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

Abstract

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\ifmmode^\circ\else\textdegree\fi{}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\ifmmode^\circ\else\textdegree\fi{}K the magnitude of the TOE constants does not vary greatly as a function of temperature. Between 77 and 3\ifmmode^\circ\else\textdegree\fi{}K, ${C}_{111}$ changes by + 3%, (${C}_{112}+4{C}_{166}$) changes by + 16%, and ($6{C}_{144}+{C}_{123}+8{C}_{456}$) changes by - 150%. All of these combinations of TOE constants are negative at 77\ifmmode^\circ\else\textdegree\fi{}K, but below 7\ifmmode^\circ\else\textdegree\fi{}K the combination ($6{C}_{144}+{C}_{123}+8{C}_{456}$) is positive. Temperature dependence of additional combinations is inferred by assuming that the "Anderson-Gr\"uneisen parameter" is independent of temperature.