8. Nonstoichiometric Phases—Composition, Properties and Phase Transitions

Nonstoichiometric phases constitute a large family of technologically important materials. Among them, the inorganic materials whose variable stoichiometry of some components originates from their exchange with surrounding atmosphere represent particular thermodynamic systems referred to a partly open system. The phase equilibria in these systems including the homogeneous crystallochemical reactions of the involved crystal defects can be effectively treated using the thermodynamic potential called hyper-free energy derived from the Gibbs free energy by Legendre transformation with respect to the amounts of free components. In this chapter, we focus on general thermodynamic description of systems with variable content of components shared with a dynamical atmosphere, their essential material quantities being influenced by variable stoichiometry, conditions for homogeneous crystallochemical equilibria as well as for phase transitions. The influence of variable stoichiometry on material properties such as isobaric thermal expansion, isothermal compressibility and in particular heat capacity is analyzed and divided into two parts: the direct effect on conventional isoplethal quantities due to deviation from stoichiometry, and so-called saturation contributions determining the difference in material properties measured under isoplethal and isodynamical conditions (constant activities of free components). In the last part, the construction of phase diagrams of partly open systems is demonstrated on several examples of oxide systems, and the relevant phase transitions are classified and discussed.