Study of the equation of states for deuterium, helium, and their mixture

Zhang Qi-Li; Zhang Gong-Mu; Zhao Yan-Hong; Liu Hai-Feng

doi:10.7498/aps.64.094702

Abstract

Equation of states for deuterium, helium, and their mixture is studied by using the quantum molecular dynamics (QMD) method. We calculate the equation of states for helium with density from 0.32 to 5 g/cm3 at temperature from 1000 to 50000 K. Results are compared with the chemical model (CM), at T less than 10000 K, and QMD is in good agreement with the CM. The shock Hugoniot curves are also calculated, and the results are in good agreement with the gas-gun experiment. The mechanism of the metal-insulator transition for helium is studied by computing its pair distribution function and density of states. The equation of states (EOS) for deuterium with density from 0.19 to 0.84 g/cm3 at temperatures from 20 to 50000 K is computed. For deuterium molecule the degree of dissociation is calculated, and the effect of the molecular vibration is accounted for using the EOS model. Theoretical Hugoniot states are also calculated and compared with the results of experiments and other theories; the maximum compressibility of hydrogen is about 4.9, and deuterium 4.4; these agree with the results of most experiments and theories. Due to the zero point motion of atoms being not taken into account, the theoretical results at low temperatures are smaller than those of experiments. The deuterium-helium mixture is studied, and its 293 points of equation of states for various xHe with densities from 0.19 to 0.84 g/cm3 at temperatures from 100 to 50000 K are calculated. The linear mixing approximation (LMA) is checked, and the maximum of the volume distinction is about 7%; the results indicate that LMA is a cursory approximation.

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References

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[22]	Ternovoi V Ya, Kvitov S V, Pyalling A A, Filimonov A S, Fortov V E 2004 JETP Lett. 79 6
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[46]	Morales M A 2009 Ph. D. Thesis (University of Illinois at Urbana-Champaign) (In United States of America)
[47]	Cui T, Zou G T 1998 Chin. Phys. Lett. 15 287
[48]	Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
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[51]	Aziz R A, Slaman M J 1991 J. Chem. Phys. 94 8047
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Cited By

