Theoretical study of the equation of state for warm dense matter

Ma Gui-Cun; Zhang Qi-Li; Song Hong-Zhou; Li Qiong; Zhu Xi-Rui; Meng Xu-Jun

doi:10.7498/aps.66.036401

Abstract

In this paper, we present in detail various theoretical models for studying the equation of state of warm dense matter, including the fluid variational theory, the chemical model, the ionization equilibrium model, the average atom model and INFERNO model. The method of calculating the equation of state of a mixture is also given. The results from the first principles molecular dynamics simulation and the quantum Monte Carlo simulation are also provided. Typical materials such as hydrogen, deuterium, helium, xenon, gold, tungsten, etc. are studied in warm dense region by using all the methods, showing the effects of dissociation and ionization in the equation of state.

Keywords:

Authors and contacts

1.
Institute of Applied Physics and Computational Mathematics, Beijing 100089, China

Corresponding author: Ma Gui-Cun, ma_guicun@iapcm.ac.cn

References

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[4]	Saumon D, Chabrier G, van Horn H M 1995 Astrophys. J. Suppl. Ser. 99 713
[5]	Saumon D, Chabrier G 1991 Phys. Rev. A 44 5122
[6]	Saumon D, Chabrier G 1992 Phys. Rev. A 46 2084
[7]	Juranek H, Redmer R 2002 J. Chem. Phys. 117 1768
[8]	Kerley G I 1986 J. Chem. Phys. 85 5228
[9]	Kerley G I 2003 Equations of State for Hydrogen and Deuterium Sandia National Laboratories Technical Report No. SAND2003-3613
[10]	Jin F Q 1999 Introduction to the Experiments of the Equation of State(Beijing:Science Press) (in Chinese)[经福谦1999实验物态方程导引(北京:科学出版社)]
[11]	Rozsnyai B F 1972 Phys. Rev. A 5 1137
[12]	Liberman D A 1979 Phys. Rev. B 20 4981
[13]	Zhu X R, Meng X J 2011 Acta Phys. Sin. 60 093103 (in Chinese)[朱希睿, 孟续军2011物理学报60 093103]
[14]	Wilson B, Sonnad V, Sterne P, Isaacs W 2006 J. Quant. Spectrosc. Radiat. Transfer 99 658
[15]	Penicaud M 2009 J. Phys.:Condens. Matter 21 095409
[16]	Barshalom A, Oreg J 2009 High Energy Density Physics 5 196
[17]	Ma G C, Zhang Q L, Lu G 2017 Chin. J. High Press. Phys. 31 1 (in Chinese)[马桂存, 张其黎, 卢果2017高压物理学报31 1]
[18]	Kress G, Furthmuller J 1996 Phys. Rev. B 54 11169
[19]	Lambert F, Clerouin J, Zerah G 2006 Phys. Rev. E 73 016403
[20]	Driver K P, Militzer B 2012 Phys. Rev. Lett. 108 115502
[21]	Hu S X, Militzer B, Goncharov V N, Skupsky S 2011 Phys. Rev. B 84 224109
