Diffusion model of internal friction in nanocrystalline materials

The stress normal and tangential components arise in grain-boundary segments differently oriented with respect to an external periodic load, causing the fluxes of vacancies and impurity atoms between neighboring segments. By solving the diffusion problem, one can find the velocity of mutual displacement of grains, the stress distribution in the segments with allowance for stress adjustment, and the amount of internal friction. The frequency dependence of the internal friction shows peaks associated with the redistribution of impurity atoms over the segments, grain sliding, and a high-temperature background.