Abstract
Of the various high pressure experimental data on a given material, the equation of state (EOS) is most amenable to theoretical treatment. Its interpretation involves, in principle,the straightforward application of electron band and lattice dynamical techniques for the calculation of pressure and internal energy as a function of volume and temperature. Though these formulations have been available since 1930’s, it is only during the last decade that considerable progress has been made in EOS computations by using these. Two reasons can be attributed for this advance. One is the considerable development of experiments involving lasers, electrically driven foils and underground nuclear explosions to study EOS at pressures above 100 GPa2–5. Very recently, experimental data on iron and aluminium shocked to ~ 500 TPa have been reported6. These data have opened up a new area in the P-V-T surface for theoretical research, where the pressure and thermal ionisation effects are important. The second is the advent of large and fast computers and improvements in energy band methods themselves. These have made computations less time consuming and have permitted evaluation of total energies of crystalline solids to such a precision that not only can bulk properties like EOS be calculated accurately but energy differences between different phases can be determined to an accuracy of 0.1 ev per atom or better.
Keywords
- Bulk Modulus
- Local Density Approximation
- Helmholtz Free Energy
- Valence Charge
- Ground State Electronic Energy
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E.P. Wigner and F. Seitz, Phys. Rev. 43: 804 (1933).
R.J. Trainor, J.W. Shaner, J.M. Auerbach and N.C. Holmes, Phys. Rev. Lett. 42: 1154 (1979).
R.C. Weingart, Lawrence Livermore Laboratory Report UCRI-52752 (1979).
C.E. Ragan III, Phys. Rev. A 21:458 (1980); Phys. Rev. A 25: 3360 (1982); Phys. Rev. A29: 1391 (1984)
A.P. Volkov, N.P. Voloshin, A.S. Vladimirov, V.N. Nogin and U.A. Simonenkov, JETP Lett. 31: 588 (1981).
A.S. Vladimirov, N.P. Voloshin, V.N. Nogin, A.V. Petrovtsev and U.A. Simonenkov, JETP Lett. 39: 82 (1984).
B.K. Godwal, S.K. Sikka and R. Chidambaram, Phys. Rep. 102: 123 (1983).
Ya. B. Zel’dovich and Yu.P. Raizer in:“Physics of Shock waves and High Temperature Hydrodynamics Phenomena,” Vols. 1amp;2, Academic Press, New York (1967).
P. Hohenberg and W. Kohn, Phys. Rev. 136:B 864 (1964).
W. Kohn and I.J. Sham, Phys. Rev. 140:A 1133 (1965).
J.C. Slater, J. Chem Phys. 57: 2389 (1972).
J. Ihm, A. Zunger and M.L. Cohen, J. Phys. C12: 4409 (1972).
J.A. Moriarty, Phys. Rev. 16:2537 (1977); Phys. Rev. B 26: 1754 (1982).
O.K. Adersen, Phys. Rev. B 12: 3060 (1975).
H.L. Skriver, in “The LMTO Method,” Springer-Verlag Berlin (1984).
T. Neal, in:“High Pressure Science and Technology”, Vol 1:80 K.D. Timmerhaus and M.S. Barber ed., Plenium, New York (1978).
H.K. Godwal, Pramana 19: 225 (1982).
M.T. Yin and M.L. Cohen, Phys. Rev. B26: 3259 (1982).
J.A. Moriarty, D.A. Young and M. Ross, Phys. Rev. B 30: 578 (1984).
A.I. Voropinov, G.M. Gandelman and V.G. Podaval’ny, Sov. Phys. Usp. 13: 56 (1970).
A. K. McMahan, B.L. Hord and M. Ross, Phys. Rev. B 15: 726 (1977).
B.K. Godwal, J. Phys. F10: 377 (1980).
B.K. Godwal, S.K. Sikka and R. Chidambaram, Phys Rev. B 20: 2362 (1979).
M. Ross, Phys. Rev B 20: 4891 (1979).
B.K. Godwal and S.K. Sikka, J. Phys. F 12: 655 (1982).
A. K. McMahan, H. L. Skriver and B. Johansson, Phys. Rev. B23: 5016 (1981).
F. Perrot, Phys. Rev. B21: 3167 (1980).
A.C. Mitchell and W.J. Nellis, J. App. Phys. 52: 3363 (1981).
S.K. Sikka and B.K. Godwal, Sol. State Comm. 38:949 (1981).
S.K. Sikka, Nuclear Physics and Solid State Phys.(India) 21 A: 83 (1978).
D.A. Young and M. Ross, Phys. Rev. B29:682 (1984).
L. Moruzzi, J.F. Jank and A.R. Williams, in:“Calculated Electric Properties of Metals”, Pergamon, New York (1978).
L. V. Al’tshuler, Sov. Phys. Usp. 8: 52 (1965).
B.J. Alder, in:“Solids under Pressure”, W. Paul and D.M. Warschauer ed., McGraw Hill, New York (1963).
D.G. Pettifor, J. Phys. F7: 613 (1977).
Y.K. Vohra, S.K. Sikka and W.B. Holzapfel, J. Phys. F 13: L107 (1983).
B.K. Godwal, S.K. Sikka and R. Chidambaram, Phys. Rev. Lett. 47: 1144 (1981).
C. A. Rouse, in:“Prog. in High Temp. Phys. and Chem.”, Vol 4, C. A. Rouse, ed., Pergamon Press, New York (1971).
B.K. Godwal, Phys. Rev. A 28: 1103 (1983).
R.M. More, Phys. Rev. A 19: 1234 (1979).
D. Liberman, Phys. Rev. B 20: 4891 (1979).
K. Takemura and K. Syassen, J. Phys. F 15: 543 (1985).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Plenum Press, New York
About this chapter
Cite this chapter
Sikka, S.K. (1986). Shock Hugoniot Equation of State - Electron Band Theory Approach. In: Gupta, Y.M. (eds) Shock Waves in Condensed Matter. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2207-8_6
Download citation
DOI: https://doi.org/10.1007/978-1-4613-2207-8_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9296-8
Online ISBN: 978-1-4613-2207-8
eBook Packages: Springer Book Archive