1. Appearance of crystals in microscope
Crystal shape – how well defined the crystal shape is
Euhedral – sharp edges, well- defined crystal shape
Anhedral – rounded edges, poorly defined shape
Subhedral – in between anhedral and euhedral
Cleavage – just as in hand samples!
Physical character – often note evidence of strain, breaking, etching on crystals – you will notice some crystals show those features better than others…

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

3. Cleavage 120° 60° 2 cleavages intersecting at ~90° pyroxene
at 60°/120°: amphibole

4. Cleavage
random fractures, no cleavage:
olivine

5. Twinning
Presence and style of twinning can be diagnostic
Twins are usually most obvious in XPL (upper polarizer in)

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

7. Twinning and Extinction Angle
Twinning is characteristic in thin section for several common minerals – especially feldspars
The twins will go from light to dark over some angle
This is characteristic of the composition
Stage of the petrographic microscope is graduated in degrees with a vernier scale to measure the angle of extinction precisely

8. Extinction angle – parallel extinction
All uniaxial minerals show parallel extinction
Orthorhombic minerals show parallel extinction
(this is because the crystal axes and indicatrix axes coincide)
orthopyroxene
XPL
PPL

9. 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

10. Habit or form acicular anhedral/irregular bladed blocky elongate
euhedral
fibrous
prismatic
rounded
tabular

11. Habit or form acicular anhedral/irregular bladed blocky elongate
euhedral
fibrous
prismatic
rounded
tabular

13. Michel-Lévy Color Chart – Plate 4.11

18. What interference color is this?

19. So far, all of this has been orthoscopic (the normal way)
All light rays are ~ parallel and vertical as they pass through the crystal
xl has particular interference color = f(biref, t, orientation)
Points of equal thickness will have the same color
isochromes = lines connecting points of equal interference color
At thinner spots and toward edges will show a lower color
Count isochromes (inward from thin edge) to determine order
Orthoscopic viewing
Fig 7-11 Bloss, Optical Crystallography, MSA

20. 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?

21. 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)

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

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

24. Uniaxial indicatrix
Circular section is perpendicular to the stem (c-axis)

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

26. 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

27. 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

28. Conoscopic Viewing
A condensing lens below the stage and a Bertrand lens above it
Arrangement essentially folds planes ® cone
Light rays are refracted by condensing lens & pass through crystal in different directions
Thus different properties
Only light in the center of field of view is vertical & like ortho
® Interference Figures Very useful for determining optical properties of xl
Fig 7-13 Bloss, Optical Crystallography, MSA

29. How interference figures work (uniaxial example)
What do we see??
Bertrand
lens nw ne
N-S polarizer
Sample
(looking down OA)
Interference figure provides a zoomed ‘picture’ of the optic axes and the areas around that which have rays which are split and refracted – must be gathered in line with optic axis!!
sub-stage
condenser W
E-W polarizer
© Jane Selverstone, University of New Mexico, 2003

30. Uniaxial Interference Figure
O E
Uniaxial Interference Figure
Circles of isochromes
Black cross (isogyres) results from locus of extinction directions
Center of cross (melatope) represents optic axis
Approx 30o inclination of OA will put it at margin of field of view
Fig. 7-14

31. Uniaxial Figure
Centered axis figure as 7-14: when rotate stage cross does not rotate
Off center: cross still E-W and N-S, but melatope rotates around center
Melatope outside field: bars sweep through, but always N-S or E-W at center
Flash Figure: OA in plane of stage Diffuse black fills field brief time as rotate
Fig. 7-14

32. Biaxial Minerals – Optic Axes
Biaxial Minerals have 2 optic axes
Recall that biaxial minerals are of lower symmetry crystal classes (orthorhombic, monoclinic, and triclinic)
The plane containing the 2 optic axes is the optic plane  looking down either results in extinction in XPL-no retardation, birefringence
The acute angle between the 2 different optic axes is the 2V angle  how this angle relates to the velocities of refracted rays in the crystal determines the sign (+ or -)

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

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

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

36. … 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

37. 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

38. 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

39. 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°

40. 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°
(+)

41. 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.

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

43. Go to your book… Chemical formula Symmetry
Uniaxial or biaxial, (+) or (-)
RIs: lengths of indicatrix axes
Birefringence (d) = N-n
2V if biaxial
Diagrams:
Crystallographic axes
Indicatrix axes
Optic axes
Cleavages
Extinction angles