Mechanism of low-frequency Raman scattering from the acoustic vibrations of dielectric nanoparticles

The depolarization ratio of the quadrupolar vibrations and the relative intensity of the symmetric l=0 and quadrupolar l=2 acoustic vibrations in the Raman spectra of some dielectric nanocrystals has been calculated. A dipole-induced-dipole model can account for the depolarized spectra from quadrupolar vibrations, but cannot be at the origin of the polarized peak from the symmetric vibration. Bond polarizability seems to be the main physical mechanism at the origin of Raman scattering from these modes. The study indicates that the quadrupolar modes or symmetric modes dominate the spectra when the dipole induced dipole or bond polarizability are more important, respectively. This result explains why semiconductor nanoparticles with covalent bonds show intense symmetric scattering, and fluoride crystals with ionic bond show Raman scattering from quadrupolar modes, and why in oxide crystals the two modes show comparable Raman activity. A comparison of the spectra of titania, zirconia, and hafnia nanocrystals offers further support to the model.