Generalized Grüneisen tensor from solid nonlinearity parameters

Anharmonic effects in solids are often described in terms of generalized Gr\"uneisen parameters which measure the strain dependence of the lattice vibrational frequencies. The relationship between these parameters and the solid nonlinearity parameters measured directly in ultrasonic harmonic generation experiments is derived using an approach valid for normal-mode elastic wave propagation in any crystalline direction. The resulting generalized Gr\"uneisen parameters are purely isentropic in contrast to the Brugger-Gr\"uneisen parameters which are of a mixed thermodynamic state. Experimental data comparing the isentropic generalized Gr\"uneisen parameters and the Brugger-Gr\"uneisen parameters are presented.