Theory of oxidation/reduction-induced valence transformations of metal ion dopants in oxide crystals mediated by oxide-vacancy diffusion: I. Thermodynamic analysis
Materials Engineering Department, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
Received 14 August 2012
Revised 22 October 2013
Accepted 9 December 2013
Available online 21 December 2013
Highlights
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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.
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The results suggest that experimental study of the different species concentrations at thermodynamic equilibrium as functions of pressure and temperature should allow assessment of various reversible reaction constants controlling the process.
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The diffusion exhibits a complex behavior; under some conditions, it may be described by a constant diffusivity, and is symmetric with respect to oxidation and reduction. However, under a wide range of conditions, the ionic state changes are highly asymmetric with respect to oxidation and reduction.
Abstract
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 of the oxygen vacancy, metal ions, holes and electrons as functions of the ambient oxygen pressure. The results suggest that experimental study of the 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.
