Lattice-dynamical study of impurity modes in mixed cuprous halides

A theoretical study of impurity modes in mixed cuprous halides ($\mathrm{Cu}{A}_{1\ensuremath{-}x}{B}_{x}$ with $A,B=\mathrm{C}\mathrm{l},\phantom{\rule{0ex}{0ex}}\mathrm{B}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{a}\mathrm{n}\mathrm{d}\phantom{\rule{0ex}{0ex}}\mathrm{I}$) in the low-concentration limit ($x\ensuremath{\ll}1$) is reported using the Green's-function technique. The perturbation caused by the halogen impurity $B$ on the phonon spectra of $\mathrm{Cu}A$ is accounted for in terms of mass change at the impurity site as well as the change in the nearest-neighbor impurity-lattice interaction. The involved lattice Green's functions have been computed by incorporating the phonons generated by an 11-parameter rigid-ion-model fit to the recent neutron data. We find that different substitutional impurities in cuprous halides may give rise to well defined symmetry vibrations both in and outside the band-mode region. The possibility is pointed out for some of the important cases to be observed by (ir or Raman) experimental techniques. In the cases of known experimental data, we have determined the force perturbation describing the impurity-host bonding in terms of our one-parameter model. The calculated force-constant changes, in particular for $\mathrm{Cu}Cl:\mathrm{Br}$ and $\mathrm{Cu}Cl:\mathrm{I}$ systems, are similar to some extent to the behavior noticed in alkali halides rather than in II-VI and III-V compounds. In view of the insufficient experimental data, the possibility of the size effect cannot be ruled out. However, more experimental data on isoelectronic substituents in cuprous halides are very much needed to arrive at a general conclusion regarding the trend of force-constant change with the size of the impurity atom.