Optical Mineralogy in a Nutshell Use of the

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 te ci l ca cal cite 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 D=retardation fast ray (low n) slow ray (high n) d mineral grain plane polarized light lower polarizer Observation: frequency of light remains unchanged during splitting, regardless of material 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…

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

Birefringence/interference colors Thickness in microns birefringence Retardation in nanometers

Remember determining optic sign last week with the gypsum plate? blue in NE = (+) Gypsum plate has constant D of 530 nm = 1 st-order pink w slo 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

Let’s look at interference colors in a natural thin section: plag ol Ifoleveryplag grain plag ol plag of the same mineral looks different, how are we ever going ol plag ol anything? ? to be able to identify ol plag Note that different grains of the same mineral show different interference colors – why? ? 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 Soccer ball (or an orange) Light travels the same distance in all directions; n is same everywhere, thus d = nhi-nlo = 0 = black

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

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

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 nw - n w = 0 therefore, d=0: grain stays black (same as the isotropic case)

Now propagate light perpendicular to c-axis ne - n w > 0 N therefore, d > 0 w nnee n wnw W nnw nw n E ne ne e S 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 clinopyroxene feldspar Now things get a lot more complicated…

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

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

… but there 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

2 V: a diagnostic property of biaxial minerals • When 2 V is acute about Z: (+) • When 2 V is acute about X: (-) • When 2 V=90°, sign is indeterminate • When 2 V=0°, mineral is uniaxial 2 V 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) n e substage condensor nw n ne w nw ne n w Effects of multiple cuts thru indicatrix 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 2 V 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 2 V: (+) 2 V=20° 2 V=40° 2 V=60° See Nesse p. 101

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? 2 V? All of these help us to uniquely identify unknown minerals.