Electronic structure of α−Al2O3 grain boundaries containing reactive element segregants

It has long been known that the addition of small quantities (``doping'') of so-called reactive elements (REs) such as Y, Zr, and Hf to high-temperature ${\text{Al}}_{2}{\text{O}}_{3}$ scale-forming alloys improves oxidation resistance. The presence of reactive elements at grain boundaries lowers the growth rate of the $\ensuremath{\alpha}\text{\ensuremath{-}}{\text{Al}}_{2}{\text{O}}_{3}$ scales, but the cause of the reduced scale growth kinetics is not fully understood. Explanations based on steric effects and explanations based on reducing the grain boundary electronic conductivity have been proposed. We have used density functional theory to study the structural and electronic properties of two $\mathrm{\ensuremath{\Sigma}}7$ bicrystal grain boundaries containing Y, Hf, and Zr substitutional defects on Al sites. The presence of RE substitutional defects plays a minimal direct role in reducing the density of electronic states near the valence-band maximum. However, ${\mathrm{Hf}}^{4+}$ or ${\mathrm{Zr}}^{4+}$ substitutions at the grain boundary repel the positively charged oxygen vacancy ${\text{V}}_{\text{O}}^{2+}$. As ${\text{V}}_{\text{O}}^{2+}$ contributes a defect state above the valence-band maximum but below the Fermi energy, this indirectly lowers the density of current-carrying holes and thus the electronic conductivity of the grain boundary. Replacing ${\mathrm{Al}}^{3+}$ ions with ${\mathrm{Hf}}^{4+}$ or ${\mathrm{Zr}}^{4+}$ ions also makes the grain boundary positively charged, further reducing the hole density.