Diffusion and Sintering in Ionic Compounds

The flux equation of lattice molecules MaXb can be derived using the flux and stoichiometry constraints. 

The flux equations for cations and anions in the form of Pick s first law can also be obtained from Eq. (13.7) using Eqs (13.3) and (13.4) they take a similar form to Eq. (13.7) with the identical effective diffusivity D. 

Concerning the effeetive diffusion coefficient, two types of expression have been, reported so far. One is  

When a compound is sintered via diffusion through various paths, the effective diffusivity is the sum of each contribution through its specific path. The effective diffusion coefficient of ion i, Dj, is then expressed as 

The contribution of grain boundary diffusion increases as the grain boundary area increases, i.e. the grain size decreases following/ oc l/G (Eq. (13.12)). Unlike grain boundary diffusion, the contribution of lattice diffusion can be considered to be independent of grain size if the volume fraction of the grain boundary is inconsiderable. For an MX compound, if  

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