Long lived acoustic vibrational modes of an embedded nanoparticle
  Classical continuum elastic calculations show that the acoustic vibrational modes of an embedded nanoparticle can be lightly damped even when the longitudinal plane wave acoustic impedances $Z_o=\rho v_L$ of the nanoparticle and the matrix are the same. It is not necessary for the matrix to be less dense or softer than the nanoparticle in order to have long lived vibrational modes. Continuum boundary conditions do not always accurately reflect the microscropic nature of the interface between nanoparticle and matrix, and a multi-layer model of the interface reveals the possibility of additional reduction of mode damping. 
Lucien Saviot, Daniel B. Murray