  In crystalline nanoparticles the Raman peak is downshifted with respect to
the bulk material and has asymmetric broadening. These effects are straightly
related to the finite size of nanoparticles, giving the perspective to use the
Raman spectroscopy as the size probe. By combining the dynamical matrix method
(DMM) and the bond polarization model (BPM), we develop a new (DMM-BPM)
approach to the description of Raman spectra for random arrays of
nanoparticles. The numerical variant of this approach is suitable for the
description of small particles, whereas its simplier to implement analytical
version allows to obtain the Raman spectra of arbitrary sized particles.
Focusing on nanodiamond powders, the DMM-BPM theory is shown to fit the most
recent experimental data much better than the commonly used phonon confinement
model (PCM), especially for small enough nanoparticles.
