Florida Atlantic University MINERALOGY -- FINAL EXAMINATION KEY

GLY4200C Name 108 points December 2, 2011 16 took exam - Numbers to the left of the question number in red are the number of incorrect responses. Instructor comments are in blue. Florida Atlantic University MINERALOGY -- FINAL EXAMINATION KEY True-False - Print the letter T or F in the blank to indicate if each of the following statements is true or false. Illegible answers are wrong. (1 point each) 3 T 1. The most common type of phase diagram for binary systems is a temperaturecomposition diagram. 2 T 2. For any angle greater than or equal to the critical angle there will be no refracted ray the light will be totally reflected. 8 F 3. If the refractive index is higher for at least some longer wavelengths, the material exhibits normal dispersion. 3 T 4. Plane-polarized radiation entering an anisotropic crystal in a direction not parallel to an optic axis, will be split into the ordinary (O) and extraordinary (E) rays, vibrating perpendicularly. 6 F 5. The fast direction of a compensator plate is marked N. The slow direction is unmarked, but is understood to be perpendicular. 4 T 6. The quarter 8 plate is especially useful in examining minerals showing bright interference colors. 7 F 7. If the slow direction of the crystal is parallel to the fast direction of the accessory plate, subtraction will occur. The new color is always less than the original color. 3 T 8. In orthoscopic mode, light rays striking a mineral grain on a thin section will be parallel. 3 T 9. If J = 0, a mineral will be extinct when viewed in crossed-nicols and its reference direction is aligned with the N-S or E-W crosshair. 5 F 10. For a uniaxial negative crystal, the optical indicatrix has the shape of a prolate ellipsoid. 1

5 F 11. The depth of focus is the range over which objects are in focus in a microscope. It increases as the magnification increases. 4 T 12. The direction of the wave normal to the wave front obeys Snell s Law for both the ordinary and the extraordinary rays. 6 F 13. In a biaxial crystal, $ is the numerical average of " and (. 5 F 14. If B xa is over Z, the mineral is biaxial negative. 2 F 15. A microscope has an objective lens whose numerical aperture is 0.70. This lens is an oil immersion lens. 1 T 16. K $ radiation is more energetic but has less intensity the K " radiation. 2 T 17. In the Bragg equation, 2 = glancing angle of incidence. 1 T 18. K " radiation is more intense than K $ because the L to K transition is far more probable than the M to K transition. 5 F 19. A critical angle may only exist when if n r > n i. (see Snell s law - sin cannot be > 1.0) 2 T 20. Three component systems may be plotted on a ternary composition diagram, with both pressure and temperature are regarded as fixed. 1 T 21. In plotting a phase diagram, it is assumed that the system is at equilibrium. 9 T 22. Inclined extinction can only occur in biaxial crystals. 3 F 23. For any angle greater than or equal to the critical angle there will be no reflected ray, because the light will be totally refracted. 6 F 24. A crystal viewed in crossed nicols shows a white interference color. When the polarizer is rotated to produce parallel nicols, the observed color becomes reddish. Thus the original color was high-order white. 11 F 25. The bonding in water (H 2 O) is more ionic than in sylvite (KCl). (Relevant electronegativities: Hydrogen, 2.1; Oxygen, 3.5: Potassium, 0.9; Chlorine, 2.9) 11 F 26. Ionically bonded substances are molecular, i.e. exhibit properties which may be explained in terms of interactions between molecules. 2

1 T 27. If the bonding mechanism is not dominantly ionic, radius ratio considerations may not be adequately used to determine the coordination number. See text, page 73 2 T 28. As nuclei grow, their surface area/volume ratio decreases. 5 T 29. Three d electrons give a large spin contribution to the magnetic moment of minerals they are in. 2 T 30. In minerals with more than one bond type, it is common for the mineral to have strongly directional properties. See text, page 64 Multiple-Choice - Choose the best response to each statement or question. Print the letter corresponding to your choice in the blank. (1 point each) 0 A 1. In the formula G = H - T)S, what does H stand for? A. Enthalpy B. Entropy C. Gibbs Free Energy D. Temperature 9 B 2. A phase diagram for a unary system, such as silica, is of what type? A. Temperature - Composition B. Pressure - Temperature C. Pressure - Composition D. Pressure 5 C 3. ds/dt is: A. Coefficient of isothermal compressibility B. Heat capacity at constant temperature C. Heat capacity at constant pressure D. None of the above 5 C 4. If a system has two components, and two phases are present, how many degrees of freedom are present? A. 0 B. 1 C. 2 D. 3 3

