Introduction to MineralogyDr. Tark Hamilton

Chapter 13: Lecture 21Optical Mineralogy &

Petrography Uniaxial & Biaxial

Camosun College GEOS 250

Lectures: 9:30-10:20 M T Th F300

Lab: 9:30-12:20 W F300

fig_13_13

Optical Indicatrix of Uniaxial Crystals (hexagonal, tetragonal)

nω < nε , cω > cε Optically positive

nω > nε , cω < cε Optically negative

Plane ofCircular section

Prolate Ellipsoid Oblate

fig_13_14

Elliptical Section has “C” Axis

Plane of Ordinary RayCircular Section

Plane of Extraordinary RayElliptical Section

2 special vibration directions in crystal: basal plane & its normal

SingleRefraction

DoubleRefraction

positive negative

fig_13_15

Vibration Directions & Extinction PositionsP-P Substage Polarizer

A-A Analyzer(Switch by ocular)

Extinction occurs when the crystal vibration directionEquals that of the polarizer & is blocked out by the analyzer

Illumination has theVector sum of vibrationDirections passing the

Analyzer.

Maximum illuminationIn 45° position

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

fig_13_16

Uniaxial Interference Figuresfor Conoscopic Light & High Power

ε-ray vibrates radiallyω-ray vibrates tangentially

Concentric isochromatic curves

Low Birefringenceδ < 0.02

Grey, white 1st yellowQuartz, Feldspar, Clays Feldspathoids

Hi Birefringenceδ > 0.03

Blue, green, hot pinkMuscovite, Epidote

W Is Tangential To Isochrome

fig_13_17

Off-Centered Uniaxial Optic Axis Figure& Clockwise Rotation of Stage

When the “C” Axis isn’t vertical,The Isogyres remain N-S & E-W

But the center precesses around the origin.

Isogyre arms of Black Cross are extinction directions.

Conoscopic illuminationCauses flaring of isogyres

fig_13_18

Determining Optic Sign from Optic Axis Figure

Accessory Plates: ¼ wave mica,rot-1 gypsum & quartz wedge

are all length fast

Slow R

adial

ε-ra

y

ε-ray is slow for optically + so colours increase:Isochromatic curves move in in quadrants I & III

Slow +

Slow

addit

ion

Slow + Fast = SubtractionIn I & III for Optically -

Optic Sign for some Uniaxial Minerals

Mineral 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 Negative

Calcite 1.658 1.486 0.172 High White 7th order colour

Negative

Corundum 1.769 1.760 0.009 White Negative

Zircon 1.920 1.967 0.047 3rd order Positive

fig_13_19

Colour Changes for Uniaxial Minerals with Rot-I Plate

Addition, ε

is slow

Subtractio

n, ε is

fast

fig_13_20

Sign of Elongation: (small crystals typically have low-grey birefringence) {δ=ω-ε}

Uniaxial (Hexagonal & Tetragonal) Crystals with elongationControlled by growth forms or prismatic cleavages often have

Optical directions that coincide with crystallographic ones.

Grain orientationNot quadrant

Grey + Red = BlueSlow + slow = add

E-ray is slow, optically +Positive elongation length slow

Grey - Red = YellowSlow + fast = subtract

E-ray is fast, optically -Negative elongation length fast

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 Minerals: Orthorhombic, Monoclinic & Triclinic

fig_13_21

Biaxial + Indicatrix: Z=Bxaβ is closer to α than to γ

Optic Plane = ZXFlash Figure, δ=γ-α

Maximum Birefringence

Optic AxesCircularSections

90° to OAs

β is intersectionof circular sections

Y is the Optic Normal

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° +

fig_13_22

Optical Orientation Diagrams for Special Sections of Barite (mmm)

Cleavage sectionsSymmetricextinction

Parallelextinction

Z Λ c = 53°Inclined ExtinctionIn Optic Plane (010)

Or Flash Section

fig_13_23

Biaxial Crystals in Convergent Polarized Light

Bxa Interference Figures

Parallel Extinction Position 45° Position Maximum Illumination2V ~ 45, Field of view = 60°

Melatopes

fig_13_24

Apparent Optic Angle (2E > 2V)

2E increases as β increases2V looks too big on BxaMelatopes too far apart

fig_13_25

Curvature of Isogyre: Centered Optic Axis Figure

2V

fig_13_26

Optic Sign tests for -Bxa & OA

Optical Properties of Biaxial Minerals

Mineral 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

fig_13_27

Reflected Light Microscopy

IsotropicAnisotropic-bireflectance

Intensity, colour oil immersion

Microindentation hardness