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42 Pages

### Symmetry and Mineral Optics

Course: GEOL 585, Fall 2008
School: WVU
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Word Count: 1711

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Helen Dr. Lang Dept. of Geology &amp; Geography p gy g p y West Virginia University SPRING 2009 GEOLOGY 585: OPTICAL MINERALOGY &amp; PETROLOGY Symmetry and Mineral Optics Optical properties obey and reflect the symmetry of the crystal structure Minerals are Grouped into Six Crystal Systems based on Symmetry System Isometric (Cubic) System Hexagonal System Tetragonal System T lS Orthorhombic...

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Helen Dr. Lang Dept. of Geology & Geography p gy g p y West Virginia University SPRING 2009 GEOLOGY 585: OPTICAL MINERALOGY & PETROLOGY Symmetry and Mineral Optics Optical properties obey and reflect the symmetry of the crystal structure Minerals are Grouped into Six Crystal Systems based on Symmetry System Isometric (Cubic) System Hexagonal System Tetragonal System T lS Orthorhombic System Monoclinic System Triclinic System Characteristic Symmetry four 3 or 3 one 6, 6, 3 or 3 one 4 or 4 three 2 and/or m one 2 and/or m 1 or 1 Crystallographic Axes Reference axes Conventional ways to hold and refer to faces on crystals Different convention for each system Crystallographic Axes: Isometric System Three perpendicular axes Coincide with three 4-fold 4 fold or 2-fold axes All equal length l l th Called a1, a2, a3 Garnet, halite, pyrite and fluorite are isometric +a3 +a2 +a1 Crystallographic Axes: Tetragonal System Must have one 4 or 4-bar axis Three perpendicular axes Vertical axis, c, coincides axis c with 4 or 4-bar axis O axis, c, is longer or One i i l shorter than other two, a1 and a2 , which are equal d hi h l +c 4-fold axis +a2 +a1 Crystallographic Axes: Orthorhombic System Has three 2-fold axes and/or one mirror plane p Three perpendicular axes coincide with 2 fold axes 2-fold or are perpendicular to mirror planes All different lengths called a, b, c ll d b +c +b b +a Crystallographic Axes: Monoclinic System +c Has one 2 fold axis or mirror 2-fold All axes different lengths Called a, b, c > 90o b axis coincides with 2-fold axis or is mirror plane c is parallel to long edges +a + a slants down to the front a b b c, angle between a b, l b t and c>90o +b b Crystallographic Axes: Triclinic System No perpendicular axes All different lengths Called a, b, c +b +a + +c There are 32 ways in which symmetry operations can be combined 32 point g p or crystal classes p groups y Hermann-Mauguin (H-M) Symbols are a simple numeric way to represent the symmetry of each class Three-place symbols y Different content for each system isometric hexagonal tetragonal orthorhombic monoclinic li i triclinic Summary of the Crystal Systems CRYSTAL SYSTEM Isometric CHARACTERISTIC SYMMETRY four 3 or AXIAL RELATIONSHIPS a1=a2=a3 *===90o a1=a2=a3c ac=90o a1a2=120o a2a3=120o a1=a2c 90 ===90o abc, c>b>a ===90o abc, ==90o , >90o abc, =>90o > or < 90o PLACES IN THE H-M SYMBOL 1symmetry of a axes 23 or (diagonal) 3other (edge to edge) 1symmetry of c axis 2symmetry of a axes 3other (between a axes) CRYSTAL CLASSES **, 3m, 432, 23 , OPTICAL CLASSIFICATION Isotropic Hexagonal one 6, , 3 or Tetragonal one 4 or Orthorhombic Monoclinic Triclinic three 2 and/or m one 2 and/or one m 1 or Uniaxial , 2m, 6mm, 622, , , 6, , 3m, 32, , 3 1symmetry of c axis Uniaxial , 2symmetry of a axes y y 2m, 4mm, 422 2m 4mm 422, 3other (between a axes) , ,4 1symmetry of a axis Biaxial , 2symmetry of b axes 222, mm2 3other (between c axes) 1symmetry of b axis y y Biaxial ,2 m 2, 11 or ,1 Biaxial * ** = bc, = ac, = ab The holohedral or highest symmetry class in each system is shown in bold letters The Petrographic Microscope Plane-polarized light from below (polarizer) EW or NS? biotite is darkest parallel to polarizer Removable "analyzer" above sample Rotatable stage Various microscopes The Petrographic (polarizing) ( l i i ) Microscope Analyzer (NS) Objectives Rotating Stage i S Polarizer (EW, (EW perpendicular to Analyzer) A l ) New Leica Microscopes The Petrographic (polarizing) ( l i i ) Microscope Analyzer (NS or EW) Rotating Stage otat g Polarizer (EW or NS, perpendicular to Analyzer) Older Olympus Microscopes Interaction of light with minerals i l Polarized light travels right through isotropic minerals, and travels at the same speed in all directions In anisotropic minerals, polarized light is split into two rays vibrating at 90 to 90 each other in two special "allowed vibration directions " the two rays travel