Modification of the van der Waals Model for Dense States of Matter

  • A. B. Medvedev
Part of the High-Pressure Shock Compression of Condensed Matter book series (SHOCKWAVE)

Abstract

Modeling the behavior of matter under various influences requires a knowledge of the equation of state. Equations of state are often required to cover a wide range, including solid, liquid, gas, and plasma states. If the material is chemically complicated, it is necessary to take possible chemical reactions into account. The problem of calculation of an equation of state from basic principles has not yet been solved by modern methods. This causes practical use of various semi-empirical models having free parameters that are chosen based on the description of experimental and theoretical data. Forms of model equations are rather varied [1]. The models have different kinds of complication, different numbers of free parameters, and describe a variety of states. Desirable properties of models are a wide range of applicability, simplicity, and the capability to describe limiting situations of high pressure and temperature where theoretical techniques of calculation are suitable. It is rather difficult to reach such a compromise, which is why models often have either local validity, agreeing with experimental data within only narrow ranges of states, or are complicated and have a large number of free parameters whose selection is often difficult because of lack of the information needed to carry it out.

Keywords

Mixture Model Sound Velocity JETP Letter Dense State Shock Compression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    A.V. Bushman and V.E. Fortov, Soy. Phys.—Usp. 26(6) pp. 465–496, (1983). [trans. from: Usp. FiiNauk 140(2) pp. 177–232 (1983).]Google Scholar
  2. [2]
    V.P. Kopyshev, J. Appt Mech Tech. Phys. 12(1) pp. 103–107 (1971). [trans. from Zh. Prikl. Mekh. Tekh. Fiz 12(1) pp. 119–122 (1971).]Google Scholar
  3. [3]
    A.B. Medvedev, VoprosyAtomnoi Nauki Tekh. Ser. Teor. Prikl. Fiz. (1), pp. 23–29 (1990).Google Scholar
  4. [4]
    A.B. Medvedev, VoprosyAtomnoi Nauki Tekh. Ser. Teor. PrikL Fiz. (1), pp. 12–19 (1992).Google Scholar
  5. [5]
    V.P. Glushko (ed.), Thermodynamic Properties of Individual Substances, Vols. 1–4, Science, (1978–1982). (in Russian)Google Scholar
  6. [6]
    W.J. Nellis, A. Mitchell, M. van Thiel, et al., J. Chem. Phys. 79(3), YPP. 1480–1486 (1983).Google Scholar
  7. [7]
    H. Shimizu, E. Brody, H. Mao, and P. Bell, Phys. Rev. Lett. 47 (2), pp. 128–131 (1981).ADSCrossRefGoogle Scholar
  8. [8]
    R.F. Trunin, MV. Zhemokletov, N.F. Kuznetsov et al., Soy. J. Chem. Phys. 11(3) p. 606–609 (1992). [trans. from Khim. Fiz. 11(3) pp. 424–432 (???).]Google Scholar
  9. [9]
    S.P. Marsh (ed.), LASL ShockHugoniotData, Univ. Calif. Press, Berkley, (1980).Google Scholar
  10. [10]
    W.J. Nellis and A.C. Mitchell, J. Chem. Phys. 73 (12), pp. 6137–6145 (1980).ADSCrossRefGoogle Scholar
  11. [11]
    V.N. Zubarev and G.S. Telegin, Dokl. Phys. Chem. Section 147(2) pp. 867–870 (1962). [trans. fromDokl. Acad. NaukSSSR 142(2) pp. 309–312 (1962).]Google Scholar
  12. [12]
    G.L. Schott, High Pressure Research 6 (3), pp 187–200 (1991).ADSCrossRefGoogle Scholar
  13. [13]
