Lattice instabilities in non-stoichiometric materials

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Abstract
Two different approaches to the problem of lattice instabilities in non-stoichiometric materials are considered. First, a semi-empirical model, which had been previously introduced to describe the composition dependence of the superconducting transition temperature of tetragonal sodium tungsten bronze, is reviewed. Second, a simple model of a material with the chemical formula ABx (0 < × < 1) is introduced and analyzed within a mean field approximation to the B atom occupation. A structural change from face centered cubic to simple cubic interpenetrating A and B lattices is shown to occur, and is accompanied by a phase separation. Considerable softening of the phonon frequencies is also obtained as the composition is varied.