Communication: three-dimensional model for phonon confinement in small particles: quantitative bandshape analysis of size-dependent Raman spectra of nanodiamonds.

Raman spectroscopy of nano-scale materials is facing a challenge of developing a physically sound quantitative approach for the phonon confinement effect, which profoundly affects the phonon Raman band shapes of small particles. We have developed a new approach based on 3-dimensional phonon dispersion functions. It analyzes the Raman band shapes quantitatively in terms of the particle size distributions. To test the model, we have successfully obtained good fits of the observed phonon Raman spectra of diamond nanoparticles in the size range from 1 to 100 nm.