Wannier functions and Born charge tensors of brookiteTiO2

Abstract

The dynamical Born charge tensor of brookite $\mathrm{Ti}{\mathrm{O}}_{2}$ has been calculated and analyzed in terms of the Wannier functions associated with the O $2s∕2p$ valence states. It is shown that the fundamental $\mathrm{O}{\mathrm{Ti}}_{3}$ triangular complex, whose opposite distortion in rutile and anatase explains the anisotropy of the Born charge in these polymorphs, is also the relevant building block for understanding this quantity in brookite. This compound consists of an equal number of distorted rutilelike and anataselike $\mathrm{O}{\mathrm{Ti}}_{3}$ structural units, which are nonplanar due to the low ${C}_{1}$ site symmetry of oxygen atoms. Born charge tensors associated with the two nonequivalent O sites correspond in terms of values and anisotropies to those for rutile and anatase, and, consistent with the acoustic sum rule, the Ti charge tensor is an ``average'' of those for the two O types. The intermediate character of brookite, between rutile and anatase, should be expected also for other physical properties.