Lattice-dynamical model for the elastic constants and Raman frequencies in (V1-xCrx)2O3.

Abstract

We report the first lattice-dynamical study of ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$ and (${\mathrm{V}}_{0.985}$${\mathrm{Cr}}_{0.015}$${)}_{2}$O $_{3}$ in the long-wavelength limit using a rigid-ion model with an effective ionic charge and various short-range interactions. The parameters of the model were determined from nonlinear least-squares fits to the experimental elastic constants and the frequencies of Raman-active modes at room temperature. The validity of the model was established by verifying that the calculated elastic constants and Raman frequencies were in good agreement with experimental data for ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$ and (${\mathrm{V}}_{0.985}$${\mathrm{Cr}}_{0.015}$${)}_{2}$O $_{3}$ as well as for ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ to which the same model was also applied. The effective ionic charge of each (${\mathrm{V}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Cr}}_{\mathrm{x}}$${)}_{2}$${\mathrm{O}}_{3}$ crystal was found to be considerably larger than that of ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ in accordance with the ionicity of ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$, estimated from the dielectric theory of Levine, being larger than that of ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$. The short-range force constants of (${\mathrm{V}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Cr}}_{\mathrm{x}}$${)}_{2}$${\mathrm{O}}_{3}$ were found to be quite different from those of ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$. It was also found that most of the model parameters for semiconducting (${\mathrm{V}}_{0.985}$${\mathrm{Cr}}_{0.015}$${)}_{2}$O $_{3}$ have values in between those of metallic ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$ and insulating ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$. The effect of alloying a small amount of ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ into ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$ on the interatomic force-field parameters is also discussed.