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Reaction dynamics of processes involving solids are extensively studied by thermal analysis methods. They are often solved almost naively by analogy with apparently gradientless homogeneous reactions. Other oversimplified approximations involve the regular shape of reacting particles that are assumed to be circles or spheres regardless of their true texture (stereology). This model never matches the results of traditional morphology observations. This article points the direction where a more rigorous solution should go by introducing a more actual state of the sample but, unfortunately, is yet unable to show the practical way how to actually bring in the challenge of entire introducing fluxes incorporation which solution makes difficult mathematical problem but it enables wide options of state of the system. Practical examples are illustrated on the flux-dependent growth of dendrites.

In this paper, we report the models of fast recrystallization processes in a-Si thin films. An important feature of the modeling of nucleation in a-Si films is the capability of allowing description of non-equilibrium solidification including the distribution of small crystalline clusters which can be responsible for visible photoluminescence. We integrate the results of the description of nucleation and growth on the phase interface of c-Si from a-Si or l-Si. The transient time, nucleation rate and growth rate were determined as a function of temperature and the position of local extremes of these functions were stated. The solidification velocity was calculated from the nucleation rate and growth rate with respect to the temperature distribution in a system. The suitability of the particular approximations and models is discussed.