Monte Carlo simulation of grain growth

Understanding and predicting grain growth in Metallurgy is meaningful. Monte Carlo methods have been used in computer simulations in many different fields of knowledge. Grain growth simulation using this method is especially attractive as the statistical behavior of the atoms is properly reproduced; microstructural evolution depends only on the real topology of the grains and not on any kind of geometric simplification. Computer simulation has the advantage of allowing the user to visualize graphically the procedures, even dynamically and in three dimensions. Single-phase alloy grain growth simulation was carried out by calculating the free energy of each atom in the lattice (with its present crystallographic orientation) and comparing this value to another one calculated with a different random orientation. When the resulting free energy is lower or equal to the initial value, the new orientation replaces the former. The measure of time is the Monte Carlo Step (MCS), which involves a series of trials throughout the lattice. A very close relationship between experimental and theoretical values for the grain growth exponent (n) was observed