Introduction of a scalable three-dimensional cellular automaton with a probabilistic switching rule for the discrete mesoscale simulation of recrystallization phenomena

The paper introduces a scalable three-dimensional (3D) kinetic cellular aut omaton model with a probabilistic switching rule for the spatial and crysta llographic prediction of mesoscale transformation phenomena that involve or ientational field variables and the motion of sharp interfaces, such as enc ountered in the field of recrystallization. The automaton is discrete in ti me, 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 transformatio n rule is formulated as a probablistic 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 functio n 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 swi tching probability using a Monte Carlo step. The transformation rule is sca led by the ratio of the local to the maximum possible grain boundary mobili ty, the local crystallographic texture, and the ratio of the local to the m aximum occurring driving force. The time step of the simulation is determin ed by the maximum occurring driving force, by the maximum occurring grain b oundary mobility and by the spacing of the grid points. The use of realisti c or even experimental input data for the boundaries allows one to make pre dictions on a real time and space scale. The transformation rule is scalabl e 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 predi cts the kinetics, the evolution of the grain size and topology, and the evo lution of the crystallographic texture during recrystallization.