A Variant of the Description of the Acoustic and Optical Branches of the Dispersion Law of High-Frequency Waves in an Elastic Medium

Abstract

This paper presents an alternative description of the acoustic and optical branches of the law of dispersion for high-frequency waves in an elastic medium. For longitudinal and transverse plane waves which propagate in an elastic media the dispersion law consists of two sections—acoustic and optical for large oscillation frequency values. The acoustic branch has a description both in mechanics of deformable solids and in solid-state physics. The optical branch is described only by solid-state physics. According to it, the oscillations of neighboring atoms in the crystal lattice for the optical branch occur in the antiphase. This can lead to the destruction of interatomic bonds and substance. Methods of solid physics for materials having complex chemical composition and structure are difficult to apply. Therefore, the description for the optical branch of the dispersion law in the framework of continuum mechanics is relevant. The paper uses a version of the moment elasticity theory which is a consequence of the nonlocal model of a continuous material, considering the pair and triple interactions between its infinitesimal particles. Another feature of the oscillations relevant for the optical branch includes by that they are similar to the thermal vibrations of atoms. They are characterized by anharmonicity—such a shift in the center of oscillations, that the average distance between atoms increases. The proposed model considers the influence of anharmonicity on the stress state of the material in the construction of the equation for conservation law of linear momentum. This equation is a balance equation for changing the total linear momentum of a substance particle for a finite, rather than infinitely small, time frame. This finite segment is a material constant. The method of its definition is specified in this work. The obtained theoretical results satisfactorily correspond to the experimental data available in the literature.