A Detailed Study of Ultrasonic Nonlinearity in Relation to other Thermodynamic Properties of Solids: Results for Silicon and Germanium between 3 and 300 K

摘要

It is shown that measurement of the ultrasonic nonlinearity parameters of solids throws light on their thermodynamic properties. Establishment of the relation between ultrasonic nonlinearity and thermal properties has been achieved for the diamond-like solids by determining the third-order elastic (TOE) constants and their variation with temperature. Study has been done on silicon and germanium. The nonlinear equation for the propagation of acoustic waves is derived and solved for longitudinal wave propagation along the pure mode directions of a cubic crystal. Because of the nonlinearity of the medium, an initially sinusoidal 30 MHz wave undergoes waveform distortion and harmonics are generated. The ultrasonic nonlinearity parameters of the medium can conveniently be determined by measuring the amplitudes of the fundamental and generated second harmonic. Such measurements are done as a function of temperature between liquid helium and room temperature using capacitive receiver. The measurements lead to the K3 parameters which are combinations of TOE constants. Temperature variation of these parameters are studied. Combining our results with an established lattice dynamical model for diamond-like solids (the Keating model) has enabled us to determine the anharmonic force constants involved in the model as a function of temperature, and subsequently to determine all the six TOE constants. The temperature variations of all the TOE constants of silicon and germanium are plotted between 3 and 300 K.