The Dynamics of Crystal Lattices

Abstract

To identify the vibrations that give rise to features in infrared and Raman spectra, we can be guided by a number of qualitative considerations. For example, lighter atoms will vibrate at higher frequencies than heavier atoms, if their bonding is of similar strength; higher bond strengths, usually associated with higher valencies or greater covalency lead to higher bond-stretching frequencies; in covalent structures, bond-stretching vibrations lie at frequencies higher than bond-angle deformations. These considerations, when combined with the results of the symmetry classification described in the last chapter, can permit intelligent guesses at the kinds of vibrations in each symmetry species. If single crystals are available, the direction of the transition moments associated with infrared absorption bands can permit up to three symmetry species to be distinguished, but often only two or one. Raman studies on single crystals can be more productive, allowing, for example, the differentiation of three symmetry species in cubic crystals, where only one species is infrared active. The recognition of some crystal vibrations is greatly simplified if there exists in the crystal some atomic grouping, a molecule or complex ion, which can be considered as dynamically isolated, i.e. when some or all of its internal vibrations lie at frequencies substantially higher than its external vibrations. Features common to the spectra of a series of compounds containing this atomic grouping can then be correlated with its internal vibrations. Here the effect of the crystal environment can be considered as a perturbation, and we have already seen that two