The paper introduces a scalable three-dimensional (3D) kinetic cellular automaton model with a probabilistic switching rule for the spatial and crystallographic prediction of mesoscale transformation phenomena that involve orientational field variables and the motion of sharp interfaces, such as encountered in the field of recrystallization. The automaton is discrete in time, physical space and Euler orientation space. It is defined on a regular 3D cubic lattice considering the first-, second- and third-neighbour shells for the calculation of the local driving forces. The kinetic transformation rule is formulated as a probabilistic analogue of the classical linearized symmetric Turnbull rate equation for grain-boundary segment motion. It is used to calculate the switching probability of each grid point as a function of its previous state and the state of the neighbouring grid points. The actual decision about a switching event is made by evaluating the local switching probability using a Monte Carlo step. The transformation rule is scaled by the ratio of the local to the maximum possible grain boundary mobility, the local crystallographic texture, and the ratio of the local to the maximum occurring driving force. The time step of the simulation is determined by the maximum occurring driving force, by the maximum occurring grain boundary mobility and by the spacing of the grid points. The use of realistic or even experimental input data for the boundaries allows one to make predictions on a real time and space scale. The transformation rule is scalable to any mesh size and to any spectrum of boundary mobility and energy data. The state update of all grid points is made in synchrony. The model predicts the kinetics, the evolution of the grain size and topology, and the evolution of the crystallographic texture during recrystallization.
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Dierk Raabe (1999) studied this question.