Integrating Research and Education > Crystallography > Directed Discovery of Crystal Structures > Summary Questions

Summary Questions

  1. What are the two basic ways that close-packed planes of oxygen can be stacked to form three dimensional crystal structures.
  2. In all of the crystal structures you have observed, the various cations have filled voids in layers of anions. Construct a chart that includes the following: number of "nearest neighbor" anions, type of coordination polyhedra, the radius ratio for cations and anions (Rc/Ra), and for silicate minerals (with O as the principal anion) the elements that would be expected to go into each site. Look at the periodic table and see if there is a pattern regarding which groups of elements are most likely to occur in different crystallographic sites.
  3. For different types of coordination polyhedra in the various models, what is the charge of the cation in the polyhedron, and how much charge is "shared" from each of the nearest neighbor anions? Is the charge on the anion balanced by shared charge from the surrounding cations? Has the overall structure achieved electrostatic neutrality? Is this generally true for the structures you have studied?
  4. Look carefully at the ways in which coordination numbers come together to form a 3-D crystal structure (the silicate structures are best to review; compare with the perspective drawings in your textbook). Do the polyhedra tend to share single points, edges, or faces? Explain this relationship.
  5. Focus on polyhedra that have small coordination numbers and contain elements with high valence. Do these polyhedra tend to be concentrated within the crystal structures, or do they tend to be displaced?
  6. You have looked at a number of different types of crystal structures that are representative of a large part of the mineral kingdom. In general, is there a large variety of crystallographic sites in any of the crystal structures, or do the types of crystallographic sites tend to be small?

  7. Linus Pauling
    Image: Linus Pauling Institute
    Compare your answers to the above questions with the discussions on "Pauling's Rules" from any mineralogy textbook. Congratulations! You have just discovered the fundamental principles of crystal structures that were first described by Linus Pauling in 1929, and which led to his award of the Nobel Prize for Chemistry in 1954.

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