Isotropic indicatrix Soccer ball or an orange Light

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

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

Conoscopic Viewing A condensing lens len below the stage and a Bertrand lens above it Arrangement essentially folds planes ® cone Fig 7 -13 Bloss, Optical Crystallography, MSA 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

How interference figures work (uniaxial example) What do we see? ? Bertrand lens n N-S polarizer e (looking down OA) W n ne w nw Sample sub-stage condenser nw ne n w 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!! E-W polarizer © Jane Selverstone, University of New Mexico, 2003

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

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 Fig. 7 -14 – 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

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 2 V angle how this angle relates to the velocities of refracted rays in the crystal determines the sign (+ or -)

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° (-)

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°

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.

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? • 2 V if biaxial • Positive or negative?

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