Raman scattering on quadrupolar vibrational modes of spherical nanoparticles

The Raman light to vibration coupling coefficients C(nu) of quadrupolar and symmetrical vibrational modes of spherical nanoparticles embedded in a matrix are calculated. In contrast to the symmetrical mode, the C(nu) of the quadrupolar modes consists of the longitudinal and transversal sound velocity contributions. It is shown that depending on the ratio of longitudinal and transverse sound velocities, these two contributions can interfere constructively or destructively resulting in enhancing or vanishing of some radial modes. The calculated results were compared to the polarized Raman spectra of CdS(x)Se(1-x) and Ge nanoparticles. By using the known size distribution of the CdS(x)Se(1-x) particles found by high-resolution transmission electron microscopy (HRTEM), the calculated low frequency (LF) polarized Raman spectra agree with the experiment. In the second case, the size distribution of Ge particles determined from the LF Raman spectra showed good agreement with the HRTEM results. The inverse problem of the determination of sound velocities of nanoparticles from the polarized low frequency Raman spectra by using the calculated C(nu) and known size distribution of the nanoparticles was demonstrated for the hafnium oxide nanoparticles in a silica matrix.