Stoichiometry and local atomic arrangements in crystals

Valence crystals have bulk stoichiometries that are electroneutral with respect to formal atomic valence, and structures in which cation sites are formed entirely by anions and vice versa. This description is shown to be equivalent to a set of stoichiometric and structural rules limiting local atomic configurations in valence crystals. Algebraic equivalents of these rules are used to derive a necessary mathematical link between bulk stoichiometry and local atomic arrangements in valence crystals. In the limit of no charge imbalances on anion sites, this link reduces to the electrostatic valence principle of Pauling. Numerical analysis shows that limits upon the coordination numbers of cations and anions severely restrict the number and type of local configurations that could ever be combined to form an electroneutral bulk stoichiometry, regardless of the valence of the anion or the magnitude of charge imbalances on anion sites.