[22]	Vorberger J, Tamblyn I, Militzer B, Bonev S A 2007 Phys. Rev. B 75 024206
[23]	Juranek H, Redmer R 2000 J. Chem. Phys. 112 3780
[24]	Nellis W J, van Thiel M, Mitchell A C 1982 Phys. Rev. Lett. 48 816
[25]	Urlin V D, Mochalov M A, Mikhailova O L 1992 High Press. Res. 8 595
[26]	Wigner E 1932 Phys. Rev. 40 749
[27]	Kirkwoord J 1933 Phys. Rev. 44 31
[28]	Andersen H C, Chandler D 1970 J. Chem. Phys. 53 547
[29]	Weeks J D, Chandler D, Andersen H C 1971 J. Chem. Phys. 54 5237
[30]	Weeks J D, Chandler D, Andersen H C 1971 J. Chem. Phys. 55 5422
[31]	Hummer D G, Mihalas D 1988 Astrophys. J. 331 794
[32]	Ebeling W, Forster A, Richert W, Hess H 1988 Physica A 150 159
[33]	Kerley G I 1980 J. Chem. Phys. 73 469
[34]	Kerley G I 1980 J. Chem. Phys. 73 478
[35]	Kerley G I 1980 J. Chem. Phys. 73 487
[36]	Nellis W J, Mitchell A C, van Thiel M, Devine G J, Trainor R J 1983 J. Chem. Phys. 79 1480
[37]	Boriskov G V, Bykov A I, II'kaev R I, Selemir V D, Simakov G V, Trunin R F, Urlin V D, Shuikin A N, Nellis W J 2005 Phys. Rev. B 71 092104
[38]	Knudson M D, Hanson D L, Bailey J E, Hall C A, Asay J R 2001 Phys. Rev. Lett. 87 225501
[39]	Da Silva L B, Celliers P, Collins G W, Budil K S, Holmes N C, Barbee T W, Hammel B A, Kilkenny J D, Wallace R J, Ross M, Cauble R, Ng A, Chiu G L B 1997 Phys. Rev. Lett. 78 483
[40]	Collins G W, Da Silva L B, Celliers P, Gold D, Foord M, Wallace R, Ng A, Weber S, Budil K, Cauble R 1998 Science 281 1178
[41]	Hicks D G, Boehly T R 2009 Phys. Rev. B 79 014112
[42]	Militzer B, Ceperley D M 2000 Phys. Rev. Lett. 85 1890
[43]	Bezkrovniy V, Filinov V S, Kremp D, Bonitz M, Schlanges M, Kraeft W D, Levashov P R, Fortov V E 2004 Phys. Rev. E 70 057401
[44]	Caillabet L, Mazevet S, Loubeyre P 2011 Phys. Rev. B 83 094101
[45]	Ross M 1998 Phys. Rev. B 58 669
[46]	Ma G C, Qi J, Wang M 2015 Chin. J. Comput. Phys. 32 361 (in Chinese)[马桂存, 齐进, 王敏2015计算物理32 361]
[47]	Novikov V G, Ovechkin A A 2011 Math. Models Comput. Simulations 3 290
[48]	Barshalom A, Oreg J 2007 High Energy Density Phys. 3 12
[49]	Barshalom A, Oreg J 2006 J. Quant. Spectrosc. Radiat. Transfer 99 35
[50]	Kerley G I 1987 Int. J. Impact. Eng. 5 441
[51]	Yokoo M, Kawai N, Nakamura K G, Kondo K 2008 Appl. Phys. Lett. 92 051901
[52]	Marsh S P 1980 Los Alamos Shock Hugoniot Data (Berkeley:University of California Press)
[53]	Al'tshuler L V, Bakanova A A, Dudoladov I P, Dynin E A, Trunin R F, Chekin B S 1981 J. Appl. Mech. Tech. Phys. 22 145
