Binary ambipolar diffusion

In the discussion so far, the diffusional and electrical fluxes of the ionic and electronic carriers were treated separately. However, as will become amply clear in this section and was briefly touched upon in Sec. 5.6, in the absence of an external circuit such as the one shown in Fig. 7.7, the diffusion of a charged species by itself is very rapidly halted by the electric field it creates and thus cannot lead to steady-state conditions. For steady state, the fluxes of the diffusing species have to be coupled such that electroneutrality is maintained. Hence, in most situations of great practical importance such as creep, sintering, oxidation of metals, efficiency of fuel cells, and solid-state sensors, to name a few, it is the coupled diffusion, or ambipolar diffusion, of two fluxes that is critical. To illustrate, four phenomena that are reasonably well understood and that are related to this coupled diffusion are discussed in some detail in the next subsections. The first deals with the oxidation of metals, the second with ambipolar diffusion in general in a binary oxide, the third with the interdiffusion of two ionic compounds to form a solid solution. The last subsection explores the conditions for which a solid can be used as a potentiometric sensor. 

Exposing a binary compound to a chemical potential gradient of one of its components results in a flux of that component through the binary compound as a neutral species. The process, termed ambipolar diffusion, is characterized by a chemical diffusion coefficient Z)chem which is related to the defect and electronic diffusivities by... 

Exposing a binary compound as a whole to a chemical potential, i.e., for diiy[x/dx 7 0, results in the ambipolar migration of both constituents of that compound down that gradient. The resulting ambipolar diffusion coefficient for an MO oxide is given by... 

Here, 8(f), 8(0), and 8(cx3) are the mean (at time f), initial (at f = 0) and final (as f —> CX3) value of oxygen nonstoichiometry, respectively. By monitoring the temporal variation of the nonstoichiometry 8(f) by either thermogravimetry or a 8-sensitive property (e.g., electrical conductivity), it is possible to determine the two kinetic parameters. With regards to binary systems, it is believed that the relaxation kinetics may be well understood. Chemical diffusion, in particular, has long been understood in the light of chemical diffusion theory [28], or in the light ofthe ambipolar diffusion theory [29]. 

If the lattice and grain boundary coefficients are additive, then for a pure binary compound the effective (or ambipolar) diffusion coefficient is given by (11)... 

Many other cases of combined transport coefficients are in use, e.g. the combined (additive) transport of oxygen and metal ions commonly that we shall address later (and exemphfy by the high temperature oxidation of metals), the combination of two diffusivities involved in interdiffusion (mixing) processes, and the mass transport in creep being rate hmited by the smallest out of cation and anion diffusivities in a binary compound. As some of these sometimes are referred to as ambipolar or chemical diffusivities, we want to stress the above simple definition of ambipolar transport coefficients as relevant for membrane applications using mixed conductors. 

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