The lab exercise is to describe one specimen from the HMNS collection in terms of all the properties you can discern or infer from various reference tables, and to compile this information on a 4"x6" index card. You will be making similar cards for other unknown minerals in subsequent labs.

The main objective of this lab is to learn how to observe and how to use this information to distinguish specific minerals. In the following weeks you will be tested on what you have learned to observe using 'unknown' minerals.

Due at beginning of next week's lab: your completed index card.

Materials needed: Crystal models and corresponding clinographic projections (perspective drawings) will be provided by the TA. Copy of Klein workbook. Colored pencils to prepare illustrations.

To turn in at beginning of next week's lab: A neat copy of the completed exercises, with the requested information summarized on the diagrams provided.

Materials needed: Structure models, materials for packing models will be provided by the TA. Bring your copy of Klein workbook, a ruler, and a set of colored pencils.

To turn in at beginning of next week's lab: Completed workbook sheets.

Please submit a written report on your activities and findings at the beginning of the next week's lab.

Please submit a written report on your activities and findings at the beginning of the next week's lab.

HW 1: Basic symmetry operations

Do Klein exercise 1 (its fun!). This exercise involves identifying simple rotational and mirror-plane symmetry operations in a number of familiar two- and three-dimensional objects.

Construct the following solid figures using the patterns in Klein:

• cube
• octahedron
• tetrahedron
• rhombohedron
• trigonal prism

For each object, determine and list ALL symmetry elements that you can discern (cf. KH 26-32). For example, what rotation axes, mirror planes, etc. are present and how many of each are there? How many distinct symmetry operators are there? Make clear perspective diagrams of each object and use colored pencils to show the symmetry operators. Label clearly! Determine the appropriate point group symmetry designation for each object.

For selected patterned cubes in the class handout, repeat the previous exercise. Note that the patterns may LOWER the symmetry present, and although each object is "CUBE-shaped" they all have different symmetry. Determine the appropriate point group symmetry designation (Hermann-Mauguin notation) and crystal class for each object (cf. K 35).

Using the clinographic drawings of two ideal crystals (class handout), determine appropriate and consistent Miller indices for each of the labelled faces ({forms}). To accomplish this task you must first designate appropriate crystallographic axes (see text or workbook for examples); neatly and accurately illustrate these axes on the diagrams provided. Remember that Miller indices for the pinacoid faces are readily ascertained on the basis of the axis that they intersect. For prism, dome, or other faces you will have to determine (approximately) the axial intercepts to calculate Miller indices. For this step, make reasonably accurate drawings of sections through the crystals showing axial intercepts of the extended faces. Remembering that parallel faces have equivalent indices, construct parallel faces that intersect one of the axes at a 'unit' translation (e.g., coincident with one of the pinacoids). Please show your complete derivation of the Miller indices for each {form}.

Do Klein exercise 5 to develop a basic understanding of how the symmetry content of an ideal crystal can be plotted quantitatively. This exercise will prepare you for Lab #3, where you will apply this stereographic plotting technique. The concepts of stereographic projection are described further in K&H and will be addressed further in lab.

To prepare for the lab, mount a copy of a stereonet on a hard surface - such as a clipboard. Before attaching in any permanent way, mount a thumbtack through the reverse side of the stereonet, so that the sharp point is located exactly at the center of the net. A sheet of tracing paper can be impaled on this point and readily rotated to plot specific data as explained in Klein. You might want to purchase say 10 sheets of tracing paper for use in this class. Your mounted stereonet will also be useful in structural geology and for amazing your friends!

Do Klein exercises 10 & 11 to get an introduction to two- and three-dimensional arrangements of motifs.

The combination of mirrors/glides and rotations in 2-D results in 17 plane groups (Klein p. 127). Exercise 10 develops the relations between these symmetry operations. Do the following parts of this exercise:

• 10.1 - determine symmetry operators (Fig. 10-7, a through f)
• 10.2 - determine appropriate unit cells (note criteria on K p. 130) and show symmetry operators (Fig. 10.8, a through f and j); what is the corresponding 'plane group' for these examples?

Exercise 11 extends our line of thought to three dimensions, incorporating the 14 Bravais lattices (K p. 152-153) to develop up to 230 space groups. Read the introductory material and recall the relations in Tables 3.2 and 3.3, then do the following parts of this exercise:

• 11.A1 - follow all steps of this exercise using Fig. 11.8 examples a and d.
• 11.B1 - determine the symmetry content and plane group symmetry symbol for the examples in Fig. 10.9.
• 11.B2 - follow the instructions for this exercise using the three examples on the second page of Fig. 11.10 (K p. 171).

