Point defects and chemical potentials in ordered alloys

We discuss the thermodynamics of point defects in an ordered A m B n alloy for small deviations from the stoichiometric composition. The concentrations of the two kinds of antisite and vacancy are function of three basic energies of formation and of the stoichiometry. We derive general formulae for them which can be solved numerically. Analytic formulae for the chemical potentials are derived in terms of the point-defect concentrations. Simple analytic formulae are derived for the concentrations which are valid when the constitutional defects (which dominate at low temperatures) continue to dominate the thermally excited defects of the same type at higher temperatures. The energies entering these formulae are defined in a general way, suitable for ab initio or semiempirical methods of calculation. We illustrate the results with calculations for NiAl using three different central N-body potentials. A significant effect is due to the temperature dependence of the formation energies.