Appearance of crystals in microscope Crystal shape how

Appearance of crystals in microscope • Crystal shape – how well defined the crystal shape is – Euhedral – sharp edges, well- defined crystal shape – Anhedral – rounded edges, poorly defined shape – Subhedral – in between anhedral and euhedral • Cleavage – just as in hand samples! • Physical character – often note evidence of strain, breaking, etching on crystals – you will notice some crystals show those features better than others…

Cleavage Most easily observed in PPL (upper polarizer out), but visible in XPL as well • No cleavages: quartz, olivine • 1 good cleavage: micas • 2 good cleavages: pyroxenes, amphiboles

Cleavage 2 cleavages intersecting at ~90° pyroxene 2 cleavages intersecting at 60°/120°: amphibole 120° 60°

Cleavage random fractures, no cleavage: olivine

Twinning Presence and style of twinning can be diagnostic Twins are usually most obvious in XPL (upper polarizer in)

Twinning - some examples Clinopyroxene (augite) • Simple twin on {100} Plagioclase • Simple (Carlsbad) twin on (010) • Polysynthetic albite twins on (010) • Pericline twin on (h 01)

Twinning and Extinction Angle • Twinning is characteristic in thin section for several common minerals – especially feldspars • The twins will go from light to dark over some angle • This is characteristic of the composition • Stage of the petrographic microscope is graduated in degrees with a vernier scale to measure the angle of extinction precisely

Extinction angle – parallel extinction • All uniaxial minerals show parallel extinction • Orthorhombic minerals show parallel extinction (this is because the crystal axes and indicatrix axes coincide) orthopyroxene PPL XPL

Extinction angle - inclined extinction Monoclinic and triclinic minerals: indicatrix axes do not coincide with crystallographic axes These minerals have inclined extinction (and extinction angle helps to identify them) extinction angle clinopyroxene

Habit or form acicular anhedral/irregular bladed blocky elongate euhedral fibrous prismatic rounded tabular

Habit or form acicular anhedral/irregular bladed blocky elongate euhedral fibrous prismatic rounded tabular

Michel-Lévy Color Chart – Plate 4. 11

What interference color is this?

So far, all of this has been orthoscopic (the normal way) All light rays are ~ parallel and vertical as they pass through the crystal Orthoscopic viewing Fig 7 -11 Bloss, Optical Crystallography, MSA • xl has particular interference color = f(biref, t, orientation) • Points of equal thickness will have the same color • isochromes = lines connecting points of equal interference color • At thinner spots and toward edges will show a lower color • Count isochromes (inward from thin edge) to determine order

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

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

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

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

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

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

Now propagate light perpendicular to c-axis ne - n w > 0 N therefore, d > 0 w nnee n wnw W nnw nw n E ne ne 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 d of the mineral

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 e (looking down OA) W n ne w nw Sample sub-stage condenser nw ne n w 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 30 o 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 2 V 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) 2 Vz The potato! There are 2 different ways to cut this and get a circle…

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

… but there 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

2 V: a diagnostic property of biaxial minerals • When 2 V is acute about Z: (+) • When 2 V is acute about X: (-) • When 2 V=90°, sign is indeterminate • When 2 V=0°, mineral is uniaxial 2 V 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 e substage condensor nw n ne w nw ne n w 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 2 V 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 2 V: (+) 2 V=20° 2 V=40° 2 V=60°

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? 2 V? 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? • 2 V 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 2 V if biaxial Diagrams: * Crystallographic axes * Indicatrix axes * Optic axes * Cleavages * Extinction angles