Third-Order Elastic Constants of Ge at Room and Liquid-Nitrogen Temperatures

Abstract

Keating's theory is applied to explain the recent experimental data of the third-order elastic moduli for Ge at room and liquid-nitrogen temperatures. The agreement between theory and experiment obtained for the new data at 293°K is better than that obtained by Keating. Also, the theory explains the experimental data at 77°K in an excellent way. It is found that unlike the other anharmonic interactions, the nearest-neighbor central one is further enhanced with the lowering of the temperature. The important parameter in Akhiezer's theory for microwave phonon attenuation in solids, called the nonlinearity constant D, has also been calculated for the said temperatures for 〈100〉 and 〈111〉 directions of ultrasonic longitudinal wave propagation, and in both the cases, it is found to be temperature dependent. The present work represents the first experimental support for our previous prediction, derived on the phonon conductivity data for Si, that D is temperature dependent and decreases at low temperatures.