Phenomenological description of the longitudinal vibrations of the quasi-one-dimensional solid PtCl: calculation of the valence defect frequencies

The longitudinal vibrations of the PtCl linear chain and those of various valence defects are described by a one-dimensional model in a first-nearest-neighbour interaction approximation. The analysis is performed as a function of the K₂/K₁ ratio (K₁ and K₂ representing the PtCl^IV-Cl and Pt^II-Cl force constants, respectively), which is shown to play an important role in the vibrational characteristics of the defects while the infrared frequencies are not strongly dependent on a particular ratio. A coherent description of the frequencies of the modes of the perfect chain and those of the polaronic defects is obtained for K₂/K₁=0.3. For this ratio the electron polaron and the electron bipolaron give rise to one Raman-active mode while at least two are predicted for the other investigated defects. The shapes of the Raman bands associated with the electron and hole polarons are explained by the chlorine isotopic effect. The vibration associated with the electron bipolaron is predicted to be at about 210 cm^-1 where a broad line grows upon photolysis. An elementary calculation based upon a Born-Mayer potential for short-range interactions, adjusted from the interionic distances, leads to force constants of the same magnitude as those adjusted from the experimental frequencies.