Optical Mineralogy in a Nutshell Use of the petrographic microscope in three easy lessons Part II © Jane Selverstone, University of New Mexico, 2003

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 w/ 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 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.

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)

Conclusions from calcite experiment single light ray coming into cc is split into two rays are refracted different amounts 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 star – 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…

Back to birefringence/interference colors Observation: frequency of light remains unchanged during splitting, regardless of material mineral grain plane polarized light fast ray (low n) slow ray (high n) lower polarizer D=retardation d F= V/l if light speed changes, l must also change l is related to color; if l changes, color also changes

Interference phenomena Light waves may be in phase or out of phase when they exit xtl When out of phase, some component of light gets through upper polarizer and displays an interference color 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. 41, 46-48…

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

Birefringence/interference colors Thickness in microns Retardation in nanometers

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

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

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?

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)

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

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

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

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

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

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

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

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

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

… 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

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

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

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

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 (+)

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.