1. Optical Mineralogy in a Nutshell
Use of the petrographic microscope in two easy lessons
Part II
© Jane Selverstone

2. Quick review
Isotropic minerals –velocity changes as light enters mineral, but then is the same in all directions thru xtl; no rotation or splitting of light.
These minerals are characterized by a single RI (because light travels with same speed throughout xtl)
Anisotropic minerals –light entering xtls is split and reoriented into two plane-polarized components that vibrate perpendicular to one another and travel with different speeds.
Uniaxial minerals have one special direction along which light is not reoriented; characterized by 2 RIs.
Biaxial minerals have two special directions along which light is not reoriented; characterized by 3 RIs.

3. 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)

4. Conclusions from calcite experiment
single light ray coming into cc is split into two rays
e ray is refracted - changes direction & speed
rays have different velocities, hence different RIs
stationary ray=ordinary, rotating ray=extraordinary
because refraction of e is so large, cc must have hi d (remember: d = nhi - nlo)
If we were to look straight down c-axis, we would see only one dot – no splitting!
C-axis is optic axis
(true for all uniaxial minerals, but unfortunately not for biaxial minerals)
More on this in a few minutes…

5. Birefringence/interference colors
Thickness in microns
Retardation in nanometers

6. Back to birefringence/interference colors
Observation: frequency of light remains unchanged during splitting, regardless of material
fast ray (low n) D
mineral grain
slow ray
(high n) d
F= V/l
if light speed changes, l must also change
plane polarized light
l is related to color; if l changes, color changes
waves from the two rays can be in phase or out of phase upon leaving the crystal
lower polarizer

7. Interference phenomena
When waves are in phase, all light gets killed
When waves are out of phase, some component of light gets through upper polarizer and the grain displays an interference color; color depends on retardation
When one of the vibration directions is parallel to the
lower polarizer, no light gets through
the upper polarizer and the grain is “at extinction” (=black)
See Nesse, p (3rd edition)

8. At time t, when slow ray 1st exits xtl:
Slow ray has traveled distance d
Fast ray has traveled distance d+D
Optional slide
D=retardation
time = distance/rate
fast ray (low n) D
mineral grain
slow ray
(high n) d
plane polarized light
D = thickness of t.s. x birefringence
lower polarizer

9. Uh oh... Let’s look at interference colors in a natural thin section:
Note that different grains of the same mineral show different interference colors – why?? ol
plag
Uh oh...
If every grain of the same mineral looks different, how are we ever going to be able to identify anything??
Different grains of same mineral are in different orientations

10. 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?

11. 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)

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

13. Uniaxial indicatrix calcite quartz
c-axis
c-axis
tangerine = uniaxial (-)
calcite
Spaghetti squash = uniaxial (+)
quartz
(this is not strictly correct, but works for our purposes…)

14. Uniaxial indicatrix nw ne nw
Circular section is perpendicular to the stem (c-axis)

15. Uniaxial indicatrix (biaxial ellipsoid)
What can the indicatrix tell us about optical properties of individual grains?

16. 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

17. Now propagate light perpendicular to c-axis
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 true d of the mineral
(highest interference colors)

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

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

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

21. … 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

22. 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

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

24. Determining if mineral is uniaxial or biaxial
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
Reminder about how to get an interference figure
Find a grain that stays dark as stage is rotated
Go to highest power objective
Insert Bertrand Lens
Look down scope and rotate stage

25. Use of interference figures, continued…
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

26. Determining optic sign with the gypsum plate - what happens?
slow
blue in NE = (+)
Optional slide
Gypsum plate has constant D of nm = 1st-order pink
Isogyres = black: D=0
Background = gray: D=150
Add to/subtract from 530 nm:
=680 nm = blue = (+)
=380 nm = yellowish = (-)
Addition = slow + slow
Subtraction = slow + fast

27. 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 or straight isogyre
determine sign w/ gypsum plate
(+)
(-)
determine 2V from curvature of isogyre
90°
60°
40°
See Nesse (p. 100, 3rd ed)

28. 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. 97, 3rd ed.)
Now do questions 1 and 2

29. Quick review of why we use indicatrix:
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.

30. Some new properties: Cleavage
Most easily observed in PPL (upper polarizer out), but visible in XN as well
No cleavages: quartz, olivine
1 good cleavage: micas
2 good cleavages: amphiboles, pyroxenes

31. Some new properties: Cleavage
2 cleavages intersecting
at ~90° pyroxene
60°
120°
2 cleavages intersecting
at 60°/120°: amphibole

32. Some new properties: Twinning
Presence and style of twinning can be diagnostic
Twins are usually most obvious in XN (upper polarizer in)

33. Twinning - some examples
Clinopyroxene (augite)
Simple twin on {100}
Plagioclase
Pericline twin on (h01)
Polysynthetic albite twins on (010)
Simple (Carlsbad) twin on (010)

34. Some new properties: Extinction angle
Extinction behavior is a function of the relationship between indicatrix orientation and crystallographic orientation
inclined extinction
parallel extinction

35. Extinction angle – parallel extinction
All uniaxial minerals show parallel extinction
Orthorhombic minerals show parallel extinction
(this is because xtl axes and indicatrix axes coincide)
orthopyroxene XN
PPL

36. Extinction angle - inclined extinction
Monoclinic and triclinic minerals: indicatrix axes do not coincide with crystallographic axes
These minerals have inclined extinction
(and extinction angle helps to identify them)
extinction angle
clinopyroxene
Now do questions 3 and 4

37. Review – techniques for identifying unknown minerals
Start in PPL:
Color/pleochroism
Relief
Cleavages
Habit
Then go to XN:
Birefringence
Twinning
Extinction angle
Uniaxial or biaxial?
2V if biaxial
Positive or negative?

38. Go to Nesse or similar book…
Chemical formula
Crystal system
Uni or biaxial, (+) or (-)
RIs: lengths of indicatrix axes
Birefringence
2V if biaxial
Diagrams:
Crystallographic axes
Indicatrix axes
Optic axes
Cleavages
Extinction angles

39. Another example Crystallographic axes: a, b, c
Optic axes
Indicatrix axes: X, Y, Z
Cleavages
Extinction angles
Then read text re color, pleochroism, habit, cleavage, twinning, distinguishing features, occurrence – make sure properties match your observations. If not, check another mineral…

40. On to real rocks…
…good luck and have fun!