Propagation velocity of longitudinal and transverse acoustic waves and anharmonicity of lattice oscillations

A linear correlation between the Grüneisen parameter and ratio of the velocities of longitudinal $(v_l)$ and transverse $(v_t)$ acoustic waves in crystals is found. It is assumed that velocities $v_l$ and $v_t$ are severally harmonic parameters, while their ratio $(v_l/v_t)$ is an anharmonic quantity and depends on the ratio between the shear and flexural rigidities of interatomic bonds.