Diffusion of oxygen in Mg-doped $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$: The corundum conundrum explained

It has been a puzzle for over two decades that the enhancement of oxygen diffusion in $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$, with respect to the amount of Mg doping, is several orders of magnitude less than expected. The standard model, which envisages that transport is mediated by oxygen vacancies induced to compensate the charge of ${\mathrm{Mg}}^{2+}$ ions substituting ${\mathrm{Al}}^{3+}$ ions, has not been able to explain this anomaly. Here, we report a detailed study of populations of point defects and defect clusters in Mg-doped $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$. By taking into account calculated defect formation energies from the literature, the condition of charge neutrality, and the environmental parameters (chemical potentials) under which the anomalous trend in oxygen diffusivities were previously observed, we are able to arrive at an explanation. A nonlinear relationship between Mg concentration in the system and key native point defects, which serve as mediators of self-diffusion in $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$, is predicted: The concentrations of such defects increase much more slowly in the supersaturation regime than in the presaturation regime, matching the anomalous result previously observed in $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$. We identify the reason for this as buffering by positively charged Mg interstitials and Mg–oxygen vacancy clusters, which compensate the negative charges of Mg substitutional defects (${\mathrm{Mg}}_{\text{Al}}^{1-}$). This study answers part of the long-standing question about self-diffusion in alumina, referred to by Heuer and Lagerlöf in 1999 as the corundum conundrum.

Figure 1

Formation energies of native $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ and Mg impurity defects, based on Ref. [7] and readjusted to the experimental temperature [6] of $T=1673.15$ K ($1400{}^{\circ }\mathrm{C}$), and partial pressure of oxygen, $p_{{\mathrm{O}}_2}=0.21\mathrm{atm}$ in (a) and, for comparison purposes, to the reductive limit in (b), which would correspond to equilibrium with metallic Al. Formation energies of Mg-containing defects are calculated using the chemical potential of Mg that was adjusted to give a total Mg content of 252 wt. ppm. The gradient of each linear segment in the defect formation energy corresponds to the dominant charge state of the defect at a given energy; a visual map relating charge state to gradient is included below the legend. The Fermi energy of the undoped (Mg-doped) $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ is marked by solid (dashed) vertical lines.

Figure 2

Defect-charge concentrations $q\left[D^q\right]$ (in $e{\mathrm{cm}}^{-3}$) for Mg-doped ${\mathrm{Al}}_2{\mathrm{O}}_3$ as a function of Mg doping concentrations under (a) ambient conditions ($P_{{\mathrm{O}}_2}=0.21$ atm) and (b) the reductive limit. Positively (negatively)-charged defects are represented by solid (dotted) lines. The calculated saturation limit for Mg (its concentration in solution if the alumina system were in equilibrium with spinel, ${\mathrm{MgAl}}_2{\mathrm{O}}_4$) is marked with a grey-vertical line. The insets are magnified parts from the top-right of the diagrams, showing more clearly the dominant defects where the Mg solution is calculated to be supersaturated.