Phonons in mixed crystals — the virtual crystal model for interacting bands with different trap depths

Abstract

Phonons in disordered molecular solids are discussed within the virtual crystal limit, suitable for small trap depths. It is shown that the self-energy due to disorder is in general non-diagonal when bands with different trap depths are interacting. The introduction of an isotopic impurity, therefore, changes the principal axes of rotation in solids. Based upon this model, a method is now available to elucidate the band—band coupling. A useful products rule is derived that is independent of the intermolecular potential provided it is the same for both components. The product rule can be used to study the isotope effect on intermolecular potentials. These theoretical results are applied to the Raman spectra of pure and mixed crystals of naphthalene.