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 intersectingat ~90° pyroxene

60°120°

2 cleavages intersectingat 60°/120°: amphibole

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)

Plagioclase

• Simple twin on {100}

• Simple (Carlsbad) twin on (010)

• Pericline twin on (h01)

• Polysynthetic albite twins on (010)

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)

PPL XPL

orthopyroxene

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)

clinopyroxene

extinction angle

Habit or form

blocky

acicular

bladed

prismatic

anhedral/irregular

elongate

rounded

fibrous

tabular

euhedral

Habit or form

blocky

acicular

bladed

prismatic

anhedral/irregular

elongate

rounded

fibrous

tabular

euhedral

Michel-Lévy Color Chart – Plate 4.11

What interference color is this?What interference color is this?

So far, all of this has been orthoscopicorthoscopic (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

• isochromesisochromes = 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 = nhi-nlo = 0 = black

anisotropic minerals - uniaxial indicatrix

quartz

calcite

c-axis

c-axis

Let’s perform the same thought experiment…

Uniaxial indicatrix

c-axisc-axis

Spaghetti squash = uniaxial (+)

tangerine = uniaxial (-)

quartz

calcite

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

Uniaxial indicatrix

Uniaxial indicatrix(biaxial ellipsoid)

n

n a=X

c=Z

b=Y

n

a=X

c=Z

nb=Y

What can the indicatrix tell us about optical properties of individual grains?

n - n = 0therefore, =0: grain stays black (same as the isotropic case)

n

n a=X

c=Z

b=Y

n

n

Propagate light along the c-axis, note what happens to it in plane of thin section

Grain changes color upon rotation. Grain will go black whenever indicatrix axis is E-W or N-S

n

n

This orientation will show the maximum of the mineral

n

n

n

n

n

n

n

n

n - n > 0therefore, > 0

N

S

W E

Now propagate light perpendicular to c-axis

Conoscopic ViewingConoscopic ViewingA condensing lencondensing lens below the stage and a

Bertrand lensBertrand lens above itArrangement 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 FiguresInterference Figures Very useful for determining optical properties of xl

Fig 7-13 Bloss, Optical Crystallography, MSA

How interference figures work (uniaxial example)How interference figures work (uniaxial example)

Bertrandlens

Sample(looking down OA)

sub-stagecondenser

W E-W polarizer

N-S polarizer

What do we see??What do we see??

n

n

n

n

nn

nn

© Jane Selverstone, University of New Mexico, 2003

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!!

Uniaxial Interference Uniaxial Interference FigureFigure

Fig. 7-14Fig. 7-14

O E

• Circles of isochromesisochromes

• Black cross (isogyresisogyres) results from

locus of extinction directions

• Center of cross (melatopemelatope)

represents optic axis

• Approx 30o inclination of OA will

put it at margin of field of view

Uniaxial FigureUniaxial Figure– CenteredCentered axis figure as 7-14: when rotate

stage cross does notnot rotate

– Off center:Off center: cross still E-W and N-S, but

melatopemelatope rotates around center

– Melatope outside field:Melatope outside field: bars sweep

through, but always N-S or E-W at center

– Flash Figure:Flash Figure: OA in plane of stage

Diffuse black fills field brief time as rotate

Fig. 7-14Fig. 7-14

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 -)

anisotropic minerals - biaxial indicatrix

clinopyroxenefeldspar

Now things get a lot more complicated…

Biaxial indicatrix(triaxial ellipsoid)

OA OA

2Vz

Y

X

Z

n

n

nn

n

n

n

n

n

n

n

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…

c

a

b

Z

X

Y

Y

aZ

bX

colivine augite

… 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 = n (lowest)

Y direction = n (intermed; radius of circ. section)

Z direction = n (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

OA OA

2Vz

Y

X

Z

n

n

n

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

How interference figures work (uniaxial example)

Bertrandlens

Sample(looking down OA)

substagecondensor

Converging lenses force light rays to follow different paths through the indicatrix

W E

N-S polarizerWhat do we see??

n

n

n

n

nn

nn

Effects of multiple cuts thru indicatrix

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 2V from curvature of isogyre

90° 60° 40°

determine sign w/ gyps

(+) (-)

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 .

Biaxial interference figures

Use this figure to get sign and 2V:

(+) 2V=20° 2V=40° 2V=60°

OA OA

2Vz

Y

X

Z

n

n

n

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 OA

2Vz

Y

X

Z

n

n

n

hi

OA OA

2Vz

Y

X

Z

n

n

n

lo

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 angleAnd 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 () = N-n• 2V if biaxial

Diagrams:* Crystallographic axes* Indicatrix axes* Optic axes* Cleavages* Extinction angles