Diffusion and Conservative Ensembles

The chemical diffusion coefficient includes, as we know from the formal treatment in Section VI..3iv., both an effective ambipolar conductivity and an effective ambipolar concentration. The latter parameter is determined by the thermodynamic factor which is large for the components but close to unity for the defects. 

If defects are not randomly distributed, in a better approximation c1/2 or c1/3 dependencies (see Section IV.5.H.) may be introduced in the thermodynamic factors of the defects (Eq. 120b). 

Formally, it will be even necessary to make corrections already in the starting flux equations. The detailed formulation of linear irreversible thermodynamics also includes coupling terms (cross terms) obeying the Onsager reciprocity relation. They take into account that the flux of a defect k may also depend on the gradient of the electrochemical potential of other defects. This concept has been worked out, in particular, for the case of the ambipolar transport of ions and electrons.230 

A more explicit procedure is to introduce chemical interactions directly There is a certain analogy with the equilibrium situation where it is possible to avoid the use of activity corrections over wide ranges by considering associates to correct for the interactions (see Section IV.5./.). The relevance of this method of treatment is particularly evident if such associates can also be detected experimentally, e.g., by spectroscopic techniques in the case of ionic defects with differing charge states. This leads to a rescaling of defect concentrations and 

In the case that Eq. (130) describes the decisive elementary reaction, the continuity Eq. (130) for B is 

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