Dielectric and vibrational properties of bixbyite sesquioxides

Most sesquioxides (X(2)O(3)) with a rare-earth cation crystallize in the cubic structure known as bixbyite, also adopted by oxides with smaller trivalent cations (e.g., Sc and Y). Here we discuss the dielectric behavior of these crystals on the basis of results of density-functional calculations for a selection of them, namely, Sc, La, Dy, and Lu binary sesquioxides. Vibrational modes can be categorized in two groups: one mostly localized on cations and with low frequencies and another with higher energies localized on oxygens. In rare-earth oxides the frequency of cation-localized modes shows a weak dependence on cation type; oxygen modes, instead, increase their energy as the cation radius decreases from La to Lu. In the case of the smaller Sc, frequencies increase for all modes and the smaller cation/oxygen mass ratio allows for a significant mixing of oxygen and cation displacements at intermediate frequencies. In the final analysis, we conclude that bixbyites all have relatively small dielectric constants and rationalize the reasons thereof.