The Chalcopyrite Structure and Solid Solution

A different kind of change in cation occurs in the common mineral chalcopyrite. The formula of chalcopyrite is usually given as CuFeSa, from which we can assume that there are two cations, Cu and Fe and one anion, (of course, there are two anions for every copper or iron cation). The anion packing is cubic closest packing, giving a sphalerite type structure. 

Assume that the structure of chalcopyrite is the sphalerite structure with either Cu or Fe in place of the ion. Moreover, assume that the cations are placed randomly in the tetrahedral voids. In other words, on average, there is a 50% chance that a particular void is occupied by Cu and a 50% chance that it is occupied by Fe . 

Would the symmetry of this randomized stracture be the same as that of sphalerite  

because, on average, half of the tetrahedral voids are occupied by an average cation. This produces the cubic symmetry of sphalerite. 

For the moment, ignore the sulfide ions and concentrate on the cations. Starting at the top of the unit ceU, there are four copper cations at the comers and one iron cation in the center. In the next layer of cations there are two copper ions on opposite faces and two iron cations on the other set of faces. Then, in the middle layer there is a layer similar to the top layer, but the ions are reversed (iron at the comers, copper in the middle). The next to bottom layer is a repeat of the second layer from the top, except that the ions are reversed. The bottom layer is, of course, a repeat of the top layer. 

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