys. 69 (1991) 2981–2986.10.1063/1.348611
|
[55] |
E. Ragan, Shock-wave experiment at threefold compression, Phys. Rev. Ser. A 29 (1984) 1391–1402.10.1103/physreva.29.1391
|
[56] |
L.V. Al'tshuler, K.K. Krupnikov, M.I. Brazhnik, Dynamical compressibility of metals under pressure from 400000 to 4 million atmospheres, Sov. Phys. JETP 7 (1958) 614–618.
|
[57] |
L.V. Al'tshuler, A.A. Bakanova, R.F. Trunin, Shock adiabats and zero isotherms of seven metals at high pressures, Sov. Phys. JETP 15 (1962) 65–74.
|
[58] |
L.V. Al'tshuler, B.S. Chekin, Metrology of high pulsed pressures, in: Proceed. of 1 All-Union Pulsed Pressures Simposium, vol. 1, VNIIFTRI, Moscow, 1974, pp. 5–22 (in Russian).
|
[59] |
L.V. Al'tshuler, N.N. Kalitkin, L.V. Kuz'mina, B.S. Chekin, Shock adiabats for ultrahigh pressures, Sov. Phys. JETP 45 (1) (1977) 167–171.
|
[60] |
L.V. Al'tshuler, A.A. Bakanova, I.P. Dudoladov, E.A. Dynin, R.F. Trunin, et al., Shock adiabats for metals. New data, statistical analysis and general regularities, J. Appl. Mech. Tech. Phys. 22 (1981) 145.10.1007/bf00907938
|
[61] |
R.F. Trunin, M.A. Podurets, B.N. Moiseev, G.V. Simakov, L.V. Popov, Relative compressibility of copper, cadmium and lead at high pressures, Sov. Phys. JETP 29 (4) (1969) 630–631.
|
[62] |
R.F. Trunin, M.A. Podurets, G.V. Simakov, L.V. Popov, B.N. Moiseev, Experimental verification of the Thomas-Fermi model for metals under high pressure, Sov. Phys. JETP 35 (3) (1972) 550–552.
|
[63] |
R.F. Trunin, L.A. Il'kaeva, M.A. Podurets, L.V. Popov, B.V. Pechenkin, et al., Measurement of shock compressibility of iron, copper, lead and titanium at pressures of 20 TPa, Teplofiz. Vys. Temp. 32 (5) (1994) 692–695 (in Russian).
|
[64] |
R.F. Trunin, Shock compressibility of condensed matters in strong shock waves caused by underground nuclear explosions, Usp. Fiz. Nauk. 164 (11) (1994) 1215–1237 (in Russian).10.3367/ufnr.0164.199411d.1215
|
[65] |
W.H. Isbell, F.H. Shipman, A.H. Jones, Hugoniot Equation of State Measurements for Eleven Materials to Five Megabars, General Motors Corp., Mat. Sci. Lab, 1968. Report MSL-68–13.
|
[66] |
S.B. Kormer, A.I. Funtikov, V.D. Ulrin, A.N. Kolesnikova, Dynamical compression of porous metals and the equation of state with variable specific heat at high temperatures, Sov. Phys. JETP 15 (1962) 477–478.
|
[67] |
R.F. Trunin, A.B. Medvedev, A.I. Funtikov, M.A. Podurets, G.V. Simakov, et al., Shock compression of porous iron, copper, and tungsten and their equation of state in terapascal pressure range, Sov. Phys. JETP 68 (2) (1989) 356–361.
|
[68] |
M.V. Zhernokletov, V.N. Zubarev, Yu. N. Sutulov, Adiabats of porous samples and expansion isentropes of copper, Zh. Prikl. Mekh. Tekhn. Fiz. 1 (1984) 119–123 (in Russian).
|
[69] |
R.F. Trunin, G.V. Simakov, Yu. N. Sutulov, A.B. Medvedev, B.D. Rogozkin, et al., Compression of porous metals in shock waves, Sov. Phys. JETP 69 (3) (1989) 580–588.
