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Unit Cells of Galena and Fluorite: Calculations and Comparisons

## Calculating Coordination and Radius Ratio for Galena

1. The images below show the unit cells for two minerals: galena (PbS) and fluorite (CaF2). Versions of the unit cells can be viewed interactively on the web using the
American Mineralogist Crystal Structure Database (AMCSD): The galena unit cell from AMCSD is the one shown below, but the fluorite version is a different one. The fluorite image below actually shows two unit cells, whereas the version on the web shows one. Both are useful.

Note that you can label the atoms on the web models by right-clicking on the cell and

choosing “Style —> Labels —> “With Element Symbol”.

In the galena model, the sulfur atoms are in yellow and the lead atoms are in grey.

Sulfur in galena exists in the 2- oxidation state.

(a) Calculate the radius ratio for the ions in galena and determine what the coordination of Pb2+ is in this mineral.

(b) How does the coordination of the atoms in galena compare to those in halite and how do the structures of these two minerals compare?

(c) Calculate the radius ratio for the ions in fluorite and determine what the coordination of Ca2+ is in this mineral.

(d) It should be clear that the structure of fluorite is different from galena (based on the unit cell models and your calculations). Why do you think they (must) have different structures?

2. In Problem Set 1 you calculated the bond strengths for fluorite and hematite in terms of their ionicity/covalency. You will have calculated the coordination for Ca in fluorite above and can determine the coordination of F from the figure above or from the AMCSD model. The coordination of Fe3+ and O2- in hematite are octahedral and tetrahedral, respectively.

(a) Calculate the relative bond strengths for these minerals using the electrostatic bond strength calculation (equation 2.1, for which you need to look up ionic radii). Use angstroms as the units for the radii.

(b) Do the hardnesses of the two minerals make sense in terms of your calculations (both from Problem Set 1 and the question above)?

3. In class we discussed how indium (In) is incorporated into sphalerite (ZnS) via a coupled substitution with Cu. Zn occurs in tetrahedral coordination in sphalerite.

(a) Explain this substitution, and, using ionic radius and electronegativity data from the online sources previously provided (also below), explain why this is reasonable in the context of Goldschmidt’s rules. Write the exchange equation for the substitution.