Lattice model of solidification with mobile impurities in the liquid phase

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Abstract
A solidification front advancing into a three-dimensional (3D) medium containing mobile impurities is implemented as a model for a semilate stage dynamical process at a first-order phase transition under the isothermal undercooling condition. The approach generalizes the dynamical epidemic model to 3D. The presence of mobile particles shifts the usual probability of the percolation transition for 3D systems from 0.65 corresponding to static hindrances, to a value numerically estimated as 0.8. Excluded volume effects caused by the impurity particles lead to an aggregation process self-organizing the particles trapped behind the front in the solid phase. The kinetics of the process early stages is studied numerically and a power law governing the front width evolution is suggested.

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