Experimental and Theoretical Study of Raman Scattering inTl+-Doped Alkali Halides

Experimental Raman spectra are presented for KCl, KBr, KI, and RbCl doped with ${\mathrm{Tl}}^{+}$ ions. The spectra are continuous and first order, being caused by the impurity-induced breakdown of the lattice periodicity, and are strongest for $E_g$ vibrations and weaker for $T_{2g}$ vibrations. No $A_{1g}$ spectra are seen. Theoretical calculations for the Raman spectra are presented and are based on the assumption that the electron-phonon interaction is linear in the displacements of the impurity's nearest neighbors. The spectra are calculated using phonons derived both from the shell model as fit to neutron data for KBr and KCl, and from the breathing-shell model computed from macroscopic parameters for all four hosts. The best agreement between theory and experiment is seen to occur using zero-force-constant changes for the $E_g$ spectra in KBr and KI and for the $T_{2g}$ spectra in all hosts. In KCl, a 10% stiffening in the force constant is necessary for the $E_g$ spectrum, and in RbCl this spectrum requires a 10% weakening. No significant differences can be seen in the spectra calculated from the two different models for the phonons, and the agreement between theory and experiment is good.