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, C₁₁₁ changes by + 3%, (C₁₁₂+4C₁₆₆) changes by + 16%, and (6C₁₄₄+C₁₂₃+8C₄₅₆) changes by - 150%. All of these combinations of TOE constants are negative at 77^∘{}K, but below 7^∘{}K the combination (6C₁₄₄+C₁₂₃+8C₄₅₆) is positive. Temperature dependence of additional combinations is inferred by assuming that the "Anderson-Gr\"uneisen parameter" is independent of temperature.