Skip to main content Accessibility help

Equation of state of condensed matter in laser-induced high-pressure regime

  • B.K. GODWAL (a1), R.S. RAO (a1), A.K. VERMA (a1), M. SHUKLA (a1), H.C. PANT (a1) and S.K. SIKKA (a1)...


We have simulated the shock Hugoniot of copper and uranium based on the results of first principles electronic structure calculations. The room temperature isotherm has been obtained by evaluating the accurate ground state total energies at various compressions, and the thermal and electronic excitation contributions were obtained by adopting isotropic models using the results obtained by the band structure calculations. Our calculations ensure smooth consideration of pressure ionization effects as the relevant core states are treated in the semi-core form at the ambient pressure. The pressure variation of the electronic Grüneisen parameter was estimated for copper using the band structure results, which leads to good agreement of the simulated shock Hugoniot with the measured shock data. The simulation results obtained for U are also compared with the experimental data available in literature and with our own data.


Corresponding author

reprint requests to: B.K. Godwal, High Pressure Physics Division, Bhabha Atomic Research Centre, Mumbai—400085, India. E-mail:


Hide All


Batani, D., Balducci, A., Beretta, D., Bernardinello, A., Löwer, T., Koenig, M., Benuzzi, A., Faral, B. & Hall, T. (2000). Equation of state data for gold in the pressure range <10 TPa. Phys. Rev. B 61, 92879294.
Batani, D., Morelli, A., Tomasini, M., Benuzzi-Mounaix, A., Philippe, F., Koenig, M., Marchet, B., Masclet, I., Rabec, M., Reverdin, Ch., Cauble R., Celliers, P., Collins, G., Da Silva, L., Hall, T., Moret, M., Sacchi, B., Baclet, P., &Cathala, B. (2002). Equation of state data for iron at pressures beyond 10 Mbar. Phys. Rev. E 88, 235502 14.
Benuzzi, A., Löwer, T., Koenig, M., Faral, B., Batani, D., Beretta, D., Dawson, C. & Kepler, D. (1996). Indirect and direct laser driven shock waves and application to copper equation of state measurements in 10–40 Mbar pressure range. Phys. Rev. E 54, 21622165.
Blaha, P., Schwarz, K., Madsen, G.K.H., Kvasnicka, D. & Luitz, J. (2001). An augmented plane wave + local orbital program for calculating crystal properties. Wien, Austria: Technische Universität.
Car, R. & Parrinello, M. (1985). Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 24712474.
Cauble, R., Perry, T.S., Bach, D.R., Budil, K.S., Hammel, B.A., Collins, G.W., Gold, D.M., Dunn, J., Celliers, P., Da Silva, L.B., Foord, M.E., Wallace, R.J., Stewart, R.E. & Woolsey, N.C. (1998). Absolute equation-of-state data in the 10–40 Mbar (1–4 TPa) regime. Phys. Rev. Lett 80, 12481251.
Collins, J.G. & White, G.K. (1964). In Progress in Low Temperature Physics (Gorter, C.J., Ed.), Vol. IV. Amsterdam: North-Holland.
Ercolessi, F. & Adams, J. B. (1994). Interatomic potential from first-principle calculations: The force matching methods. Euro. Phys. Lett. 26, 583588.
Godwal, B.K., Sikka, S.K. & Chidambaram R. (1979). Electronic Grüneisen parameter in the shock Hugoniot equation of state of aluminum. Phys. Rev. B 20, 23622365.
Godwal, B.K., Sikka, S.K. & Chidambaram, R. (1981). Model for the equation of state of condensed matter in the “intermediate” pressure (about 0.5–10 TPa) region. Phys. Rev. Lett. 47, 11441147.
Godwal, B.K., Sikka, S.K. & Chidambaram, R. (1983). Equation of state theories of condensed matter up to about 10 GPa. Phys. Rep. 102, 121197.
Godwal, B.K. & Jeanloz, R. (1989). First-principles equation of state of gold. Phys. Rev. B 40, 75017507.
Godwal, B.K. & Jeanloz, R. (1990). Pressure-induced s → d transfer and the equation of state of molybdenum. Phys. Rev. B 41, 74407445.
Godwal, B.K. (1995). Condensed matter at ultra-high pressures. Curr. Sci. 68, 10871095.
Godwal, B.K., Meenakshi, S., Modak, P., Rao, R.S., Sikka, S.K., Vijayakumar, V., Bussetto, E. & Lausi, A. (2002). Evidence of a Lifshitz transition in the high-pressure behavior of the intermetallic compound AuIn2. Phys. Rev. B 65, 140101 14. [Rapid commun.].
Godwal, B.K., Modak, P. & Rao, R.S. (2003). On the high pressure electronic topological transitions in zinc. Solid State Commun. 125, 401405.
