Optical MineralogyOptical MineralogyUse of the petrographic microscope John Winter, Whitman College with some slides Jane Selverstone, University of New Mexico, 2003

Why use the microscope??Identify minerals (no guessing!)Determine rock typeDetermine crystallization sequenceDocument deformation historyObserve frozen-in reactionsConstrain P-T historyNote weathering/alteration Jane Selverstone, University of New Mexico, 2003

The petrographic microscopeAlso called a polarizing microscopeIn order to use the scope, we need to understand a little about the physics of light, and then learn some tools and tricks Jane Selverstone, University of New Mexico, 2003

What happens as light moves through the scope?Frequency = # of waves/sec to pass a given point (hz)f = v/l v = velocity(in physics v = c, but no longer) Jane Selverstone, University of New Mexico, 2003

Electromagnetic spectrum & visible portionViolet (400 nm) Red (700 nm)White = ROYGBV

(can be separated by dispersion in a prism)

RefractionIncident ray and reflected ray:1) of incidence i = of reflection r'2) coplanar plane of incidence(^ plane of interface)

Refracted ray: 1) Slower in water (or glass) 2) r iDepends on D velocityIncidentReflectedairRefractedwaterirr

For a substance x:nx = vair/vxnair = ?? light is slower in water, glass, crystalsIs nwater greater or less than 1??Larger n associated with slower V !!Snells Law: ni sin i = nr sin rfor 2 known media (air/water) sin i/sin r = nr / ni = constSo can predict angle change (or use to determine nr)Index of refraction

Light beam = numerous photons, each vibrating in a different planeVibration in all directions ~ perpendicular to propagation directionvibration directionspropagation directionWhat happens as light moves through the scope?Polarized LightUnpolarized LightEach photon vibrates as a wave form in a single planeLight beam = numerous photons, all vibrating in the same planeplanes of vibration

1) Light passes through the lower polarizerUnpolarized light Jane Selverstone, University of New Mexico, 2003

2) Insert the upper polarizerwest (left)east (right)Now what happens?What reaches your eye?Why would anyone design a microscope that prevents light from reaching your eye???XPL=crossed nicols (crossed polars) Jane Selverstone, University of New Mexico, 2003

The Optical IndicatrixShows how ni varies with vibration direction.Vectors radiating from centerLength of each proportional to ni for light vibrating in the direction of the vectorIndicatrix = surface connecting tips of vectors (a representational construct only!)Isotropic media have all ni the same (by definition)What is the shape of an isotropic indicatrix? Amorphous materials or isometric crystals are (optically) isotropic with a spherical indicatrix

The Isotropic IndicatrixA section through the center of an indicatrix all n for light propagating ^ the sectionConventions:1) Indicatrix w/ center on interface surface2) n (radial vectors of circular section in this case) same in all possible vibration directionsIncoming light can (and will) vibrate in the same direction(s) it did prior to entryIf unpolarized, it will remain so.Only effect is slower velocity (rep. by closer symbol spacing)

Liquids, gases, amorphous solids such as glass, and isotropic minerals (isometric crystal system) stay black in all orientationsReview: With any isotropic substance (spherical indicatrix), when the analyzer is inserted (= crossed-nicols or XPL) no light passes extinct, even when the stage is rotatedNote: the gray field should also be extinct (glass and epoxy of the thin section are also isotropic), but is left lighter for illustration

Mineral properties in PPL: relief Relief is a measure of the relative difference in n between a mineral grain and its surroundings Relief is determined visually, in PPL Relief is used to estimate ngarnet:n = 1.72-1.89quartz:n = 1.54-1.55epoxy:n = 1.54Quartz has low reliefGarnet has high relief

Mineral properties in PPL: relief Relief is a measure of the relative difference in n between a mineral grain and its surroundings Relief is determined visually, in PPL Relief is used to estimate n Jane Selverstone, University of New Mexico, 2003

What causes relief?Difference in speed of light (n) in different materials causes refraction of light rays, which can lead to focusing or defocusing of grain edges relative to their surroundings Jane Selverstone, University of New Mexico, 2003

