1. Optical Mineralogy in a Nutshell
Use of the petrographic microscope in three easy lessons
Part III
Slides borrowed/adapted from Jane Selverstone (University of New Mexico) and John Winter (Whitman College)

2. Today we’ll break down anisotropic minerals into
Some review…
Optical mineral properties ONLY visible in PPL:
Color – not an interference color! (for that, see below)
Pleochroism – is there a color change while rotating stage?
Relief – low, intermediate, high, very high?
Optical mineral properties visible in PPL or XPL:
Cleavage – number and orientation of cleavage planes
(may need higher magnification and at different grains)
Habit – characteristic form of mineral (sometimes better in XPL)
Optical mineral properties ONLY visible in XPL:
Birefringence – use highest order interference color to describe
Twinning – type of twinning, orientation
Extinction angle – parallel or inclined? Angle?
Isotropic vs. anisotropic minerals – 100% extinct in XPL?
Today we’ll break down anisotropic minerals into
uniaxial or biaxial…

3. Some generalizations and vocabulary
All isometric minerals (e.g., garnet) and glass are isotropic – they cannot reorient light. These minerals are always black in crossed polars.
All other minerals are anisotropic – they are all capable of reorienting light.
All anisotropic minerals contain one or two special directions (the “optic axes”) that do not reorient light.
Minerals with one special direction are called uniaxial
Minerals with two special directions are called biaxial
• Uniaxial and biaxial minerals can be subdivided into
optically positive and optically negative, depending on the
orientation of fast and slow rays relative to the xtl axes

4. All anisotropic minerals can resolve light into two plane polarized components that travel at different velocities and vibrate in planes that are perpendicular to one another
Some light is now able to pass through the upper polarizer
fast ray
slow ray
mineral grain
When light gets split:
velocity changes
rays get bent (refracted)
2 new vibration directions
usually see new colors
plane polarized light W E
lower polarizer

5. Calcite experiment and double refraction
O E
Fig 6-8 Bloss, Optical Crystallography, MSA
Fig 6-7 Bloss, Optical Crystallography, MSA

6. We’ve talked about minerals as magicians - now let’s prove it!
calcite
calcite
calcite
calcite
calcite
ordinary
ray, w
(stays stationary)
extraordinary
ray, e
(rotates)

7. How light behaves depends on crystal structure (there is a reason you took mineralogy!)
Isotropic
Uniaxial
Biaxial
Isometric
All crystallographic axes are equal
Hexagonal, trigonal, tetragonal
– All axes  c are equal but c is unique
Orthorhombic, monoclinic, triclinic
– All axes are unequal
Let’s use all of this information to help us identify minerals

8. Simple guide to interference figures
• Get a good interference figure;
• Distinguish uniaxial and biaxial figures;
• Determine optic sign; and
• Estimate 2V
1) Choose a grain showing the lowest interference colors
2) Move to the high-powered objective lens and refocus
3) Open the sub-stage diaphragm as wide as possible
4) Insert the condenser lens
5) Cross the polars
6) Insert the Bertrand lens

9. Use of interference figures, continued…
You will see a very small, circular field of view with one or more black isogyres -- rotate stage and watch isogyre(s)
uniaxial
If uniaxial, isogyres define cross; arms remain N-S/E-W as stage is rotated
biaxial or
If biaxial, isogyres define curve that rotates with stage, or cross that breaks up as stage is rotated

10. Use of interference figures, continued…
Now determine the optic sign of the mineral:
Rotate stage until isogyre is concave to NE (if biaxial)
Insert gypsum accessory plate
Note color in NE, immediately adjacent to isogyre --
Blue = (+)
Yellow = (-)
uniaxial
(+)
(+)
biaxial
Without plate
Gypsum plate inserted

11. Remember determining optic sign last week with the gypsum plate?
slow
blue in NE = (+)
Gypsum plate has constant D of nm = 1st-order pink
Isogyres = black: D=0
Background = gray: D=100
Add or subtract 530 nm:
=630 nm = blue = (+)
=430 nm = yellowish = (-)
Addition = slow + slow
Subtraction = slow + fast

12. Time for some new tricks: the optical indicatrix
Thought experiment:
Consider an isotropic mineral (e.g., garnet)
Imagine point source of light at garnet center; turn light on for fixed amount of time, then map out distance traveled by light in that time
What geometric shape is defined by mapped light rays?

