Temperature variation of acoustic attenuation and nonlinearity constant in Ge and GaAs

The temperature dependence of the nonlinearity constant in pure germanium has been estimated for longitudinal waves along [110] and [111] directions and for shear waves along [110] direction with polarization along [11̄0] and [001] directions in the temperature range 25–293 K. The nonlinearity constant estimated from second order elastic constants and third order elastic constants has been further used to evaluate the ultrasonic attentuation at 475 MHz in Ge for (i) longitudinal waves along the [110] direction and (ii) for shear waves along the [110] directions. We have also estimated the nonlinearity constant and ultrasonic attenuation for longitudinal waves at 306 MHz along the [111] direction. The estimated values of attenuation have been compared with the experimental values of attenuation available in the literature. They are found to be in good agreement with the experimental values. The estimated values of nonlinearity constant increases with temperature for longitudinal waves whereas it shows a negative temperature coefficient for shear waves. The results are similar for Si and Cu. The nonlinearity constant for GaAs at 298 K is estimated from elastic moduli data for longitudinal waves along [111] direction and for shear waves along [110] direction with polarization along [001] direction and then the frequency dependence of ultrasonic attenuation have been estimated. Comparison with the experimental values available in literature shows that the results are quite satisfactory. It is worthwhile to mention that the Mason’s nonlinearity constant D is deceptively similar to the nonlinearity parameter β defined by Breazeale and coworkers. The nonlinearity constant D is evaluated from the knowledge of the Gruneisen number γ ji for various modes and directions and other data, whereas the nonlinearity parameter β is the negative ratio of coefficients of nonlinear term to the linear term of the (dissipationless) nonlinear wave equation. Both D and β are in general temperature dependent.