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Fractional kinetics of subdiffusion-limited decomposition of a supersaturated solid solution

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  • Sibatov, R.T.
  • Svetukhin, V.V.

Abstract

Precipitation of atoms and defects can substantially change mechanical, electrical and optical properties of materials. Its kinetics is usually described by some model of diffusion-limited process. Evidence of anomalous diffusion of impurities and defects in disordered solids stimulates to develop generalized models. In present work, we study the kinetics of subdiffusion-limited growth and dissolution of nanoprecipitates in disordered solids on the base of subdiffusion equations with fractional derivatives. Analytical results are compared with Monte Carlo simulation data. Foundation of the fractional model of subdiffusion-limited Ostwald ripening is proposed.

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  • Sibatov, R.T. & Svetukhin, V.V., 2015. "Fractional kinetics of subdiffusion-limited decomposition of a supersaturated solid solution," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 519-526.
    • Handle: RePEc:eee:chsofr:v:81:y:2015:i:pb:p:519-526
    DOI: 10.1016/j.chaos.2015.04.002
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    1. Gorenflo, Rudolf & Mainardi, Francesco & Moretti, Daniele & Pagnini, Gianni & Paradisi, Paolo, 2002. "Fractional diffusion: probability distributions and random walk models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 106-112.
    2. Piryatinska, A. & Saichev, A.I. & Woyczynski, W.A., 2005. "Models of anomalous diffusion: the subdiffusive case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 375-420.
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    Cited by:

    1. Vyacheslav Svetukhin, 2021. "Nucleation Controlled by Non-Fickian Fractional Diffusion," Mathematics, MDPI, vol. 9(7), pages 1-11, March.
    2. Pakhare, Sumit S. & Daftardar-Gejji, Varsha & Badwaik, Dilip S. & Deshpande, Amey & Gade, Prashant M., 2020. "Emergence of order in dynamical phases in coupled fractional gauss map," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).

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