Role of atomic radius andd-states hybridization in the stability of the crystal structure ofM2O3(M=Al, Ga, In) oxides

Abstract

We study the stability of the corundum, gallia, and bixbyite structures of ${\mathrm{Al}}_{2}{\mathrm{O}}_{3},{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$, and ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ with density functional theory calculations. To artificially control the relative position of the $d$ states within the band structure, we add a Hubbard-like on-site Coulomb interaction to the $d$ states. We quantitatively show that smaller (larger) atomic radii favor the corundum (bixbyte) structure, which supports empirical models based on the atomic radius ratio between the cation and anions and the spacing-filling condition. Thus, ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ and ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ crystallizes in the corundum and bixbyite structures, which is consistent with experimental observations. The empirical models based on atomic radius and space filling would predict a corundum or bixbyite structure for ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. However, as expected from experimental observations, we find gallia to be the most stable structure for ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. Our results explain why ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ crystallizes in the gallia structures instead of the corundum or bixbyite as follows. The stability of gallia increases as the hybridization of the Ga $d$ states with the O $2s$ states grows and the $p\text{\ensuremath{-}}d$ splitting increases, which is maximized by the presence of fourfold cation sites. The presence of the fourfold cation sites in gallia is a key structural feature that increases its relative stability compared with the corundum and bixbyite structures for ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$, which contain only sixfold cation sites, so that the effect of the $d$ states is unimportant.