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

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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.

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