Slide 1Uniaxial indicatrix (biaxial ellipsoid)Conoscopic ViewingSlide 4Uniaxial Interference FigureUniaxial FigureBiaxial Minerals – Optic AxesSlide 8Biaxial indicatrix (triaxial ellipsoid)Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Isotropic indicatrixSoccer ball(or an orange)Light travels the same distance in all directions;n is same everywhere, thus = nhi-nlo = 0 = blackUniaxial indicatrix(biaxial ellipsoid)nna=Xc=Zb=Yna=Xc=Znb=YWhat can the indicatrix tell us about optical properties of individual grains?Conoscopic ViewingConoscopic ViewingA condensing lencondensing lens below the stage and a Bertrand lensBertrand lens above itArrangement essentially folds planes  coneLight rays are refracted by condensing lens & pass through crystal in different directionsThus different propertiesOnly light in the center of field of view is vertical & like ortho Interference FiguresInterference Figures Very useful for determining optical properties of xlFig 7-13 Bloss, Optical Crystallography, MSAHow interference figures work (uniaxial example)How interference figures work (uniaxial example)BertrandlensSample(looking down OA)sub-stagecondenserW E-W polarizerN-S polarizerWhat do we see??What do we see??nnnnnnnn© Jane Selverstone, University of New Mexico, 2003Interference 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!!Uniaxial Interference Uniaxial Interference FigureFigureFig. 7-14Fig. 7-14O E•Circles of isochromesisochromes•Black cross (isogyresisogyres) results from locus of extinction directions•Center of cross (melatopemelatope) represents optic axis•Approx 30o inclination of OA will put it at margin of field of viewUniaxial FigureUniaxial Figure–CenteredCentered axis figure as 7-14: when rotate stage cross does notnot rotate–Off center:Off center: cross still E-W and N-S, but melatopemelatope 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 rotateFig. 7-14Fig. 7-14Biaxial 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 -)anisotropic minerals - biaxial indicatrixclinopyroxenefeldsparNow things get a lot more complicated…Biaxial indicatrix(triaxial ellipsoid)OAOA2VzYXZnnnnnnnnnnnThe potato!2VzThere are 2 different ways to cut this and get a circle…Alas, the potato (indicatrix) can have any orientation within a biaxial mineral…cabZXYYaZbXcolivineaugite… but there are a few generalizations that we can makeThe potato has 3 perpendicular principal axes of different length – thus, we need 3 different RIs to describe a biaxial mineralX 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 axesOAOA2VzYXZnnn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 uniaxial2V is measured using an interference figure… More in a few minutesHow interference figures work (uniaxial example)BertrandlensSample(looking down OA)substagecondensorConverging lenses force light rays to follow different paths through the indicatrixW EN-S polarizerWhat do we see??nnnnnnnnEffects of multiple cuts thru indicatrixBiaxial interference figuresThere are lots of types of biaxial figures… we’ll concentrate on only two1. Optic axis figure - pick a grain that stays dark on rotationWill see one curved isogyredetermine 2V from curvature of isogyre90° 60° 40°determine sign w/ gyps(+) (-)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 figuresUse this figure to get sign and 2V:(+)2V=20° 2V=40° 2V=60°OAOA2VzYXZnnn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 sectionOAOA2VzYXZnnnhi OAOA2VzYXZnnnlo Isotropic? Uniaxial? Biaxial? Sign? 2V?All of these help us to uniquely identify unknown minerals.Review – techniques for identifying unknown mineralsStart in PPL:• Color/pleochroism• Relief• Cleavages• HabitThen go to XPL:• Birefringence• Twinning• Extinction angleAnd Confocal lense:• Uniaxial or biaxial?• 2V if biaxial• Positive or negative?Go to your book…• Chemical formula• Symmetry• Uniaxial or biaxial, (+) or (-)• RIs: lengths of indicatrix axes• Birefringence () = N-n• 2V if biaxialDiagrams:* Crystallographic axes* Indicatrix axes* Optic axes* Cleavages* Extinction