Reactions in inhomogeneous media

The quantitative description of most diffusional processes in single-phase media is based upon the assumption of local defect equilibrium. Therefore, in this section we shall first of all examine processes by which defect equilibrium is attained. In this regard, two important fundamental types of defect reactions should be discussed 1. Following a sudden change in temperature or pressure, a reaction between defects and lattice atoms occurs at sites of repeat-able growth such as inner or outer surfaces and dislocations. For a crystal with Schottky disorder, the reaction equation may be formulated as  

Let us assume that the heterogeneous reaction (6-6 a) takes place on infinitely extended laminar plates. In the zeroth approximation, this can be taken as a description of the mosaic structure of the crystal. The fluxes of vacancies in the cation and anion sublattices are given by  

Because of the condition of electroneutrality, the local concentrations and must be equal to each other at all times, even during the equilibration reaction. Therefore, yV is always equal to. By using this condition, we can eliminate the diffusion potential (j) from the flux equations. Furthermore, the laws of ideal dilute solutions may be used in the present case. Setting rji = fXi 4- ZiF i and pi = /i H- i T In Cf, we obtain the following equation for the flux  

For the assumed geometry of the system, the initial and boundary conditions for lamellar plates of thickness 2a are  

The solution of this equation has already been given in eq. (5-47). For times greater than Sa lln D, the series can be terminated after the first term without introducing serious errors. The relaxation time is then given as  

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