Behavior-type analysis of the polarized Raman spectra of halogen-perturbed interstitial hydrogen atoms in alkali halides

The behavior-type analysis method of the polarized Raman scattering intensities on preferentially or randomly oriented defects described in the preceding paper was applied to study two types of perturbed interstitial hydrogen atom (${\mathrm{H}}_i^0$) centers in alkali halides doped with halogen impurities $Y^{-}$, heavier than the host halogen ion $X^{-}$. This method allows one to determine the symmetry of the defect, the nature of its vibrational modes, and the components of the Raman tensor. In a series of six crystals we have identified the $A_1$ and $E$ modes of the ${\mathrm{H}}_i^0$ center perturbed by a single substitutional $Y^{-}$ ion, the ${\mathrm{H}}_i^0\left(Y^{-}\right)$ center, which possesses $C_{3\nu }\mathrm{}\left[111\right]\mathrm{}$ symmetry. Compared to the $T_2$ mode frequency of the unperturbed ${\mathrm{H}}_i^0$ center the $E$ mode is unshifted or slightly higher, while the $A_1$ mode exhibits a much larger (up to 14%) shift to lower frequencies. The relative values of the elements of the Raman tensors of the $A_1$ and $E$ modes have been determined, and the $Y^{-}$ halogen impurity is found to have a stronger influence on the $E$-mode tensor than on the $A_1$-mode tensor. A calculation of these elements within the framework of the valence optical theory provides an understanding of their behavior. A localized vibration of the doubly perturbed ${\mathrm{H}}_i^0$ defect, the ${\mathrm{H}}_i^0\left(Y^{-}{Y}^{-}\right)$ center, is also detected at still lower energies and is shown to belong to the $B_2$ representation of the point group $C_{2\nu }\mathrm{}\left[001\right](110,1\mathrm{}\overline{1}0)$. The relationships between the mode frequencies of the various ${\mathrm{H}}_i^0$- type centers are discussed.