0 T 1. When twinning occurs in minerals of low symmetry, it may cause the mineral to appear to possess more symmetry than it actually does.

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1 GLY4200C Name 90 points October 26, 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 -- MIDTERM 2 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) 0 T 1. When twinning occurs in minerals of low symmetry, it may cause the mineral to appear to possess more symmetry than it actually does. 9 T 2. The formula for pyrrhotite is Fe 1-x S. If x = 0.0, pyrrhotite will be more magnetic than if x = 0.2. X>0 implies Fe 3+ is present, leading to e - exchange, and thus magnetism 0 F 3. Infra-red radiation has a shorter wavelength than ultraviolet radiation. 2 T 4. A prism is an open form. 2 T 5. Above the Curie temperature ferromagnetic materials become paramagnetic. 6 T 6. Purple fluorite gets its color from a type of Frankel defect, in which an electron replaces a fluorine anion. 1 T 7. The symbol (032) represents a plane parallel to the x-axis. 9 F 8. Three d electrons give a large orbital contribution to the magnetic moment of minerals they are in. 1 F 9. The external appearance of the crystal must reflect its internal symmetry. 1 T 10. In the term Point Group, group refers to a collection of mathematical operations which, taken together, define all possible, nonidentical, symmetry combinations. 3 F 11. Complex operations involve a combination of two simple operations, both of which must exist independently. 2 F 12. Polysynthetic twinning is a type of multiple penetration twinning. Exams to date /180 % Grade 1

2 0 T 13. It is possible for one crystal to exhibit twinning according to multiple twin laws. Gridiron or tartan twinning in microcline is an example. 1 F 14. Isometric {100} is the same as tetragonal {100} 4 T 15. Many vectorial properties vary discontinuously as direction is changed 8 F 16. 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. 0 T 17. Faces composed of all anions or all cations are very high energy. They attract ions of opposite sign, grow rapidly, and may grow themselves out of existence. 3 F 18. If two ions have the same charge, the larger ion will enter a crystal structure preferentially. 1 F 19. As nuclei grow, their surface area/volume ratio increases. 0 F 20. Red light has a shorter wavelength than blue light. 4 F 21. A twin operation must 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) 2 B 1. Hematite and corundum are X 2 O 3 oxides. What is the charge on X? A. +2 B. +3 C. +4 D C 2. What color has next longer wavelength after orange in the visible spectrum? A. Blue B. Yellow C. Red D. Green 3 A 3. The general symbol for a zone axis is: A. [uvw] B. (hkl) C. {hkl} D. hkl 2

3 6 C 4. 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 1 D 5. A form with all four faces parallel to a common axis is a(n): A. Scalenohedron B. Pinacoid C. Pyramid D. Prism 6 D 6. Which type of magnetic susceptibility is described as, "Transition metals ions are present but the magnetic moments are randomly distributed. The net field is zero, although an external field will produce some alignment of dipoles, which disappears when the external field is removed. The alignment of the magnetic dipoles produces a small positive magnetic susceptibility and these minerals are attracted to a magnet in a strong magnetic field. Example olivine (Mg, Fe) 2 SiO 4." A. Diamagnetic B. Ferrimagnetic C. Ferromagnetic D. Paramagnetic 3 A 7. A mineral has a low magnetic susceptibility which increases with increasing temperature up to the Néel temperature. Above the NÉel temperature, the susceptibility falls and the mineral becomes paramagnetic. It was originally: A. Antiferromagnetic B. Diamagnetic C. Ferrimagnetic D. Ferromagnetic 4 B 8. Which set of conditions is true for the monoclinic system? A. a b c, α = β = γ = 90 B. a b c, α = γ = 90, β 90 C. a = b c, α = β = γ = 90 D. a b c, α β γ 3

4 0 A 9. The symmetry operation inversion is associated with which type of symmetry element? A. Point B. Axis C. Plane D. Cube 2 A 10. The notation 213 indicates: A. A point B. A line C. A plane D. An even number 2 A 11. Which of the following is not a closed form? A. Ditrigonal prism B. Hexagonal dipyramid C. Scalenohedron D. Tetrahexahedron 2 B 12. Minor elements are those elements whose abundances lie within what range, expressed in weight per cent? A. 1-10% B % C % D % 6 B 13. [301 ]is parallel to which crystallographic axis? A. X B. Y C. Z D. More information is needed 6 C 14. What crystal system does (111 1) belong to? A. Isometric B. Tetragonal C. Hexagonal D. Triclinic 0 D 15. Why is milky quartz white? A. Fluoride ion occurs as interstitial impurities B. Replacement of Si 4+ by Al 3+ C. Cr 3+ ion replaces some Si 4+ D. Inclusions of water occur as quartz is precipitated from hydrothermal solution 4