Now insert a thin section of a rock in XPLwest (left)east (right)Light vibrating E-WHow does this work??Unpolarized lightnorthsouth Jane Selverstone, University of New Mexico, 2003

Conclusion has to be that minerals somehow reorient the planes in which light is vibrating; some light passes through the upper polarizerBut, note that some minerals are better magicians than others (i.e., some grains stay dark and thus cant be reorienting light)olivineplagPPLXPL

Anisotropic crystalsCalcite experiment and double refractionFig 6-7 Bloss, Optical Crystallography, MSAO-ray (Ordinary) Obeys Snell's Law and goes straightVibrates ^ plane containing ray and c-axis (optic axis)E-ray (Extraordinary)deflectedVibrates in plane containing ray and c-axis..also doesn't vibrate ^ propagation, but we'll ignore this as we said earlier

Both rays vibrate parallel to the incident surface for normal incident light, so the interface x-section of the indicatrix is still valid, even for the E-rayThus our simplification of vibration ^ propagation works well enoughFrom now on we'll treat these two rays as collinear, but not interacting, because it's the vibration direction that countsFig 6-7 Bloss, Optical Crystallography, MSAIMPORTANT: A given ray of incoming light is restricted to only 2 (mutually perpendicular) vibration directions once it enters an anisotropic crystalCalled privileged directionsEach ray has a different nw = noe = nE in the case of calcite w < e which makes the O-ray dot appear above E-ray dot

Some generalizations and vocabularyAmorphous materials and isometric minerals (e.g., garnet) are isotropic they cannot reorient light. These minerals are always extinct in crossed polars (XPL).All other minerals are anisotropic they are all capable of reorienting light (acting as magicians).All anisotropic minerals contain one or two special propagation directions that do not reorient light.Minerals with one special direction are called uniaxialMinerals with two special directions are called biaxial Jane Selverstone, University of New Mexico, 2003

n > 1 for anisotropic substancesn = f(vibration direction) Indicatrix no longer a sphereIndicatrix = ellipsoid Note: continuous function, smooth ellipsoid.Hexagonal and tetragonal crystals have one unique crystallographic axis (c axis) ^ 2 identical ones The optical properties reflect this as well: ellipsoid of rotation about c (optically uniaxial) and c = the optic axis

Uniaxial ellipsoid and conventions:Fig 6-11 Bloss, Optical Crystallography, MSA

Circular Section^ optic axis: all w'sPrincipal Sections have w and true e: max & min n'sRandom Sections (e' and w) All sections have w!!

Any non-circular cut through the center of a uniaxial indicatrix will have w as one semiaxis and e' (or true e) as the otherDepending on light propagation we can have:

Fig 6-7 Bloss, Optical Crystallography, MSAFig 6-8 Bloss, Optical Crystallography, MSACalcite experiment and double refraction

Circular Section: all rays are O-rays and vibrate parallel w

Random Section: O-ray vibrates parallel w E-ray vibrates parallel e'Fig 6-13 Bloss, Optical Crystallography, MSA

Principal section:This is essentially the same as random, but here e' is really true e.In this case both rays really do vibrate ^ propagation & follow same path (as we have simplified the random case)We shall consider random and principal as alike, only the value of e varies.Fig 6-13 Bloss, Optical Crystallography, MSA

Essentially 2 possibilities(light coming toward you)1. Circular sectionLight prop. || OAAll vibration directions ^c are the same nOptic AxisFig 6-13 Bloss, Optical Crystallography, MSALike isotropic(no unique plane containing ray and c-axis)Only one ray (O-ray) with n = w (doesnt split to two rays)Extinct with analyzer in and stays that way as rotate stage (behaves as though isotropic)If incident light is unpolarized it will remain so

Essentially 2 possibilities(light coming toward you)2 raysOnly 2 privileged vibration directionsO-ray with n = wE-ray with n = e or e (depending on section)Does not stay same as rotate (more later)2. Elliptical sectionAny orientation other than circular

B-C: Polarized parallel e and wTransmits only one ray! (no component parallel to the other privileged direction) Note convention here: Light slows upon entering xl. Since frequency (& color) is about same, the slowing is illustrated by more compressed wave forms (they spend more time in the xl), so vibrate more times (vibrate more per length traveled) A: Unpolarized Ray splits into e and wThis figure rotates the light source(we rotate the crystal)Fig 6-17 Bloss, Optical Crystallography, MSA

