Temperature dependence of elastic constants using thermal energy for geophysical minerals

Abstract

In this paper, we have developed relationship to predict temperature dependence of elastic constants for geophysical minerals by using a formulation for volume dependence of isothermal Anderson–Grünesien parameter which is valid up to extreme compression limit [Formula: see text] or [Formula: see text]. An alternative formulation based on thermal pressure or thermal energy has also been used for determining elastic constants as a function of temperature. The basic idea used in this study is to generalize the expression of bulk modulus for determining temperature dependence of elastic constants. The results thus obtained for MgO, CaO, Mg2SiO4 and Al2O3 from the two different methods are very close to each other and also experimental data. The good agreement reveals the validity of the formulations given in this study.