Do Klein exercises 12 & 13 to familiarize yourself with graphical representations of the 230 distinct space groups (cf. Table 12.3) that are produced by application of mirrors, glides, and rotations in three dimensions. Read the introductory material, then complete the following:

• 12.3 - in this example you are asked to show all symmetry elements that are compatible with the drawing in top panel of Fig. 12.10, and to specify the space group to which it belongs. It might be helpful for you to work the preceeding examples.

Exercise 13 takes the space group concept further into the realm of actual crystal structures. Read the introductory material, then complete the following parts of the exercise: (the objective is to determine an appropriate space group notation in each case)

• 13.1-3 - these three examples (Figs. 13.3 and 13.4) deal with simple stacking arrangements of spheres and will help prepare you for lab 4. Hint, for the third case, it will be useful to refer to Table 10.1
• 13.7 - this example (Fig. 13.8) concerns the mineral sanidine - a common feldspar.
• 13.8 - this example (Fig. 13.9) concerns the mineral diopside - a representative clinopyroxene.

A few words about crystal structure diagrams in the last two examples. Each figure shows two views of the mineral. The first (a) is a representation of the spatial distribution of individual atoms, with coordinates indicating percent of the 'b' translation distance above the plane of the page (note that 'b' is normal to the page for these cases).
For sanidine [KAlSi₃O₈], the solid circles represent randomly mixed Si & Al atoms (in a 3:1 ratio) and open circles with numbers inside are O atoms; four O atoms are coordinated with each Si (or Al) atom (solid lines represent bonds) to form 'SiO₄ tetrahedra'. Smaller open circles represent K atoms. The second view (b) is a 3-D representation of the crystal structure as viewed normal to the 'b' crystallographic direction; in this diagram, the 'SiO₄ tetrahedra' are represented by shaded tetrahedral forms labeled T1 or T2 to denote slight differences between them. Note the existence of a mirror plane normal to 'b'.
For diopside [CaMgSi₂O₆], (a) the unit cell is shown as viewed along the 'b' axis. Si (small circles) and O (large circles with coordinates inside) are linked by bonds to again form 'SiO₄ tetrahedra'; other atoms are Ca and Mg, as labeled, each of which is in 6-fold, or octahedral, coordination with O atoms. A second view (b) shows the structure as viewed normal to 'b' in terms of the arrangement of 'coordination polyhedra' ('SiO₄ tetrahedra' and variants of the Ca- (M2) or Mg-filled (M1) octahedra; note that the latter differ in shape and size depending on which cation fills the octahedron, Ca ions being larger than Mg ions). The tetrahedra and octahedra form 'chain-like' structures [n € SiO₃] elongated along the 'c' direction; note the obvious glide planes in this structure.
You will find it instructive to read the specific descriptions of these minerals, and especially their crystallography, in Klein & Hurlbut.

Using the in-class handout, this problem concerns application of simple principles to understanding the structure of NaCl (halite).

Use the resources in your textbook to explain this fundamental concept in a brief essay. Discuss the sources and magnitudes of uncertainty in such measurements. Upon what assumptions is the concept of ionic radius based?

The following exercise will help you grasp the concept of chemical systems and projections of mineral formuli into a simple tetrahedral compositional diagram.

1. Determine the standard chemical formuli for the following "endmember" minerals:
   • enstatite
   • forsterite
   • periclase
   • pyrope
   • grossularite
   • anorthite
   • corundum
   • kyanite
   • quartz
   • diopside
   • wollastonite

2. All of these minerals can be considered parts of a single "system" or compositional space defined by four oxide components. Make a tetrahedral diagram showing this system and plot the locations of each of the above minerals in it.

Buckyballs are not strictly minerals (why is this statement true?). Nevertheless, they are highly symmetric entities. Using the template provided, construct your own BB model and determine the symmetry operators present in this object. What rotation axes/mirrors are present, and how many of each can you find? Try to assign an appropriate point group symmetry designation to a BB; be creative.

Write a brief description of the project you have selected, giving the reasons why you choose it. Provide at least three references (other than standard mineralogy textbooks) that you will use in completing your project, and a brief outline of the content of your report.

- with answers!