Temperature effects on the universal equation of state of solids

TLDR

A universal equation of state for solids has been proposed, but its application to pressure–volume relations requires three temperature‑dependent parameters and is limited to regimes without phase transitions. This study demonstrates that the data required to predict high‑temperature thermodynamic properties can be drastically reduced. By using only four reference‑temperature parameters—zero‑pressure bulk modulus, its pressure derivative, volume, and thermal expansion—the authors generate predictions for high‑temperature isotherms, thermal expansion, and temperature dependence of bulk modulus and its derivative, which are then validated against experimental data for gold, sodium chloride, and xenon. The predictions show good agreement with experimental measurements.

Abstract

Recently it has been argued, based on theoretical calculations and experimental data, that there is a universal form for the equation of state of solids. This observation was restricted to the range of temperatures and pressures such that there are no phase transitions. The use of this universal relation to estimate pressure-volume relations (i.e., isotherms) required three input parameters at each fixed temperature. In this paper we show that for many solids the input data needed to predict high-temperature thermodynamical properties can be dramatically reduced. In particular, only four numbers are needed: (1) the zero pressure (P=0) isothermal bulk modulus, (2) its P=0 pressure derivative, (3) the P=0 volume, and (4) the P=0 thermal expansion; all evaluated at a single (reference) temperature. Explicit predictions are made for the high-temperature isotherms, the thermal expansion as a function of temperature, and the temperature variation of the isothermal bulk modulus and its pressure derivative. These predictions are tested using experimental data for three representative solids: gold, sodium chloride, and xenon. Good agreement between theory and experiment is found.