Density of constitutional and thermal point defects in ${L1\mathrm{}}_2$ ${\mathrm{Al}}_3\mathrm{Sc}$

The energy of constitutional and thermal point defects in ${L1\mathrm{}}_2$ ${\mathrm{Al}}_3\mathrm{Sc}$ are calculated within a first principles, local density functional theory framework. Relaxed structures and energies for vacancies and antisites are calculated using a plane-wave pseudopotential method. The resulting energies are used within a dilute-solution thermodynamic formalism to estimate the equilibrium point defect densities as functions of temperature and alloy composition. The first-principles-based thermodynamic calculations predict that ${\mathrm{Al}}_3\mathrm{Sc}$ forms antisite constitutional defects for both Al- and Sc-rich alloys. Also, the density of thermal vacancies is found to be very sensitive to the underlying stoichiometry. At 1000 K the Sc-sublattice vacancy concentration increases by ten orders of magnitude as the alloy goes from Sc to Al rich. At this temperature, the density of Sc-sublattice vacancies is predicted to be comparable to the concentration of Al antisite defects for Al-rich alloys.