Low frequency Raman scattering of anatase titanium dioxide nanocrystals

TiO₂ nanoparticle of size 7.8 nm are synthesized by wet chemical route and characterized by low-frequency Raman scattering (LFRS), transmission electron microscopy (TEM) and X-ray diffraction. The low frequency peaks in the Raman spectra have been explained using the Lamb's theory that predicts the vibrational frequencies of a homogeneous elastic body of spherical shape. Our results show that the observed low-frequency Raman scattering originates from the spherical (l=0) and quadrupolar vibrations (l=2) of the spheriodal mode due to the confinement of acoustic vibrations in TiO₂ nanoparticles. In addition to the low-frequency peak due to the vibrational quadrupolar and spheriodal modes, a band is also observed, which is assigned to the Raman forbidden torsional l=2 mode originating from the near spherical shape of the TiO₂ nanoparticles. The size distribution is also obtained from LFRS, which is in good agreement with TEM.