Geol 311 - Mineralogy
Homework & Lab Assignments
by W.P. Leeman

Return to GEOL 311 Information

Homework assignments

Lab assignments

Study resources

Homework policy

click here to return to Bill's Home Page.
Updated: 30 Aug 2000

Geology 311 Homework Assignments:

  1. HW#1 - symmetry elements - Klein exercise 1
  2. HW#2 - symmetry of solid figures
  3. HW#3 - symmetry of patterned blocks
  4. HW#4 - Miller indices
  5. HW#5 - stereograms - Klein exercise 5
  6. HW#6 - 2-D & 3-D symmetry - Klein exercises 10, 11
  7. HW#7 - space groups & crystal structures - Klein exercises 12, 13
  8. HW#8 - ionic radii
  9. HW#9 - explain measurement of ionic radii
  10. HW#10 - mineral chemistry
  11. HW#11 - mineral formuli and projections
  12. HW#12 - buckyball exercise
  13. HW#13 - retardation effects (practice exam question)
  14. HW#14 - uniaxial optics (practice exam question)
  15. HW#15 - biaxial worksheet
  16. HW#16 - crystal optics problem (practice exam question)
  17. HW#17 - student project prospectus (abstract/outline)
  18. HW#18 - optics grain scenarios

Geology 311 Lab Assignments:

  1. Lab#1 - Physical properties of minerals
  2. Lab#2 - Crystal Symmetry, Miller indices
  3. Lab#3 - Stereographic projections, interfacial angles
  4. Lab#4 - Packing, coordination, crystal structures
  5. Lab#5 - Mineral chemistry, electron microprobe demo
  6. Lab#6 - X-ray diffraction, XRD demo
  7. Lab#7 - Complete XRD exercises
  9. Lab#9 - Petrographic microscope & Isotropic minerals
  10. Lab#10 - Uniaxial minerals
  11. Lab#11 - Biaxial minerals
  12. Lab#12 - Minerals in thin section
  13. Lab#13 - OPTICS LAB EXAM 4-Dec

Laboratory assignments

Lab 1: Mineral physical properties - Read Klein exercises 22, 23 to familiarize yourself with such properties as habit, cleavage, parting, fracture, luster, color/streak, hardness, tenacity, specific gravity, etc. Especially study the lab specimens to learn how to recognize the observable properties and to get a relative feel for specific gravity.

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.

Lab 2: Crystal Symmetry, Miller indices - This lab draws on what we have covered in class concerning recognition of crystal symmetry and indexing of crystal faces and forms.

We will follow the format of Klein exercises 2, 3, and 4, but using a selection of designated crystal models (wooden blocks) and corresponding perspective diagrams. Review the information in these exercises. Assignments are as follows for each model:

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.

Lab 3: Stereographic projections, interfacial angles - The purpose of this lab is to solidify the relation between the external morphology of crystals and their inherent symmetry. In essence, you will learn how to prepare stereographic projections of 'poles' to crystal faces, and from these derive the symmetry following Klein exercises 5, 6, and 8. The first of these exercises (#5) is to be completed prior to the lab as Homework #5.

For simplicity, in exercise #6 we will use some of the crystal models that you studied in the previous lab. Exercise #8 will illustrate the utility of stereographic projections in predicting the development of crystal forms as a consequence of specified point group symmetry; it may be completed outside of the lab. Assignments are as follows:

Materials needed: Crystal models, corresponding clinographic projections (perspective drawings), and contact goniometers will be provided by the TA. Bring your copy of Klein workbook, a stereonet mounted on a clipboard or hard surface (as explained in class and HW#5), and 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 well-labelled diagrams (trace them from examples in Klein if necessary, but be sure they are accurate).

Lab 4: Packing, coordination, crystal structures - This lab aims to solidify concepts of atomic packing, coordination polyhedra, ionic radii, and charge balance. We will follow Klein exercises 17 and 18. Assignments are as follows:

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.

Lab 5: Mineral chemistry - This lab consists of two distinct parts, beginning with a brief demonstration of the departmental electron microprobe facility. Among other things, this facility is used to perform chemical analyses of micron size spots on mineral samples. We will then follow Klein exercises 19, 20, 21, and 35 to illustrate how such chemical data are routinely manipulated to obtain maximum information. Assignments are as follows:

Materials needed: Bring your copy of Klein workbook, a calculator, and a set of colored pencils.

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

Lab 6: X-ray diffraction - demonstration of XRD lab facility, analysis of unknown mineral.

