Migration and Diffusion of Charge Carriers in Solids

The most important driving forces for the motion of ionic defects and electrons in solids are the migration in an electric field and the diffusion under the influence of a chemical potential gradient. Other forces, such as magnetic fields and temperature gradients, are commonly much less important in battery-type applications. It is assumed that the fluxes under the influence of an electric field and a concentration gradient are linearly superimposed, which 

It is important to realize that the migration in an electric field depends on the magnitude of the concentration of the charged species, whereas the diffusion process depends only on the concentration gradient, but not on the concentration itself. Accordingly, the mobility rather than the concentration of electrons and holes has to be small in practically useful solid electrolytes. This has been confirmed for several compounds which have been investigated in this regard so far [13]. 

In the predominantly electronically conducting electrodes it is the chemical diffusion of the ions which controls the electrical current of the galvanic cell. This includes the internal electric field which is built up by the simultaneous motion of ions and electrons to establish charge neutrality [14]  

The chemical diffusion coefficient D is the product of the diffusivity of the ions Dj and the Wagner factor S na.J r lncv, [3], 

It should be kept in mind that all transport processes in electrolytes and electrodes have to be described in general by irreversible thermodynamics. The equations given above hold only in the case that asymmetric Onsager coefficients are negligible and the fluxes of different species are independent of each other. This. should not be confused with chemical diffusion processes in which the interaction is caused by the formation of internal electric fields. Enhancements of the diffusion of ions in electrode materials by a factor of up to 70000 were observed in the case of Li3Sb [15]. 

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