Florida Atlantic University MINERALOGY -- FINAL EXAMINATION KEY

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1 GLY4200C Name 108 points December 14, 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) 1 T 1. A solvus line separates a region with one solid phase from a region with two distinct solid phases. 1 F 2. A minimum melting point is the same thing as a eutectic point in a binary phase diagram. 10 F 3. In a binary system plotted on a temperature-composition diagram, suppose there are two solid phases. As the system cools, one of the phases begins a phase change to a different crystal structure. While this process is going on, there is one degree of freedom. 3 T 4. In any binary diagram, there are always two components present. 2 T 5. A stoichiometric relationship between substances reduces the number of components necessary to fully describe a system by one. 2 T 6. In orthoscopic mode, the higher the value of the numerical aperture, the better the resolution. 0 F 7. For any angle greater than or equal to the critical angle there will be no reflected ray, because the light will be totally refracted. 4 F 8. A crystal viewed in crossed nicols shows a white interference color. When the polarizer is rotated to produce parallel nicols, the observed color remains white. Thus the original color was 1 white. 1 T 9. Interference colors for an anisotropic crystal will be brightest when viewed 45 off extinction. 5 F 10. In the indicatrix for a biaxial crystal, the optical axis labeled X is the direction of the slow ray. 1

2 5 T 11. X-ray radiation has a shorter wavelength than ultraviolet radiation. This allows X-rays to penetrate deeper into matter, and makes them more dangerous to living systems. 4 T 12. β is normal to the OAP plane. 6 F 13. Addition occurs when the slow direction of a mineral is parallel to the fast direction of the compensator. 6 F 14. The index of refraction is independent of the frequency of light used to measure it. 0 T 15. In plotting a phase diagram, it is assumed that the system is at equilibrium. 5 F 16. Phase diagrams show the stable phase at any point in the diagram, and the stable phase always has the highest value of G. 5 T 17. The Reitveld Refinement Method allows structural information about a mineral to be obtained from powder x-ray patterns. 5 F 18. The interior of an x-ray tube is filled with argon, an inert gas. 1 T 19. There are two circular sections in any biaxial indicatrix. 9 F 20. X-ray fluorescence spectroscopy is used for determining the crystal structures of unknown minerals. See page 321 of text. 1 F 21. Incongruent melting means melting of a substance directly to a liquid that is of the same composition as the solid. 2 T 22. In orthoscopic mode, light rays striking a mineral grain on a thin section will be parallel. 1 T 23. If τ = 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. 3 F 24. In a biaxial crystal, β is the numerical average of α and γ. 8 F 25. Ionic radii increase with increasing oxidation state. 4 T 26. In minerals with more than one bond type, it is common for the mineral to have strongly directional properties. See text, page 64 3 T 27. As the difference in electronegativity between the cation and anion increases, so does the percent ionic bonding between them. 2

3 1 T 28. Among ions with identical charge and differing radii, the smaller ions will be incorporated into crystal structures first. This is why garnets show preferential concentration of heavy rare earth elements. 5 F 29. Three d electrons give a large orbital contribution to the magnetic moment of minerals they are in. 11 F 30. When crystal field splitting occurs, the average of the energy levels of the split d orbital levels moves up or down depending on the electronic environment of the ion in question. 2 T 31. A twin operation cannot belong to the normal symmetry operations of a mineral. 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. What type of phase diagram would be used to represent the system CaSiO3, MgSiO3, and FeSiO3? A. Ternary (composition) B. Binary eutectic (temperature and composition) C. Temperature and pressure D. Binary solid solution (temperature and composition) 12 C 2. What type of phase diagram is used to represent the leucite-k-feldspar-silica system? A. Ternary (composition) B. Binary eutectic (temperature and composition) C. Binary peritectic (temperature and composition) D. Binary solid solution (temperature and composition) 4 A 3. At the eutectic point in a binary temperature-composition diagram, how many degrees of freedom are there? A. 0 B. 1 C. 2 D. 3 3 C 4. What type of phase diagram is used to represent the silica system? A. Ternary (composition) B. Binary eutectic (temperature and composition) C. Temperature and pressure D. Binary solid solution (temperature and composition) 3