This lab will provide a hands-on example of a typical application of our diffractometer, specifically the determination of the composition of an unknown mineral. In addition, you are asked to complete Klein exercises 14 and 15 to familiarize yourself with interpretation of data obtained using a powder camera and a scanning diffractometer [do the complete exercises and submit these at the next week's lab].

Using data obtained from the Rice XRD, repeat exercise 15 for one sample and determine the mineral identity and, if possible, further details of its composition. More on this in lab...

Lab 7: X-ray diffraction - continue exercises. This week, in addition to hand sample identification, your assignment is to complete Klein exercise 16. This introduces another important application of XRD data to determine the unit cell dimensions of a relatively simple isometric mineral as explained in Klein.

Lab 8: PRACTICAL MINERAL ID EXAM - cumulative test of mineral identification from hand specimens; closed book but mineral index cards can be used.

Lab 9: Petrographic microscope & Isotropic minerals - We will assign individual petrographic microscopes and explain how they are used. It is very important that you have read the first few chapters in Nesse before coming to lab. You should be familiar with the general features of a petrographic microscope and the optics for isotropic materials!

As explained in a lab handout, your assignment will be to learn the basic methods of refractometry using oil immersion techniques using grains of known materials. You will then use this method to determine the refractive index on an unknown mineral and, based on all your observations, determine what it is.

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

Lab 10: Uniaxial minerals - This lab will extend what you have learned to the study of anisotropic materials, specifically uniaxial minerals. Following the lab handout your assignments are to:

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

Lab 11: Biaxial minerals - This lab will extend what you have learned to the study of biaxial minerals. Following the lab handout your assignments are to:

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

Lab 12: Minerals in thin section - In this lab you will become familiar with the optical properties of a variety of common rock-forming minerals in thin section. A simple optical method for the determination of plagioclase composition will also be introduced.

Lab 13: OPTICS LAB EXAM - will cover practical applications of the petrographic microscope; closed book, any necessary tables/figures will be provided.

Study resources

It is your responsibility to do all assigned reading and exercises. You should be able to answer the review and thought questions at the end of each chapter of the textbook. See supplementary readings, refrences, and WWW links for further information.

Homework philosophy

HW questions will help you understand the course material. Moreover, these are the kinds of questions you are likely to see on the exams! Attempt to answer them and come to class each day prepared to ask your own questions and to participate in class discussion. You may work with friends or study groups - anything that works for you and is enjoyable. Assignments should be legible and organized and include your name! All will be discussed and self-assessed in class, then turned in so the instructor can see how you are doing. Although there will be no official grade, completed HW assignments turned in on time will be counted for extra credit.

Homework assignments

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.

HW 2: Symmetry in solid figures

Construct the following solid figures using the patterns in Klein:

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.

HW 3: Symmetry in patterned blocks

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).

HW 4: Miller indices

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}.

HW 5: Stereograms

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!

HW 6: Space groups

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:

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:

HW 7: Space groups

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:

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)

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.

HW 8: Ionic radii

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

HW 10: Mineral chemistry problems

  1. Do the following calculations:

    • (a) Calculate weight % of constituent oxides for labradorite (plagioclase) having the formula Ab50An50 where:

      • An (anorthite) = CaAl2Si2O8 (or CaO*Al2O3*2SiO2)

      • Ab (albite) = NaAlSi3O8 (or 0.5Na2O*0.5Al2O3*3SiO2)

    • (b) Calculate the structural formula for this mineral using the analysis derived in (a) (i.e., cation proportions on the basis of 8 oxygens). From these cation proportions show that the feldspar can be represented by 50% An, 50% Ab. This is a check on your computations.

  2. Using the above information and similar calculations for Fo80 (from class lecture), give the oxide wt % analysis of a rock consisting of 40 wt % olivine (Fo80) and 60 wt % plagioclase (An50).

  3. Determine the formuli and identify the minerals represented by the following analyses (wt %).

    1. (a) Cu: 63.3, Fe: 11.1, S: 25.6

    2. (b) SiO2: 38.0, Al2O3: 21.5, FeO: 26.6, MgO: 6.3, MnO: 7.6

    3. (c) SiO2: 51.5, FeO: 30.8, MgO: 17.7

HW 9: Explain how is ionic radius determined

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?

HW 11: Mineral formuli and chemical systems

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.

HW 12: Buckyball (BB) exercise

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.

HW 13: Concept of retardation (optically speaking)

HW 14: Uniaxial optics

HW 15: Biaxial worksheet

HW 16: Crystal optics problem

HW 17: Student project prospectus

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.

HW 18: Optics scenarios with mineral grain mounts

- with answers!