Ultrasonic second-harmonic generation in various crystalline systems: Coupling parameters in terms of elastic moduli and propagation directions

The ultrasonic second- and third-order coupling parameters, K2 and K3, determined by ultrasonic second-harmonic generation, are evaluated in terms of the second- and third-order elastic moduli, for a number of crystalline systems. It is shown that K2 and K3 turn out simply to be the values of the elastic moduli C11 and C111, transformed into the direction of propagation. The possibility of evaluating the complete set of third-order elastic moduli from measurements of second-harmonic generation and hydrostatic pressure dependence of the sound velocity for pure mode propagation is discussed. Symmetries considered: cubic, hexagonal, rhombohedral, tetragonal, and orthorhombic