Substitution of the Same Cation on Several Non-equivalent Sites

Substitution of the Same Cation on Several Non-equivalent Sites 

In the olivine example above, two different cations exchange on one equivalent site. With garnet we had three different sites (X, Y, and Si) each of which could exchange different ions here, could substitute on either the octahedral Y sites or the tetrahedral Si sites. To round out the possibilities, we should discuss how to handle such situations, where one species (ion, molecule, or whatever) substitutes on two or more different sites in a crystal—something which is very common in minerals. 

If you prefer to write the formulas for orthopyroxene and ferrosilite with the more conventional stoichiometries (Fe, Mg)Si03 and FeSi03, then the activities become 

This is because the structural formula for this stoichiometry would have to be written as Mlo.5M2o.5Si03, making n = 1/2 in equation (15.5). In these examples, as always, ai = and the 7j s have been omitted for simplicity. In these cases of multi-site mixing, 7 can differ for each specific site. 

Using the above reasoning, we can write a general equation for the activity of a cation i (or of its pure end-member) distributed over j different crystal sites  

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