1 / 36

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

Introduction to Mineralogy Dr. Tark Hamilton Chapter 6: Lecture 23-26 Crystallography & External Symmetry of Minerals. Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300. Rotoinversion Inside a Sphere (Stereonet). fig_06_14.

ebony
Télécharger la présentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related