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Optical Mineralogy Interference Figures 1. Uniaxial Figures Optical Indicatrix and Interference Figures: LAB TS-3: Uniaxial minerals Interference figures Optic sign Pleochroic scheme LAB TS-4: Biaxial minerals Interference figures Optic sign Pleochroic scheme Optical Indicatrix and Interference Figures: 1. Optical Indicatrix 2. Uniaxial Interference Figures 3. Biaxial Interference Figures Polarisation in the petrographic microscope upper polarising filter (analyser) what happens here??? sensitive tint plate LAB TS-2 what happens mineral sample (thin section) here??? conoscopic light what happens here??? LAB TS-1 LAB TS-3,4 condenser lens plane polarised light (PPL) lower polarising filter (polariser) unpolarised light light source Optical Indicatrix constructed as a sphere or ellipsoid with radii parallel to the principal vibration directions and lengths of axes proportional to refractive index in 2D: nmax (slow) nmin = nmax circle: isotropic nmin nmin (fast) nmin < nmax ellipse: anisotropic nmax in 3D: indicatrix for isotropic mineral is a sphere (of no further interest) indicatrix for anisotropic mineral is an ellipsoid 2 cases: uniaxial and biaxial Case 1: Uniaxial minerals (hexagonal, tetragonal: a1 = a2 = c) principal axes: ne // c nw // a e: “extraordinary” ray w: “ordinary” ray X=Y<Z X<Y=Z Nesse, 2000; Fig. 7.23 X-Y plane: circular section (all planes perpendicular to Z) Z = optic axis (c-axis = slow) Y-Z plane: circular section (all planes perpendicular to X) X = optic axis (c-axis = fast) ne > nw +ve ne < nw -ve Case 1: Uniaxial minerals (hexagonal, tetragonal: a1 = a2 = c) principal axes: ne // c nw // a e: “extraordinary” ray w: “ordinary” ray optic axis // plane of section plane of section contains optic axis I plane of section both nw and ne : plane of section contains maximum d only nw : minimum d (extinct!) random section: contains nw and ne’ < ne intermediate d Nesse, 2000; Fig. 7.25 Optic Sign how do we figure this out??? Case 1: Uniaxial minerals: Case 2: Biaxial minerals: Z = optic axis (c-axis = slow) ne > nw +ve + ve where Bxa // Z -ve where Bxa // X X = optic axis (c-axis = fast) ne < nw -ve c = OA = Z Z Z +ve -ve c = OA = X a +ve X a -ve X Optic Sign how do we figure this out??? Requires: conoscopic light (condenser lens in place) interference figures (viewed with Bertrand lens) use of STP to determine fast and slow directions Nesse, Ch. 7, p. 139 -143 (uniaxial) p. 143 - 151 (biaxial) Extinction Angles: where optic axis is normal to plane of thin section mineral will appear extinct for full stage rotation! applies to both uniaxial and biaxial minerals how distinguished from isotropic minerals? (also requires interference figures: stay tuned.....) Optical Indicatrix and Symmetry isometric system: a1 = a2 = a3; all angles = 90o indicatrix is a sphere; minerals extinct in XN hexagonal, trigonal, tetragonal systems: a1 = a2 (= a3) = c all angles either 90o or 120o uniaxial: indicatrix is ellipsoid; X < Y < Z c-axis = optic axis = e (either X or Z) parallel extinction orthorhombic system: a = b = c; all angles = 90o biaxial: indicatrix is ellipsoid; X < Y < Z X, Y, Z // crystallographic axes 2 circular sections I 2 optic axes parallel extinction 2. Uniaxial Interference Figures (Nesse Ch. 7 p. 139-143) optic axis = c crystallographic axis ne // c; nw // a e can be either fast or slow Interference Figures require conoscopic light result: interference figure Bertrand lens (on eyepiece tube) rays focused through centre of sample: concentric interference rings when viewed through Bertrand lens condenser lens (sub-stage) Nesse Fig. 7.36 Interference Figures uniaxial optic axis figure result: interference figure isochrome OA melatope isogyre number of rings (isochromes) birefringence OA sample oriented with optic axis normal to plane of section (in XN, grain appears extinct through 360o rotation) Nesse Fig. 7.36 Interference Figures uniaxial optic axis figure isochrome what it really looks like: melatope isochromes melatope isogyre isogyre number of rings (isochromes) birefringence sample oriented with optic axis normal to plane of section (in Xn, grain appears extinct through 360o rotation) cross-hairs optic axis figure (OAF) for high d mineral (e.g., calcite) Interference Figures uniaxial optic axis figure isochrome melatope isogyre number of rings (isochromes) birefringence