Pressure Dependence of the Elastic Constants for Aluminum from 77° to 300°K

Abstract

To study the anharmonic properties of Al at low temperatures, the pressure derivatives of the elastic constants have been measured from 77° to 300°K. The isothermal elastic constants are obtained as a function of pressure by a self‐consistent analysis of the ultrasonic data. The most probable values for the pressure derivatives are calculated from the results of six measurements of different combinations of the elastic constants. The pressure derivatives are found to be almost constant below Θ_D/3 and increasing for higher temperatures. Using the quasiharmonic approximation, the Grüneisen constant γ is calculated from our results and found to be about 15% higher than the thermal γ in the temperature range studied. We have calculated the elastic γ for T≪Θ_D from the extrapolated values of the pressure derivatives. It turns out to be 2.51, a value in excellent agreement with the low‐temperature lattice thermal γ. The equation of state in the Murnaghan form and in a series expansion of the volume change in terms of pressure is discussed for Al. A good agreement can be obtained between the ultrasonic and the static and shock compression results if the latter data are analyzed according to the Murnaghan equation of state.