Application of the grand canonical ensemble to the study of equilibrium point defect concentrations in binary intermetallic phases with the B2-structure

Abstract

A statistical thermodynamic model of ordering in nonstoichiometric B2-phases is developed, based on the oldest and simplest theory of ordering, the mean-field approximation with constant pair-wise interaction energies between nearest-neighbor atoms. This approximation is limited to the description of the distribution of atoms and vacancies on the different sublattices, a possible short-range ordering tendency of point defects is neglected. The expressions for the point defect concentrations as a function of composition and temperature are derived from the grand canonical ensemble. In B2-phases the vacancy concentration depends on composition and temperature and it is therefore necessary to consider an open system, where the transfer of atoms to or from the outside is allowed. In B2-phases not only one defect equilibrium is involved, but there are four defect equilibria to be considered. It is shown that, if a series of defect equilibria is involved, it is necessary to apply the principle of microscopic reversibility to formulate the required number of independent equilibrium conditions. Expressions for the activities and partial molar enthalpies of the alloy components as a function of composition and temperature are derived, and a comparison with experimental data for β′-FeAl is given, which shows the practicability of this approach.