Phase Transformations in Solids

AgI-type solid electrolytes

Publisher Summary The chapter presents a study on the relationship between structure, vibrational dispersion relations, and band structure for chalcopyrite and related compounds. The essential step in this procedure is the “folding” of the dispersion relations [ ω (k) or E (k)] for the simplest structure into the smaller Brillouin zone of the more complicated one. In one-dimensional models, such folding is trivial enough and is discussed in relation to the nearly free electron approximation, Peierls instability, and so on. In three dimensions, it is more complex and therefore merits the detailed and concentrated description that is presented in this chapter. In addition to the chalcopyrites, the chapter includes certain quaternary and “defect” or “vacancy” compounds, such as HgIn 2 Te 4 . The vacancy compounds may be considered to have tetrahedral structures with a sublattice of unfilled sites. In this case, it is questionable whether the compound is to be regarded as derived from its parent structure by a small perturbation, as is often assumed for chalcopyrites. Compounds that have tetrahedrally coordinated structures generally have an average number of four valance electrons per atom. This is the Grimm–Sommerfeld rule.

J. A. A. Ketelaar

Papers

The relation between electrolytic conduction in solids and crystal structure