Isotropic indicatrix Soccer ball or an orange Light travels the same distance in all directions n is same everywhere thus nhi nlo 0 black Uniaxial indicatrix biaxial ellipsoid c Z c Z n n b Y n a X n b Y What can the indicatrix tell us about optical properties of individual grains a X 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 n n n n Sample looking down OA sub stage condenser W n n n 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 30o 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 2V 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 OA Z 2Vz OA 2Vz n Y n n n n The potato X n n n n n n There are 2 different ways to cut this and get a circle Alas the potato indicatrix can have any orientation within a biaxial mineral Y c a Z Z olivine c augite b Y b X a X 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 2V a diagnostic property of biaxial minerals OA Z OA When 2V is acute about Z 2Vz When 2V is acute about X When 2V 90 sign is n Y n n indeterminate X 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 n substage condensor n n n n n n n 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 2V 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 Z grain with intermediate OA OA 2Vz n Y n n Use this figure to get sign and 2V 2V 20 2V 40 2V 60 X 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 OA Z OA hi 2Vz n n n Y OA Z X OA lo 2Vz n Y n n X Isotropic Uniaxial Biaxial Sign 2V 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 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 biaxial Diagrams Crystallographic axes Indicatrix axes Optic axes Cleavages Extinction angles