    W.J. Nellis, F.H. Ree, A.C. Mitchell, and M. van Thiel, J. Chem. Phys. 75 (6), pp. 3055–3063 (1981).ADSCrossRefGoogle Scholar
  14. [14]
    N.B. Vargaftik, Handbook on Thermophysical Properties of Gases and Fluids, FIFML (1963). (in Russian)Google Scholar
  15. [15]
    B.I. Verkin (ed.), Properties of Condensed Phases of Hydrogen and Oxygen, Naukova Dumka, Kiev, (1984). (in Russian)Google Scholar
  16. [16]
    V.P. Kopyshev and V.V. Khrustalev, Zh. Prikl. Mekh. Tekh. Fiz. 1, pp. 122–128 (1971).Google Scholar
  17. [17]
    M.P. Vukalovich and I.I. Novikov, Equation of State ofReal Gases, Gosenergoizat, (1948). (in Russian)Google Scholar
  18. [18]
    C.L. Mader, Numerical Modeling ofDetonations, University of California Press, Berkeley (1979), p. 270.Google Scholar
  19. [19]
    Dobratz B.M. LLNL Explosives Handbook LLL Calif.: Univ. Calif., 1981.Google Scholar
  20. [20]
    H. Hornberg, Propellants, Explosives, Pyrotechnics, 11 (1), pp. 23–31 (1986).CrossRefGoogle Scholar
  21. [21]
    I-Feng Lan, Sheng-Chin Hung, Chun-Yu Cher, et al., Propellants, Explosives, Pyrotechnics, 18, pp. 18–24 (1993).CrossRefGoogle Scholar
  22. [22]
    A.B. Medvedev, Khim. Fin 14 (2–3), pp. 56–64 (1995).Google Scholar
  23. [23]
    A.V. Bushman B.N. Lomakin, V.A. Sechenov, V.E. Fortov, O.E. Shchekotov, and I.I. Sharipdzhanov, Sov. Phys.-JETP 42(5), pp. 828–831(1976) [trans. from Zh. Eksp. Teor. Fiz. 69 (5), pp. 1624–1633 (1975).ADSGoogle Scholar
  24. [24]
    I.Ya. Dikhter and V.A. Zeigarnik, High Temperature 15(1) pp.167–169 (1977). [trans. from Teplofiz. Vys. Temp. 15(1) pp.196–198 (1977).]Google Scholar
  25. [25]
    I.N. Makasenko, H.M. Nikolaenko, and S.M. Stishov: Liquid Metals-1976 (ed. R. Evans and D.A. Greenwood) Institute of Physics, Bristol, (1977), pp. 79–89.Google Scholar
  26. [26]
    V.F. Kozhevnikov, Sov. Phys.-JETP 70(2) pp. 298–310 (1990). [Trans. from Zh. Eksp. Teor. Fiz. 97(2) pp. 541–558 (1990).]Google Scholar
  27. [27]
    N.B. Vargaftik, L.D. Volyak, V.G. Stepanov, V. D. Sheherbakov and P.I. Baumshtein, High Temperature 15(1) pp. 550–556 (1977). [trans. from Teplofiz. Vys. Temp. 23(4) pp. 692–698 (1985).]Google Scholar
  28. [28]
    B.G. Braviy, S.P. Vetchinin, A.V. Kirillin, and A.T. Kunavin High Temperature 15(1) pp. 1–6 (1977). [trans. from Teplofiz. Vys. Temp. 15(1) pp. 1–7 (1977).]Google Scholar
  29. [29]
    V.P. Kopyshev and A.B. Medvedev, Soy. Tech. Rev. B. Therm. Phys. Rev. 5, pp. 37–93 (1993).Google Scholar
  30. [30]
    V.P. Kopyshev and A.B. Medvedev, Thermodynamic Model of Compressed Covolume, VNIIEF, Sarov (1995), p. 121.Google Scholar
  31. [31]
    M.V. Zhemokletov, A.B. Medvedev, and G.V. Simakov, Khim. Fiz. 14(2–3) pp. 49–55 (1995).]Google Scholar
  32. [32]
    R.F. Trunin and G.V. Simakov, Math Modelirovanie 5 (8), pp. 108–117 (1993).Google Scholar
  33. [33]
    L.V. Al’tshuler, A.A. Bakanova, I.P. Dudoladov, E.A. Dynin, R.F. Trunin, and B.S. Chekin, J. Appl. Mech. Tech. Phys. 22(2) pp. 145–169 (1981). [trans. from Prikl. Mekh. Tekh. Fiz. 2 pp. 3–34 (1981).]Google Scholar
  34. [34]
    K.K. Krupnikov, A.A. Bakanova, M.I. Brazhnik, and R.F. Trunin, Soy. Phys. Doklady (Physics) 8(2), pp. 205–208 (1963). [trans. from Dokl. Acad. Nauk SSSR 148(6), pp. 1302–1305 (1963).]Google Scholar
  35. 13.
