A Simple, Potential-Free Model to Calculate Elastic Constants of Solids at High Temperature

Abstract

A simple method for the determination of temperature dependent second order elastic constants (SOEC) of MgO, CaO, Mg2SiO4 and Grossular garnet[Ca3Al2(SiO4)3] using a potential free model based on thermodynamical relationships, has been proposed. The equations developed here are based on the linear relationship between elastic constants at temperatures higher than the Debye temperature. The extrapolated data for elastic constants at very high temperatures obtained in the present study are useful to understand the thermoelastic properties of given solids. It is found that the calculated values of elastic constants, in general, decrease with temperature. The theoretical predictions incorporating the concept of Debye temperature, reported in this paper, are well supported by the available experimental data. The proposed empirical relationship provides a method to estimate the thermoelastic properties of geophysical minerals and solids at high temperature range.