  Vibrational mode frequencies and damping are calculated for an elastic sphere
embedded in an infinite, homogeneous, isotropic elastic medium. Anisotropic
elasticity of the sphere significantly shifts the frequencies in comparison to
simplified calculations that assume isotropy. New low frequency Raman light
scattering data are presented for silicon spheres grown in a SiO2 glass matrix.
Principal features of the Raman spectrum are not correctly described by a
simple model of the nanoparticle as a free, isotropic sphere, but require both
matrix effects and the anisotropy of the silicon to be taken into account.
Libration, not vibration, is the dominant mechanism.
