A Monte Carlo program for simulating segregation and diffusion utilizing chemical potential calculations
Joubert, Heinrich Daniel
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Bulk-to-surface segregation plays a major role in the engineering of alloy surfaces. An increase in surface sensitive analysis techniques in recent years have led to big advances in the engineering of surface properties. The focus of this study is the development of a Chemical Potential Monte Carlo (CPMC) model which is based on the modified Darken model. This model is capable of simulating diffusion and segregation in crystals with a uniform concentration as well as crystals consisting of thin layers. The chemical potential equations used for the calculations by the modified Darken model are rewritten to include the segregation energy associated with the surface layer. The change in chemical potential directs atomic motion and simulations involving the change in chemical potential are performed on a 2-dimensional matrix containing two elements: the solute and the solvent elements. A random selection of an atom inside the matrix initiates the model. The change in chemical potential due to an atomic jump of a randomly selected atom to an adjacent layer is calculated. The largest change in chemical potential directs the atomic motion, complying with the conditions associated with the lowering of the Gibbs free energy; the driving force of atomic motion is therefore the lowering of the total crystal energy. Inclusion of the segregation energy (for jumps involving the surface layer) limits the number of atomic jumps from the surface layer to the bulk. Simulated segregation profiles generated by the CPMC model were compared with profiles calculated with both the modified Darken and Fick model. The comparisons show that the CPMC successfully describes both the kinetic and equilibrium conditions associated with surfa ce segregation. A reduction in calculation time was also achieved by implementing the CPMC model in parallel.