D: Polarized at random angle

Resolves into components parallel e and parallel w

Rotating the stage

Anisotropic minerals with an elliptical indicatrix section change color as the stage is rotated; these grains go black 4 times in 360 rotation-exactly every 90o

Consider rotating the crystal as you watch:B = polarizer vibration direction parallel e only E-ray Analyzer in extinct

C = polarizer vibration direction || w only O-ray also extinct with analyzerewwe

Consider rotating the crystal as you watch:

DPolarized light has a component of eachSplits two raysone is O-ray with n = wother is E-ray with n = eWhen the rays exit the crystal they recombine

ew

REVIEWCalcite: Fig 6-72 rays, each polarizedvibrate ^ each other & in plane of incidence Indicatrix- uniaxialRandom SectionO-ray vibrates parallel wE-ray vibrates parallel e'Principal sectionCircular sectione' and w = privileged vibration directions

InterferenceA: Particles in phase if displaced from rest position by same amount in same directiona1 - a2 - a3 are all in phaseb1 - b2 - b3 are also all in phase (but not with a1)particles perfectly out of phase: equal-but-opposite displacementb1 and c1 are not, since in an instant it won't workFig 7-1 Bloss, Optical Crystallography, MSAPath Difference (D) = distance between any 2 points on a wave formusually expressed as xlD between any 2 points in phase = il (i=any integer)D between any 2 points perf. out of phase = ((2i+1)/2) l

B: Instant later with a second ray enteringC: Shows algebraic sum interference composite rayIf both waves in phase constructive interference with amplitude greater than either (intensity = A2)

InterferenceInterference of light polarized in perpendicular planesThis works in air & isotropic media, but not in crystals where vibrate independentlyNow we're ready for a big step

InterferencePlane polarized light enters xl. & resolved into 2 rays (if not || optic axis), which vibrate ^ each other & travel at different velocities (since have different n)Will thus travel diff # of l (even if frequency same or similar)So if in phase when enter, won't be when exit!!The path diff (D) between O-ray and E-ray = t (|w-e'|) (t = thickness)absolute value because the crystal can be (+) or (-)D then = t(N-n) and each mineral has a ~unique w and e, D is thus a function of the thickness, the mineral observed, and the orientation

Interference2 crystals of equal t, but different Dni A: n = 1/2 Nn=small ref index N=large " "slow ray requires 2 periods & fast only onethus come out polarized in same plane as entered no transmission by analyzer in XPL

Interference2 crystals of equal t, but different Dni B: n = 3/4 NSlow ray requires 2 periods & fast 1.5 100% transmission by analyzer in XPL

Transmission by the AnalyzerDetermined by:a) Angle between analyzer and polarizer (fixed at 90o)b) Angle between polarizer and closest privileged direction of xlWhen polarizer || either privileged vibration direction extinct, since only one ray & it's cancelledEvery crystal goes extinct 4 times in 360o rotation (unless isotropic)

Transmission by the Analyzerc) D = path difference = t (N-n) Fig. 7-4 t(N-n) = 1l 0% transmissiont(N-n) = 1.5l 100% transmission

Transmission by the AnalyzerDetermined by:d) l of lighta new conceptin part (c) D has been expressed in terms of l...but it's really an absolute retardation, some finite # of nm (or A or miles)If the transmitted light is white (mixed), each wavelength will be retarded t(N-n) by the same absolute distance, which will be a different x/l

Transmission by the AnalyzerExample: assume xl has t(N-n) that will retard D = 550 mm & viewed 45o off extinction (max intensity)

retardation 550550550550550550selected light l 40044048955062973313/8 l11/4 l11/8 l1 l7/8 l3/4 lYou can see 550 mm gets no transmission & others varying amount

retardation 550550550550550550selected light l 400440489550629733 13/8 l 11/4 l 11/8 l 1 l7/8 l3/4 l Fig 7-7 Bloss, Optical Crystallography, MSA

retardation 800800800800800800 800selected light l 400426457550581711 800 2 l 17/8 l 13/4 l 11/2 l 7/8 l1 1/8 l 1 l Fig 7-7 Bloss, Optical Crystallography, MSA

