Third-order elastic constants of germanium between 300 and 3°K

The ultrasonic harmonic-generation technique has been improved to the point that both amplitude and phase of the second harmonic of an initially sinusoidal ultrasonic wave in a solid can be measured between room temperature and 3°K. By measuring along the principal crystallographic directions, we have been able to determine temperature dependence of linear combinations of third-order elastic (TOE) constants of germanium. Between room temperature and 77°K the magnitude of the TOE constants does not vary greatly as a function of temperature. Between 77 and 3°K, $C_{111}$ changes by + 3%, ($C_{112}+4\mathrm{}{C}_{166}$) changes by + 16%, and ($6C_{144}+C_{123}+8\mathrm{}{C}_{456}$) changes by - 150%. All of these combinations of TOE constants are negative at 77°K, but below 7°K the combination ($6C_{144}+C_{123}+8\mathrm{}{C}_{456}$) is positive. Temperature dependence of additional combinations is inferred by assuming that the "Anderson-Grüneisen parameter" is independent of temperature.