Quadrupole terms in defect energies in transition metal oxides

Abstract

In a previous paper it was shown that, for defects in transition metal oxides, there was evidence for an additional term in the potential energy beyond the usual monopole and dipole terms of the shell model. This appeared to be a quadrupole term in which the open 3d shells of the host ions, as well as any impurities, responded to local electric field gradients. Quantitative estimates are made which confirm our hypothesis and, in CoO, show that the effect is sufficient to bring theory into accord with experimental measurements. Such quadrupole interactions will also be relevant to other systems with host ions or impurities having incomplete electric shells.