Electronic structure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>Al</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> grain boundaries containing reactive element segregants

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