Temperature Dependence of the Raman Spectrum in Anatase TiO₂

Abstract

The frequency and linewidth of the four Raman active modes in anatase have been investigated over the temperature range 20 to 1100 K. The temperature ( T ) dependence of the frequency of the 639 cm -1 mode showed typical behavior in normal ionic crystals, whereas the other modes at 399, 197 and 144 cm -1 did anomalous behavior. These T dependent results were combined with pressure dependent results, thermal expansion and compressibility data to evaluate the pure-volume and pure-temperature contributions to the T dependence of each frequency. The results indicate that the anomalous T dependence of the 399 cm -1 mode reflects the near cancellation of the cubic and quartic contributions to the frequency shift, and that of the modes at 197 and 144 cm -1 arises from strong quartic contributions. The T dependence of the linewidth is well explained qualitatively in terms of simple anharmonic effects involving three phonon processes.