Simulations of Aluminum-Magnesium Alloys in a hexagonal close-packed Lattice based on the Cluster Expansion Method.

Abstract

By using the density-functional theory and adopting the approach of Kohn and Sham, together with the cluster expansion method for Monte Carlo simulations, aluminum-magnesium alloys on a hcp lattice have been studied. The exchange-correlation energy functional mainly considered is the Perdew-Burke-Ernzerhof functional which belongs to the class of generalized gradient approximations. To perform calculations the open-source density-functional theory Python code named GPAW has been used. This in turn uses the projector-augmented wave method and the atomic simulation environment ASE. In conclusion, this thesis highlights the ability of the cluster expansion method combined with density-functional theory and Monte Carlo simulations to predict phases of an alloy on a given lattice. A cluster expansion model is developed for aluminum-magnesium alloys on a hcp lattice ranging in concentration from 25 % to 100 % magnesium. MC simulations reveal an Mg3Al phase emerging at temperatures below 300 K and its phase boundaries have been further studied in canonical and grand-canonical ensembles.