Light ray overview Rays are split into 2 orthogonal rays (e and w) – these rays are slowed to different degrees (apparent birefringence, d related to the refractive index, n; d=ne-nw), and can go in different directions, resulting in a different length to get through a mineral (retardation, D, which is a function of both birefringence and thickness of the mineral)

When the rays exit the crystal they recombine Polarized light going into the crystal splits  into two rays, going at different velocities one is O-ray with n = w other is E-ray with n = e When the rays exit the crystal they recombine When rays of different wavelength combine  what things happen? e w polarizer

Michel-Lévy Color Chart – Plate 4.11

Example: Quartz w = 1.544 e = 1.553 w e 1.544 1.553 Data from Deer et al Rock Forming Minerals John Wiley & Sons

What interference color is this?

Color can be quantified numerically: d = nhigh - nlow Colors one observes when polars are crossed (XPL) Color can be quantified numerically: d = nhigh - nlow

Rotation of crystal? Retardation also affected by mineral orientation! As you rotate a crystal, observed birefringence colors change Find maximum interference color for each in practice

Extinction When you rotate the stage  extinction relative to the cleavage or principle direction of elongation is extinction angle Parallel, inclined, symmetric extinction Divided into 2 signs of elongation based on the use of an accessory plate made of gypsum or quartz (which has a retardation of 550 nm) which changes the color  for a grain at 45º from extinction look for yellow (fast) or blue (slow)

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 shape is defined by mapped light rays?

Isotropic indicatrix Light travels the same distance in all directions; n is same everywhere, thus d = nhi-nlo = 0 = black Soccer ball (or an orange)

Uniaxial indicatrix calcite quartz c-axis c-axis tangerine = uniaxial (-) calcite Spaghetti squash = uniaxial (+) quartz

Uniaxial indicatrix Circular section is perpendicular to the stem (c-axis)

Propagate light along the c-axis, note what happens to it in plane of thin section nw - nw = 0 therefore, d=0: grain stays black (same as the isotropic case) nw

This orientation will show the maximum d of the mineral Now propagate light perpendicular to c-axis N S W E ne - nw > 0 therefore, d > 0 ne nw ne nw ne nw ne nw ne nw Grain changes color upon rotation. Grain will go black whenever indicatrix axis is E-W or N-S This orientation will show the maximum d of the mineral

Biaxial indicatrix (triaxial ellipsoid) The potato! 2Vz There are 2 different ways to cut this and get a circle…

Alas, the potato (indicatrix) can have any orientation within a biaxial mineral… augite olivine

anisotropic minerals - biaxial indicatrix feldspar clinopyroxene Now things get a lot more complicated…

anisotropic minerals - uniaxial indicatrix c-axis Let’s perform the same thought experiment… c-axis calcite quartz

Uniaxial indicatrix (biaxial ellipsoid) What can the indicatrix tell us about optical properties of individual grains?

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 uniaxial 2V is measured using an interference figure… More in a few minutes

Conoscopic Viewing A condensing lens below the stage and a Bertrand lens above it Arrangement essentially folds planes ® cone 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 Fig 7-13 Bloss, Optical Crystallography, MSA

How interference figures work (uniaxial example) What do we see?? Bertrand lens nw ne N-S polarizer Sample (looking down OA) 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!! sub-stage condenser W E-W polarizer © Jane Selverstone, University of New Mexico, 2003

Uniaxial Interference Figure O E Uniaxial Interference Figure Circles of isochromes Black cross (isogyres) results from locus of extinction directions Center of cross (melatope) represents optic axis Approx 30o inclination of OA will put it at margin of field of view Fig. 7-14

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 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 Fig. 7-14

Optic Sign Find NE-SW quadrants of the field Slide the full wave (550nm) plate (aka gypusm plate) in This slows the ray aligned NE-SW relative to the retardation - if that ray is more retarded it turns blue (adds 550 nm of retardation)

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 -)

… 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 = na (lowest) Y direction = nb (intermed; radius of circ. section) Z direction = ng (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

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 grain with intermediate d. Use this figure to get sign and 2V: 2V=20° 2V=40° 2V=60° (+)

Isotropic? Uniaxial? Biaxial? Sign? 2V? 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 hi d lo d 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 (d) = N-n 2V if biaxial Diagrams: Crystallographic axes Indicatrix axes Optic axes Cleavages Extinction angles