    Modification of the van der Waals Model for Dense States of Matter 433Google Scholar
  36. [35]
    L.V. Altshuler, A.A. Bakanova, and R.F. Trunun, Sov. Phys.-JETP 42(1) pp. 91104 (1962).]Google Scholar
  37. [36]
    L.V. Al’tshuler, K.K. Krupnikov, and M.I. Brazhnik, Sov. Phys.-JETP 34(7), pp. 614–619 (1958). [Trans. from, Zh. Eksp. Teor. Fiz. 34(4), pp. 886–893 (1958).]Google Scholar
  38. [37]
    L.V. Alttshuler, S.B. Kormer, A.A. Bakanova, and R.F. Trunin, Sov. Phys.-JETP 11, pp. 573–579 (1960). [trans from Zh. Eksp. Teor. Fiz. 38(3), pp. 790–798 (1960).]Google Scholar
  39. [38]
    L.V. Altshuler and B.S. Chekin, in: The first All-Union Symposium on Pulse Pressures VNIIFTRI, (1974), pp. 5–22.Google Scholar
  40. [39]
    A.C. Mitchell and W.J Nellis, J. Appl. Phys. 52 (5), p. 3363–3374, (1981).ADSCrossRefGoogle Scholar
  41. [40]
    L.V. Al’thhuler, S.B. Kormer, M.I. Brazhnik, L.A. VladimirovGoogle Scholar
  42. M.P. Speranskaya, and A.I. Funtikov, Sov. Phys.-JETP 11 pp. 766–775 (1960). [trans. from: Zh. Eksp: Teor. Fiz. 38(4) pp. 1061–1073 (1960).]Google Scholar
  43. [41]
    L.V. Altthhuler, B.N. Moiseev, L.V. Popov, G.V. Simakov, and R.F. Trunin, Soy. Phys.-JETP 27 pp. 420–422 (1968). [trans. from: Zh. Eksp. Teor. Fiz. 54(3), pp. 785–789 (1968).]Google Scholar
  44. [42]
    R.F. Trunin, M.A. Podurets, B.N. Moiseyev, G.V. Simakov, and L.V. Popov, Sov. Phys.JIfIP 29(4), pp. 630–631 (1969). [trans. from Zh. Eksp. Teor. Fiz. 56(4), pp. 1172–1174 (1969).]Google Scholar
  45. [43]
    R.F.Trunin, M.A. Podurets, G.V. Simakov, L.V. Popov, and B.N. Moiseev, Sov. Phys.-JETP 35, pp. 550–552 (1972). [trans. from Zh. Eksp. Teor. Fiz. 62(3), pp. 1043–1048 (1972).]Google Scholar
  46. [44]
    C.E. Ragan, Phys. Rev. A 25(6), pp.. 3360–3375 (1982).Google Scholar
  47. [45]
    C.E. Ragan, Phys. Rev. A. 29 (3), pp. 1391–1402 (1984).ADSCrossRefGoogle Scholar
  48. [46]
    B.L. Glushak, A.P. Zharkov, M.V. Zhernokletov, V.Ya. Ternovoi, A.S. Filmonov, and V.E. Fortov, Sov. Phys.-JETP 69(4), pp. 739–749 (1989). [trans. from Zh. Eksp. Teor. Fiz. 96(4), pp. 1301–1318 (1989).]Google Scholar
  49. [47]
    B.K. Vodolaga XXVIII EHPRG annual meeting “Materials and high pressures”. Booklet of the abstracts. Bordeanx. France. 1990.Google Scholar
  50. [48]
    A.C. Mitchell, W.J. Nellis, N.C. Holmes, et al. in: Shock waves in Condensed Matter-1983 (eds. J.R. Asay, R.A. Graham, and G.K. Straub) North-Holland, Amsterdam (1984), pp. 81–83.Google Scholar