[54]	Jones A H, Isbell W M, Maiden C J 1966 J. Appl. Phys. 37 3493
[55]	Zhu X R, Meng X J, Tian M F 2008 Acta Phys. Sin. 57 4049 (in Chinese)[朱希睿, 孟续军, 田明峰2008物理学报57 4049]
[56]	Militzer B 2005 J. Low. Temp. Phys. 139 739
[57]	Zhang Q L, Zhang G M, Zhao Y H, Liu H F 2015 Acta Phys. Sin. 64 094702 (in Chinese)[张其黎, 张弓木, 赵艳红, 刘海风2015物理学报64 094702]
[58]	Danel J F, Kazandjian L 2015 Phys. Rev. E 91 013103
[59]	Car R, Parrinello M 1985 Phys. Rev. Lett. 55 2471
[60]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[61]	Wang Y, Perdew J P 1991 Phys. Rev. B 44 13298
[62]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[63]	Nose S C 1984 J. Chem. Phys. 81 511
[64]	Nellis W J, Holmes N C, Mitchell A C, Trainor R J, Governo G K, Ross M, Young D A 1984 Phys. Rev. Lett. 53 1248
[65]	Zhang Q L, Zhao Y H, Ma G C 2014 Chin. J. High Press. Phys. 28 18 (in Chinese)[张其黎, 赵艳红, 马桂存2014高压物理学报28 18]
[66]	Ma G C, Pei W B, Wang M 2005 Annual Report of ICF 272(in Chinese)[马桂存, 裴文兵, 王敏2005 ICF科技年报272]
[67]	Koenig M, Faral B, Boudenne J, Batani D, Benuzzi A, Bossi S, Remond C, Perrine J P, Temporal M, Atzeni S 1995 Phys. Rev. Lett. 74 2260
[68]	McQueen R, Marsh S 1960 J. Appl. Phys. 31 1253
[69]	Al'tshuler L, Krupnikov K, Brazhnik M I 1958 Sov. Phys. JETP 7 614
[70]	Konstantin D L, Pavel N G, Dorogokupets P I, Igor S S, Shatskiy A, Fei Y W, Pashchenko S V, Seryotkin Y V, Higo Y J, Funakoshi K, Ohtani E 2013 J. Appl. Phys. 113 133505
[71]	Kubo R 1957 J. Phys. Soc. Jpn. 12 570
[72]	Greenwood D A 1958 Proc. Phys. Soc. London 715 585
[73]	Mott N 1984 Rep. Prog. Phys. 47 909
[74]	Korobenko V N, Rakhel A D 2013 Phys. Rev. B 88 134203
[75]	Ceperley D M 1995 Rev. Mod. Phys. 67 279
[76]	Pierleoni C, Ceperley D M, Bernu B, Magro W R 1994 Phys. Rev. Lett. 73 2145
[77]	Magro W R, Ceperley D M, Pierleoni C, Bernu B 1996 Phys. Rev. Lett. 76 1240
[78]	Filinov V S, Bonitz M, Ebeling W, Fortov V E 2001 Plasmas Phys. Controlled Fusion 43 743
[79]	Filinov V S, Fortov V E, Bonitz M, Kremp D 2000 Phys. Lett. A 274 228
[80]	Filinov V S, Bonitz M, Kremp D, Kraeft W D, Ebeling W, Levashov P R, Fortov V E 2001 Contrib. Plasmas Phys. 41 135
[81]	Wang C, Zhang P 2013 Phys. Plasmas 20 092703
[82]	Holst B, Redmer R, Desjarlais M P 2008 Phys. Rev. B 77 184201
[83]	Redmer R, Ropke G 2010 Contrib. Plasma Phys. 50 970
[84]	Militzer B 2013 Phys. Rev. B 87 014202

