Formation Kinetics of Double Salts

Since both the oxide reactant and the spinel are ternary (nonstoichiometric) compounds when equilibrated with each other, at a given P and T, the boundaries (A, B)0/spinel and spinel/(B, A)203 are not invariant. They become invariant (and thus provide unique boundary conditions for the reaction) only if an additional intensive thermodynamic variable can be predetermined. This is a consequence of Gibbs phase rule. 

Spinel formation is usually treated under some tacit assumptions which do not always hold. For example, it is tacitly assumed that the oxygen potential of the surrounding gas atmosphere prevails throughout the reaction product during reaction. In other words, it is assumed that d,u0 = 0. Although this inference reduces the number of variables by one and simplifies the formal treatment, the subsequent analysis will show that the assumption is normally not adequate. 

Let us systematize the possible boundary conditions for cation diffusion in a spinel. Since in the ternary system (at a given P and T) the chemical potentials of two components are independent, we may distinguish between three different transport situations. If A denotes a change across the product layer and O and AO are chosen as the independent components, the possibilities are 

An analogous equation holds for The Gibbs-Duhem equation requires that VpBO = - ]/2-VjuA0 for compounds with a sufficiently narrow range of homogeneity. 

In the classical cation counterdiffusion experiment, oxygen gas is excluded from the interfaces and rM = 0 (Fig. 6-6 a). Thus the coupling condition is simply 

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