  51. [49]
    V.A. Simonenko, N.P. Voloshin, A.S. Vladimirov, A.P. Nagibin, V.N. Nogin, V.A. Popov, V.A. Vasilenko, and Yu. A. Shoidin, Sov. Phys.-JETP 61(4), pp. 869–873 (1985). [trans. from Zh. Eksp. Teor. Fiz. 88(4), pp. 1452–1469 (1985).]Google Scholar
  52. [50]
    L.P. Volkov, N.P. Voloshin, A.S. Vladimirov, V.N. Nogin and V.A. Simonenko, Soy. Phys.-JETP Letters 31(11), pp. 588–592 (1980). [trans. from: Pis ‘ma Zh. Eksp. Teor. Fiz. 31(11), pp. 623–627 (1980).]Google Scholar
  53. [51]
    S.B. Kormer, A.I. Funtikov, V.D. Urlin, and A.N. Kolesnikova, Sov. Phys.-JETP 15, pp. 477–488 (1962). [trans. from Zh. Eksp. Teor. Fiz 42(3), pp. 686–702 (1962).]Google Scholar
  54. [52]
    L.V. Alttshuler and A.A. Bakanova, Sov. Phys.-Usp. 11(5), pp. 678–689, (1968). [trans. from Usp. Fizich. Nauk 96(2), pp. 193–215 (1968).]Google Scholar
  55. [53]
    R.F. Trunin, Izvestiya Earth Phys. 22(2) p. 103 (1986). [transi. from Izvestia Akad. NaukSSSRFizika Zemli. (2) p. 26 (1986).]Google Scholar
  56. [54]
    R.G. McQueen, J.N. Fritz, and C.E. Morris, in: Shock Compression of Condensed Matter-1983 (eds. J.R. Asay, R.A. Graham, and G.K. Straub), North-Holland, Amsterdam, pp. 95–98 (1984).Google Scholar
  57. [55]
    J.M.Brown and R.G. McQueen, Geophys. Res. Lett. 91, p. 7485–7494 (1986).Google Scholar
  58. [56]
    R.S. Hixson, D.A. Boness, J.W. Shaner, and J.A. Moriarty, Phys. Rev. Lett. 62 (6), p. 637–640 (1989).ADSCrossRefGoogle Scholar
  59. [57]
    J.M. Brown and J.W. Shaner, in: Shock Compression of Condensed Matter-1983 (eds. J.R. Asay, R.A. Graham, and G.K. Straub), North-Holland, Amsterdam, pp. 91–94 (1984).Google Scholar
  60. [58]
    D.A. Boness, J.M. Brown, and J.W. Shaner, in: Shock Waves in Condensed Matter-1987 (eds. S.C. Schmidt and N.C. Holmes) North-Holland (1988), pp. 115–118.Google Scholar
  61. [59]
    E.N. Avrorin, B.K. Vodolaga, N.P. Voloshin, V. F. Kuropatenko, G.V. Kovalenko, V.A. Simonenko, and B.T. Chemovolyuk, JETP Letters 43(5) pp. 308–311 (1986). [trans. from: Pis ‘ma Zh. Eksp. Teor. Fiz. 43(5) pp. 241–244 (1986).]Google Scholar
  62. [60]
    I.Sh. Model’, A.T. Narozhny, A.I. Kharchenko, S.A. Kholin, and V.V. Khrustalev, JETP Letters 41(6), pp. 332–334 (1985). [trans. from Pis ‘ma Zh. Eksp. Teor. Fiz. 41 (6), pp. 270–272 (1985).Google Scholar
  63. [61]
    A.S. Vladimorov, N.P. Voloshin, V.N. Nogin, V.A. Nogin, A.V. Petrovtsev, and V.A. Simonenko, JETP Letters 39(2) pp. 82–85 (1984). [trans. from Pis ‘ma Zh. Eksp. Teor. Fiz. 39(2) pp. 69–72 (1984).]Google Scholar
