Third-Order Elastic Moduli of Germanium

Abstract

Measurements have been made for all six third-order elastic moduli of germanium by measuring ultrasonic velocities in selected directions when directed static stresses are applied to the crystal. Three measurements are obtained by using hydrostatic pressures, three by using a static compression along the <001> axis, and six by stressing the <110> axis with measurements being made along the <001> direction and the <11̄0> direction. Using the finite strain formulas of Murnaghan, the measured velocities are related to the three second-order elastic moduli and the six third-order elastic moduli for a cubic crystal. The 12 sets of measurements provide considerable overlap, and the probable errors are shown to be moderate.