[1]	Chabrier G 2007 Astrophys. J. 391 817
[2]	Goncharov A F, Hemley R J, Mao H k 2011 J. Chem. Phys. 134 174501
[3]	Stixrude L, Jeanloz R 2008 Proc. Natl. Acad. Sci. U.S.A. 105 11071
[4]	Mao H K, Hemley R J, Wu Y, Jephcoat A P, Finger L W, Zha C S, Bassett W A 1988 Phys. Rev. Lett. 60 2649
[5]	Goncharov A F, Gregoryanz E, Hemley R J, Mao H k 2001 Proc. Natl. Acad. Sci. U.S.A. 98 14234
[6]	Loubeyre P, Occelli F, LeToullec R 2002 Nature 416 613
[7]	Subramanian N, Goncharov A, Struzhkin V, Somayazulu M, Hemley R 2011 Proc. Natl. Acad. Sci. U.S.A. 108 6014
[8]	Nellis W J, Weir S T, Mitchell A C 1999 Phys. Rev. B 59 3434
[9]	Gu Y J, Chen Q F, Cai L C, Chen Z Y, Zheng J, Jing F Q 2009 J. Chem. Phys. 130 184506
[10]	Knudson M D, Hanson D L, Bailey J E, Hall C A, Asay J R, Deeney C 2004 Phys. Rev. B 69 144209
[11]	Knudson M D, Hanson D L, Bailey J E, Hall C A, Asay J R 2003 Phys. Rev. Lett. 90 035505
[12]	Knudson M D, Hanson D L, Bailey J E, Hall C A, Asay J R 2001 Phys. Rev. Lett. 87 225501
[13]	Boehly T R, Hicks D G., Celliers P M, Collins T J B, Earley R, Eggert J H, Jacobs-Perkins D, Moon S J, Vianello E, Meyerhofer D D, Collins G W 2004 Phys. Plasmas 11 L49
[14]	Collins G W, Celliers P M, Da Silva L B, Cauble R, Gold D M, Foord M E, Holmes N C, Hammel B A, Wallace R J, Ng A 2001 Phys.Rev. Lett. 87 165504
[15]	Mostovych A N, Chan Y, Lehecha T, Schmit A, Sethian J D 2000 Phys. Rev. Lett. 85 3870
[16]	Da Silva L B, Celliers P, Collins G W, Budil K S, Holmes N C, Barbee T W, Jr. Hammel B A, Kilkenny J D, Wallace R J, Ross M, Cauble R 1997 Phys. Rev. Lett. 78 483
[17]	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 2005 Phys. Rev. B 71 092104
[18]	Hicks D, Boegly T, Celliers P, Eggert J, Moon S, Meyerhofer D, Collins G 2009 Phys. Rev. B 79 014112
[19]	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
[20]	Eggert J, Brygoo S, Loubeyre P, Mc Williams R S, Celliers P M, Hicks D G., Boehly T R, Jeanloz R, Collins G W 2008 Phys. Rev. Lett. 100 124503
[21]	Chen Q F, Cai L C, Chen D Q, Jing F Q 2004 Physica B 348 299
[22]	Ternovoi V Ya, Kvitov S V, Pyalling A A, Filimonov A S, Fortov V E 2004 JETP Lett. 79 6
[23]	Gu Y J, Chen Q F, Cai L C, Chen Z Y, Zheng J, Jing F Q 2009 J. Chem. Phys. 130 184506
[24]	Brush S G, Sahlin H L, Teller E 1966 J. Chem. Phys. 45 2102
[25]	Jones M D, Ceperley D M 1996 Phys. Rev. Lett. 76 4572
[26]	Galam S, Hansen J P 1976 Phys. Rev. A 14 816
[27]	Liberatore E, Pierleoni C, Ceperley D M 2011 J. Chem. Phys. 134 184505
[28]	Ross M, Ree F, Young D 1983 J. Chem. Phys. 79 1487
[29]	Jaranek H, Redmer R 2000 J. Chem. Phys. 112 3780
[30]	Kerley G I 2003 Sandia National Laboratories Technical Report No. SAND 2003-3613
[31]	Nagara H, Nakamura T 1992 Phys. Rev. Lett. 68 2468
[32]	Städele M, Martin R M 2000 Phys. Rev. Lett. 84 6070
[33]	Pickard C J, Needs R J 2007 Nature Phys. 3 473
[34]	Zhang L J, Niu Y L, Cui T, Li Y, Wang Y, Ma Y M, He Z, Zou G T 2006 J. Phys. Condens. Matter 18 9917
[35]	Desjarlais M 2003 Phys. Rev. B 68 064204
[36]	Militzer B 2006 Phys. Rev. Lett. 97 175501
[37]	Holst B, Redmer R, Desjarlais M 2008 Phys. Rev. B 77 184201
[38]	Caillabet L, Mazevet S, Loubeyre P 2011 Phys. Rev. B 83 094101
[39]	Morales M A, Benedict L X, Clark D S, Schwegler E, Tamblyn I, Bonev S A, Correa A A, Haan S W 2012 High Energy Density Phys. 8 5
[40]	Wang C, He X T, Zhang P 2012 Physics 41 462 (in Chinese) [王聪, 贺贤土, 张平 2012 物理 41 462]
[41]	Ceperley D M, Alder B J 1987 Phys. Rev. B 36 2092
[42]	Natoli V, Martin R M, Ceperley D M 1993 Phys. Rev. Lett. 70 1952
[43]	Militzer B, Ceperley D 2000 Phys. Rev. Lett. 85 1890
[44]	Khairallah S, Shumway J, Draeger E 2011 arXiv:1108.1711
[45]	Filinov V, Levashov P, Bonitz M, Fortov V 2005 Plasma Phys. Rep. 31 700
[46]	Morales M A 2009 Ph. D. Thesis (University of Illinois at Urbana-Champaign) (In United States of America)
[47]	Cui T, Zou G T 1998 Chin. Phys. Lett. 15 287
[48]	Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[49]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[50]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[51]	Aziz R A, Slaman M J 1991 J. Chem. Phys. 94 8047
[52]	Sano T, Ozaki N, Sakaiya T, Shigemori K, Ikoma M, Kimura T, Miyanishi K, Endo T, Shiroshita A, Takahashi H 2011 Phys. Rev. B 83 054117
[53]	Dick R, Kerley G 1980 J. Chem. Phys. 73 5264
[54]	Nellis W, Mitchell A, McCandless P, Erskine D, Weir S 1992 Phys. Rev. Lett. 68 2937

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