Temperature variation of some combinations of third-order elastic constants of silicon between 300 and 3 °K

The ultrasonic harmonic generation technique has been used to determine the nonlinearity parameters of silicon between room temperature and 3 °K. By measuring the amplitude of the second harmonic of an initially sinusoidal longitudinal ultrasonic wave propagating along the three principal directions, the temperature dependence of three linear combinations of third-order elastic (TOE) constants of silicon have been studied. Between room temperature and 77 °K, the magnitude of the TOE constants does not vary much as a function of temperature. Between 77 and 3 °K, C111 changes by 3.5%, C112+4C166 changes by 11.7%, and C123+6C144+8C456 changes by −207%. All these combinations are negative at room temperature as well as at low temperatures except C123+6C144+8C456 which is positive below 8 °K. Room-temperature values of the strain generalized Grüneisen parameters of silicon have been calculated from measured nonlinearity parameters and are compared with existing values. Complete sets of third-order elastic constants at 298, 77, and 4 °K have been calculated by combining our nonlinearity parameters with pressure derivatives of elastic constants measured by Beattie and Schirber [Phys. Rev. B 1, 1548 (1970)].