Cited By

[1]	Xu X S, Zhang W X 1986 Introduction to the Theory of Equation of State (Beijing:Science Press) (in Chinese)[徐锡申, 张万箱1986实用物态方程理论导引(北京:科学出版社)]
[2]	Rogers F J, Young D A 1997 Phys. Rev. E 56 5876
[3]	Fortov V, Iakubov I, Khrapak A 2006 Physics of Strongly Coupled Plasma (Oxford:Oxford University Press)
[4]	Saumon D, Chabrier G, van Horn H M 1995 Astrophys. J. Suppl. Ser. 99 713
[5]	Saumon D, Chabrier G 1991 Phys. Rev. A 44 5122
[6]	Saumon D, Chabrier G 1992 Phys. Rev. A 46 2084
[7]	Juranek H, Redmer R 2002 J. Chem. Phys. 117 1768
[8]	Kerley G I 1986 J. Chem. Phys. 85 5228
[9]	Kerley G I 2003 Equations of State for Hydrogen and Deuterium Sandia National Laboratories Technical Report No. SAND2003-3613
[10]	Jin F Q 1999 Introduction to the Experiments of the Equation of State(Beijing:Science Press) (in Chinese)[经福谦1999实验物态方程导引(北京:科学出版社)]
[11]	Rozsnyai B F 1972 Phys. Rev. A 5 1137
[12]	Liberman D A 1979 Phys. Rev. B 20 4981
[13]	Zhu X R, Meng X J 2011 Acta Phys. Sin. 60 093103 (in Chinese)[朱希睿, 孟续军2011物理学报60 093103]
[14]	Wilson B, Sonnad V, Sterne P, Isaacs W 2006 J. Quant. Spectrosc. Radiat. Transfer 99 658
[15]	Penicaud M 2009 J. Phys.:Condens. Matter 21 095409
[16]	Barshalom A, Oreg J 2009 High Energy Density Physics 5 196
[17]	Ma G C, Zhang Q L, Lu G 2017 Chin. J. High Press. Phys. 31 1 (in Chinese)[马桂存, 张其黎, 卢果2017高压物理学报31 1]
[18]	Kress G, Furthmuller J 1996 Phys. Rev. B 54 11169
[19]	Lambert F, Clerouin J, Zerah G 2006 Phys. Rev. E 73 016403
[20]	Driver K P, Militzer B 2012 Phys. Rev. Lett. 108 115502
[21]	Hu S X, Militzer B, Goncharov V N, Skupsky S 2011 Phys. Rev. B 84 224109
[22]	Vorberger J, Tamblyn I, Militzer B, Bonev S A 2007 Phys. Rev. B 75 024206
[23]	Juranek H, Redmer R 2000 J. Chem. Phys. 112 3780
[24]	Nellis W J, van Thiel M, Mitchell A C 1982 Phys. Rev. Lett. 48 816
[25]	Urlin V D, Mochalov M A, Mikhailova O L 1992 High Press. Res. 8 595
[26]	Wigner E 1932 Phys. Rev. 40 749
[27]	Kirkwoord J 1933 Phys. Rev. 44 31
[28]	Andersen H C, Chandler D 1970 J. Chem. Phys. 53 547
[29]	Weeks J D, Chandler D, Andersen H C 1971 J. Chem. Phys. 54 5237
[30]	Weeks J D, Chandler D, Andersen H C 1971 J. Chem. Phys. 55 5422
[31]	Hummer D G, Mihalas D 1988 Astrophys. J. 331 794
[32]	Ebeling W, Forster A, Richert W, Hess H 1988 Physica A 150 159
[33]	Kerley G I 1980 J. Chem. Phys. 73 469
[34]	Kerley G I 1980 J. Chem. Phys. 73 478
[35]	Kerley G I 1980 J. Chem. Phys. 73 487
[36]	Nellis W J, Mitchell A C, van Thiel M, Devine G J, Trainor R J 1983 J. Chem. Phys. 79 1480
[37]	Boriskov G V, Bykov A I, II'kaev R I, Selemir V D, Simakov G V, Trunin R F, Urlin V D, Shuikin A N, Nellis W J 2005 Phys. Rev. B 71 092104
[38]	Knudson M D, Hanson D L, Bailey J E, Hall C A, Asay J R 2001 Phys. Rev. Lett. 87 225501
[39]	Da Silva L B, Celliers P, Collins G W, Budil K S, Holmes N C, Barbee T W, Hammel B A, Kilkenny J D, Wallace R J, Ross M, Cauble R, Ng A, Chiu G L B 1997 Phys. Rev. Lett. 78 483
[40]	Collins G W, Da Silva L B, Celliers P, Gold D, Foord M, Wallace R, Ng A, Weber S, Budil K, Cauble R 1998 Science 281 1178
[41]	Hicks D G, Boehly T R 2009 Phys. Rev. B 79 014112
[42]	Militzer B, Ceperley D M 2000 Phys. Rev. Lett. 85 1890
