How to enhance the applicability of Murnaghan equation of state

Abstract

The paper presents the brief overview of known isothermal equations of state for solids and of theoretical background to construct them, focusing on widely used Murnaghan equation. Since the latter has a limited range of application, failing to reproduce reliably both near-equilibrium and high-pressure regions simultaneously, the paper proposes simple, but rather efficient way to improve it. The suggested modification favors its applicability at high pressures, allowing to expand considerably the region of reliable reproducing of experimental or computational data. The proposed improved equation has been tested in fitting of U(V) data, obtained within ab initio computations, as well as of experimental V-P data for a representative selection of solids. In comparison with ordinary Murnaghan equation, it has found significant advantages, extending the range, where the computational data may be reproduced trustworthy (from the equilibrium state to the pressures, appreciably higher, the ordinary equation could). As for the fitting of experimental data, the proposed improved Murnaghan equation reproduces them, in the presented examples, at least not worse than other well-known equations (Vinet, Birch-Murnaghan, Mao) do. Some aspects of fitting process, as well as some alternative approaches to obtain the proposed equation of state in various forms are also discussed.