Iterative Procedure to Estimate the Values of Elastic Constants of a Cubic Solid at High Pressures from the Sound Wave Velocity Measurements

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Abstract
In order to estimate accurately the values of the elastic constants of a solid at high pressure and at an arbitrary temperature T from the ultrasonic measurements of the velocities of elastic waves propagated in solids as a function of pressure at the temperature T, it is necessary to know a priori the compressibility of the solid as a function of pressure at the temperature T. However, this latter information is not always available. Hence, one has to make some kind of approximation to estimate the values of the elastic constants of solids at high pressure. The procedure developed here is more consistent than previous procedures. It requires a priori knowledge of the following values: the thermal expansion coefficient, its temperature derivative, the specific heat at constant pressure of a solid at one atmosphere, and the travel-time measurements of the elastic waves propagated through the solid as a function of pressure at a temperature T or at more than one temperature.

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