Kinetic Monte Carlo Method to Model Diffusion Controlled Phase Transformations in the Solid State

  • Martin G
  • Soisson F
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Abstract

The classical theories of diffusion-controlled transformations in the solid state (precipitate-nucleation,-growth,-coarsening, order-disorder transformation , domain growth) imply several kinetic coefficients: diffusion coefficients (for the solute to cluster into nuclei, or to move from smaller to larger precipitates. . .), transfer coefficients (for the solute to cross the interface in the case of interface-reaction controlled kinetics) and ordering kinetic coefficients. If we restrict to coherent phase transformations, i.e., transformations, which occur keeping the underlying lattice the same, all such events (diffusion, transfer, ordering) are nothing but jumps of atoms from site to site on the lattice. Recent progresses have made it possible to model, by various techniques , diffusion controlled phase transformations, in the solid state, starting from the jumps of atoms on the lattice. The purpose of the present chapter is to introduce one of the techniques, the Kinetic Monte Carlo method (KMC). While the atomistic theory of diffusion has blossomed in the second half of the 20th century [1], establishing the link between the diffusion coefficient and the jump frequencies of atoms, nothing as general and powerful occurred for phase transformations, because of the complexity of the latter at the atomic scale. A major exception is ordering kinetics (at least in the homogeneous case, i.e., avoiding the question of the formation of microstructures), which has been described by the atomistic based Path Probability Method [2]. In contrast, supercomputers made it possible to simulate the formation of microstructures by just letting the lattice sites occupancy change in course of time following a variety of rules: the Kinetic Ising model (KIM) in particular has been (and 2223 S. Yip (ed.), Handbook of Materials Modeling, 2223-2248. c 2005 Springer. Printed in the Netherlands.

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Martin, G., & Soisson, F. (2005). Kinetic Monte Carlo Method to Model Diffusion Controlled Phase Transformations in the Solid State. In Handbook of Materials Modeling (pp. 2223–2248). Springer Netherlands. https://doi.org/10.1007/978-1-4020-3286-8_115

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