2 B 5. The property determined by the equation n(8) = A + B/8 2 + C/8 4 is: A. Birefringence B. Dispersion C. Refraction D. Retardation 8 C 6. In optical mineralogy, ) is: A. A measure of the change in the property which follows ) (i.e. )T means a change in temperature) B. Dispersion C. Path difference D. Refraction angle 3 B 7. Which of the following is not anisotropic? A. Crystals belonging to the hexagonal system B. Crystals belonging to the isometric system C. Crystals belonging to the monoclinic system D. Crystals belonging to the orthorhombic system 6 C 8. Index of refraction oils with n greater than 1.8 are often dangerous. Why? A. They are unstable compounds which degrade with time, forming vibration sensitive solids with a tendency to explode B. They are highly flammable, whose vapors often catch fire C. They contain poly-chlorinated biphenyls, compounds known to be highly carcinogenic D. All of the above 8 C 9. In a biaxial crystal, the slowest ray travels along which optical axis? A. X B. Y C. Z D. Either X or Z, depending on whether the crystal is positive or negative 5 B 10. The index of refraction associated with the circular section of a biaxial crystal is: A. " B. $ C. ( D. 8 4 D 11. The section through a biaxial indicatrix labeled OAP: A. Is the optic axial plane B. Shows the maximum possible birefringence C. Contains the optical axes X and Z D. All of the above 4

9 A 12. What is the minimum birefringence possible in a biaxial mineral. A. 0 B. (' - $ C. (' - " D. ( - " 4 D 13. If a sample is in continuous extinction: A. It is isometric B. It is viewed along an optic axis C. It is isotropic D. Any of the above 9 D 14. The X-ray line labeled L $ is a transition between which levels? A. n = 2 to n = 1 B. n = 3 to n = 1 C. n = 4 to n = 1 D. n = 4 to n = 2 7 A 15. In order to filter K $ an iron X-ray tube, which element should be used as a filter? A. Mn B. Co C. Ni D. Cu 9 A 16. The condition for successful reinforcement of X-ray waves reflected off different layers in a crystal structure is given by which equation? A. Bragg B. Brewster C. Cauchy D. Snell 2 D 17. Extinction which looks like a wave passing across a crystal as the stage is rotated is said to be: A. Inclined B. Parallel C. Symmetric D. Undulatory 3 C 18. Which of the following phases is a high pressure phase of silica? A. Cristabolite B. Quartz C. Stishovite D. Tridymite 5

8 B 19. In the expression, I/I 0 = e -kt, what does t refer to? A. Temperature B. Thickness C. Time D. None of the above 7 A 20. Minerals from which of the following systems would be uniaxial? A. Hexagonal - the only one with a high-order axis B. Monoclinic C. Orthorhombic D. Triclinic 6 D 21. Parallel or straight extinction is not possible in what type of crystals? A. Hexagonal B. Monoclinic C. Orthorhombic D. Triclinic 4 B 22. One nanometer is equivalent to how many centimeters? A. 10-9 B. 10-7 C. 10 7 D. 10 9 5 A 23. The bonding within the graphene layers in graphite is due to what type of bonds? Read question carefully - Within the layer, not between layers A. Covalent B. Ionic C. Van der Waals D. Metallic 3 A 24. When minerals with metallic luster weather they may appear to have which of the following lusters? A. Dull B. Glistening C. Semi-metallic D. Waxy 3 C 25. Moving electrical currents generate magnetic forces. What is the source(s) of magnetic force in a transition metal ion? A. Electrons orbiting the nucleus B. Electrons spinning around their own axes C. Both A and B D. None of the above 6

3 D 26. The symbol {121} represents: A. Point B. Line C. Plane D. Form 3 A 27. Which of the following forms of radiation is the most energetic? A. Gamma B. Infra-red C. Ultraviolet D. Visible 3 A 28. Which quantum number determines the shape of the electronic orbital? A. Azimuthal quantum number, R (see text, page 40) B. Magnetic quantum number, m C. Principal quantum number, n D. Spin quantum number, s Fill-Ins - Write in the word or words which best completes each statement or answers each question. (1 point per blank) 3 1. An INTENSIVE PROPERTY does not depend on the amount of material present. Examples of such properties include density and temperature. 3 2. The ratio of the speed of light in vacuum to the speed of light in a medium, such as a mineral, is the INDEX OF REFRACTION. 1 3. Many colored anisotropic minerals, viewed in plane polarized light, will show a change in color as the stage is rotated. This phenomenon is known as PLEOCHROISM. 3,5 4-5 2V x is 34. What is the optical class? 4) BIAXIAL What is the optical sign? 5) NEGATIVE 7 6. When light passes from a medium of low index of refraction to one of higher refractive index, the light will be refracted TOWARD the normal. 7 7. How many significant figures are expressed in the number 0.00470 (± 0.00002)? THREE 7 8. Elements whose valance electrons may be denoted as ns2 are called ALKALINE EARTHS. 8 9. Luster observed on cleavage faces that are parallel to perfect cleavage planes is often PEARLY. 7

