Analysis of Diffusion Reactions in the Solid State

Let us now turn to diffusion in the general case, without wonting about the exact mechanism or the rates of diffusion of the various species. As an example to illustrate how we would analyze a dlffusion-Umlted solid state reaction, we use the general equation describing formation of a compound with spinel (cubic) structure and stoichiometry (Spinel is the name applied to both one particular compound, i.e.- MgAl204, and a group of compounds all having the same cubic structure and composition). 

A and B are two different metallic ions and O is the oxygen atom (as the oxide). Spinel is a cubic mineral composed of magnesium alimiinum oxide or any member of a group of rock-forming minerals. AU of these are 

Blasse (1964) listed close to 200 spinels having either a normal or inverted spinel structure. What this means is that the cations normally occupying the A site would occupy the B site would be exchanged, depending upon the ionic radius of the two cations. Thus, if we could make Mg smaller in radius, and Al were made larger, we would have Al MgO as an inverted spinel. In normal spinels, the divalent cations occupy tetrahedral sites while the trivalent cations occupy the octahedral sites. The Inverted state depends upon which cations are involved and their relative ionic size. Thus, we have two cation sub-lattices in the spinel lattice, the tetrahedrcd or A-sublattlce and the octahedral B-sublattice. 

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