Analysis of finite-strain equations of state for solids under high pressures

We have reformulated equations of state (EOS) for solids based on Lagrangian and Eulerian strains following the method developed by Stacey [Phys. Earth Planet. Inter. 128 (2001) 179]. The expressions thus obtained are used conveniently to assess the validity of various EOS for different types of solids. The logarithmic EOS based on the Hencky measure of finite-strain is also modified by including the higher terms arising from the fourth-order contribution in the Taylor series expansion of the free energy. The results are obtained for pressure (P), isothermal bulk modulus (K-T) and its pressure derivative (dK(T)/dP) for Ne, Ar, Al, Cu, LiH and MgO solids for a wide range of compressions (V/V-0) down to 0.5. The results determined from the finite-strain equations are compared with those obtained from the Vinet-Rydberg equation and the Shanker equation, which are based on the interatomic potential energy functions. The results are also compared with the ab inito values reported by Hama and Suito [J. Phys.: Condens. Matter 8 (1996) 67] determined from first-principles calculations using the augmented plane wave method and the quantum statistical model. The EOS based on the K finite-strain theory due to Keane and Stacey are also discussed, emphasising the importance of K'(infinity), in the limit P --> infinity. (C) 2004 Elsevier B.V. All rights reserved.