4 6 C 5. A rock contains orthoclase, quartz, and albite. How many phases are present? A. 1 B. 2 C. 3 D. 4 9 C 6. If the rock in question 5 is heated, the quartz melts, leaving albite and orthoclase. How many phases are present? A. 1 B. 2 C. 3 D. 4 9 B 7. If a system has only pressure as a variable, and there are two components and two phases present, the number of degrees of freedom is: A. 0 B. 1 C. 2 D. 3 3 D 8. Parallel or straight extinction is not possible in what type of crystals? A. Hexagonal B. Monoclinic C. Orthorhombic D. Triclinic 1 D 9. When a mineral viewed in plane polarized light shows color, it is: A. 1 B. 2 C. High order D. Natural color 4 C 10. What shape does an isotropic indicatrix have? A. Oblate ellipsoid B. Prolate ellipsoid C. Sphere D. Triaxial ellipsoid 1 A 11. The maximum birefringence possible in a biaxial crystal is: A. γ - α B. γ - β C. β - α D. 0 4

5 6 D 12. If B xa is over X, the mineral is: A. Uniaxial positive B. Uniaxial negative C. Biaxial positive D. Biaxial negative 4 C 13. Which of the following X-ray methods is used for powder samples? A. Laue B. Precession C. Hagg-Guinier D. Weissenberg 9 C 14. Minerals from which of the following systems would be uniaxial? A. Monoclinic B. Orthorhombic C. Tetragonal - the only one with a high-order axis D. Triclinic 3 B 15. The section containing the greatest index of refraction (γ) and the least (α) is: A. The optic normal B. The optical axial plane C. A random plane D. A circular section 10 B 16. An X-ray photon knocks a 1s electron away from a copper atom. An electron from the 3p subshell falls to the 1s level. What type of radiation is released? A. K α B. K β C. L α D. L β 1 A 17. The ports, where x-rays emerge from an x-ray machine before entering a camera, are covered with which metal? A. Be B. Cu C. Fe D. Mo 1 B 18. In order for extinction to occur, assuming the stage is empty, the privileged directions of two polaroids must be: A. Parallel B. Perpendicular C. 45 to each other D. The respective positions is irrelevant to extinction 5

6 8 A 19. In biaxial crystals, how many high-order axes are present? A. 0 B. 1 C. 2 D. 3 5 A 20. The K shell in x-ray crystallography corresponds to a shell whose n value is what? A. 1 B. 2 C. 3 D. 4 0 C 21. The line separating a vapor and a solid phase in a phase diagram might be called: A. Critical point B. Fusion curve C. Sublimation curve D. Vaporization curve 8 C 22. Which of the following phases is a high-pressure form of silica? A. β-quartz B. Cristobalite C. Stishovite - review the diagram shown in class! D. Tridymite 4 D 23. 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 5 B 24. The value of the index of refraction in a circular section of a biaxial indicatrix is: A. α B. β - review diagrams seen in class C. γ D. Any of the above 4 B 25. The property determined by the equation n(λ) = A + B/λ 2 + C/λ 4 is: A. Birefringence B. Dispersion C. Refraction D. Retardation 6

7 5 C 26. In optical mineralogy, Δ is: A. A measure of the change in the property which follows Δ (i.e. ΔT means a change in temperature) B. Dispersion C. Path difference D. Refraction angle 9 A 27. What is the minimum birefringence possible in a biaxial mineral. A. 0 B. γ' - β C. γ' - α D. γ - α 9 C 28. The quantum number for a given orbital is one. What letter designates this orbital? A. d B. f C. p D. s 4 A 29. The bonding within the graphene layers in graphite is due to what type of bonds? (Hint: Read question carefully.) Within the layer, not between layers A. Covalent B. Ionic C. Van der Waals D. Metallic 7 C 30. The bond angle in perfect tetrahedral coordination is: A. 180 B. 120 C D B 31. The second column from the left in the periodic table is known as: A. Alkali metals B. Alkaline earths C. Halogens D. Nobel gases 0 C 32. The equation F (Z 1 Z 2 )/r 2 is: A. Bragg s equation B. Brewster s Law C. Coulomb s Law D. Einstein s equation 7

