Low-Frequency Raman Spectroscopy of Pure and La-Doped $TiO_2$ Nanopowders Synthesized by Sol-Gel Method

Pure and La-doped titania $(TiO_2)$ nanopowders are synthesized by sol-gel technology. The crystallite sizes determined by X-ray diffraction measurements range from 10 to 15 nm. Dependence of structural and morphological characteristics of nanopowders on synthesis conditions and $La^{3+}$ content is investigated by the Raman spectroscopy. Very intensive modes observed in the Raman spectra of all nanopowder samples are assigned to anatase phase of $TiO_2$. Additional Raman modes of extremely low intensity can be related to the presence of a small amount of brookite amorphous phase in nanopowders, which is in accordance with the results of X-ray diffraction analysis. The particle size distribution in TiO_2 nanopowders was estimated from the low frequency Raman spectra, using the fact that the phonon modes in nanosized $TiO_2$ observed in the low frequency region (ω <40 $cm^{-1}$) can be well described by the elastic continuum model, assuming that nanoparticles are of perfect spherical shape and isotropic. The nanosized particle distribution obtained by this method is used for the calculation of the frequency and shape of the most intensive $E_g$ Raman mode in anatase $TiO_2$ by the phonon confinement model. The calculated broadening of this mode, associated with the particle size distribution, coincides well with the characteristics of $E_g$ mode observed in measured Raman spectra of $TiO_2$ nanopowders. This confirms the Raman spectroscopy method as a powerful tool for determination of particle size distribution in nanosized materials.