Mineralogy 231Recitation 2: Uniaxial IndicatrixSept. 5, 2003Mineralogy 231Recitation 2: Uniaxial IndicatrixreadingsThurs., Sept. 11: biaxial indicatrix and optic sign: Chap. 7, Nesse, p. 133-136optional readings in Bloss, F.D. (1961) An Introduction to the Methods of Optical Crystallographypractical aspects of measuring RI(1) use parallel light source (medium magnification, medium illumination, “Kohler arrangement”)(2) to see Becke line, gently raise objective, in reality one is lowering the stagecounterclockwise motion of right focusing knob (clockwise motion of left knob)(3) view grain under uncrossed polars as stage is lowered(4) watch for movement of faint light line (Becke line) on margin of grain(5) estimate how close RI is to unknown by relief(6) choose next oil with this info in handAnisotropic Crystalsanisotropic crystals: those with variable velocity of light in different directions through crystaluniaxial mineralsplane with ordinary index, , normal to vector with extraordinary index, two possibilities:  < (positive), and  > (negative)birefringence defined as or = / - why defined in terms of absolute value?examplesquartz:  = 1.544, = 1.553,  = 0.009, positivecalcite:  = 1.658, = 1.486,  = 0.172, negativeas compared with biaxial mineralsthree orthogonal indices,  <  < , where  is “fast” (lowest RI) and is “slow” (highest RI)anisotropy of calciteillustrates splitting of incident light into two mutually  waves, one // c, the other  c Fig. 7.13optical effect is to see two dots, because one is refracted differently than the other Figs. 7.24, 7.26use polaroid paper to see that the rays of the two dots are mutually perpendicularretardationthe differential RI of the two  waves means that one is slower than the other Fig. 7.14consider only a plane-polarized light sourceif the grain is oriented so that one is looking down the c axis, velocity in both perpendicular directions isthe same, and the grain appears isotropic under crossed polarswhen the two  waves re-emerge from the crystal and recombine, the resolved wave is in general rotatedfrom the incoming polarized light waveif the second polar is inserted above the crystal (crossed polar condition), light still passes through toyour eye, and the grain looks “birefringent” Fig. 7.15the new resolved direction rotates as a function of the thickness of the crystal, going in and out ofextinction and with maximum light transmitted when it is  to the bottom polar Fig. 7.16use of polychromatic light is much more complicated because each  is different Fig. 7.17variable birefringence,  = / - / or ( - and orientation ontrol amount of effective rotationcolor seen for polychromatic light a mix of wavelengths near extinction and far from extinctionbirefringent colorsFig. at back of book shows color sequence w/ increasing retardation for white light Plate 1first order colors: black - grey - light yellow - redsecond order: violet - blue - green - yellow - orange - carmine redthird order: intense blue - intense green - yellow green - lighter pinkish redhigh order: cream colors, more or less uniform, called “high-order white” (>5 orders)easiest to count order using red bands onlyconsider a grain as an ideal lens: bands of colors seen correspond to color sequence on graphtotal effect is shown on colored retardation graphthickness vertical: in mm (to convert to microns or micrometers, m, multiply by 1000)standard thin section is 35 m (0.035 mm) thickin oils, grains are not of fixed thickness, so retardation colors may varyif grain has known orientation and , can calculate its thicknessmore useful to know thickness of a thin section and calculate the accessory plateretardation is 550 nm (first order red), “gypsum” plate (usually made of quartz), 1 plateorientation of plate is slow direction at +45° to NS (oriented NE-SW)allows one to tell which of two mutually perpendicular waves in crystal is slow, which is fast“slow on slow” gives increased retardation Fig. 7.20a“slow on fast” gives decreased retardation Fig. 7.20bactual procedure Fig. 7.21definition of optical indicatrix: a three dimensional shape with axes are proportional to the refractive indexin each direction through the crystalellipsoid with length of axis = RI in that directionisotropic indicatrix a sphere because RI or n is constant in all directions, any cross-section a circleuniaxial indicatrixthe uniaxial indicatrix is an ellipsoid with a circular cross-section,  perpendicular to unique axis, referred to as a biaxial ellipsoid in solid geometrythe c axis of hexagonal and tetragonal minerals is parallel to the unique axis of the ellipsoidif  < , the indicatrix is prolate; if > , the indicatrix is oblatecircular cross-section has constant velocity, orientation same as isotropic indicatrixa uniaxial grain in such an orientation appears to be isotropica random cross-section through the uniaxial indicatrix is an ellipse with one direction of  and the otherthat is ’  a crystal in any orientation can be used for measurement of the only cross-section through the indicatrix that contains  is normal to the circular cross-section any plane that contains c allows measurement of