Bulk-to-surface segregation was studied with a Monte Carlo model based on the modified Darken model. Chemical potentials were used to represent the local energy of a randomly chosen atom, while the largest positive change in chemical potential directs atomic motion, complying with the conditions associated with the lowering of the Gibbs free energy. An adjustment was made to the calculations to compensate for the segregation energy associated with the surface layer. The current model simulates segregation in binary alloys, represented by a crystal matrix containing two constituent elements. A random selection of an atom initiates the calculation process, after which the energy of the selected atom, represented by the chemical potential, was calculated for an area that included nearest and next nearest neighbors. In addition, only nearest neighbor exchanges were allowed, resulting in a maximum of four possible moves. A test move was performed to each of the four move directions, and the chemical potential for each new configuration was calculated. The change in chemical potential for all four exchanges could be calculated, and the probabilities associated with these moves could also be calculated. The exchange that represents the largest positive change in chemical potential will possess the largest probability of motion. By including the segregation energy (associated with the surface) in the calculations, the frequency of jumps from the surface to the bulk was significantly reduced.

A Monte Carlo Model Utilizing Local Chemical Potentials for Simulating Segregation and Diffusion. Part 1 - Theory. H.D.Joubert, H.C.Swart, J.J.Terblans: Surface and Interface Analysis, 2005, 37[11], 1027-30