Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300

1. Introduction to MineralogyDr. Tark HamiltonChapter 6: Lecture 23-26Crystallography & External Symmetry of Minerals Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300

2. Rotoinversion Inside a Sphere (Stereonet) fig_06_14

3. 2- , 3- , 4- & 6- Rotoinversion Projections 2-fold = m 3-fold = 3 + i 4-fold = 4 + m 6-fold = 3 + m fig_06_15

4. 32 Bravais Lattices table_06_02

5. table_06_03

6. Tetragonal 422 & Hexagonal 622 Phosgenite Pb2Cl2CO3 Oblique perspective 422 1-A4 , 4-A2’s Equatorial Plane (Primitive circle) 622 1-A6 , 6-A2’s Equatorial Plane (Primitive circle) 422 Oblique view Of symmetry axes 622 Oblique view Of symmetry axes 422 β-High Quartz fig_06_16

7. Stereoprojection normal to 3, II to 2 Hexagonal: 1-A3 , 3-A2 ‘s Original motif In lower hemisphere Diad-Rotated motif In upper hemisphere Motifs produced By triad normal to page α-Quartz fig_06_17

8. 4-, 3- & 2-fold Symmetry Axes in a Cube Triads connect Along body diagonals Diads Connect Along Edge Diagonals Tetrads Connect Along Face Normals fig_06_18

9. Rotational Axes Normal to Mirrors Solid dot upper hemisphere m lies along primitive fig_06_19

10. Mirrors in the Tetragonal System Tetrad Axis with Parallel m’s, Upper only Point groups preclude m’s Rotational Axes with Perpendicular m’s: Up & Down + Side by Side fig_06_20

11. Intersecting Mirror Planes:Reflected reflections = Rotations Orthorhombic Perspective Tetragonal Perspective Plan Views Tetragonal Perspective Orthorhombic Perspective fig_06_21

12. NaCl Cube + Octahedron & Symmetry 54°44’ fig_06_22

13. 32 Possible Point Groups & Symmetry fig_06_23

14. Motifs & Stereonet Patterns for 32 point groups 7 Tetragonal Point Groups 3 Monoclinic patterns: 2nd setting 3 Orthorhombic Point Groups 2 Triclinic Point Groups fig_06_24

15. Motifs & Stereonet Patterns Cont’d 5 Isometric Groups 12 Hexagonal Groups fig_06_24cont

16. 21 11 What Symmetry element makes the center of symmetry appear? table_06_04

17. Only 6 Different Crystal SystemsDetermined by Axial Lengths & Angles Triclinic a≠ b ≠ c α≠β≠γ≠90° Monoclinic a≠ b ≠ c α = γ = 90°, β > 90° Tetragonal a =b ≠ c α = β = γ = 90° Orthorhombic a≠ b ≠ c α = β = γ = 90° Isometric a =b =c α = β = γ = 90° Hexagonal a1 = a2 = a3 @ 120°, c@ 90° fig_06_25

18. Crystal Morphology & Crystallographic Axes b is pole to β > 90° plane c is Zone Axis a & b ~symmetric a b a1 a2 a3 are poles to faces in equatorial zone & 4, 2 rotational axes Hey! Somebody Has to be Perfect! fig_06_26

19. table_06_05

20. Orientation & Intercepts of Crystal Faces, Cleavages & Mirror Planes Intercepts at Integral Valuesof Unit Cell Edges Forms Correspond To Faces, Edges& Corners of Unit Cell fig_06_27

21. Orthorhombic Crystal with 2 Pyramidal Forms Olivine 2/m2/m2/m (Similar forms in Scheelite 4m CaWO4) fig_06_28

22. Miller Indices • Are integers derived from the intercepts on the a, b, & c axes • Intercepts are expressed in terms of logical unit cell edge dimensions (the fundamental translation unit in the lattice) • If a = 10.4 Å , then an intercept at 5.2 Å on the a axis is ½ • Fractions are cleared by multiplying by a common denominator • e.g. a plane cutting at [⅓ ⅔ 1/∞ ] X 3 = (1 2 0)

23. Isometric Lattice, Intercepts & Miller Indices What would be the difference between crystals which had Cleavages or other planes along (100) versus (400)? fig_06_29

24. Miller Indices for Positive & Negative Axes This Crystal like Diamond, Fluorite or Spinel has all Faces of the “form” (111) fig_06_30

25. A Crystal Form • A Crystal Form is a group of Like crystal faces • All faces of a given form have the same relationship to the symmetry of the crystal • In Isometric Crystals the general form (100) includes: (010) (001) (-100) (0-10) and (00-1) through the 4-fold, 3-fold, 2-fold axes and Mirror Planes • These faces will all tilt or intersect at 90° • Triclinic forms: (100) (010) & (001) all have different pitches; so they do not belong to a single common form • For 2 & 2/m Monoclinic forms (101) = (-10-1) ≠ (-101)

26. Hexagonal 4-digit Miller-Bravais Indices a1 a2 a3 c 1 Form : Prismatic (1010) (1100) (0110) (1010) (1100) (0110) 1 Form : Pyramidal (1121) (2111) (1211) (1121) (2111) (1211) fig_06_31

27. Crystal Zones & Zone Axes Zone Axis [001] Zone : m’ a m b • Which Forms are : • Prismatic • Pyramidal? (hkl) = a single face [hkl] = a form or pole • What is the • General form • Of the miller • Index for : • m • r’ Zone Axis [100] Zone : r’ c r b fig_06_32

28. Conventional Lettering of Forms General Miller Indices For each form (hkl)? What symmetry makes p=p, m=m ? fig_06_33

29. The (111) Form in 1 & 4/m 3 2/m Triclinic : Inversion Center Makes only (111) & (111) Isometric : Generates full Octahedron (111) fig_06_34

30. Distinct Forms Manifest Different Details Striation patterns & directions differ for cube & pyritohedon forms on 2/m 3 Pyrite Striation patterns & directions differ For forms on Quartz Apophyllite KCa4(Si4O10)2 F – 8H2O 4/m 2/m 2/m Base : Pearly, others vitreous fig_06_35

31. 18 Open Forms Faces ≤ 4 15 Closed Forms Faces ≥ 4 table_06_06

32. 15 Closed Forms table_06_07

33. 11 Open Non-Isometric Forms & Symmetry 2 Dihedrons: 1 Pedion & 1 Pinacoid Sphenoid = Angles Dome 7 Prisms 11 Open Forms fig_06_36a

34. 14 Pyramidal Crystal Forms & Symmetry Pyramids: 7 Open Forms Rhombic & Trigonal, Ditrigonal & etc. for both Dipyramids 7 Closed Forms fig_06_36b

35. 8 Non & 8 Isometric Crystal Forms & Symmetry 8 Non-isometric Forms 3 Trapezohedrons (4≠angles, 4≠edges) 2 Scalenohedrons (3≠angles, 3≠edges) Rhombic equilateral 2 Disphenoids: Tetragonal isosceles 1 Rhombohedron (2 pairs=angles, 1 edge) Tristetrahedron, Trisoctahedron & Tertahexahedrons have isosceles triangle faces Both Octahedrons & Tetrahedrons have Equilateral [111] forms 8 Isometric Forms fig_06_36c

36. 7 Isometric Crystal Forms & Symmetry Dodecahedron & Deltoid 12 have Sym. Trapezoids Pyritohedron, Tetartoid & Gyroid (Pentagon faces) fig_06_36d