Measurement of Third-Order Moduli of Silicon and Germanium

Experimental techniques for determining third‐order moduli of single crystals by means of ultrasonic wave propagation are described. Results for silicon and germanium demonstrate a good degree of self‐consistency among the basic experimental data obtained with both hydrostatic and uniaxial pressure. In units of 10¹² dyn/cm² and for 25°C, the third‐order moduli are: $$\begin{array}{ccc}\mathrm{Modulus}& \mathrm{Value\; for\; Si}& \mathrm{Value\; for\; Ge}\\ {\mathrm{C}}_{111}& \text{−8.25±0.10}& \text{−7.10±0.06}\\ {\mathrm{C}}_{112}& \text{−4.51±0.05}& \text{−3.89±0.03}\\ {\mathrm{C}}_{123}& \text{−0.64±0.10}& \text{−0.18±0.06}\\ {\mathrm{C}}_{144}& \text{+0.12±0.25}& \text{−0.23±0.16}\\ {\mathrm{C}}_{166}& \text{−3.10±0.10}& \text{−2.92±0.08}\\ {\mathrm{C}}_{456}& \text{−0.64±0.20}& \text{−0.53±0.07}\end{array}$$ Thermodynamic definitions for the moduli (K. Brugger, Phys. Rev. 133, A1611 (1964)] have been used.