5 2 B 16. In the tetragonal system, {100} includes which of the following faces? A. (100), (010), (001), (1 00), (01 0), (001 ) B. (100), (010), (1 00), (0 1 0) C. (100), (010), (001) D. (01 0), (001 ) 3 B 17. The unit cell vector b is associated with which crystal axis? A. X B. Y C. Z D. It depends on the crystal system 2 B 18. Which region of the earth is believed to be composed of 80% iron and 20% nickel? A. Crust B. Inner core C. Mantle D. Outer core 0 D 19. Which region of the earth ranges from 2900 to 5100 kilometers below the surface of the earth? A. Crust B. Inner core C. Mantle D. Outer core 6 D 20. Goethite after pyrite is an example of what? A. Omission substitution B. Polymorphism C. Polytypism D. Pseudomorphism 3 A 21. The angle γ lies between which crystallographic axes? A. X and Y B. X and Z C. Y and Z D. It depends on the crystallographic system 9 C 22. 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 5

6 8 D 23. Which type of twinning occurs when a preexisting crystal undergoes a change in structure due to a change in pressure or temperature A. Deformation B. Glide C. Growth D. Transformation Fill-Ins - Write in the word or words which best completes each statement or answers each question. (1 point per blank) 1-2. The Twin Law must specify two things. These are: 2 1) TWIN ELEMENT and 2 2) ORIENTATION OF THE TWIN ELEMENT { } is the symbol for a FORM 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 5 5. Fe 3+ has five 3d electrons, while Fe 2+ has six 3d electrons. Which ion has the larger magnetic moment? Fe Which crystal system has a = b c, and α = β = γ = 90? TETRAGONAL 9 7. The ratio of induced magnetization to the strength of an external magnetic field is known as the MAGNETIC SUSCEPTIBILITY Name three different ways crystals grow in nature. 3 8) CRYSTALLIZE FROM AN AQUEOUS SOLUTION, 1 9) CRYSTALLIZATION FROM A MAGMA, 2 10) CRYSTALLIZATION FROM VAPOR 6

7 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) 0 B 1. The lattice shown here is: A. C B. F C. I D. P 3 A 2. The lattice shown here is: A. C B. F C. I D. P 6 C 3.The form shown is a: A. Pinacoid B. Pyramid C. Sphenoid D. Dome 0 C 4. The form illustrated here is a: A. Dipyramid B. Dome C. Prism D. Sphenoid 3 D 5. The axes system shown here belongs to which crystal system? A. Hexagonal B. Monoclinic C. Tetragonal D. Triclinic 3 A 6. The axes system shown here belongs to which crystal system? A. Hexagonal B. Monoclinic C. Tetragonal D. Triclinic 7

8 0 A 7. The operation shown here is known as: A. Inversion B. Reflection C. Rotation D. Roto-reflection 0 A 8. The form illustrated here is a: A. Dipyramid B. Dome C. Prism D. Sphenoid 4 B 9. The complex symmetry operation shown here is a: A. 2 B. 4 C. 2 tilda D. 4 tilda 0 T 10. (T-F) The picture illustrates dendritic crystal habit. 2 C 11. This pie chart illustrates the major element composition of the earth. The pinkish color on the left represents: A. Aluminum B. Oxygen C. Silicon D. Sodium 0 A 12. The type of crystal defect illustrated here is a: A. Frenkel defect B. Grain boundary defect C. Schottky defect D. Stacking defect 2 B 13. The type of crystal defect illustrated here is a: A. Frenkel defect B. Grain boundary defect C. Schottky defect D. Stacking defect 2 A 14. The picture illustrates what phenomenon associated with minerals? A. Ex-solution B. Glass C. Metamict D. Pseudomorphism 8

9 0 D 15. The pictures shown here illustrate twinning in which mineral? A. Microcline B. Pyrite C. Rutile D. Staurolite 16. The object shown here is called: (Take your pick) A. The Great Pumpkin 0 B. Jack O Lantern 11 Jack is making this look easy (7 years in a row) C. Toothy 2 D. All of the above 4 9

