Cellular automata diffusion-kinetic model of dendritic growth

A mathematical crystallization model in the meso scale (the intermediate dimension scale between interatomic distance in solids and grain size in metals and alloys) is presented with the use of a kinetic-diffusion cellular automaton model. The proposed model differs from other models by including the diffusion of elements and heat conductivity effects on the physical phenomena at the solid-liquid interface. The model considers the non-equilibrium character of real processes of phase transformation, where the kinetic undercooling of the solid-liquid interface is a measure of this non-equilibrium level. The anisotropy of interface mobility is assumed. The growth of individual dendrites was simulated for different initial conditions and growth parameters. The modelling results are compared to the experimental data.