Ab initio studies of defect concentrations and diffusion in metal oxides

Abstract

This work presents a methodology for determining the concentrations and diffusion coefficients of point defects in metal oxides using ab initio calculations of defect formation energies and diffusion barriers, and the binding energies of defect-impurity clusters. The methodology is applied to analyse the long-standing mysteries surrounding the mechanism of self-diffusion in α-Al2O3. Al2O3 is a prototypical large band gap ceramic with extensive applications, many of which depend on its defect chemistry. In particular, point defect concentrations, that vary with temperature and impurity doping, govern diffusion properties such as creep, sintering, or the oxidation rate of Al-containing alloys. Experimental measurements of the self-diffusion coefficients in bulk alumina reveal three important truths that theory cannot reconcile, collectively termed the ’corundum conundrum’. First, large experimental activation energies for oxygen and aluminum diffusion and low theoretical formation energies imply unreasonably high diffusion barriers of ∼ 5eV. Second, aluminum diffusion is orders of magnitude faster than oxygen diffusion. Third, the oxygen diffusion coefficient is relatively insensitive to aliovalent doping, increasing by a factor of 100 on heavy Mg2+-doping, and decreasing by a similar amount on Ti4+-doping. We attempt to resolve this conundrum by calculating the formation energies and binding energies of a raft of native point defects and defect-impurity clusters as functions of temperature T and oxygen partial pressure pO2 , and the diffusion barriers of the native defects, using density functional theory. We then use a thermodynamic mass action approach to determine the concentrations of the defects and clusters, and the diffusion coefficients of the defects, as functions of T, pO2 , and the concentrations of aliovalent dopants, [Mg2+] and [Ti4+]. In the process, we discover new ground-state defect structures for the aluminum vacancy and oxygen interstitial, and demonstrate that diffusion of aluminum vacancies and interstitials occurs by extended vacancy and interstitialcy mechanisms, and oxygen interstitials by a dumbbell interstitialcy mechanism, all of which yield much lower migration barriers than previous theory. Unfortunately, the results do not demonstrate the experimentally-found insensitivity of the oxygen diffusivity to aliovalent doping. This could be an artefact of approximations within density functional theory and our methodology, and we show that modest changes in the calculated binding energies lead to significant defect clustering. This defect clustering could result in a buffering mechanism that can explain the insensitivity of the diffusivity to aliovalent doping, and may occur in other ionic materials. More accurate calculations, employing hybrid functionals or quantum Monte Carlo methods, may be necessary to elucidate this effect, but are currently computationally intractable for our purposes.