Pressure and Temperature Dependence of the Static Dielectric Constants and Raman Spectra of TiO2(Rutile)

Abstract

The effects of temperature [(4-500)\ifmmode^\circ\else\textdegree\fi{}K] and hydrostatic pressure (0-4 kbar) on the static dielectric constants ${\ensuremath{\epsilon}}_{a}$ and ${\ensuremath{\epsilon}}_{c}$ and on the frequencies of the four Raman-active phonons ${B}_{1g}$, ${E}_{g}$, ${A}_{1g}$, and ${B}_{2g}$ of single-crystal rutile were investigated. The temperature and pressure dependence of the frequency of the infrared-active soft ferroelectric (FE) mode ${A}_{2u}$ were deduced from the dielectric-constant data. The Gr\"uneisen parameter $\ensuremath{\gamma}$ of each of the modes was determined. Particularly important are the results that $\ensuremath{\gamma}({A}_{2u})$ is large and increases with decreasing temperature-unique properties of the FE mode-and that $\ensuremath{\gamma}({B}_{1g})$ is relatively large and negative. This latter result, which is in agreement with an earlier measurement, may be significant from the standpoint of a pressure-induced phase transition in rutile. The temperature and pressure results are combined with thermal expansion and compressibility data to evaluate the pure-volume and pure-temperature contributions to the isobaric temperature dependence of each of the frequencies and dielectric constants. The results yield some important conclusions about the lattice dynamics of rutile. The pure-temperature contribution arises from cubic and quartic anharmonicities. It plays a dominant role in determining the anharmonic self-energy shift of the FE mode and accounts for 20% of the mode energy at 300 \ifmmode^\circ\else\textdegree\fi{}K. The Szigeti effective ionic-charge ratio for rutile is found to be $\frac{{e}^{*}}{e}=0.64$ at 4 \ifmmode^\circ\else\textdegree\fi{}K and 0.62 at 296 \ifmmode^\circ\else\textdegree\fi{}K. These results are discussed briefly.