Kinetics of subdiffusive growth of new phase particles in supersaturated solid solutions

摘要

The kinetics of the subdiffusion-limited growth of spherical precipitates is studied. The process is described by the equation of anomalous diffusion with a fractional derivative with respect to time. It is shown that a decrease in the concentration of monomers is described by the law exp(-kt (3 alpha/2)) at the initial stage and the power law t (-alpha) at large times, where 0 < alpha a parts per thousand currency sign 1 is the dispersion parameter coinciding with the order of time derivative in the subdiffusion equation. The time dependence of the size of a spherical precipitate is obtained. The results generalize the Ham diffusion theory and are in agreement with the Monte Carlo simulation data.