Low Wavenumber Raman Scattering of Nanoparticles and Nanocomposite Materials

Low wavenumber Raman scattering of the acoustic vibrational modes of nanoparticles was used for the determination of the size distribution of free dielectric and semiconductor nanoparticles and of nanoparticles embedded in matrices. The theoretical background as well as the experimental results for the free noninteracting nanoparticles and for the nanoparticles in strong interaction with a surrounding matrix is described. The approach is based on a 1/ dependence of the Raman light-to-vibration coupling coefficient and on the fact that each nanocrystallite of diameter D vibrates with its eigenfrequency 1/D. The model calculation considers the inhomogeneous broadening due to contribution from the particles of different sizes, and homogeneous broadening due to interaction of particles with the matrix. The comparison of the calculated and experimental low wavenumber Raman spectra are presented for SnO2, TiO2 and CdS free nanoparticles and TiO2, CdSxSe1-x and HfO2 nanoparticles embedded in a glass matrix. The particle-size distributions determined by Raman scattering were compared to those found by TEM measurements. Raman spectroscopy proved to be a simple, fast and reliable method for size-distribution measurements. By an inverse procedure, starting from the Raman spectra and known particle-size distribution, a new method for the determination of the mean sound velocities of longitudinal and transverse phonons of nanoparticles is described.