A new statistical thermodynamic theory for substoichiometric fluorite structure compounds and its application: I. An order-disorder model theory for the thermodynamic functions of substoichiometric fluorite structure compounds

In this work an attempt is made of constructing the (G, T, x) curves for the case of substoichiometric oxides of the fluorite structure on the basis of a statistical model. Considering the fluorite structure as a repitition of oxygen ions tetrahedrically coordinated, the hypothesis is made of a local bond between the reduced cations and the oxygen vacancy in the tetrahedron (“tetrahedral defect”).This “tetrahedral defect” constitutes the building block of the low temperature sub-phases often encountered in these systems; at higher temperatures its packing in the lattice gives rise to “residual structures”.One can express all thermodynamic functions, at given oxygen/metal ratio, as a function of an “ordering parameter” p, representing larger and larger packings of the tetrahedral defects, in such a way making this model a typical order-disorder treatment.Introducing the formalism of chemical equilibria in the equilibria between the various defect species it is also possible to obtain thermodynamic functions by the solution of a system of pseudo-chemical equilibrium equations, when probability functions f are employed in place of the activities of the defects species.