8 5 D 33. The general symbol for a zone axis is: A. hkl B. (hkl) C. {hkl} D. [uvw] 3 C 34. When electrons are delocalized, the hopping of electrons between adjacent ferrous and ferric ions, produces a blue color, seen in minerals such as kyanite, glaucophane, crocidolite, and sapphire. This process is called: A. Selective absorption B. Crystal field transition C. Charge transfer transition D. Dispersion 7 C 35. [31 0]is parallel to which crystallographic axis? A. X B. Y C. Z D. More information is needed 6 C 36. What crystal system does (111 1) belong to? A. Isometric B. Tetragonal C. Hexagonal D. Triclinic 5 D 37. Quartz after fluorite is an example of what? A. Omission substitution B. Polymorphism C. Polytypism D. Pseudomorphism 3 C 38. 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 - electrons are moving in both cases D. None of the above 8

9 Fill-Ins - Write in the word or words which best completes each statement or answers each question. (1 point per blank) 4 1. When a mineral possesses cleavage in two or more directions what property, in addition to the number of cleavage directions present, must be specified? THE ANGLE BETWEEN THE CLEAVAGE PLANES MUST BE SPECIFIED 5 2. What is N in the formula N = c/c m? INDEX OF REFRACTION Crystals which are elongated are said to be LENGTH - FAST if the slow direction of the crystal is perpendicular to the long direction of the crystal In the Bragg equation what is θ? Θ IS THE GLANCING ANGLE OF INCIDENCE 5-6 Suppose a crystal of tourmaline is observed in a standard 30 micron thin section. Omega is and epsilon is ) The crystal is (Optical class and sign): Uniaxial negative 11 6) The fast direction is: epsilon 5 7. The heads of an infinite collection of vectors, equal in magnitude to the index of refraction, all pointing outward from the origin, would describe the geometrical figure called the optical INDICATRIX Elements whose valance electrons may be denoted as ns 1 are called ALKALI METALS When a mineral is tested with dilute hydrochloric acid, and it effervesces, what gas is released? CARBON DIOXIDE Both covellite (Cu 2 S) and acanthite (Ag 2 S) are gray to black. Why aren t they colored, like many other sulfide minerals? BOTH METAL IONS ARE IN THE +1 STATE; THEREFORE, THEY ARE D 10 (either 3D or 4D), AND NO D-D TRANSITIONS ARE POSSIBLE The ratio of induced magnetization to the strength of an external magnetic field is known as the MAGNETIC SUSCEPTIBILITY. 9

10 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 Column 2 6 H 1. The idea of a geometrical representation of the variance of the index of refraction was first described in The Optical Indicatrix and the Transmission of Light in Crystals (London, 1892). Who wrote this book? 4 I 2. He is known for the discovery of the dark absorption lines in the Sun's spectrum. 10 L 3. Some of the first experiments on polarized light were performed on calcite crystals by this man 7 P 4. Austrian physicist who designed a moving film x-ray technique that allows unambiguous indexing of each refraction 0 J 5. The free energy equation G = H - TΔS is named for this scientist. 3 N 6. 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. 6 E 7. An American Crystallographer who developed the precession camera. A. Roy G. Biv B. Sir William Henry Bragg C. Sir William Lawrence Bragg D. Sir David Brewster E. Martin J. Buerger F. Augustin Louis Cauchy G. Albert Einstein H. Sir Lazarus Fletcher I. Joseph von Fraunhofer J. Josiah Willard Gibbs K. Michel Levy L. William Nicol M. Wilhelm C. Roentgen N. Willebrod Snellius O. Max Theodore Felix von Laue P. Karl Weissenburg 10

