First-Principles Calculated Structures and Carbon Binding Energies of Σ11 ${{\left\{ {10\bar{1}1} \right\}} \mathord{\left/ {\vphantom {{\left\{ {10\bar{1}1} \right\}} {\left\{ {10\bar{1}\bar{1}} \right\}}}} \right. \kern-0pt} {\left\{ {10\bar{1}\bar{1}} \right\}}}$ Tilt Grain Boundaries in Corundum Structured Metal Oxides

Abstract

To give a basic understanding of the experimentally observed difference between Cr₂O₃ and Al₂O₃ scales on carbon permeation, we employed the first-principles calculation methods to predict atomistic structures, formation energies, and carbon binding energies of Σ11 ${{\left\{ {10\bar{1}1} \right\}} \mathord{\left/ {\vphantom {{\left\{ {10\bar{1}1} \right\}} {\left\{ {10\bar{1}\bar{1}} \right\}}}} \right. \kern-0pt} {\left\{ {10\bar{1}\bar{1}} \right\}}}$ tilt grain boundaries (GB) in both α-Al₂O₃ and α-Cr₂O₃ with a corundum structure. Owing to different surface terminations, we predicted two distinct kinds of stable atomistic structures for the GB: one with measurable voids and high formation energy, and the other with a compact interface and low formation energy. The predicted GB structures agree with experimental images. No significant structural difference was found for the same GB in α-Al₂O₃ and α-Cr₂O₃. Moreover, we predicted that atomic carbon would bind to the Σ11 ${{\left\{ {10\bar{1}1} \right\}} \mathord{\left/ {\vphantom {{\left\{ {10\bar{1}1} \right\}} {\left\{ {10\bar{1}\bar{1}} \right\}}}} \right. \kern-0pt} {\left\{ {10\bar{1}\bar{1}} \right\}}}$ GB in α-Cr₂O₃ appreciably more strongly than in α-Al₂O₃. Therefore, our computational results suggest that chemical affinity rather than geometric structure of the GBs is related to different carbon permeation behaviors in Al₂O₃ and Cr₂O₃ scales.

Graphic Abstract