Simple model for the vibrations of embedded elastically cubic nanocrystals

The purpose of this work is to calculate the vibrational modes of an elastically anisotropic sphere embedded in an isotropic matrix. This has important application to understanding the spectra of low-frequency Raman scattering from nanoparticles embedded in a glass matrix. First some low-frequency vibrational modes of a free cubically elastic sphere are found to be nearly independent of one combination of elastic constants. This is then exploited to obtain an isotropic approximation for these modes which enables to take into account the surrounding isotropic matrix. This method is then used to quantitatively explain recent spectra of gold and copper nanocrystals in glasses.