Transport phenomenon and groups of elementary steps

The space model that we retained above requires transportation of the matter from the grain toward the neck. 

This transfer will occur by diffusion, only if concentration gradients exist between the two ends of the transfer and the difference of curvature causes this difference of concentrations, which is the driving force of these transfers. We mainly distinguish three cases of diffusions. 

Of course, these three diffusions can intervene simultaneously but then we have three parallel ways and on assumption of a rate-determining step, this is the fastest one, which will be retained. If diffusion in the solid is retained, generally it will be the strrface diffusion for the relatively low temperatrues and the bulk diffusion for higher temperatures. In these two cases, diffusiorrs that ate ettsttred by point defects can be  

In case of solids made up of several main comporrents (e.g. oxides, chlorides, etc.), the two entities anions and cations must be transported. In case of gas diffusiotr, it is necessary that the transfer is of either two gas species or a complex species so that the stoichiometry of the initial solid is preserved. In case of diffusion in solid state, it is necessary to use an anion diffusion and a cation diffusiotr, that is, the Wagner approximation for the prevalent defect (see section 2.3.2) could not be strictly retained. However, we will be able to consider the relative evaluation of the concentrations of the defects, in particnlar to simplify the electric eqrration of neutrality in the approximation of Bronwer (see section 3.7.2). 

Various kinetic modes with rate-determining steps 

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