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Nonlinear diffusion in spinodal decomposition: a numerical solution

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Abstract

The numerical solution of the one-dimensional nonlinear diffusion equation with a negative diffusion coefficient (up-hill diffusion) by a five-point approximation central difference scheme is considered. The stability criteria are discussed in detail and a numerical solution is provided for a specific case in which the time evolution of a periodic composition wave is presented with growth eventually leading to a stationary configuration. A critical comparison of the numerical solution with existing analytical solutions is shown. This leads to a simple semi-empirical growth law for studying the kinetics of spinodal decomposition in alloys.

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Authors and Affiliations

  1. Department of Mechanics and Material Science, Rutgers University, P.O. Box 909, 08854, Piscataway, New Jersey, USA

    T. Tsakalakos

  2. RCA Solid State Technology Center, Route 202, Somerville, New Jersey, USA

    M. P. Dugan

Authors
  1. T. Tsakalakos
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  2. M. P. Dugan
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Tsakalakos, T., Dugan, M.P. Nonlinear diffusion in spinodal decomposition: a numerical solution. J Mater Sci 20, 1301–1309 (1985). https://doi.org/10.1007/BF01026326

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  • DOI: https://doi.org/10.1007/BF01026326

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