Optical Mineralogy in a Nutshell Use of the petrographic microscope in three easy lessons Part III Slides borrowed/adapted from Jane Selverstone (University of New Mexico) and John W inter (W hitman College) Some review… Optical mineral properties ONLY visible in PPL: Color – not an interference color! (for that, see below) Pleochroism – is there a color change while rotating stage? Relief – low, intermediate, high, very high? Optical mineral properties visible in PPL or XPL: Cleavage – number and orientation of cleavage planes (may need higher magnification and at different grains) Habit – characteristic form of mineral (sometimes better in XPL) Optical mineral properties ONLY visible in XPL: Birefringence – use highest order interference color to describe Twinning – type of twinning, orientation Extinction angle – parallel or inclined? Angle? Isotropic vs anisotropic minerals – 100% extinct in XPL? Today we’ll break down anisotropic minerals into uniaxial or biaxial… Some generalizations and vocabulary • All isometric minerals (e.g., garnet) and glass are isotropic – they cannot reorient light These minerals are always black in crossed polars • All other minerals are anisotropic – they are all capable of reorienting light • All anisotropic minerals contain one or two special directions (the “optic axes”) that not reorient light – Minerals with one special direction are called uniaxial – Minerals with two special directions are called biaxial • Uniaxial and biaxial minerals can be subdivided into optically positive and optically negative, depending on the orientation of fast and slow rays relative to the xtl axes All anisotropic minerals can resolve light into two plane polarized components that travel at different velocities and vibrate in planes that are perpendicular to one another Some light is now able to pass through the upper polarizer fast ray slow ray mineral grain plane polarized light W E lower polarizer When light gets split: -velocity changes -rays get bent (refracted) -2 new vibration directions -usually see new colors Calcite experiment and double refraction O E Fig 6-8 Bloss, Optical Crystallography, MSA Fig 6-7 Bloss, Optical Crystallography, MSA We’ve talked about minerals as magicians now let’s prove it! calcite ca lc it e ca l calcite cit e calcite ordinary ray, ω (stays stationary) extraordinary ray, ε (rotates) How light behaves depends on crystal structure (there is a reason you took mineralogy!) Isotropic Isometric – All crystallographic axes are equal Uniaxial Hexagonal, trigonal, tetragonal – All axes ⊥ c are equal but c is unique Biaxial Orthorhombic, monoclinic, triclinic – All axes are unequal Let’s use all of this information to help us identify minerals Simple guide to interference figures • Get a good interference figure; • Distinguish uniaxial and biaxial figures; • Determine optic sign; and • Estimate 2V 1) Choose a grain showing the lowest interference colors 2) Move to the high-powered objective lens and refocus 3) Open the sub-stage diaphragm as wide as possible 4) Insert the condenser lens 5) Cross the polars 6) Insert the Bertrand lens Use of interference figures, continued… You will see a very small, circular field of view with one or more black isogyres rotate stage and watch isogyre(s) or uniaxial If uniaxial, isogyres define cross; arms remain N-S/E-W as stage is rotated biaxial If biaxial, isogyres define curve that rotates with stage, or cross that breaks up as stage is rotated Use of interference figures, continued… Now determine the optic sign of the mineral: Rotate stage until isogyre is concave to NE (if biaxial) Insert gypsum accessory plate Note color in NE, immediately adjacent to isogyre - Blue = (+)  Yellow = (-) uniaxial (+) (+) biaxial Without plate Gypsum plate inserted anisotropic minerals - uniaxial indicatrix c-axis c-axis calcite quartz Let’s perform the same thought experiment… Uniaxial indicatrix c-axis c-axis tangerine = uniaxial (-) Spaghetti squash = uniaxial (+) quartz calcite Uniaxial ellipsoid and conventions: Fig 6-11 Bloss, Optical Crystallography, MSA (-) crystal: ω>ε → oblate (+) crystal: ε>ω → prolate Propagate light along the c-axis, note what happens to it in plane of thin section nω χ=Ζ nω nε νω β=Ψ α=Ξ nω - nω = therefore, δ=0: grain stays black (same as the isotropic case) Now propagate light perpendicular to c-axis nε - nω > N therefore, δ > ω nnε ε n ωnω W nnω nω n nε nε ε 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 δ of the mineral anisotropic minerals - biaxial indicatrix clinopyroxene feldspar Now things get a lot more complicated… Biaxial indicatrix (triaxial ellipsoid) OA Z 2Vz OA 2Vz νγ Y nβ νβ να nβ The potato! X nγ nγ να νβ nα νβ There are 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 perpendicular principal axes of different length – thus, we need different RIs to describe a biaxial mineral X direction = nα (lowest) Y direction = nβ (intermed; radius of circ section) Z direction = nγ (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 indeterminate νγ • When 2V=0°, mineral is uniaxial Y nβ να X 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 we see?? Sample (looking down OA) n ε substage condensor nω n nε ω nω nε n ε n ω 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 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° See Nesse p 103 (-) Estimating 2V OAP Fig 11-5A Bloss, Optical Crystallography, MSA Biaxial interference figures 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 Z intermediate δ OA OA 2Vz νγ Y nβ να X Use this figure to get sign and 2V: (+) 2V=20° 2V=40° 2V=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 OA Z OA hi δ 2Vz νγ να nβ Y OA Z X OA lo δ 2Vz νγ Y nβ να X Isotropic? Uniaxial? Biaxial? Sign? 2V? All of these help us to uniquely identify unknown minerals [...]... will show the maximum δ of the mineral anisotropic minerals - biaxial indicatrix clinopyroxene feldspar Now things get a lot more complicated… Biaxial indicatrix (triaxial ellipsoid) OA Z 2Vz OA 2Vz νγ Y nβ νβ να nβ The potato! X nγ nγ να νβ nα νβ 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... directions; n is same everywhere, thus δ = nhi-nlo = 0 = black anisotropic minerals - uniaxial indicatrix c-axis c-axis calcite quartz Let’s perform the same thought experiment… Uniaxial indicatrix c-axis c-axis tangerine = uniaxial (-) Spaghetti squash = uniaxial (+) quartz calcite Uniaxial ellipsoid and conventions: Fig 6-11 Bloss, Optical Crystallography, MSA (-) crystal: ω>ε → oblate (+) crystal: ε>ω... ∆=100 Add or subtract 530 nm: 530+100=630 nm = blue = (+) 530-100=430 nm = yellowish = (-) Addition = slow + slow Subtraction = slow + fast 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... need 3 different RIs to describe a biaxial mineral X direction = nα (lowest) Y direction = nβ (intermed; radius of circ section) Z direction = nγ (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:... OAP Fig 11-5A Bloss, Optical Crystallography, MSA 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 Z intermediate δ OA OA 2Vz νγ Y nβ να X Use this figure to get sign and 2V: (+) 2V=20° 2V=40° 2V=60° See Nesse p 101 Quick review: Indicatrix gives us a way to relate optical phenomena to... to relate optical phenomena to crystallographic orientation, and to explain differences between grains of the same mineral in thin section OA Z OA hi δ 2Vz νγ να nβ Y OA Z X OA lo δ 2Vz νγ Y nβ να X Isotropic? Uniaxial? Biaxial? Sign? 2V? All of these help us to uniquely identify unknown minerals ... 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 indeterminate νγ • When 2V=0°, mineral is uniaxial Y nβ να X 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