The search for a universal equation of state correct up to very high pressures

Abstract

The universal equations of state of solids recently proposed by several authors have been examined by comparing them with the theoretical results calculated by the augmented-plane-wave method and the quantum-statistical model proposed by Kalitkin and Kuz'mina from low to ultra-high pressures. It has been shown that the Vinet equation is in good agreement with the theoretical results both for the P - V relation and for the pressure dependence of the isothermal bulk modulus up to for monatomic solids and up to for diatomic solids. The Kumari - Dass and the Dodson equations become less successful below if the zero-pressure values for and are used. For monatomic solids the Holzapfel equation has a very similar structure to that of the Vinet equation at low and medium compressions and it is in good agreement with the theoretical values up to ultra-high pressures. For the application to polyatomic solids a remedy for the shortcomings of the Vinet equation at very high pressures is given on the basis of the quantum-statistical model. The resulting equation is in good agreement with the theoretical values from low to ultra-high pressures both for monatomic and for diatomic solids.