Heine, V. (1994). Ab initio simulation of complex processes in solids. Condens. Matter Phys. 16, 379385.
Hohenberg, P.C. & Kohn, W. (1964). Inhomogeneous electron gas. Phys. Rev. B 136, 864871.
Koenig, M., Faral, B., Bondenne, J.M., Batani, D., Benuzzi, A., Bossi, S., Remond, C., Perrine, J.P., Temporal, M. & Atzeni, S. (1995). Relative consistency of equation of state by laser driven shock waves. Phys. Rev. Lett. 74, 22602263.
Kohn, W. & Sham, L.J. (1965). Self-consistent equations including exchange and correlation effects. Phys. Rev. A 140, 11331138.
Marsh, S.P. (ed.). (1980). LASL Shock Hugoniot Data, Los Angeles: University of California Press.
McMahan, A.K. & Ross, M. (1977). High-temperature electron-band calculations. Phys. Rev. B 15, 718725.
Mermin, N.D. (1965). Thermal properties of the inhomogeneous electron gas. Phys. Rev. A 137, 14411443.
Mitchell, A.C., Nellis, W.J., Moriarty, J.A., Heinle, R.A., Holmes, N.C., Tipton, R.E. & Repp, G.W. (1991). Equation of state of Al, Cu, Mo and Pb at shock pressures up to 2.4 TPa (24 Mbar). J. Appl. Phys. 69, 29812986.
Narasimhan, S. & Gironcoli, S. (2002). Ab initio calculation of the thermal properties of Cu: Performance of the LDA and GGA. Phys. Rev. B 65, 064302 18.
Nellis, W.J., Moriarty, J.A., Mitchell, A.C., Ross, M., Dandrea, R.G., Ashcroft, N.W., Holmes, N.C. & Gathers, G.R. (1988). Metal physics at ultrahigh pressure: Al, Cu and lead as prototypes. Phys. Rev. Lett. 60, 14141417.
Pant, H.C., Shukla, M., Senecha, V.K., Bandyopadhyay, S., Rai, V.N., Khare, P., Bhat, R.K., Godwal, B.K. & Gupta, N.K. (2002). Equation of state studies using laser driven shock wave propagation through layered foil targets. Curr. Sci. 82, 149157.
Perdew, J.P., Burke, K. & Ernzerhof, M. (1996). Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 38653868.
Perdew, J.P., Kurth, S., Zupan, A. & Blaha, P. (1999). Accurate density functional with correct formal properties: A step beyond the generalized gradient approximation. Phys. Rev. Lett. 82, 25442547.
Pickett, W.E., Freeman, A.J., & Koelling, D.D. (1980). Self-consistent linearized augmented-plane-wave study of the electronic structure and superconductivity of fcc lanthanum under pressure. Phys. Rev. B 22, 26952715.
Ragan, C.E., III (1982). Shock compression measurements at 1 to 7 TPa. Phys. Rev. A 25, 33603375.
Rai, V.N., Shukla, M., Pant, H.C. & Bhawalkar, D.D. (1995). Development of picosecond time resolution optical and X-ray streak cameras. Sadhana 20, 937954.
Rao, R.S., Godwal, B.K. & Sikka, S.K. (1992). Thorium: A 5f-band metal at ultrahigh pressures. Phys. Rev. B 46, 57805782.
Rao, R.S., Godwal, B.K., Sikka, S.K. & Chidambaram, R. (1994). Occupancy of central sites in the Zn49Mg32 quasicrystal from total-energy computations on its crystal approximant. Phys. Rev. B 50, 1563215635.
Rao, R.S., Modak, P., Godwal, B.K. & Sikka, S.K. (1999). Stability of the pressure-induced orthorhombic phase of iron. Phys. Rev. B 59, 1349813500.
Ross, M. & Young, D.A. (1993). Theory of equation of state at high pressure. Annu. Rev. Phys. Chem. 44, 6187.
Rothman, S.D., Evans, A.M., Harsfield, C.J., Graham, P. & Thomes, B.R. (2002). Impedance match equation of state experiments using indirectly laser driven multimegabar shocks. Phys. Plasmas 9, 17211733.
Struzhkin, V.V., Timofeev, Y.A., Hemley, R.J. & Mao, H. (1997). Superconducting Tc and electron-phonon coupling in Nb to 132 GPa: Magnetic susceptibility at megabar pressures. Phys. Rev. Lett. 79, 42624265.
T-4 Group (1983). SESAME report on the Los Alamos Equation-of-State Library, LANL Report No.LALP-83-4. Los Alamos, NM: Los Alamos National Laboratory.
Vladimirov, A.S., Voloshin, N.P., Nogin, V.N., Petrovtsev, A.V. & Simonenko, V.A. (1984). Shock compressibility of aluminum at P ≥ 1 Gbar. JETP Lett. 39, 8285.
Wang, Y., Chen, D. & Zhang, X. (2000). Calculated equation of state of Al, Cu, Ta, Mo, and W to 1000 GPa. Phys. Rev. Lett. 84, 32203223.
Zel'dovich, Ya.B. & Raizer, YuP. (1976). Physics of shock waves and high temperature hydrodynamics phenomena, vol. 1 and 2. New York: Academic Press.


Equation of state of condensed matter in laser-induced high-pressure regime

  • B.K. GODWAL (a1), R.S. RAO (a1), A.K. VERMA (a1), M. SHUKLA (a1), H.C. PANT (a1) and S.K. SIKKA (a1)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed