Geol 311 - Mineralogy
Review Questions
by W.P. Leeman Optical Mineralogy leeman@rice.edu
Updated: 1 Sep 2000 ## Review questions - Crystallography

1. Understand how symmetry operators work and be able to develop point group representations (e.g., dots/circles on a stereographic projection). Try generating the point-group arrangements on the circular diagrams given the presence of various vertical rotation axes (one at a time, of course) either || to mirrors or normal to other rotation axes. See K., p. 10-16, 87-88, 174-182).

2 Determine point group symmetry for blocks having various decorations on their sides - examples attached (cf. K., p. 20).

3. Determine point group symmetry for external morphology of wooden crystal models (cf. K., p. 20-27, examples in exercise 2) - this determines the crystal class as well.

4. Discuss (list) the crystal systems and their distinctions in terms of symmetry. What is their relation to point groups, space groups, or Bravais lattices (see definitions, below)? How are these different classification tools used in developing a systematic concept of mineralogy?

5. Be familiar with the relationship of Hermann-Mauguin symbols to coordinate axes in crystals - know the hierarchical system by which the symbol elements are assigned (cf. K., p. 35).

6. Be familiar with the concept of Miller indices (K. p. 53-60) and be able to index relatively simple crystal forms (cf. K., exercises 2 and 3 for practice examples).

7. Given a representative space group symbol, be able to specify the crystal system, define the symmetry operators present, and discuss the their relation to the crystal axes and to each other.

8. Given simple crystal structure diagrams (e.g., K. Ex 13), discuss the various symmetry operators present (rot- and screw-axes, mirrors, glides), show their locations, and give the space group symbol consistent with these operators - see diopside (K., p. 211) or sanidine (K., p. 209) structure diagrams.

9. Derive Braggs law for x-ray diffraction (XRD). Discuss how it enables determination of d-spacings within mineral structures.

10. The following XRD methods are described in KH (pp. 279-288): Laue method, rotation method, Debye-Scherrer camera method, powder diffractometer method. Given certain types of mineral material (small well-formed single crystal, massive lump of poorly formed mineral, mineral with highly-developed basal cleavage such as mica), what kind of data results from each of these methods? What are the advantages or disadvantages of each? (K. Ex 14, 15).

11.The concepts of electrostatic (ionic) bonding and ionic radii are widely used to describe structures of minerals (especially the silicates) (KH Ch. 4). What factors control/affect the magnitude of ionic radii?

12. How do effective ionic radii change with atomic structure or with P, T, coordination, ionic charge, structural site, etc.? Explain in general terms of atomic structure (KH Ch. 4). Provide mineral examples for these concepts.

13. What other types of bonding are represented in silicate minerals? Give mineral examples and especially relate to specific parts of the crystal structures (e.g., amphiboles, micas, clay minerals).

14. For the other mineral groups we have covered in the lab, what is the prevailing style of bonding (cf. KH, Ch. 4, 10, 11, etc.)? Again consider mixed bonding types. Refer to Table 4.11 (KH, p. 208) concerning bonding types. (e.g., native elements, oxides, hydroxides, halides, etc.)

15. Discuss compositional variations (e.g., between end members) and describe substitutions of the major cations in the following mineral groups :

• feldspars
• pyroxenes
• amphiboles
• olivines
• garnets

(you should be generally familiar with all of these examples and know the end-member chemical formuli).

16. Select the components that best describe the compositional systems containing the above minerals, aluminosilicates, silica minerals, and/or carbonates and plot their end member compositions on simplified binary, ternary, or quaternary projections (molar basis). Note that the system required (and the components too) will depend on which mineral groups you choose to consider.

17. Discuss the structural classification system for silicate minerals (based on combinations of [SiO4]-4 tetrahedra); list the subgroups and give at least one mineral example (with chemical formula) for each (cf. KH, p. 214-216, Ch. 13).

18. Precisely, what is a solid solution? Discuss the three main types of solid solution and provide mineral examples for each (KH, pp. 233-236):

• substitutional
• omission (or defect)
• interstitial

19. Describe substitutional solid solutions in terms of structural, P, T effects. This is best done for a specific mineral group (e.g., plagioclases, pyroxenes, olivines). Explain immiscibility and when/why it occurs - again with respect to specific minerals (cf. KH, ch. 4, 5, & 13).

20. Explain how temperature and crystal structure affect solid solutions of (a) pyroxenes, and (b) alkali feldspars (cf. KH, pp. 236-240; 321, 325-326). Give some details as to why exsolution occurs and how and why the coexisting phases vary in composition along the solvus curve as temperature decreases. Use the relevant phase diagrams to illustrate. Describe what the crystalline material will look like, texturally speaking.

21. Explain the "phase rule" and be prepared to apply it to simple phase diagrams, such as that for the aluminosilicates (andalusite, sillimanite, kyanite)or silica (a-b quartz, cristobalite, tridymite, etc.). What do the terms bivariant, univariant, and invariant mean (again relate these to a simple phase diagram)? (KH, ch. 9)

22. What is the effect of pressure and temperature on Gibbs free energy (G)? How do responses of G to P, T affect mineral stabilities? (KH, ch. 9)

23. What are "mineral facies" diagrams and how are they affected by changing P, T, bulk composition? (KH, ch. 9)

24. Discuss how mineral physical properties may be determined or controlled by crystal structure and/or chemical composition; give specific mineral examples for each (KH, ch. 4):

• hardness
• cleavage
• melting point
• density (specific gravity)
• tenacity

25. Definition of terms - you should develop good precise definitions of the following:

• mineral
• crystal classes (cf. K., pp. 15-16)
• crystal systems (cf. K., pp. 35-36)
• Bravais lattices (cf. K., pp. 150-151)
• point group (cf. K., pp.15-16, 87-88)
• space group (cf. K., pp. 177)
• Miller indices (cf. K., ex. 4)
• x-ray diffraction (KH, ch. 7)
• chemical system (KH, ch. 9)
• chemical component (KH, ch. 9)
• mineral phase (KH, ch. 9)
• polymorph (KH, p. 153)
• pseudomorph (KH, p. 161)
• phase diagram (KH, ch. 9)
• solidus (KH, ch. 9)
• liquidus (KH, ch. 9)
• miscibility gap (KH, ch. 5, 9)
• solvus (KH, ch. 5, 9)
• entropy (KH, ch. 9)
• Gibbs free energy (KH, ch. 9)
• molar volume (KH, ch. 9)
• Clausius-Clapyron slope (KH, ch. 9)
• Herman-Mauguin symbols (cf. K., pp. 35)

I suggest you prepare brief discussions/answers to the above questions and develop precise definitions for the terms listed above. The most efficient approach might be to split up the questions among yourselves to provide frameworks that you can share and embellish individually. This should not be as formidable as appears, as we have been emphasizing the above topics throughout the semester.

For the Crystallography Exam, I will prepare specific questions from this material (and may take some of them more or less directly). Questions likely will involve application of concepts or principles rather than request simple recitation of facts. The crystallography exam will include some definitions and at least five questions taken from above.

## Review questions - Optical Mineralogy (refer to N = Nesse)

The following are examples of the kinds of questions that you should be able to answer readily. However, it is unlikely that the quiz will have questions exactly like those given below.

1. What is the relation between velocity, wavelength, and frequency for light?

2. How does white light differ from monochromatic light?

3. What is Snell's law and why is it useful? Explain with detailed drawings.

4. What is dispersion? Sketch this effect for both white and monochromatic light passing through a crystal prism.

5. Explain polarization and provide two examples of how light can be polarized.

6. Become familiar with the parts of a petrographic microscope and identify them on a drawing. Explain the function of each. What is the basic difference between orthoscopic and conoscopic observation?

7. Define refractive index.

8. Explain why Becke lines form (using drawings) and show how they are used to determine relative refractive indices.

9. Draw realistic dispersion curves for a hypothetical crystal. What does nD indicate?

10. List and describe at least 4 methods for determining accurate refractive indices. (e.g., dispersion method, double dispersion method [using temperature variation], refractometry, monochromatic vs. polychromatic light source). Explain the principle of each method using drawings.

11. Explain isotropic and anisotropic. What is the relation between these properties and crystal structure? Give at least 3 examples of materials with each property.

12. For uniaxial crystals, define ordinary and extraordinary rays, and explain how they originate.

13. Draw examples of typical cleavage fragments you are likely to see in isotropic and uniaxial materials.

14. What is a ray velocity surface? Draw cross sections of ray velocity surfaces for isotropic, uniaxial positive, and uniaxial negative materials assuming that the crystallographic c-axis is both parallel and perpendicular to the plane of your paper.

15. Define optic sign in terms of both light velocity and refractive index.

16. Draw examples of indicatrices for uniaxial positive and negative minerals. Give at least two mineral examples for each.

17. Define extinction and provide drawings to explain this phenomenon.

18. Define retardation (optically speaking) and explain its relation to (a) phase difference and interference color, (b) thickness (length of optical path), and (c) refractive indices. What is the retardation for isotropic minerals?

19. Define birefringence. How would you use the color chart to estimate birefringence in an mineral in a typical thin section?

20. List the crystallographic classes corresponding to isotropic, uniaxial, and biaxial materials. Give mineral examples for each.

21. Think about the kinds of optical characteristics you could observe for specific cleavage sections of isotropic and uniaxial crystals. E.g., {001}, {111}, {110}, {100}, {0001}, prismatic cleavage.

22. Explain what uniaxial interference figures are, how they are observed, and draw optic axis and flash figures for both uniaxial negative and positive crystals.

23. Define the following terms and provide sketches where appropriate:

• isochromes
• isogyres
• pleochroism
• first order red
• melatrope
• sign of elongation
• length-fast and length-slow

25. Sketch and label all relevant parts of the biaxial (-) and (+) principal sections (X-Z, Y-Z, and X-Y planes). Include optic directions, optic axes, Bxa, Bxo, optic normal, 2V angle, etc.

26. Be able to define each of the components listed in the #25 above (N ch. 9).

27. Sketch and label the following biaxial interference figures: Bxo, Bxa, OA, ON (flash). Show vibration directions in each, along with positions of optic directions, optic axes, isogyres, isochromes, etc. where appropriate. Be able to do this for grains in both the extinction and 45° positions (N 87-99).

28. Describe at least four methods for determining 2V angle in biaxial minerals (Tobi, Kamb, Mertie diagrams, Wright method); note that the Mertie diagram (Nesse, fig. 7.3) is related to mathematical derivation of 2V from measured refractive index values. Also explain under what conditions each method can be applied (i.e., advantages vs. disadvantages; see N 79-80, 99-104).

29. Explain relations between biaxial indicatrices and crystallographic axes for orthorhombic, monoclinic, and triclinic minerals (N 105-107, handouts).

30. Be able to relate cleavages and crystal faces to corresponding optic parameters - e.g., using standard 3-D drawings of crystals (as in N ch 9-15). Explain the types of extinction expected in these examples.

31. Explain pleochroism and pleochroic formulae (N 104).

32. Explain how dispersion occurs in biaxial minerals, and show typical effects on the respective interference figures. How is this useful?

33. Explain how a thin section is made (Nesse, appendix A)