Successive perturbation of phonon bands in an organic alloy

Successive perturbation of the phonon bands is presented as a method to determine the criteria for formation of localized phonons in an organic alloy. The method is applied to the p-dihalobenzenes. The host is p-C₆H ₄Cl₂. The other isomorphic p-dihalobenzenes are used as guests with increasing perturbation in the order p-C₆H ₄ClBr, p-C₆H₄Br₂, p-C ₆H₄ClI, and p-C₆H₄BrI. It is found that the phonon bands remain amalgamated throughout the entire range of concentration for all perturbation strengths. The absence of localized phonons indicates either a large bandwidth (k dispersion) for the various phonon subbands (branches), or a significant coupling among the various phonon subbands. Several theoretical approaches for mixed crystals are summarized with a comparison of their relative merits. The highest frequency phonon exhibits the behavior predicted by the virtual crystal approximation. However, the more sophisticated average T-matrix approximation is required to adequately explain the line position and linewidths of the lowest frequency phonon.