  64. N.N. Kalitkin, Soy. Phys.-JETP 11(5) pp. 1106–1110 (1960) [trans. from Zh. Eksp. Teor. Fiz. 38(5) pp., 1534–1540 (1960).Google Scholar
  65. [63]
    V.P. Kopyshev, in: Numerical Methods of Continuous Media Mechanics 8(6) (1977), pp. 54–67. (in Russian)Google Scholar
  66. [64]
    H.K. Mao, P.M. Bell, J.W. Shaner, and D.J. Steinberg, J. Appl. Phys. 49 (6) pp. 3276–3283 (1978).ADSCrossRefGoogle Scholar
  67. [65]
    J. Wu, H.K. Mao, and P.M. Bell, High Temp. High Press. 16, pp. 495–499 (1984).Google Scholar
  68. [66]
    H.K. Mao, Y. Wu, L.C. Chen, et al. in: High Pressure Science and Technology. (ed. W.B. Holzapfel and P.G. Johansen) Gordon and Breach, New York (1989), pp. 773–775.Google Scholar
  69. [67]
    L.V. Al’tshuler, M.I. Brazhnik, and G.S. Telegin, J. AppL Mech Tech. Phys. 12 pp. 921–926 (1971). [trans. from Prikl. Mekh. Tekh. Fiz. 6 pp. 159–166 (1971).]Google Scholar
  70. [68]
    M.V. Zhemokletov, V.N. Zubarev, and Yu.N. Sutulov, AppL Mech. Tech. Phys. 25(1) pp. 107–110 (1984). [trans. from Prikl. Mekh. Tekh. Fiz. 25(1) pp. 119–123 (1984).]Google Scholar
  71. [69]
    R.F. Trunin, G.V. Simakov, Yu.N. Sutulov, A.B. Medvedev, B.D. Rogozkir, and Yu.E. Fedorov, Sov. Phys. JETP 69(3) pp 580–588 (1989). [trans. from: Zh. Eksp. Teor. Fiz. 96(3) pp. 1024–1038 (1989).]Google Scholar
  72. [70]
    M. van Thiel (ed.), Compendium of Shock WaveData, Lawrence Livermore National Laboratory report UCRL-50108, Vol. 1, Livermore, CA, (1977).Google Scholar
  73. [71]
    R.S. Hixon, M.A. Winkler, and J.W. Shaner, High Temp. High Press. 18, pp. 635638 (1986).Google Scholar
  74. [72]
    R.S. Hixon, M.A. Winkler, and J.W. Shaner, Physica 139/140, pp. 893–896 (1986).Google Scholar
  75. [73]
    L.V. A1’tshuler, A.V. Bushman, M.V. Zhemokletov, V.N. Zubarev, A.A. Leont’ev, and V.E. Fortov Soy. Phys.—JETP 51(2) pp. 373–383 (1980). [trans. from Zh. Eksp. Teor. Fiz. 78(2) p. 741–760, (1980).]Google Scholar
  76. [74]
    P. De Beaumont and J. Leygonie, in: Proc. Fifth Symp. (International) on Detonation, Report ACR-184, Office of Naval Research, Arlington, VA, (1970) pp. 430–439.Google Scholar
  77. [75]
    L.V. A1’tshuler, A.A. Bakanova, A.V. Bushman et al., Soy. Phys.—JETP 46(5) pp. 980–983 (1986). [trans. from: Zh. Eksp. Teor. Fiz. 73(11) pp. 1866–1872 (1977).]Google Scholar

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