Theory of oxidation/reduction-induced valence transformations of metal ion dopants in oxide crystals mediated by oxide-vacancy diffusion: I. Thermodynamic analysis

• We consider theoretically valence transformations of doping metal ions in oxide crystals induced by changes in ambient oxygen partial pressure.
• Experimental study at thermodynamic equilibrium allows assessment of various reversible reaction constants controlling the process.
• In the companion paper II, the diffusion study reveals complex behavior: symmetric or asymmetric with respect to oxidation and reduction.

We consider theoretically valence transformations of doping metal ions in oxide crystals induced by oxidation and reduction obtained by changes in the ambient oxygen partial pressure. Three types of oxygen vacancies are assumed to mediate transformations: neutral, singly ionized, and doubly ionized. We provide thermodynamic equilibrium analyses, yielding concentration relations among the oxygen vacancy, metal ions, holes and electrons as functions of the ambient oxygen pressure. The results suggest that experimental study of different species concentrations at thermodynamic equilibrium as functions of pressure and temperature should allow assessment of various reversible reaction constants controlling the process. In the Part II companion paper, the kinetic (diffusion) characteristics are considered in detail.