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

The effects of temperature [(4-500)°K] and hydrostatic pressure (0-4 kbar) on the static dielectric constants ${\epsilon }_a$ and ${\epsilon }_c$ 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 Grüneisen parameter $\gamma$ of each of the modes was determined. Particularly important are the results that $\gamma \left(A_{2u}\right)$ is large and increases with decreasing temperature-unique properties of the FE mode-and that $\gamma \left(B_{1g}\right)$ 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 °K. The Szigeti effective ionic-charge ratio for rutile is found to be $\frac{e^{*}}{e}=0.64\mathrm{}$ at 4 °K and 0.62 at 296 °K. These results are discussed briefly.