directions, at different speeds = =retarda ation Light passing thru an anisotropic mineral If recombined wave is perpendicular to Analyzer, no light li h passes, mineral is dark If recombined wave is parallel to the Analyzer, Analyzer all light passes, mineral appears brightest In an ani n isotrop min pic the "s slow" ray lag r "slow rayfast" rabehind the "fast" ra w" "f ay, d sho long ort "fast" ray, long g "slow" ray slow short se, 2004) ) Lagging of the "slow" ray behind gg g y the "fast" ray is called Retardation When the two rays recombine at the Analyzer, they interfere (constructively or y , y ( y destructively) with each other and there is g generally a component of light p y p g parallel to the Analyzer Different colors of light experience different amounts of Retardation Retardation and Interference Q Quartz Wedge g between Crossed Polaroid Films in Monochromatic (NaD; =590nm) Light Note constructive and destructive dd i interference Interference Colors Constructive (bright) and Destructive Interference (black) for different colors sums to the interference colors ( t the l (at th bottom) for white light (Phillips, 1971) Interference Colors depend on: The amount of retardation caused by the mineral in a certain direction How anisotropic is the mineral? maximum difference in refractive index , And the thickness of the mineral (typically a 30 m thin section) hi i ) Interference Colors Plag Qtz birefringence Cpx Muscovite 0.03 Olivine Th hickness (mm) s Calcit te retardation Properties viewed in Planepolarized light (PPL) Relief (relative) Becke lines bright line moves toward medium with higher refractive index ( g (distance increased) ) Color Pleochroism Grain shape Cleavages Cl Alteration Others? Properties in Cross-polarized light li ht (XPL) Birefringence None, zero isotropic Interference colors anisotropic How high? low, medium, high, extremely high E ti ti Extinction parallel extinction? extinction angle? Others? Optical Groupings Isotropic Same properties in all directions Li ht t Light travels at th same speed i all di ti l t the d in ll directions Isometric symmetry Uniaxial One unique axis, one direction in which the mineral appears isotropic = optic axis = c axis pp p p Tetragonal or Hexagonal symmetry Biaxial Three principal refractive indices, two directions in which the mineral appears isotropic = optic axes angle between them is 2V Orthorhombic, Monoclinic or Triclinic symmetry Uniaxial and Biaxial Optics David Hirsch Uniaxial Indicatrix Movie http://almandine geol wwu edu/ dave/courses/40 http://almandine.geol.wwu.edu/~dave/courses/40 7resources/UniPosIndicatrix.mov David Hirsch Biaxial Indicatrix Movie http://almandine.geol.wwu.edu/~dave/courses/40 7resources/BiaxialNegativeIndicatrix.mov 7resources/BiaxialNegativeIndicatrix mov A really good Optical Mineralogy course Dr Greg Finn, Brock University, Canada Dr. Finn University http://www.brocku.ca/earthsciences/people/gfinn/ optical/222lect.htm optical/222lect htm Uniaxial Minerals The optic axis (direction along which mineral appears isotropic) is always parallel to c , the ordinary ray, vibrates perpendicular to the c axis , the extraordinary ray, vibrates parallel to th t the c axis i Positive > V < V is fast ray Quartz Leucite co Zircon Rutile Negative < V > V is slow ray Beryl Tourmaline Apatite pat te Calcite, Dolo Corundum Uniaxial U i i l Indicatrix d ca > Greg Finn-Brock U. g < Determining the Optic Sign Obtaining an interference figure C Conoscopic Li ht microscope setup i Light i t Uniaxial Minerals Centered Optic Axis figure Looking down the c-axis Biaxial Minerals Several options, Bxa, Bxo or Optic Axis p , , p (OA) I suggest Optic Axis figure, easiest to find gg p g , likely grains Uniaxial Figure & Optic Sign if > , is the "fast ray" and the optic sign is negative g g if > is the slow ray and the optic , sign is positive Uniaxial Mineral Conoscopic Light Greg Finn-Brock U. Uniaxial sign and interference figure > V>V fast NW-SE fast on slow subtraction yellow > V>V slow NW-SE NW SE slow on slow addition blue Biaxial Minerals X vibration direction of fastest ray refractive index of light vibrating in X direction lowest refractive index Y vibration direction of light traveling along OA refractive index of light vibrating to Optic Axis intermediate refractive index Z vibration direction of slowest ray refractive index of li ht vibrating i Z di ti f ti i d f light ib ti in direction highest refractive index birefringence = = (always) < < (always) Biaxial Indicatrix Greg Finn-Brock U. Biaxial Relationships p () () () Y (...

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