Equilibrium vacancy concentrations in Al-Σ=33(554)[1(1)over-bar0] by grand canonical Monte Carlo simulations

A Monte Carlo simulation of equilibrium thermal vacancies is extended to grain boundaries in Al. The vacancy localization is explored by intensive molecular-dynamics simulations. It is found that, in the symmetrical tilt boundary Sigma=33(554)[1 (1) over bar0], the reference lattice, based on the coincident site lattice geometrical model, is good enough to describe the microstates of the system up to T=700 K in the presence of vacancies and vacancy clusters. A microstate is therefore defined by site occupancies and continuous displacements from the lattice nodes. This model, intermediate between an Ising model and the representation of states in classical statistical mechanics, is used to perform grand canonical Monte Carlo simulations. Vacancy concentrations along the grain boundary are computed from the average site occupancies. Vacancy alignment along the tilt axis is reported. The results are analyzed in the framework of a one-dimensional Ising model which incorporates vacancy free formation energies and pair interaction free energies.