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 2 cleavages intersecting at ~90° pyroxene 60° 120° 2 cleavages intersecting 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) Plagioclase Simple twin on {100} Simple (Carlsbad) twin on (010) Pericline twin on (h01) Polysynthetic albite twins 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) PPL XPL orthopyroxene

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) clinopyroxene extinction angle

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

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

13. Michel-Lévy Color Chart – Plate 4.11

18. What interference color is this?

19. orthoscopic So far, all of this has been orthoscopic (the normal way) All light rays are ~ parallel and vertical as they pass through the crystal Orthoscopic viewing Fig 7-11 Bloss, Optical Crystallography, MSA xl has particular interference color = f(biref, t, orientation) Points of equal thickness will have the same color isochromesisochromes = 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

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 Soccer ball (or an orange) Light travels the same distance in all directions; n is same everywhere, thus  = n hi -n lo = 0 = black

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

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

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

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

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

27. Grain changes color upon rotation. Grain will go black whenever indicatrix axis is E-W or N-S nn nn This orientation will show the maximum  of the mineral nn nn nn nn nn nn nn nn n  - n  > 0 therefore,  > 0 N S WE Now propagate light perpendicular to c-axis

28. Conoscopic Viewing condensing len Bertrand lens 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  Interference Figures Very useful for determining optical properties of xl Fig 7-13 Bloss, Optical Crystallography, MSA

29. How interference figures work (uniaxial example) Bertrand lens Sample (looking down OA) sub-stage condenser WE-W polarizer N-S polarizer What do we see?? nn nn nn nn nn nn nn nn © Jane Selverstone, University of New Mexico, 2003 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!!

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

31. Uniaxial Figure –Centered not –Centered axis figure as 7-14: when rotate stage cross does not rotate –Off center: melatope –Off center: cross still E-W and N-S, but melatope rotates around center –Melatope outside field: –Melatope outside field: bars sweep through, but always N-S or E-W at center –Flash Figure: –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 clinopyroxene feldspar Now things get a lot more complicated…

34. Biaxial indicatrix (triaxial ellipsoid) The potato! 2V z 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… olivine augite

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 = n  (lowest) Y direction = n  (intermed; radius of circ. section) Z direction = n  (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) Bertrand lens Sample (looking down OA) substage condensor Converging lenses force light rays to follow different paths through the indicatrix WE N-S polarizer What do we see?? nn nn nn nn nn nn nn nn Effects of multiple cuts thru indicatrix

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 2V from curvature of isogyre 90°60°40° determine sign w/ gyps (+)(-)

40. 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 . Biaxial interference figures Use this figure to get sign and 2V: (+) 2V=20°2V=40°2V=60°

41. 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  lo  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 (  ) = N-n 2V if biaxial Diagrams: * Crystallographic axes * Indicatrix axes * Optic axes * Cleavages * Extinction angles