Introduction to Mineralogy Dr Introduction to Mineralogy Dr. Tark Hamilton Chapter 13: Lecture 21 Optical Mineralogy & Petrography Uniaxial & Biaxial Camosun College GEOS 250 Lectures: 9:30-10:20 M T Th F300 Lab: 9:30-12:20 W F300

Optical Indicatrix of Uniaxial Crystals (hexagonal, tetragonal) Prolate Ellipsoid Oblate Calcite Quartz Plane of Circular section nω < nε , cω > cε Optically positive nω > nε , cω < cε Optically negative fig_13_13

Elliptical Section has “C” Axis Plane of Extraordinary Ray Elliptical Section Double Refraction Plane of Ordinary Ray Circular Section Single Refraction positive negative 2 special vibration directions in crystal: basal plane & its normal fig_13_14

Vibration Directions & Extinction Positions A-A Analyzer (Switch by ocular) P-P Substage Polarizer Illumination has the Vector sum of vibration Directions passing the Analyzer. Maximum illumination In 45° position Extinction occurs when the crystal vibration direction Equals that of the polarizer & is blocked out by the analyzer fig_13_15

Birefringence in Uniaxial Crystals Birefringence depends on the difference in refractive indices and the path length (mineral thickness), so bigger crystals look prettier than little ones under crossed polars This is the same as the amount of double refraction For the principle or flash section the 45° position of maximum illumination shows the full value δ=[ω-ε] For other random inclinations (tilts other than vertical) birefringence is less because δ=[ω-ε’] δ is low for Quartz & Apatite, Extreme for Zircon & Calcite

Uniaxial Interference Figures for Conoscopic Light & High Power ε-ray vibrates radially ω-ray vibrates tangentially Concentric isochromatic curves WITTI Hi Birefringence δ > 0.03 Blue, green, hot pink Muscovite, Epidote W Is Tangential To Isochrome Low Birefringence δ < 0.02 Grey, white 1st yellow Quartz, Feldspar, Clays Feldspathoids fig_13_16

Off-Centered Uniaxial Optic Axis Figure & Clockwise Rotation of Stage Isogyre arms of Black Cross are extinction directions. When the “C” Axis isn’t vertical, The Isogyres remain N-S & E-W But the center precesses around the origin. Conoscopic illumination Causes flaring of isogyres fig_13_17

Determining Optic Sign from Optic Axis Figure Slow Radial ε-ray Slow + Slow addition ε-ray is slow for optically + so colours increase: Isochromatic curves move in in quadrants I & III Slow + Fast = Subtraction In I & III for Optically - Accessory Plates: ¼ wave mica, rot-1 gypsum & quartz wedge are all length fast fig_13_18

Optic Sign for some Uniaxial Minerals ω ε δ = birefringence Optic sign Nepheline 1.537 1.534 0.003 Dark grey Negative Quartz 1.544 1.553 0.009 White Positive Apatite 1.649 1.644 0.005 Grey Calcite 1.658 1.486 0.172 High White 7th order colour Corundum 1.769 1.760 Zircon 1.920 1.967 0.047 3rd order

Colour Changes for Uniaxial Minerals with Rot-I Plate Addition, ε is slow Subtraction, ε is fast fig_13_19

Sign of Elongation: (small crystals typically have low-grey birefringence) {δ=ω-ε} E-ray is fast, optically - Negative elongation length fast Grain orientation Not quadrant Grey + Red = Blue Slow + slow = add Grey - Red = Yellow Slow + fast = subtract E-ray is slow, optically + Positive elongation length slow Uniaxial (Hexagonal & Tetragonal) Crystals with elongation Controlled by growth forms or prismatic cleavages often have Optical directions that coincide with crystallographic ones. fig_13_20

Biaxial Minerals: Orthorhombic, Monoclinic & Triclinic Index Relative value Direction Ray Velocity Alpha=nx=nα α-Lowest X Fastest Beta=nY=nβ β-Intermediate Y Intermediate Gamma=nγ γ-Highest Z Slowest

Biaxial + Indicatrix: Z=Bxa β is closer to α than to γ β is intersection of circular sections Optic Axes Circular Sections 90° to OAs Optic Plane = ZX Flash Figure, δ=γ-α Maximum Birefringence Y is the Optic Normal fig_13_21

2V: The Optic Angle in Biaxial Crystals Light moving along the Optic Axes in Biaxial Crystals has n=β and no birefringence 2V is the angle between the Optic Axes of which Z is the Acute Bisectrix (Z=Bxa) for + V the optic angle is related to the shape of the indicatrix and thus the 3 indices of refraction Cos2Vx = [ γ2(β2-α2) / β2(γ2-α2) ], where V is Bxo Cos2V’x =~ (β-α) / (γ-α) V’ < V not accurate for large V, δ birefringence Since V is for Bxo, V<45° is negative, V>45° +

Optical Orientation Diagrams for Special Sections of Barite (mmm) Parallel extinction Symmetric extinction Cleavage sections Z Λ c = 53° Inclined Extinction In Optic Plane (010) Or Flash Section fig_13_22

Biaxial Crystals in Convergent Polarized Light Bxa Interference Figures Melatopes Parallel Extinction Position 45° Position Maximum Illumination 2V ~ 45, Field of view = 60° fig_13_23

Apparent Optic Angle (2E > 2V) 2E increases as β increases 2V looks too big on Bxa Melatopes too far apart fig_13_24

Curvature of Isogyre: Centered Optic Axis Figure

Optic Sign tests for -Bxa & OA fig_13_26

Optical Properties of Biaxial Minerals α β γ δ Sign Stilbite 1.494 1.498 1.500 0.006 - Gypsum 1.520 1.523 1.530 0.010 + Sanidine 1.521 1.526 1.528 0.007 Muscovite 1.556 1.602 1.603 0.047 Forsterite 1.635 1.651 1.670 0.035 Epidote 1.733 1.755 1.765 0.032

Other Optical Properties Absorption e.g. X>Y>Z (intensity varies in any light) Pleochroism e.g. Straw-Yellow-Brown, Pale Green-Olive-Green Brown (colour varies with crystal orientation, Fe minerals, only in Plane Polarized Light) Cleavage, Habit, Twinning, Zoning, Z Λ C, inclusion patterns, radiation haloes, metamict, alteration phases

Reflected Light Microscopy Isotropic Anisotropic-bireflectance Intensity, colour oil immersion Microindentation hardness fig_13_27