Mixed Tetrahedral Solids

Because of the polar nature of the mixed tetrahedral solids, there is stong coupling between electromagnetic radiation and lattice vibrations. This has allowed direct experimental study of the vibrational spectra through examination of infrared... 

Given this description of the forces, there is no difficulty in carrying out the calculation of the full vibration spectrum for an ionic solid in the manner described in Chapter 9. At least for the compounds we have considered here the structures are sufficiently simple that the complications which arose in calculating the spectra for the mixed tetrahedral solids are not present. The elastic con.stants describe the low-frequency lattice vibrations and there is no reason to expect the description at high frequencies to be cither worse or better. (Some discussion of the vibration spectra of ionic crystals is given, for example, by Wallis, 1965 a number of properties related to anharmonicily are described by Cowley, 1971.)... 

Universal matrix elements were not available at the time of Pantelides s study, but now we may use them for a direct prediction of the susceptibility in the alkali halides. This is closely analogous to the calculation of susceptibility for the tetrahedral solids, done in terms of bond dipoles in Section 5-A by means of Eq. (5-7), and the corresponding calculation for the mixed tetrahedral solids. Since now we do not have independent two-electron bonds, however, the. susceptibility must be formulated differently the final result will be equivalent to the extreme polar limit of the tetrahedral solids. 

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