11 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, and must be shown where requested. Points as shown State the general case of the phase rule in a formula, and clearly define each symbol used. (5 points) where: f = c - p + x f = # degrees of freedom. The number of intensive parameters that must be specified in order to completely determine the system. Intensive variables usually include pressure, temperature, and composition, and may include magnetic and/or electric fields, that can be changed independently without loss of a phase. p =number of phases - phases are mechanically separable constituents c = minimum number of components, which are chemical constituents that must be specified in order to define all phases x is the number of intensive variables, pressure, temperature, composition, and possibly magnetic and electric fields, that can be changed independently without loss of a phase. The results of this question are very disappointing. You did a number of homeworks involving the phase rule, yet three students left this page blank. The question asked you to define quantities, but quite a few students merely named the quantity. Many of the definitions were confused or inaccurate. 11

12 How could we obtain a nearly monochromatic source of copper K α radiation? Why does this technique work? (3 points) A nickel filter is placed in the X-ray beam before it hits the sample. Nickel is chosen because the absorption edge of an element one atomic number lower than the metal X-ray source, in this case copper, has an absorption edge at an energy slightly higher than the Cu K α peak, but well below the copper K β peak, thus effectively removing K β radiation Why is the wavelength range of X-ray significant in mineralogy? (2 points) X-rays have wavelengths which are comparable to the interatomic spacing in crystals. They interact with the crystals in ways which allow us to determine information about the atomic arrangement within the crystal. 12

13 Diagrams and Figures - Several diagrams are shown.. Each was previously seen in class. Diagrams may have been altered to remove labels, etc. Answer each question. (1 point each, unless otherwise indicated) 1. Each of the following questions pertain to Figure 1.(1 point each) Figure 1 What is the physical state of the following regions? 20 A Solid (Ice) 0.5 B Liquid 3 C Vapor What are the following points? 7 D Triple point 7 E Critical point Eutectic and peritectic appeared frequently as answers for D and E. These words belong on binary diagrams, not a unary diagram. And a couple of students thought region C was solid, despite the obvious high temperatures. 13

14 Problems - Do each of the following problems. Show all work. Label answers, including units, if any. Express answers to the correct number of significant figures. 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. Given: c vacuum = x 10 8 m/s If f = x Hz, what is λ (expressed in nm)? (2 points) 2. Use Figure 3 (next page) Outline the liquidus line in green, and the solidus line in brown. Start at 70% An and 1600 C. Assume the temperature is slowly decreased until the temperature reaches 1000 C. Show the path followed by the solid in blue, and the path followed by the liquid in red. (2 points) Then answer the following questions. (1 point each) 3 A. At what temperature does the first solid form? 1500 C 6 B. What is the composition of the first solid phase? An C. What phases (type and composition) are present at 1450 C? Liquid, An 51 ; Solid, An D. What is the percentage of each phase present at 1450 C? (Show calculations below) Liquid 37%, Solid 63% LF + SF = 38 LF = 14 SF = 24 Liquid = 14/38 *100 = 37% Solid = 24/38*100 = 63% 7.5 E. At what temperature does the last liquid disappear? 1370 C 10 F. What is the composition of the final liquid? An 30 7 G. How many components are there? Two 5 H. How many phases are present at 1550 C? One 11 I. How many degrees of freedom are there at 1550 C? Two 2 J. How many phases are there at 1450 C? Two 7 K. How many degrees of freedom are there at 1450 C? One 7 L. How many phases are presen1200 C? One 14

15 1 Brown 2 Green 4.5 Red 5 Blue 15

16 If light travels from air into sodalite, and the angle of incidence is 15.8, what is r? n for sodalite = (3 points) If the angular aperture is 42.1, and n = 1.544, what is N.A.? (2 points) HAVE A GREAT VACATION AND A VERY HAPPY AND SAFE NEW YEAR! 16

17 Final Exam results A B B 87.5 B C MEDIAN = D+ MEAN = 79.5 (73.6%) D 67.0 D F TOTAL EXAMINATION RESULTS (OUT OF 288; 48% OF FINAL GRADE) Examinations are worth 48% of the total grade A A B B B- MEDIAN = MEAN = C C D F 17

18 Previous Years Results -Final Examination Term, Year Mean, % Fall, Fall, Fall, Fall, Fall, Fall, Fall, Fall, Spring, Fall, Fall, Fall, Spring, Fall, Spring, Spring, Fall, Fall, Fall, Fall, Fall, Fall, Fall, Fall, Fourteenth out of twenty-four 18