10-11 Viktor Goldschmidt described two rules, really empirical observations, governing ionic substitution. What are these rules? 8.5 10) CHARGE ON THE IONS CANNOT DIFFER BY MORE THAN ONE 7 11) FREE SUBSTITUTION OCCURS IF SIZE DIFFERS BY LESS THAN 15%, AND LIMITED SUBSTITUTION OCCURS IF SIZE DIFFERENCES BETWEEN IONS ARE BETWEEN 15 AND 30% Diagrams and Figures - A series of slides will be shown. Each of these is a photo or a diagram previously seen in class. Diagrams may have been altered to remove labels, etc. Answer each question as the slide is shown. (1 point each) 3 C 1. The diagram shown here is a: A. Binary solid solution diagram B. Binary congruent melting diagram C. Binary incongruent melting diagram D. Binary minimum melting diagram 2 A 2. Point 12 on this diagram has what composition? A. 30 % Limestone, 60 % sandstone, 10 % shale B. 60 % Limestone, 10 % sandstone, 30 % shale C. 10 % Limestone, 30 % sandstone, 60 % shale D. 10 % Limestone, 60 % sandstone, 30 % shale 4 D 3. The diagram shown here is a: A. Binary solid solution diagram B. Binary congruent melting diagram C. Binary incongruent melting diagram D. Binary minimum melting diagram 6 F 4. (T-F) The figure shown is the indicatrix for a biaxial crystal. 4 A 5. The plane shown in pink is: A. Circular section B. Elliptical section C. Principal section D. Random section 0 T 6. (T-F) The diagram shown pertains to an anisotropic crystal. 8

4 D 7. What is the optical class and sign of the mineral represented by the section shown? A. Uniaxial positive B. Uniaxial negative C. Biaxial positive D. Biaxial negative 13 8. What name is given to the section shown? IT IS THE OPTICAL AXIAL PLANE (OAP) SECTION 9-13 pertain to figure 1: Figure 1 - Phase diagram for water What are the following regions? 2 9. Region A Solid (Ice) 3 10. Region B Liquid 5 11. Region C Vapor What are the following points? 8 12. Point D Triple point 10 13. Point E Critical point 9

Matching - Match the discovery in column one with the person associated with the discovery in column two. Answers may be used once, more than one, or not at all (One point each) Column 1 0 K 1. A mathematical formula, which relates the angle of incidence to the angle of refraction, was discovered by several people, one of whom was a Dutch mathematician, for whom it was named. 2 I 2. One of the greatest American scientists of the 19 th century, he was awarded the first Doctor of Engineering in the U.S., and was appointed Professor of Mathematical Physics at Yale in 1871. His name is now attached with rule that is of great importance in geochemistry, mineralogy, and petrology, as well as many areas outside of the geosciences. 3 D 3. The condition for maximum polarization of reflected and refracted rays is named for this Scottish physicist. 9 L 4. German physicist who won the Nobel Prize in Physics in 1914 for the discovery of diffraction of X-rays by crystals 0 E 5. An American Crystallographer who developed the precession camera. Column 2 A. Roy G. Biv B. Sir William Henry Bragg C. Sir William Lawrence Bragg D. Sir David Brewster E. Martin J. Buerger F. Albert Einstein G. Sir Lazarus Fletcher H. Joseph von Fraunhofer I. Josiah Willard Gibbs J. Wilhelm C. Roentgen K. Willebrod Snellius L. Max Theodore Felix von Laue M. Karl Weissenburg 10

Problems - Do each of the following problems. Show all work. Label answers, including units, if any. List any formula used, and define all symbols used in the formula. Miraculous answers, unsupported by all necessary calculations, will receive little or no credit. 10 1. 1. Dolomite belongs to the hexagonal crystal system, with, = 1.500 and T = 1.681. What is the optical class and sign of dolomite? (2 points) Uniaxial negative 19.5 2. What is the retardation, expressed in nm, of a crystal of dolomite of standard thickness, which shows the maximum possible birefringence? (2 points) = t(n n) mm (. 1681 1500. ) 0. 030 (. 0181) 3 540. x 10 mm 5400 nm 16 3. Given: c vacuum = 2.998 x 10 8 m/s If f = 5.66 x 10 14 Hz, what is 8 (expressed in nm)? (3 points) 11

21 4. Hercynite has the formula FeAl 2 O 4, and has n = 1.80. If light passes from hercynite into air, what is the critical angle? (3 points) 16.5 5. Assuming a standard thin section thickness of 30 microns, what is the retardation value for cassiterite (tetragonal, T = 1.997,, = 2.093)? Express your answer in nanometers. (2 points) () = (2.093-1.997) x 0.03 mm x 10 6 nm/mm) = 2880 nm ) = 2900 nm 12