sample oriented with optic axis normal to plane of section (in XN, grain appears extinct through 360o rotation) w e Nesse Fig. 7.35 e oriented radially w oriented tangentially insert tint plate! Interference Figures: Determining Optic Sign uniaxial optic axis figure w e if e slow: mineral is +ve if e fast: mineral is -ve observe colour change in SE-NW quadrants ? ? Nesse Fig. 7.40 Interference Figures: Determining Optic Sign down uniaxial optic axis figure down colours go down (subtraction) w = fast e = slow + ve w e if e slow: mineral is +ve if e fast: mineral is -ve up up - ve colours go up (addition) w = slow e = fast Interference Colour Chart low d optic axis figure addition: grey blue 30 mm subtraction: grey yellow what do addition and subtraction look like? Interference Colour Chart low d optic axis figure addition: grey blue high d optic axis figure addition: 2nd order red 3rd order red 30 mm subtraction: grey yellow subtraction: 2nd order red 1st order red what do addition and subtraction look like? colours go down (subtraction) w = fast e = slow Interference Figures: Determining Optic Sign uniaxial optic axis figure Y + ve colours go up (addition) w = slow e = fast Y SE-NW quadrant: if colours go from grey-white to yellow (subtraction; “down”) mineral is +ve (YAY!) - ve colours go down (subtraction) w = fast e = slow Interference Figures: Determining Optic Sign uniaxial optic axis figure B + ve colours go up (addition) w = slow e = fast B SE-NW quadrant: if colours go from grey-white to blue (addition; “up”) mineral is -ve (BOO!) - ve colours go down (subtraction) w = fast e = slow Interference Figures: Determining Optic Sign high d mineral (many isochromes) no tint plate + ve colours go up (addition) w = slow e = fast low order colours (grey-white) near centre of figure - ve colours go down (subtraction) w = fast e = slow Interference Figures: Determining Optic Sign high d mineral (many isochromes) no tint plate + ve colours go up (addition) w = slow e = fast tint plate in + (rings move in) (rings move out) - ve colours go down (subtraction) w = fast e = slow Interference Figures: Determining Optic Sign high d mineral (many isochromes) no tint plate + ve colours go up (addition) w = slow e = fast tint plate in + (rings move in) (rings move out) mineral is uniaxial -ve - ve Interference Figures Practical problem(s): 1. How to find a grain with optic axis normal to plane of thin section? 2. What if you can’t find a suitably oriented grain? Interference Figures Practical problem(s): 1. How to find a grain with optic axis normal to plane of thin section? look for grain that is extinct for full rotation of stage (opaque? isotropic? hole in slide? optic axis grain?) 2. What if you can’t find a suitably oriented grain? Interference Figures Practical problem(s): 1. How to find a grain with optic axis normal to plane of thin section? look for grain that is extinct for full rotation of stage (opaque? isotropic? hole in slide? optic axis grain?) 2. What if you can’t find a suitably oriented grain? look for low d grain with minimum change during rotation “off-centre” figure: not ideal, but may be best possible in your section Interference Figures “off-centre” uniaxial figure: obtained from low d grain with minimum colour change during rotation not ideal, but may be best possible in your section slightly off-centre (melatope visible) OK to use way off-centre (melatope not visible) best avoided Nesse Fig. 7.38 Interference Figures Flash Figures: both e and w in plane of section (maximum d) useless for determining optic sign field of view light dark very quickly as stage rotated very similar for both uniaxial and biaxial Nesse Fig. 7.39 Uniaxial Minerals: Pleochroic Scheme Nesse, 2000; Fig. 7.30 1. In PPL, find grain with minimum colour change as stage rotated (w in plane of section); observed colour = w (= a) 2. In PPL, find grain with maximum colour change as stage rotated (both w and e in plane of section); w colour already determined other colour = e (= c) 3. Can also be determined by finding fast and slow rays + optic sign Optic Sign: Summary Case 1: Uniaxial minerals: Case 2: Biaxial minerals: Z = optic axis (c-axis = slow) ne > nw +ve + ve where Bxa // Z -ve where Bxa // X X = optic axis (c-axis = fast) ne < nw -ve Z c = OA = Z Z c = OA = X a +ve X a +ve Bxa -ve X -ve Bxa determined from OA figure determined from Bxa or OA figure