Determining the site preference of trivalent dopants in bixbyite sesquioxides by atomic-scale simulations

Oxides with the bixbyite structure $(Ia\overline{3})$ have two crystallographically unique cation sites, namely (in Wyckoff notation) $24d$ and $8b$. Since the symmetries of these two sites are different (${C}_{2}$ and ${S}_{6}$, respectively), properties related to solute cations will vary depending on the site preference. Therefore, we have employed atomic scale simulation techniques to systematically investigate the solution site preference of a range of trivalent cations ranging from ${\mathrm{Sc}}^{3+}$ to ${\mathrm{La}}^{3+}$ in ${A}_{2}{\mathrm{O}}_{3}$ bixbyite oxides (where $A$ ranges from Sc to La). Results reveal that when the solute cation is smaller than the host lattice cation, the $24d$ site is energetically favorable, but when the solute cation is larger than the host lattice cation, the $8b$ site is preferred. We also discuss the tendency for solute cations to cluster, as well as corroboration of this work by first principles methods.