The effect of native point defect thermodynamics on off-stoichiometry in β-Mg ₁₇Al ₁₂

The mechanical strength of Mg-Al-Zn alloys can be affected by a fine spatial dispersion of β-Mg ₁₇Al ₁₂ precipitates in the Mg matrix. In an effort to understand the phase stability and the unusual asymmetric off-stoichiometry observed in β-Mg ₁₇Al ₁₂, we have performed a series of first-principles density functional theory (DFT) calculations of bulk and defect properties of Mg ₁₇Al ₁₂. Specifically, we consider native point defects (i.e. vacancies and anti-sites) in all four sublattices of Mg ₁₇Al ₁₂, i.e. 2a, 8c, 24g (Mg) and 24g (Al). The T = 0 K static energies of defect Mg ₁₇Al ₁₂ supercells indicate that anti-site defects are energetically favored over vacancies, and the lowest anti-site defect formation energies are in 24g sites for both Al _Mg and Mg _Al. These Al-rich and Mg-rich anti-site defect formation energies are similar in magnitude, and thus do not explain the asymmetric off-stoichiometry of Mg ₁₇Al ₁₂. We also investigate the effect of atomic vibrations via DFT phonon calculations on native point defect free energies of Mg ₁₇Al ₁₂ and combine these entropic contributions with the point defect formation energies to evaluate the thermodynamics of off-stoichiometry in this phase. We find that the formation of the Al _Mg anti-site is not strongly stabilized by vibrational entropy. Thus, we conclude that the observed asymmetry in the off-stoichiometry of the β-Mg ₁₇Al ₁₂ phase in the Mg-Al phase diagram is not explained by simple native point defect thermodynamics, and must involve a more complicated defect formation mechanism, such as multi-defect clustering.