1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. Optic Sign for some Uniaxial Mineralsω 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
rd order

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

11. 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

12. 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

13. 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

14. 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° +

15. 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

16. 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

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

18. Curvature of Isogyre: Centered Optic Axis Figure

19. Optic Sign tests for -Bxa & OA
fig_13_26

20. Optical Properties of Biaxial Mineralsα 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

21. 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

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