10 Matching - Match the discovery in column one with the person(s) associated with the discovery in column two. Answers may be used once, more than one, or not at all (One point each) Column 1 1 I 1. The discovery that in antiferromagnetic materials the magnetic susceptibility is low, but increases up to a temperature is named for this man, and the material them becomes paramagnetic. 0 A 2. He wrote Études Crystallographiques in 1849 in which he showed the fourteen patterns which meet the requirements for a lattice. 0 H 3. British mineralogist and crystallographer, in 1839, devised a universally accepted system of indices used to describe the orientation of crystallographic planes and crystal faces relative to crystallographic axes. 1 A 4. The statement. Common crystal faces are parallel to lattice planes that have high lattice node density is known as the Law of 1 F 5. Swiss-born Norwegian mineralogist and petrologist who made the observation that, for ions of similar radius but different charges, the ion with the higher charge enters the crystal preferentially Column 2 A. Auguste Bravais B. Jacques Curie C. Marie Curie D. Pierre Curie E. Yakov Frankel F. Victor M. Goldschmidt G. René J. Huay H. William Hallows Miller I. Louis E.F. Néel J. Linus Carl Pauling K. Walter H. Schottky L. Nicolaus Steno 3 K 6. First described a type of crystal defect in which an atom or ion is missing from its proper place in the crystal structure. 11 G 7. He showed that crystals could be built by stacking together tiny identical blocks, which he called integral molecules. He later followed this with the Law of Rational Indices. 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. Points as shown Refer to figure 1. What color is emerald? Ruby? Explain why these colors are seen. What ion is responsible for the color in both minerals? Why are the colors different? (6 points) EMERALD IS GREEN, RUBY IS RED. RUBY HAS STRONG ABSORPTION IN BOTH THE BLUE AND THE GREEN TO YELLOW PARTS OF THE SPECTRUM. THE LEAST ABSORPTION IS IN THE RED. EMERALD ABSORBS STRONGLY IN THE BLUE AND THE RED, LEAVING GREEN. EMERALD IS A GEM VARIETY OF BERYL, Be 3 Al 2 Si 6 O 18. RUBY IS A GEM VARIETY OF CORUNDUM, Al 2 O 3. IN BOTH MINERALS, SMALL AMOUNTS OF CR 3+ REPLACE AL 3+. IN BERYL, ALUMINUM OR CHROMIUM IONS ARE IN DISTORTED OCTAHEDRAL COORDINATION WITH OXYGEN FROM SiO 4 OR BeO 4 TETRAHEDRA. THE BONDING IS RESONANT BETWEEN IONIC AND COVALENT. THE COVALENT COMPONENT WEAKENS THE CRYSTAL FIELD AROUND THE ALUMINUM OR CHROMIUM IONS. IN CORUNDUM, OXYGEN FORMS HEXAGONAL CLOSE-PACKED LAYERS, WITH THE ALUMINUM OR CHROMIUM IONS IN INTERSTICES BETWEEN LAYERS. THIS RESULTS IN A STRONG CRYSTAL FIELD AROUND THESE CATIONS. THE SPECTRA OF EMERALD AND BERYL CLEARLY REFLECT THE STRENGTH OF THE CRYSTAL FIELD. 11

12 2. In the mineral beryllonite, Na {Be(PO 4 )}, the beryllium is in tetrahedral coordination with the oxygen (BeO 4 tetrahedra). The phosphorus is also in tetrahedral coordination with the oxygens (PO 4 tetrahedra).(clearly a better review of Pauling s Rules was in order for all but one of you) 26.5 a. The BeO 4 tetrahedra share an element with the PO 4 tetrahedra. Would you expect this to be a face, an edge, or a corner? Why? (2 points) A corner. Both Be and P are small ions with high charge. According to Pauling s Rules, they cannot share more than a corner because of the repulsion between the two nuclei. If they share an edge or a face, the inter-nucleus distance would decrease and the repulsive forces would become very large b. No PO 4 tetrahedra share an element with each other. Why? (l point) The P cations have a charge of 5+. The Z 1 Z 2 charge term is 25. The repulsion is thus very large c. Ionic radii: Be 2+, 0.35Å, P 5+, 0.35Å, 0 2-, 1.40Å The observed Be-O bond lengths are in the range Å, and the observed P-O bond lengths Å. Are these longer or shorter than you would expect? Why? (2 points) Shorter. The bonds are partially covalent, and they are stronger than pure ionic bonds, hence shorter. 9.5 d. Why are P - O bond lengths shorter than Be - O bond lengths? (1 point). The P has a higher charge so the ionic bond portion of the PO 4 tetrahedron bonds is stronger than the BeO 4 tetrahedron bonds. 12

13 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 defined all symbols used in the formula. Miraculous answers, unsupported by all necessary calculations, will receive little or no credit Calculate the zone axis of the following planes. (031), (22 1) (3 points) (3 + 2, 2-0, 0-6) = [5 2 6 ] 6 2. Enargite is orthorhombic with the following unit cell dimensions. a = o.641 nm b = nm c = 6.15 nm Calculate the Miller index for a plane with the following intercepts: (4 points) x' = nm y' = nm z' = HAPPY HALLOWEEN! 13

14 Midterm 2 Results 87.5 A A 81.5 A MEDIAN = B MEAN = 75.2 (83.5%) B C 65.0 C D+ Exams to Date A A B MEDIAN = B MEAN = 149.1(82.8%) B C C D- 14

15 Previous Years Results - Midterm 2-6th out of 24 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,

CHAPTER 4. Crystal Structure

CHAPTER 4. Crystal Structure CHAPTER 4 Crystal Structure We can assume minerals to be made of orderly packing of atoms or rather ions or molecules. Many mineral properties like symmetry, density etc are dependent on how the atoms