Boundary layers and grain boundaries

The relationships are more complex for chemical diffusion and tracer diffusion. 

Let us consider first the chemical transport of oxygen in an oxide along an interface (x-y plane, see Fig. 6.41, right) as a consequence of a sudden chemical potential change in the ambient. As we do for the bulk we assume local equilibrium L Since no gradients occur in the electrochemical potentials or in the chemical potential perpendicular to the interface at the start of the experiment, the flux, at a given position, is completely determined by a dfio/dy. It would be wrong, however, to assume that the flux lines would be parallel to the interface for the whole experiment, and that the effective diffusion coefficient Dq could be obtained from an arithmetic mean of the local DQ(y) values, as it was for in the conductance experiment with 

A greatly simplified treatment can be achieved, if it is possible to assume that the lateral diffusion into the bulk is absolutely negligible with respect to the core diffusion (Fig. 6.42, left). The bulk transport then takes place on a completely separate 

Even if, in a polycrystalline sample, the grain boundary resistance dominates completely, the thermodynamic factor (or chemical capacitance) is still determined by the bulk, provided the density of boundaries is not too great. In other words, the largest part of the stoichiometric change (d/xo/dco) takes place there (Fig. 6.42, right). In this case we obtain, for hardly permeable boundaries, the sruprisingly simple relationship 

We neglect isotope effects on the mobility which is certainly incorrect in the case of the proton. 

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