Theory of the vibrational structure of the Raman spectra of impure crystals

Abstract

1. If the frequency of the incident light is considerably closer to the frequencies of impurity centres than to those absorbed by the pure crystal, the vibrational structure of the Raman spectra may be appreciably determined by the local dynamics of the lattice and the vibronic interaction in the impurity centre. For lack of the first order Raman spectrum of the pure crystal the matrix conditions of observing this vibrational structure are favourable in systems such as impure alkali-halide crystals. 2. It is shown that the Raman spectra would have in the Born-Oppenheimer adiabatic approximation quasi linear vibrational structure analogous to that of the absorption (luminescence) spectra : in the absence of local modes the spectrum consists of a sharp no-phonon line (the Raman analogue of the Mossbauer line) and of a considerably wider phonon band (the Raman analogue of the phonon wing of the Mossbauer line) ; a local (or pseudo-local) mode causes in addition to this aspect a series of vibrational lines. 3. For various models of the impurity centre the intensity distribution and temperature dependence of the vibrational structure are calculated. If the frequency of the incident light is close to the maximum of the impurity absorption band and the Stokes-shift is appreciable, the distribution of the intensity in a vibrational series is no longer monotonic and the maximum intensity will now belong to a vibrational line whose frequency differs from the frequency of the incident light by nω, where ω is the frequency of the local mode and n is an integer, n > 1. 4. The theoretical conclusions are compared with the experimental results of Stekhanov and Eliashberg on the Raman spectra of impure alkali-halide crystals.