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Physical contradictions and remedies using simple polythermal equations of state

¹ Department of Earth Sciences, University of Bristol, Wills Memorial Building, Queen’s Road, Bristol BS8 1RJ, U.K.
² Institute for Mineralogy and Petrography, ETH Zurich, Sonneggstrasse 5, 8092 Zurich, Switzerland

Correspondence: ^* E-mail: george{at}geology.bristol.ac.uk

Simple polythermal extensions to two widely used isothermal equations of state, the Murnaghan and the Birch-Murnaghan, can lead to non-physical material behavior without proper parameterization: the thermal expansivity at high pressure can become negative. We show how this arises and propose a remedy using an approximation to the thermal relaxation of the bulk modulus. Using the revised equation of state for thermodynamic equilibrium calculations leads to low-pressure and -temperature behavior indistinguishable from the unmodified equation of state, yet extrapolates to high pressure and temperature without non-physical behavior.

Key Words: Thermodynamics • equation of state properties • phase equilibria • calculation • high-pressure studies • expansivity measurements • negative expansivity