[43]	Bezkrovniy V, Filinov V S, Kremp D, Bonitz M, Schlanges M, Kraeft W D, Levashov P R, Fortov V E 2004 Phys. Rev. E 70 057401
[44]	Caillabet L, Mazevet S, Loubeyre P 2011 Phys. Rev. B 83 094101
[45]	Ross M 1998 Phys. Rev. B 58 669
[46]	Ma G C, Qi J, Wang M 2015 Chin. J. Comput. Phys. 32 361 (in Chinese)[马桂存, 齐进, 王敏2015计算物理32 361]
[47]	Novikov V G, Ovechkin A A 2011 Math. Models Comput. Simulations 3 290
[48]	Barshalom A, Oreg J 2007 High Energy Density Phys. 3 12
[49]	Barshalom A, Oreg J 2006 J. Quant. Spectrosc. Radiat. Transfer 99 35
[50]	Kerley G I 1987 Int. J. Impact. Eng. 5 441
[51]	Yokoo M, Kawai N, Nakamura K G, Kondo K 2008 Appl. Phys. Lett. 92 051901
[52]	Marsh S P 1980 Los Alamos Shock Hugoniot Data (Berkeley:University of California Press)
[53]	Al'tshuler L V, Bakanova A A, Dudoladov I P, Dynin E A, Trunin R F, Chekin B S 1981 J. Appl. Mech. Tech. Phys. 22 145
[54]	Jones A H, Isbell W M, Maiden C J 1966 J. Appl. Phys. 37 3493
[55]	Zhu X R, Meng X J, Tian M F 2008 Acta Phys. Sin. 57 4049 (in Chinese)[朱希睿, 孟续军, 田明峰2008物理学报57 4049]
[56]	Militzer B 2005 J. Low. Temp. Phys. 139 739
[57]	Zhang Q L, Zhang G M, Zhao Y H, Liu H F 2015 Acta Phys. Sin. 64 094702 (in Chinese)[张其黎, 张弓木, 赵艳红, 刘海风2015物理学报64 094702]
[58]	Danel J F, Kazandjian L 2015 Phys. Rev. E 91 013103
[59]	Car R, Parrinello M 1985 Phys. Rev. Lett. 55 2471
[60]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[61]	Wang Y, Perdew J P 1991 Phys. Rev. B 44 13298
[62]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[63]	Nose S C 1984 J. Chem. Phys. 81 511
[64]	Nellis W J, Holmes N C, Mitchell A C, Trainor R J, Governo G K, Ross M, Young D A 1984 Phys. Rev. Lett. 53 1248
[65]	Zhang Q L, Zhao Y H, Ma G C 2014 Chin. J. High Press. Phys. 28 18 (in Chinese)[张其黎, 赵艳红, 马桂存2014高压物理学报28 18]
[66]	Ma G C, Pei W B, Wang M 2005 Annual Report of ICF 272(in Chinese)[马桂存, 裴文兵, 王敏2005 ICF科技年报272]
[67]	Koenig M, Faral B, Boudenne J, Batani D, Benuzzi A, Bossi S, Remond C, Perrine J P, Temporal M, Atzeni S 1995 Phys. Rev. Lett. 74 2260
[68]	McQueen R, Marsh S 1960 J. Appl. Phys. 31 1253
[69]	Al'tshuler L, Krupnikov K, Brazhnik M I 1958 Sov. Phys. JETP 7 614
[70]	Konstantin D L, Pavel N G, Dorogokupets P I, Igor S S, Shatskiy A, Fei Y W, Pashchenko S V, Seryotkin Y V, Higo Y J, Funakoshi K, Ohtani E 2013 J. Appl. Phys. 113 133505
[71]	Kubo R 1957 J. Phys. Soc. Jpn. 12 570
[72]	Greenwood D A 1958 Proc. Phys. Soc. London 715 585
[73]	Mott N 1984 Rep. Prog. Phys. 47 909
[74]	Korobenko V N, Rakhel A D 2013 Phys. Rev. B 88 134203
[75]	Ceperley D M 1995 Rev. Mod. Phys. 67 279
[76]	Pierleoni C, Ceperley D M, Bernu B, Magro W R 1994 Phys. Rev. Lett. 73 2145
[77]	Magro W R, Ceperley D M, Pierleoni C, Bernu B 1996 Phys. Rev. Lett. 76 1240
[78]	Filinov V S, Bonitz M, Ebeling W, Fortov V E 2001 Plasmas Phys. Controlled Fusion 43 743
[79]	Filinov V S, Fortov V E, Bonitz M, Kremp D 2000 Phys. Lett. A 274 228
[80]	Filinov V S, Bonitz M, Kremp D, Kraeft W D, Ebeling W, Levashov P R, Fortov V E 2001 Contrib. Plasmas Phys. 41 135
[81]	Wang C, Zhang P 2013 Phys. Plasmas 20 092703
[82]	Holst B, Redmer R, Desjarlais M P 2008 Phys. Rev. B 77 184201
[83]	Redmer R, Ropke G 2010 Contrib. Plasma Phys. 50 970
[84]	Militzer B 2013 Phys. Rev. B 87 014202

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