Temperature dependence of Elastic Constants and Bulk Modulus of metals

The temperature dependence of bulk modules was given by Q. Liu & Q. He13 using fundamental thermodynamic relations. The assumption in this theory was that volume thermal expansion coefficient is quadratic function of temperature. The new expressions and formulations were also derived by Tallon14. In the present study temperature of elastic constants is based on the combination of above mentioned formulations. A method to estimate the temperature dependence of bulk modules is developed with the approximation that coefficient of volume thermal expansion depends linearly on temperature. This approximation is valid only for small expansions in low temperature range.