Vacancies and antisite defects in ordered alloys

Equations for the concentrations of vacancies and antisite defects in ordered alloys in thermodynamic equilibrium at and near stoichiometry have been derived as functions of defect energies and a Lagrangian parameter. While the resulting equations cannot be solved analytically and in general require iterative calculations, an approximation is given that permits simple numerical evaluation with just a minor loss of accuracy. Using defect energies obtained from an embedded-atom method calculation for Cu₃Au, it is found that the adjustment for off-stoichiometric compositions is accounted for primarily by the creation of antisite defects rather than vacancies, and the vacancy concentration on Au sites is orders of magnitude less than that on Cu sites. There is a significant increase in the Au vacancy concentration but a slight decrease in the net vacancy content with increasing Cu fraction.