1. Optical Mineralogy in a Nutshell Use of the petrographic microscope in three easy lessons Part II © 2003 Prof. Jane Selverstone Used and modified with permission

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. Anisotropic minerals –light entering xtls is split and reoriented into two plane-polarized components that vibrate perpendicular to one another and travel w/ 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. These minerals are characterized by a single RI (because light travels w/ same speed throughout xtl)

3. Determining if mineral is uniaxial or biaxial Uniaxial If Uniaxial, isogyres define a cross; arms remain N-S/E-W as stage is rotated Biaxial or If Biaxial, isogyres define a curve that rotates with stage, or cross that breaks up as stage is rotated Reminder about how to get an interference figure 1.Find a grain that stays dark as stage is rotated 2.Go to highest power objective 3.Swing the condenser in and open the diaphragm iris 4.Insert the Bertrand Lens (if present) or remove the eyepiece. 5.Look down the scope and then rotate stage

4. Determining optic sign Now determine the optic sign of the mineral: 1.Rotate stage until isogyre is concave to NE (if biaxial) 2.Insert gypsum accessory plate 3.Note color in NE, immediately adjacent to isogyre --  Blue = (+)  Yellow = (-) Uniaxial Biaxial (+) (-)

5. We’ve talked about minerals splitting light - here’s what it looks like. calcite ordinary ray,  (stays stationary) extraordinary ray,  (rotates)

6. single light ray coming into cc is split into two  ray is refracted - changes direction & speed rays have different velocities, hence different RIs stationary ray=ordinary, rotating ray=extraordinary because refraction of  is so large, Calcite must have hi   remember:  = n hi - n lo  Conclusions from calcite experiment If we were to look straight down c-axis, we would see only one dot – no splitting! The c-axis is the optic axis for Calcite (true for all Uniaxial minerals, but unfortunately not for Biaxial minerals)

7. Birefringence/interference colors Retardation in nanometers Thickness in microns birefringence

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

9. 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 Interference phenomena lower polarizer, no light gets through the upper polarizer and the grain is “at extinction” (=black)

10. mineral grain plane polarized light fast ray (low n) slow ray (high n) lower polarizer  =retardation d At time t, when slow ray 1 st exits xtl: Slow ray has traveled distance d Fast ray has traveled distance d+  time = distance/rate Slow ray: t = d/V slow Fast ray: t= d/V fast +  /V air Therefore: d/V slow = d/V fast +  /V air  = d(V air /V slow - V air /V fast )  = d(n slow - n fast )  = d   = thickness of t.s. x birefringence

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

12. 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 Different grains of same mineral are in different orientations

13. Time for another concept: 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?

14. 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

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

16. Uniaxial indicatrix c-axis Spaghetti squash = Uniaxial (+) tangerine = Uniaxial (-) quartz calcite The shapes reflect the relative sizes of indices of refraction

17. Circular section is perpendicular to the stem (c-axis) Uniaxial indicatrix nn nn nn nn

18. Uniaxial Indicatrix What can the indicatrix tell us about optical properties of individual grains? Uniaxial (+) Uniaxial (-)

19. 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

20. 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

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

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

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

24. … 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

25. 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

26. 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? Effects of multiple cuts thru indicatrix        

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 isogyre determine 2V from curvature of isogyre 90°60°40° See Nesse or handout determine sign w/ gypsum plate (+)(-)

28. 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° See handout/Nesse

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  lo  Isotropic? Uniaxial? Biaxial? Sign? 2V? All of these help us to uniquely identify unknown minerals.