Computer simulation of grain growth-I. Kinetics

A novel Monte Carlo procedure is applied to the study of the kinetics of grain growth in two dimensions. The model employed maps the microstructure onto a discrete lattice. Each lattice site is assigned a number, between 1 and Q, which indicates the local crystallographic orientation. The initial distribution of orientations is chosen at random and the system evolves so as to reduce the number of nearest neighbor pairs of unlike crystallographic orientation. The temporal evolution of the microstructure is monitored to yield the time dependence of the size and shapes of the grains. The microstructures produced are in good correspondence with experimental observations of soap bubbles, foams and cross-sections of isotropic metallurgical specimens. Examination of the temperature and lattice dependence of the kinetics shows the existence of a number of universal features. The model properly reproduces the kinetics of the Ising model in the limit that Q approaches 2. For large Q, power law kinetics [R^m(t) - R^m(0) = Bt] are observed with the growth exponent, m, is found to be independent of Q with a value of approximately 2.4. The deviation of the growth exponent from the mean field value of 2 is discussed in terms of the role of vertices.