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

Color chartShows the relationship between retardation, crystal thickness, and interference color550 mm red violet800 mm green1100 mm red-violet again (note repeat )0-550 mm = 1st order 550-1100 mm = 2nd order 1100-1650 mm = 3rd order...Higher orders are more pastel

1) Find the crystal of interest showing the highest colors (D depends on orientation)2) Go to color chartthickness = 30 micronsuse 30 micron line + color, follow radial line through intersection to margin & read birefringenceSuppose you have a mineral with second-order greenWhat about third order yellow?Estimating birefringence

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

Example: Quartz w = 1.544 e = 1.553Sign?? (+) because e > w e - w = 0.009 called the birefringence (d) = maximum interference color (when seen?)What color is this?? Use your chart.

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

Example: Quartz w = 1.544 e = 1.553Sign?? (+) because e > w e - w = 0.009 called the birefringence (d) = maximum interference color (when see this?)What color is this?? Use your chart.For other orientations get e' - w progressively lower colorRotation of the stage changes the intensity, but not the hueExtinct when either privileged direction N-S (every 90o) and maximum interference color brightness at 45o360o rotation 4 extinction positions exactly 90o apart

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

If this were the maximum interference color seen, what is the birefringence of the mineral?

Conoscopic ViewingA condensing lens below the stage and a Bertrand lens above itArrangement essentially folds planes of Fig 7-11 coneLight rays are refracted by condensing lens & pass through crystal in different directionsThus different propertiesOnly light in the center of field of view is vertical & like ortho Interference Figures Very useful for determining optical properties of xlFig 7-13 Bloss, Optical Crystallography, MSA

How interference figures work (uniaxial example)BertrandlensSample(looking down OA)sub-stagecondenserConverging lenses force light rays to follow different paths through the indicatrixWE-W polarizerN-S polarizerWhat do we see?? Jane Selverstone, University of New Mexico, 2003

Uniaxial Interference FigureCircles of isochromesNote vibration directions: w tangential e' radial & variable magnitudeBlack cross (isogyres) results from locus of extinction directionsCenter of cross (melatope) represents optic axisApprox 30o inclination of OA will put it at margin of field of view

Uniaxial FigureCentered axis figure as 7-14: when rotate stage cross does not rotateOff center: cross still E-W and N-S, but melatope rotates around centerMelatope outside field: bars sweep through, but always N-S or E-W at centerFlash Figure: OA in plane of stage Diffuse black fills field brief time as rotate

Accessory PlatesWe use an insertable 1-order red (gypsum) plate

Accessory PlatesWe use an insertable 1-order red (gypsum) plateSlow direction is marked N on plateFast direction (n) || axis of plateThe gypsum crystal is oriented and cut so that D = (N-n) 550nm retardation it thus has the effect of retarding the N ray 550 nm behind the n rayIf insert with no crystal on the stage 1-order red in whole field of viewFig 8-1 Bloss, Optical Crystallography, MSA

Accessory PlatesSuppose we view an anisotropic crystal with D = 100 nm (1-order gray) at 45o from extinctionIf Ngyp || Nxl AdditionRay in crystal || Ngyp already behind by 100nm & it gets further retarded by 550nm in the gypsum plate100 + 550 650nmWhat color (on your color chart) will result?Original 1o grey 2o blue

Accessory PlatesNow rotate the microscope stage and crystal 90o Ngyp || nxl (D still = 100 nm)Ngyp || nxl Subtraction Ray in the crystal that is parallel to Ngyp is ahead by 100nm 550mm retardation in gypsum plate 450nm behindWhat color will result?1o orange

What will happen when you insert the gypsum plate?

What will happen when you insert the gypsum plate?

