Diffusion Involving Internal Boundaries

While Dq directly reflects the ionic conductivity measured in a steady state experiment, the relationships are more complex for chemical diffusion and tracer diffusion. For simplicity we assume that the transport is so slow that local relaxation effects occur instantaneously.240 

The treatment is greatly simplified, if the lateral diffusion into the bulk is absolutely negligible with respect to the boundary diffusion. The bulk transport then just takes place on a completely separate time scale the effective diffusion length of the ceramic is the grain size (X) rather than the sample size (L), but capacitive (oc lcs) and resistive terms (oc Me/) are unchanged compared to the bulk values (cf. Section VI.3.tv.). In the case of the chemical experiment, 

Donor-doped BaTi03 and SrTi03 are relevant examples. There bulk diffusion is very slow because of the very low Vq concentration and the low mobility of the metal vacancies. If a perovskite ceramic, 

Let us briefly highlight the effect of equilibrium space charges on the transport in our prototype oxide (with just O and h as defects).244 The situation becomes particularly clear if we assume equal mobilities and equal bulk conductivities. Since in the case of chemical diffusion x0. and crh. are, as it were, in series, a space charge splitting 

In a polycrystalline sample the situation is more complicated. Again, a simple result is only arrived at even if we assume extreme chemical resistance ratios for bulk and boundary values. Even if the 

---

Reactor design in the presence of internal diffusion involves simultaneous solution of the reactor and pellet equations (see Chapter 12). These are given in Table 20.9 along with the boundary conditions in both dimensional and nondimensional forms. 

---