Lattice Vibrations of Solid Solutions; Infrared Absorption Spectra of Nitrate Ions in Alkali Halides

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Abstract
Infrared-absorption spectra of alkali halide single crystals with nitrate-ion impurities show a fine structure on the internal vibrational bands of the nitrate ion that must be ascribed to combinations with the lattice modes of the crystal. A part of these combinations arises from lattice modes that are practically the same as for the unperturbed lattice. Specific heats calculated from the observed spectra are in excellent agreement with the calorimetrically determined values for the pure alkali halide crystals. Other features in the experimentally obtained spectra must be ascribed to combinations with local modes. Group-theoretical considerations lead to selection rules for first-order transitions involving these lattice modes, as well as for absorption due to combinations with the internal vibrational or electronic transitions. A model calculation gives the frequencies of the local modes in terms of the eigenvectors and eigenfrequencies of the unperturbed lattice with the ratio of the masses of the substituted ion and the impurity ion as parameter. Calculated local-mode frequencies are compared with the observed frequencies and with frequencies that have been reported in the literature.