Optic Sign DeterminationFor all xls remember e' vibrates in plane of ray and OA, w vibrates normal to plane of ray and OA1) Find a crystal in which the optic axis (OA) is vertical (normal to the stage). How would you do that?2) Go to high power, insert condensing and Bertrand lenses to optic axis interference figure(+) crystal: e > w so w faster

Fig 7-13 Bloss, Optical Crystallography, MSA

Optic Sign DeterminationInserting plate for a (+) crystal: subtraction in NW & SE where n||N addition in NE & SW where N||NWhole NE (& SW) quads add 550nmisochromes shift up 1 orderIsogyre adds redIn NW & SE where subtractEach isochrome loses an order Near isogyre (~100nm) get 450 yellow in NW & SE (100-550)and 650 blue in NE & SW (100+550)(+) crystal: e > w so w fasteraddaddsubsub

(+) OA Figure with plateYellow in NW is (+)(+) OA Figure without plate

Optic Sign DeterminationInserting plate for a (-) crystal: subtraction in NE & SW where n||N addition in NW & SE where N||NWhole NW (& SE) quads add 550nmisochromes shift up 1 orderIsogyre still adds redIn NE & SW where subtractEach isochrome loses an order Near isogyre (~100nm) get 650 blue in NW & SE and 450 yellow in NE & SW(-) crystal: e < w so w sloweraddsubaddsub

(-) OA Figure with plateBlue in NW is (-)(-) OA Figure without plate(same as (+) figure)

Can determine the refractive index of a mineral by crushing a bit up and immersing the grains in a series of oils of known refractive index.When the crystal disappears perfectly nmineral = noilThe trick is to isolate w and true e by getting each E-W (parallel to the polarized light)Orienting crystals to determine w and e

To measure w only (if all grains of a single mineral):1) Find a grain with low interference colors- ideally a grain that remains extinct as the stage is rotated2) (check for centered OA figure)3) Determine optic sign while you're at it (for use later)4) Back to orthoscopic : all rays are w 5) Compare nxl to noilOrienting crystals to determine w and e

Now look at the other crystals of the same mineral:If the crystals are randomly oriented in a slide or thin section you may see any interference color from gray-black (OA vertical) to the highest color possible for that mineral (OA in plane of stage and see w and true e). Orienting crystals to determine w and e

To measure e :1) Find a grain with maximum interference colors2) (Check for flash figure?)3) Return orthoscopic at lower power4) Rotate 45o from extinction (either direction)

5) Figure out whether e is NE-SW or NW-SE & rotate it to E-W extinction6) Then only e coming through!Oils are then used nmust redo with each new oil as get closer! Ugh!Orienting crystals to determine w and e

Changes in absorption color in PPL as rotate stage (common in biotite, amphibole)Pleochroic formula:Example: Tourmaline: e = dark green to bluish w = colorless to tanCan determine this as just described by isolating first w and then e E-W and observing the colorPleochroism

Hornblende as stage is rotated

Biotite as stage is rotated

Biaxial CrystalsOrthorhombic, Monoclinic, and Triclinic crystals don't have 2 or more identical crystal axesThe indicatrix is a general ellipsoid with three unequal, mutually perpendicular axesOne is the smallest possible n and one the largest a = smallest n(fastest) b = intermediate n g = largest n(slowest)

The principal vibration directions are x, y, and z ( x || a, y || b, z || g)

By definition a < a' < b < g '< gFig 10-1 Bloss, Optical Crystallography, MSA

Biaxial CrystalsIf a < b < g then there must be some point between a & g with n = bBecause = b in plane, and true b is normal to plane, then the section containing both is a circular sectionHas all of the properties of a circular section! If look down it:all rays = bno preferred vibration directionpolarized incoming light will remain sounpolarized thus appear isotropic as rotate stagegaLooking down true b= b

Biaxial CrystalsIf a < b < g then there must be some point between a & g with n = bgaLooking down true b= b^ optic axis by definitionOA

Biaxial CrystalsIf a < b < g then there must be some point between a & g with n = b^ optic axis by definition

And there must be two! Biaxial

Orthorhombic, Monoclinic, and Triclinic minerals are thus biaxial and Hexagonal and tetragonal minerals are uniaxial

Biaxial CrystalsNomenclature:2 circular sections 2 optic axes Must be in a-g plane = Optic Axial Plane (OAP)Y || b direction ^ OAP = optic normalFig 10-2 Bloss, Optical Crystallography, MSAAcute angle between OA's = 2VThe axis that bisects acute angle = acute bisectrix = Bxa The axis that bisects obtuse angle = obtuse bisectrix = Bxo