13. Isotropic indicatrix
Light travels the same distance in all directions;
n is same everywhere, thus d = nhi-nlo = 0 = black
Soccer ball
(or an orange)

14. anisotropic minerals - uniaxial indicatrix
c-axis
Let’s perform the same thought experiment…
c-axis
calcite
quartz

15. Uniaxial indicatrix calcite quartz c-axis c-axis
tangerine = uniaxial (-)
calcite
Spaghetti squash = uniaxial (+)
quartz

16. Uniaxial ellipsoid and conventions:
(-) crystal:
w > e
 oblate
(+) crystal:
e > w
 prolate
Fig 6-11 Bloss, Optical Crystallography, MSA

17. Propagate light along the c-axis, note what happens to it in plane of thin section
nw - nw = 0
therefore, d=0: grain stays black
(same as the isotropic case) nw

18. This orientation will show the maximum d of the mineral
Now propagate light perpendicular to c-axis N S W E
ne - nw > 0
therefore, d > 0 ne nw ne nw ne nw ne nw ne nw
Grain changes color upon rotation. Grain will go black whenever indicatrix axis is E-W or N-S
This orientation will show the maximum d of the mineral

19. anisotropic minerals - biaxial indicatrix
feldspar
clinopyroxene
Now things get a lot more complicated…

20. Biaxial indicatrix (triaxial ellipsoid)
The potato!
2Vz
There are 2 different ways to cut this and get a circle…

21. Alas, the potato (indicatrix) can have any orientation within a biaxial mineral…
augite
olivine

22. … but there are a few generalizations that we can make
The potato has 3 perpendicular principal axes of different length – thus, we need 3 different RIs to describe a biaxial mineral
X direction = na (lowest)
Y direction = nb (intermed; radius of circ. section)
Z direction = ng (highest)
Orthorhombic: axes of indicatrix coincide w/ xtl axes
Monoclinic: Y axis coincides w/ one xtl axis
Triclinic: none of the indicatrix axes coincide w/ xtl axes

23. 2V: a diagnostic property of biaxial minerals
When 2V is acute about Z: (+)
When 2V is acute about X: (-)
When 2V=90°, sign is indeterminate
When 2V=0°, mineral is uniaxial
2V is measured using an interference figure…
More in a few minutes

24. How interference figures work (uniaxial example)
Converging lenses force light rays to follow different paths through the indicatrix
Bertrand
lens
N-S polarizer
What do we see??
Sample
(looking down OA) nw ne
Effects of multiple cuts thru indicatrix
substage
condensor W E

25. Biaxial interference figures
There are lots of types of biaxial figures… we’ll concentrate on only two
1. Optic axis figure - pick a grain that stays dark on rotation
Will see one curved isogyre
determine sign w/ gyps
(+)
(-)
determine 2V from curvature of isogyre
90°
60°
40°
See Nesse p. 103

26. Estimating 2V
Fig 11-5A Bloss, Optical Crystallography, MSA
OAP

27. Biaxial interference figures
2. Bxa figure (acute bisectrix) - obtained when you are looking straight down between the two O.A.s. Hard to find, but look for a grain with intermediate d.
Use this figure to get sign and 2V:
2V=20°
2V=40°
2V=60°
See Nesse p. 101
(+)

28. Isotropic? Uniaxial? Biaxial? Sign? 2V?
Quick review:
Indicatrix gives us a way to relate optical phenomena to crystallographic orientation, and to explain differences between grains of the same mineral in thin section
hi d
lo d
Isotropic? Uniaxial? Biaxial? Sign? 2V?
All of these help us to uniquely identify unknown minerals.