Vibrational relaxation in a structurally disordered organic solid: Temperature dependence of Raman active phonons in p-bromochlorobenzene and p-dichlorobenzene

A theoretical discussion is presented to show that for a highly delocalized phonon motion, the line shapes derived from disorder and from vibrational relaxation due to anharmonic phonon-phonon scattering are both approximately Lorentzians. The linewidths obtained from disorder and vibrational relaxation are additive. A temperature dependence of the linewidth can be used to identify the mechanism and obtain the rate of vibrational relaxation. An experimental study is presented on the lowest frequency Raman active phonon of p-bromochlorobenzene which in the solid state shows an orientational disorder. The result is compared with that on the corresponding phonon in the isomorphic p-dichlorobenzene crystal which does not involve any orientational disorder. Experimental findings are in agreement with the theoretical predictions. The experimental study shows that in p-bromochlorobenzene at 2°K, the line broadening due to disorder is almost an order of magnitude larger than that due to anharmonic phonon-phonon scattering. Yet the overall line shape is a Lorentzian and the two linewidths are additive. The temperature dependence reveals that in both p-bromochlorobenzene and p-dichlorobenzene the mechanism of line broadening involves a T₁-relaxation process in which the optical phonon decays into two phonons of half its frequency by cubic anharmonic interactions.