Structure of δ-Bi₂O₃ from density functional theory: A systematic crystallographic analysis

A systematic crystallographic analysis of the 〈110〉 and 〈111〉 vacancy-ordered structure of cubic δ-Bi₂O₃ obtained from electronic-structure calculations is presented. The ordering of vacancies leads to a doubling of the unit-cell that results in a 2×2×2 fluorite super-structure, with an associated reduction in its space group symmetry from Fm over(3, -) m to Fm over(3, -). The Bi atoms present inside the 〈111〉 vacancy-ordered oxygen sublattice have equal Bi-O bond lengths, whereas, those present inside the 〈110〉 vacancy-ordered oxygen sublattice have three different pairs of Bi-O bond lengths. The specific ionic displacements and electronic charge configurations also depend on the nature of vacancy ordering in the oxygen sub-lattice.