Biaxial CrystalsB(+) defined as Z (g) = Bxa Thus b closer to a than to g

Biaxial CrystalsB(-) defined as X (a) = Bxa Thus b closer to g than to agaLooking down true b= b= bOAOA

Let's see what happens to unpolarized light travelling in various directions through a biaxial crystal Light will propagate with normal incidence to:Both = O-raysBoth polarized, and vibrate ^ each other (as uniaxial)One ray vibrates || Z and has n = g and the other vibrates || Y and n = b...or Z and X or Y and X1) Principal Plane - Includes 2 of the 3 true axes or principal vibration directions

Let's see what happens to unpolarized light travelling in various directions through a biaxial crystal Light will propagate with normal incidence to:This is identical to uniaxial:1 O-ray and 1 E-ray g and a' or b and g' ... vibration in incident plane so indicatrix works!2) Semi-random Plane Includes one principal vibration direction

Vibration directions of 2 rays in all 3 cases are mutually perpendicular, and || to the longest and shortest axes of the indicatrix ellipse cut by the incident planeThis is the same as with uniaxial, only the names change3) Random Plane No principal vibration directions 2 E-rays One vibrates in the OWZ' plane and || OZ with n = g' The other vibrates in the OWX' plane and || OX with n = a

4) Circular Section (either one)Acts as any circular section:Unpolarized remains soPolarized will pass through polarized in the same direction as entered with n = b extinct in XPL and remains so as rotate stage

ReviewFig 10-10 Bloss, Optical Crystallography, MSA

Biaxial Interference FiguresBxa figure (Bxa is vertical on stage)As in uniaxial, condensing lens causes rays to emanate out from OOX OS OA results in decreasing retardation (color) as g bOA OT OUIncrease again, but now because b aOX OQ OP incr retardation (interference colors)OR is random with a' and g'Fig 10-14 Bloss, Optical Crystallography, MSA

Biaxial Interference FiguresBxa figure

Result is this pattern of isochromes for biaxial crystalsFig 10-15 Bloss, Optical Crystallography, MSA

Biaxial Interference FiguresBiot-Fresnel Rule: for determining privileged vibration directions of any light ray from path and optic axesCalcite Expt: no longer a single plane containing ray and OAVibration directions bisect angle of planes as shown

Biaxial Interference FiguresApplication of B-F rule to conoscopic view Bxa figure+ = bisectrices of optic axis planes Isogyres are locus of all N-S (& E-W) vibration directionsSince incoming light vibrates E-W, there will be no N-S component extinctFig 10-16 Bloss, Optical Crystallography, MSA

Biaxial Interference FiguresCentered Bxa FigureFig 10-16 Bloss, Optical Crystallography, MSA

Biaxial Interference FiguresSame figure rotated 45oOptic axes are now E-WClearly isogyres must swingDemonstration

As rotate Centered Optic Axis Figure Large 2V:

Bxa Figure with Small 2V:Not much curvatureMakes use of Bxa awful

Always use optic axis figuresEasiest to find anyway. Why?Bxo looks like Bxa with 2V > 90oRandom Figures: Isogyre sweeps through field (not parallel x-hair at intersection, so can recognize from uniaxial even with this odd direction)Useless if far from OA

Biaxial Optic SignB(-)a = Bxa thus b closer to gaddaddsubtract100 gray + 550 650 blue100 gray - 550 450 yellow

Biaxial Optic SignB(-) a = Bxa thus b closer to g (in stage)Centered Bxa 2V = 35oCentered Bxa 2V = 35oWith accessory plate

Biaxial Optic SignB(+) g = Bxa thus b closer to a (in stage)subsubadd

Always use Optic Axis Figure & curvature of isogyre to determine optic signHow find a crystal for this?Blue in NW is (-) still works

Estimating 2VOAPFig 11-5A Bloss, Optical Crystallography, MSA

Sign of ElongationgIf g || elongation will always add length slowIf a || elongation will always subtract length fastU(+) will also length slowU(-) will also length fasta

Sign of ElongationbIf b || elongationSometimes will add length slowSometimes will subtract length fastgba