Figure 2 Answer each of the following questions which pertain to figure 2. (1 point each) 0 6. Show all liquidus lines in green. 9 7. Show all solidus lines in yellow. 4.5 8. Starting at point A in the diagram, trace the path followed by the liquid in red as the system cools to 900 C. 9.5 9. Trace the path followed by the solid(s) from the point of first crystallization to 900 C in blue. 3 10. What is point B called? PERITECTIC 0 11. What is point C called? EUTECTIC 7.5 12. At what temperature does solid X disappear? 1190 C 6.5 13. What is the composition of the liquid at 1100 C? 38% Z 9 14. What is the percent liquid at 1100 C? 16% 11 15. What is the percent solid at 1100 C? 84% 13

Discussion questions - Write a complete, concise answer to each of the following questions. Diagrams (labeled) may be used to supplement your written answers, where appropriate. Points as shown 1. Make a labeled sketch of an X-ray tube showing the following features:(5 points) 7 A. Focusing shield 4 D. Water conduit 6 B. Target 3 E. Path followed by electron stream 6 C. X-ray ports 14

22 2. Describe how X-rays are produced in an X-ray tube. Why is it necessary to cool an X-ray tube with water? (3 points) X-RAYS ARE PRODUCED BY BOMBARDING A METAL TARGET WITH ELECTRONS BOILED OFF AN ELECTRODE AN ACCELERATED THROUGH VACUUM BY A LARGE VOLTAGE DIFFERENCE. THE ELECTRONS HIT THE TARGET WITH VERY HIGH KINETIC ENERGY, KNOCKING OUT THE INNER ELECTRONS ON THE TARGET NUCLEI, WHICH THEN EMIT X-RAYS AS ELECTRONS DROP INTO VACANT INNER ORBITAL POSITIONS. THE KINETIC ENERGY OF THE ELECTRONS MAKES THE TARGET VERY HOT, AND WOULD SOON VAPORIZE IT IF IT WERE NOT COOLED 18 3. Both calcite and quartz occur as transparent uniaxial crystals, but only calcite is capable of showing double refraction in a crystal whose dimensions are 2-3 centimeters. Why? (3 points) THE DIVERGENCE OF THE ORDINARY AND EXTRAORDINARY RAYS IN A CRYSTAL PRODUCE DOUBLE REFRACTION. WHEN THE BIREFRINGENCE IS SMALL, THE ANGLE BETWEEN THE TWO RAYS IS VERY SMALL, AND ONLY ONE IMAGE IS SEEN. THIS IS THE CASE FOR QUARTZ. IN HIGHLY BIREFRINGENT MINERALS, LIKE CALCITE, THE RAYS QUICKLY SPREAD APART, AND TWO IMAGES ARE SEEN. HAVE A GREAT VACATION AND A VERY HAPPY AND SAFE NEW YEAR! 15

Final Examination Grades 107.0 106.0 105.5 A+ 100.0 98.5 A- 96.0 B+ 89.0 B- 83.5 C+ MEDIAN = 82.8 82.0 C MEAN = 82.2 (76.1%, C) 72.0-2 71.0 68.0 D 59.0 55.5 49.5 F 16

Previous Years Results -Final Examination Term, Year Mean, % Fall, 2011 76.1 Fall, 2010 70.0 Fall, 2009 68.8 Spring, 2009 75.6 Fall, 2007 73.9 Fall, 2006 73.7 Fall, 2005 69.0 Spring, 2004 89.7 Fall, 2002 73.2 Spring, 2001 69.7 Spring, 2000 87.2 Fall, 1998 66.8 Fall, 1997 76.8 Fall, 1996 71.5 Fall, 1995 76.1 Fall, 1994 69.6 Fall, 1993 79.6 Fall, 1992 73.2 Fall, 1991 73.8 Tied for fourth of out 19 17

TOTAL EXAMINATION RESULTS (OUT OF 288; 48% OF FINAL GRADE) 271.5 A 263.0 260.5 A- 257.0 254.5 B+ 248.0 B 226.0 C+ 219.0 MEAN = 219.3 (76.1%) 217.5 C MEDIAN = 218.3 208.0 206.5 C- 193.5 193.0 D+ 174.5 D- 170.0 145.5 F In 2010, the highest grade on the exams was 247.5, so part of this group did well. However, the 2010 Mean was also 219.3, so some students did not do as well. DO PREREQUISITES MATTER? Judge for yourself Students missing some or all prerequisites - average = 71.7% (C-) Students with proper prerequisites - average = 89.4 % (B+) 18