Elastic properties and anharmonicity of solids

The squares of the velocities of the longitudinal and transverse acoustic waves separately are practically not associated with anharmonicity, and their ratio $(\nu_L^2/\nu_S^2)$ turns out to be a linear function of the Gruneisen parameter $\gamma$ – the measure of anharmonicity. The obtained dependence of $(\nu_L^2/\nu_S^2)$ on $\gamma$ is in satisfactory agreement with the experimental data. The relationship between the quantity $(\nu_L^2/\nu_S^2)$ and anharmonicity is explained through its dependence on the ratio of the tangential and normal stiffness of the interatomic bond $\lambda$, which is a single-valued function of the Gruneisen parameter $\lambda(\gamma)$. The relationship between Poisson's ratio $\mu$ and Gruneisen parameter $\gamma$, established by Belomestnykh and Tesleva, can be substantiated within the framework of Pineda's theory. Attention is drawn to the nature of the Leont'ev formula, derived directly from the definition of the Gruneisen parameter by averaging the frequency of normal lattice vibration modes. The connection between Gruneisen, Leontiev and Belomestnykh–Tesleva relations is considered. The possibility of a correlation between the harmonic and anharmonic characteristics of solids is discussed.