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

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{sup 3α/2}) at the initial stage and the power law t{sup −α} at large times, where 0 < α ≤ 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.
Authors:
;  [1]
  1. Ulyanovsk State University (Russian Federation)
Publication Date:
OSTI Identifier:
22472309
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 120; Journal Issue: 4; Other Information: Copyright (c) 2015 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; COMPUTERIZED SIMULATION; CONCENTRATION RATIO; DIFFUSION; DIFFUSION EQUATIONS; MONOMERS; MONTE CARLO METHOD; PRECIPITATION; SOLID SOLUTIONS; SPHERICAL CONFIGURATION; TIME DEPENDENCE