Dispersion of longitudinal waves propagating in materials with point defects

The paper investigates the propagation of harmonic waves in materials with point defects. The problem is described by a system of differential equations, which includes a dynamic equation of the theory of elasticity and kinetic equations of defect densities taking into account the mutual influence of defects and a propagating wave, as well as mutual recombination of defects. We consider both limit cases, materials with one type of point defects (vacancies, interstitials), and the general case if the material contains both types of point defects (vacancies and interstitials). We analyzed the effect on the amplitude and velocity of the harmonic wave of the parameters of point defects characterizing the diffusion of defects, the rate of their recombination on drains and the change in the volume of the material when one point defect is formed in it. It has been shown that in media with vacancies, longitudinal waves of low frequency have a higher amplitude and velocity than in media with interstitials. At the same time, in media with vacancies, the velocities of low-frequency perturbations reach large values, and in media with interstitials they reach smaller values, compared to high-frequency perturbations. A frequency range has been identified in which the dispersion of longitudinal waves is significant, in media with vacancies it is normal, and in media with interstitials it is abnormal. The increasing diffusion coefficient or the decreasing dilation parameter contributes to a weaker dispersion. It is noted that the diffusion coefficients of defects do not affect the existence of an additional low-frequency wave. For high frequency waves, media with vacancies and interstitials are practically indistinguishable; the presence of any point defects almost does not affect the propagation rate of high-frequency perturbations and their amplitude.