Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

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

Citation:

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

Zhang Qi-Li, Zhang Gong-Mu, Zhao Yan-Hong, Liu Hai-Feng
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • 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.
    [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

  • [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

  • [1] Qin Meng-Fei, Wang Ying-Min, Zhang Hong-Yu, Sun Ji-Zhong. Molecular dynamics simulation of dynamic migration of $\boldsymbol {\langle 100\rangle} $ interstitial dislocation loops under (010) surfaces of pure W and W containing helium impurity. Acta Physica Sinica, 2023, 72(24): 245204. doi: 10.7498/aps.72.20230651
    [2] Tian Bao-Xian, Wang Zhao, Hu Feng-Ming, Gao Zhi-Xing, Ban Xiao-Na, Li Jing. Equation-of-state measurements for polystyrene under high presure driven by HEAVEN-I laser facility. Acta Physica Sinica, 2021, 70(19): 196401. doi: 10.7498/aps.70.20210240
    [3] Tang Wen-Hui, Xu Bin-Bin, Ran Xian-Wen, Xu Zhi-Hong. Equations of state and thermodynamic properties of hot plasma. Acta Physica Sinica, 2017, 66(3): 030505. doi: 10.7498/aps.66.030505
    [4] Zhou Hong-Qiang, Yu Ming, Sun Hai-Quan, He An-Min, Chen Da-Wei, Zhang Feng-Guo, Wang Pei, Shao Jian-Li. Calculation of equation of state of a material mixture. Acta Physica Sinica, 2015, 64(6): 064702. doi: 10.7498/aps.64.064702
    [5] Zhang Bao-Ling, Song Xiao-Yong, Hou Qing, Wang Jun. Molecular dynamics study on the phase transition of high density helium. Acta Physica Sinica, 2015, 64(1): 016202. doi: 10.7498/aps.64.016202
    [6] Jia Guo, Huang Xiu-Guang, Xie Zhi-Yong, Ye Jun-Jian, Fang Zhi-Heng, Shu Hua, Meng Xiang-Fu, Zhou Hua-Zhen, Fu Si-Zu. Experimental measurement of liquid deuterium equation of state data. Acta Physica Sinica, 2015, 64(16): 166401. doi: 10.7498/aps.64.166401
    [7] Wang Xin-Xin, Zhang Ying, Zhou Hong-Bo, Wang Jin-Long. Effects of niobium on helium behaviors in tungsten:a first-principles investigation. Acta Physica Sinica, 2014, 63(4): 046103. doi: 10.7498/aps.63.046103
    [8] Han Yong, Long Xin-Ping, Guo Xiang-Li. Prediction of methane PVT relations at high temperatures by a simplified virial equation of state. Acta Physica Sinica, 2014, 63(15): 150505. doi: 10.7498/aps.63.150505
    [9] Jiang Shao-Ning, Wan Fa-Rong, Long Yi, Liu Chuan-Xin, Zhan Qian, Ohnuki Somei. Effects of helium and deuterium on irradiation damage in pure iron. Acta Physica Sinica, 2013, 62(16): 166801. doi: 10.7498/aps.62.166801
    [10] Yuan Du-Qi. Maximum trap range and equation of state for Fermi gas in potential trap. Acta Physica Sinica, 2011, 60(6): 060509. doi: 10.7498/aps.60.060509
    [11] Chen Min. Molecular dynamics study of small helium cluster diffusion in titanium. Acta Physica Sinica, 2011, 60(12): 126602. doi: 10.7498/aps.60.126602
    [12] Song Ping, Cai Ling-Cang. Grüneisen parameter and high temperature and high pressure equation of state for aluminum. Acta Physica Sinica, 2009, 58(3): 1879-1884. doi: 10.7498/aps.58.1879
    [13] Zhang Chao, Sun Jiu-Xun, Tian Rong-Gang, Zou Shi-Yong. Analytic equations of state and thermo-physical properties for the α, β, and γ-Si3N4. Acta Physica Sinica, 2007, 56(10): 5969-5973. doi: 10.7498/aps.56.5969
    [14] Guo Zeng-Yuan, Cao Bing-Yang, Zhu Hong-Ye, Zhang Qing-Guang. State equation of phonon gas and conservation equations for phonon gas motion. Acta Physica Sinica, 2007, 56(6): 3306-3312. doi: 10.7498/aps.56.3306
    [15] Li Hong, Zhang Yong-Qiang, Cheng Jie, Wang Lu-Xia, Liu De-Sheng. Laser pulse control of ultrafast heterogeneous electron transfer——The multiple vibrational mode three electronic state system. Acta Physica Sinica, 2007, 56(6): 3589-3595. doi: 10.7498/aps.56.3589
    [16] Zhang Ying, Chen Qi-Feng, Gu Yun-Jun, Cai Ling-Cang, Lu Tie-Cheng. Self-consistent variational calculation of the dense fluid helium plasma in the region of partial ionization. Acta Physica Sinica, 2007, 56(3): 1318-1324. doi: 10.7498/aps.56.1318
    [17] Tian Chun-Ling, Liu Fu-Sheng, Cai Ling-Cang, Jing Fu-Qian. Many-body contributions to the equation of state for highly compressed solid helium. Acta Physica Sinica, 2006, 55(2): 764-769. doi: 10.7498/aps.55.764
    [18] Zheng Si-Xiao, Luo Shun-Zhong, Liu Zhong-Yang, Long Xing-Gui, Wang Pei-Lu, Peng Shu-Ming, Liao Xiao-Dong, Liu Ning. Preservation dose of helium-implanted in nanocrystal titanium films. Acta Physica Sinica, 2004, 53(2): 555-560. doi: 10.7498/aps.53.555
    [19] Tian Chun-Ling, Liu Fu-Sheng, Cai Ling-Cang, Jing Fu-Qian. Contributions of fourbody interactions to compressibility of solid helium. Acta Physica Sinica, 2003, 52(5): 1218-1221. doi: 10.7498/aps.52.1218
    [20] . Acta Physica Sinica, 2002, 51(2): 337-341. doi: 10.7498/aps.51.337
Metrics
  • Abstract views:  5023
  • PDF Downloads:  299
  • Cited By: 0
Publishing process
  • Received Date:  09 October 2014
  • Accepted Date:  04 November 2014
  • Published Online:  05 May 2015

/

返回文章
返回