# The Conditions of Equilibrium of "Non-Stoichiometric" Chemical Compounds

J. S. Anderson

## Abstract

The conditions are discussed under which a crystalline binary compound may exist over a relatively wide, but finite, range of chemical composition-e.g. the existence of pyrrhotite, nominally FeS, up to a composition approximately FeS$_{1\cdot 2}$. On the hypothesis that the lattice defects (interstitial atoms or vacant sites), introduced by departure from stoichiometric composition, interact with one another when in adjacent lattice positions, the problem reduces to a form similar to that of Fowler's treatment of regular localized monolayers. It follows that below a certain temperature, determined by the energy of interaction of lattice defects, the phase is stable only when the concentration of defects is less than some limiting value. If this is exceeded, the phase breaks up into a two-phase system. Hence the range of existence of any compound is limited on either side by the compositions at which, for example, the concentration of vacant cation sites and of interstitial atoms reach limiting values. The dependence of these limits on the partial pressure of the volatile component and the degree of lattice disorder in the stoichiometric phase is worked out. The conditions emerge under which (a) the stoichiometric compound may be metastable (e.g. FeS) and (b) the phase is incapable of existence. Experimental pressure-composition isotherms for the systems Pt-PtS-PtS$_{2}$, MS-MS$_{2}$ (M = Fe, Co or Ni), and UO$_{3}$-U$_{3}$O$_{8}$ are compared with the model. The general form of the equilibrium diagrams is satisfactorily reproduced, and the limitations of the model are shown. The formation of anomalous solid solutions between compounds of different formula type (e.g. YF$_{3}$ and CaF$_{2}$) is finally discussed and shown to fall within the scope of the theory.