Abstract
We study the stability of the corundum, gallia, and bixbyite structures of , and with density functional theory calculations. To artificially control the relative position of the states within the band structure, we add a Hubbard-like on-site Coulomb interaction to the 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, and 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 . However, as expected from experimental observations, we find gallia to be the most stable structure for . Our results explain why crystallizes in the gallia structures instead of the corundum or bixbyite as follows. The stability of gallia increases as the hybridization of the Ga states with the O states grows and the 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 , which contain only sixfold cation sites, so that the effect of the states is unimportant.
- Received 9 July 2014
- Revised 7 September 2014
DOI:https://doi.org/10.1103/PhysRevB.90.155206
©2014 American Physical Society