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  1. What are the coordination numbers for Si, Mg, and K?
  2. How are the Si tetrahedra connected to each other in this structure (i.e., how many oxygen in each tetrahedron are shared with another tetrahedron? In what crystallographic direction do the unconnected corners of the tetrahedra point?
  3. Note that the basic structure consists of layers of Si tetrahedra on the top and bottom of octahedral (Mg, Fe) sheets. This is the "T-O-T" structure. How does this T-O-T structure differ from that of amphiboles or pyroxenes?
  4. Consider the three cations: Si4+, K+ and Mg2+. What is the coordination number of each and what is the strength of its bonds to oxygen? So, where would you expect cleavage to occur in biotite?
  5. Orient the structure so that the a and b axes are within the plane of the screen. You should be looking perpendicular to the T-O-T sheets. What is the symmetry of the "rings" of tetrahedra? (Hint: Look closely).
  6. If the rings of tetrahedra in one layer lie directly above the rings in adjacent layers, then they are related by a 90° translation and biotite must belong to the hexagonal crystal system. If the rings are offset in any direction, then biotite is monoclinic. Now rotate the structure so that you are looking directly down the b-axis. Do the layers stack directly on top of one another? What does this suggest as to the crystal system of biotite?--is it hexagonal (trigonal) or monoclinic?
  7. You've already partially answered this question, but compare the biotite structure to the structures of tremolite and diopside. How are they similar, and how are they different?