Activities with Multi-site Mixing

With olivine the substitution of Mg and Fe occurs on the same crystal site (to a good approximation). What happens if there is more than one type of site on which mixing can occur This is very common with silicates such as micas, hornblendes, garnets, and so on. With olivine of the composition and formula (Feo.75Mgo.2. i)2Si04, 

Here the activity of FeSio.502 would be 0.75 according to (15.5). The activity of the fayalite component written as Fc2Si04 is (0.75).  

Next let s take a mineral such as garnet where substitution can occur on two different groups of sites instead of one. The general formula for garnet can be written X3Y2Si30i2 (remember that this choice for the formula now fixes our choice of n in equation (15.5)). The X sites are cubic (8-coordinated) and we will assume they accept Al and Fe ions. The Y sites are octahedral (6-fold), and let s assume they accept only Mg , Fe , and The Si site is tetrahedral (4 fold), and it can also hold AP ions. The total configurational entropy for this mineral must be the sum of the entropies on all three of these sites, or 

Here n equals 3, 2, and 3 on the cubic (X), octahedral (Y) and tetrahedral (Si) sites, respectively. 

One can see from this that a general equation for the configurational entropy or entropy of dissolution involved in forming a solution is 

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In carrying out calculations for multi-site mixing such as this, you can either use equation (15.10) directly, or work through the problem stepwise and ion by ion as with (15.8) the two methods are equivalent. Further details are given by Powell (1977). It is possible using analytic techniques such as X-ray diffraction, Mossbauer spectroscopy and infra-red, Raman and UV-visible spectroscopy to analyze for the concentration of different ions on specific crystal sites. Thus the activities, configurational entropies, and other such properties of solid solutions can often be calculated. This provides detailed information on the stability and structure of crystalline solutions. 

Langmuirian view, the active catalytic surface is comprised of a uniform distribution of static sites that do not interact with one another. This is sharply contrasted by the Taylor view, which proposes vacancies and topologically unique surface atom configurations as the centers of reactivity. The Langmuirian idea of a catalytically reactive surface leads to the ensemble effect that ascribes the changes in the selectivity for an alloy surface to the dilution of multi-atom surface ensembles in the alloy induced by mixing inert components into the active surface. In this view, the selectivity of a particular reaction depends predominantly on the number of reactive surface atoms that participate in elementary reaction events. 

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