|
[70] |
V.K. Gryaznov, V.E. Fortov, M.V. Zhernokletov, G.V. Simakov, R.F. Trunin, et al., Shock compression and thermodynamics of highly nonideal metallic plasma, Sov. Phys. JETP 87 (4) (1998) 678–690.10.1134/1.558710
|
[71] |
Sizu Fu, Xiuguang Huang, Minxun Ma, Hua Shu, Jiang Wu, et al., Analysis of measurement error in the experiment of laser equation of state with impedance-match way and the Hugoniot data of Cu up to ∼2.24 TPa with high precision, J. Appl. Phys. 101 (2007) 043517.10.1063/1.2538097
|
[72] |
Xiuguang Huang, Sizu Fu, The Experiment of Laser Equation of State, Report in Shanghai Institute of Laser Plasma (unpublished), 2014.
|
[73] |
W.J. Nellis, A.C. Mitchell, D.A. Young, Equation-of-state measurements for aluminum, copper, and tantalum in the pressure range 80-440 GPa (0.8-4.4 Mbar), J. Appl. Phys. 93 (1) (2003) 304–310.10.1063/1.1529071
|
[74] |
Bakanova, I.P. Dudoladov, M.V. Zhernokletov, V.N. Zubarev, G.V. Simakov, On evaporation of shock-compressed metals under expansion, J. Appl. Mech. Tech. Phys. 24 (1983) 204.
|
[75] |
Yu. L. Alekseev, B.P. Ratnikov, A.P. Rybakov, Shock adiabats of porous metals, Zh. Prikl. Mekh. Tekhn. Fiz. 2 (1971) 101–106 (in Russian).
|
[76] |
D.J. Steinberg, S.G. Cochran, M.W. Guinan, A constitutive model for metals applicable at high strain rate, J. Appl. Phys. 51 (3) (1980) 1498–1503.10.1063/1.327799
|
[77] |
D. Hayes, R. Hixson, R. McQueen, High pressure elastic properties, solid-liquid phase boundary and liquid equation of state from release wave measurement in shock-loaded copper, in: M.D. Furnish, L.C. Chhabildas, R.S. Hixson (Eds.), Shock Compression of Condensed Matter-1999, 2000, pp. 483–488. Melville, New York.
|
[78] |
Yuyin Yu, Measurement of Sound Velocity of Copper in Inverse Impact, Report in Institute of Fluid Physics, 2006 (unpublished).
|
[79] |
Pengjian Xiang, Comparative Study of Johnson-cook Constitutive Model and Steinberg Constitutive Model (Ph. D thesis), Graduate of China Academy Engineer Physics, Mianyang, 2006.
|
[80] |
Ke Jin, Measurement of Sound Velocity of Copper under shock loading, Report in Institute of Fluid Physics, 2012 (unpublished).
|
[81] |
Ping Song, Lingcang Cai, Xianming Zhou, Hua Tan, Experimental investigation of the release isentropes of OFHC copper, Chin. J. High Press. Phys. 19 (2) (2005) 174.
|
[82] |
L.V. Al'tshuler, S.B. Kormer, M.I. Brazhnik, L.A. Vladimirov, M.P. Speranskaya, et al., The isentropic compressibility of aluminum, copper, lead at high pressures, Sov. Phys. JETP 11 (4) (1960) 766–775.
|
[83] |
K.B. Broberg, Shock Wave in Elastic and Plastic Media, 1965.
|
[84] |
C.E. Morris, J.N. Fritz, B. E. Holian, LA-Ur -81.
|
[85] |
Jinbiao Hu, Qian Jingfu, Juxin Cheng, Sound velocities at high pressures and shock-melting of copper, Chin. J. High Press. Phys. 3 (3) (1989) 187.
|
[86] |
J.H. Nguyen, M.C. Akin, R. Chau, D.E. Fratanduono, W.P. Ambrose, et al., Molybdenum sound velocity and shear modulus softening under shock compression, Phys. Rev. B 89 (2014) 174109.10.1103/physrevb.89.174109
|