Optical Mineralogy in a Nutshell

Use of the petrographic microscope in three easy lessons

Part II

© Jane Selverstone

Courtesy of Jane SelverstoneUniversity of New Mexico

Quick review• Isotropic minerals –velocity changes as light enters

mineral, but then is the same in all directions thru xtl; no rotation or splitting of light.

• Anisotropic minerals –light entering xtls is split and reoriented into two plane-polarized components that vibrate perpendicular to one another and travel w/ different speeds.

• Uniaxial minerals have one special direction along which light is not reoriented; characterized by 2 RIs.

• Biaxial minerals have two special directions along which light is not reoriented; characterized by 3 RIs.

These minerals are characterized by a single RI(because light travels w/ same speed throughout

xtl)

Determining if mineral is uniaxial or biaxial

uniaxialIf uniaxial, isogyres define cross; arms remain N-S/E-W as stage is rotated

biaxial

or

If biaxial, isogyres define curve that rotates with stage, or cross that breaks up as stage is rotated

Reminder about how to get an interference figure1. Find a grain that stays dark as stage is rotated2. Go to highest power objective3. Insert Bertrand Lens4. Look down scope and rotate stage

Determining optic signNow determine the optic sign of the mineral:1. Rotate stage until isogyre is concave to NE (if biaxial)2. Insert gypsum accessory plate3. Note color in NE, immediately adjacent to isogyre --

Blue = (+)Yellow = (-)

uniaxial

biaxial

(+)

(+)

We’ve talked about minerals as magicians -now let’s prove it!

calcite calcite

calcite

calcitecalcite

ordinaryray, ω

(stays stationary)extraordinary

ray, ε(rotates)

• single light ray coming into cc is split into two• ε ray is refracted - changes direction & speed• rays have different velocities, hence different RIs• stationary ray=ordinary, rotating ray=extraordinary• because refraction of ε is so large, cc must have hi δ

(remember: δ = nhi - nlo)

Conclusions from calcite experiment

If we were to look straight down c-axis, we would see only one dot – no splitting!

C-axis is optic axis(true for all uniaxial minerals, but unfortunately not for biaxial minerals)

More on this in a few minutes…

Birefringence/interference colors

Retardation in nanometers

Thic

knes

s in

mic

rons

birefringence

Back to birefringence/interference colors

Observation: frequency of light remains unchanged during splitting, regardless of material

F= V/λif light speed changes, λ must also change

λ is related to color; if λ changes, color changes

• waves from the two rays can be in phase or out of phase upon leaving the crystal

mineral grain

plane polarized light

fast ray (low n)

slow ray(high n)

lower polarizer

∆=retardation

d

• When waves are in phase, all light gets killed• When waves are out of phase, some component of light

gets through upper polarizer and the grain displays an interference color; color depends on retardation

• When one of the vibration directions is parallel to the

Interference phenomena

lower polarizer, no light gets through the upper polarizer and the grain is “at extinction” (=black)

mineral grain

plane polarized light

fast ray (low n)

slow ray(high n)

lower polarizer

∆=retardation

d

At time t, when slow ray 1st exits xtl:Slow ray has traveled distance dFast ray has traveled distance d+∆

time = distance/rate

Slow ray: t = d/Vslow

Fast ray: t= d/Vfast + ∆/Vair

Therefore: d/Vslow = d/Vfast + ∆/Vair

∆ = d(Vair/Vslow - Vair/Vfast)∆ = d(nslow - nfast)∆ = d δ

∆ = thickness of t.s. x birefringence

Determining optic sign with the gypsum plate - what happens?

slow

blue in NE = (+)

Gypsum plate has constant ∆ of 530 nm = 1st-order pink

Isogyres = black: ∆=0Background = gray: ∆=150

Add to/subtract from 530 nm:

530+150=680 nm = blue = (+)530-150=380 nm = yellowish = (-)

Addition = slow + slowSubtraction = slow + fast

Let’s look at interference colors in a natural thin section:

Note that different grains of the same mineral show different interference colors – why??

ol

ol

olol ol

ol plagplag

plag

plag

plag

plag

Different grains of same mineral are in different orientations

If every grain of the same mineral looks different, how are we ever going to be able to identify anything??

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 δ = nhi-nlo = 0 = black

anisotropic minerals - uniaxial indicatrix

quartz

calcite

c-axis

c-axis

Let’s perform the same thought experiment…

Uniaxial indicatrixc-axis

c-axis

Spaghetti squash = uniaxial (+)

tangerine = uniaxial (-)

quartz

calcite

(this is not strictly correct, but works for our purposes…)

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

Uniaxial indicatrix

nω

nε

nω

nω

Uniaxial indicatrix(biaxial ellipsoid)

nε

nω a=X

c=Z

b=Y

nε

a=X

c=Z

nωb=Y

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

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

nε

nω a=X

c=Z

b=Ynω

nω

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 indicatrixaxis is E-W or N-S

nε

nω

This orientation will show the maximum δ of the mineral

nε

nω

nε

nω

nε

nω

nε

nω

nε - nω > 0therefore, δ > 0

N

S

W E

Now propagate light perpendicular to c-axis

anisotropic minerals - biaxial indicatrix

clinopyroxenefeldspar

Now things get a lot more complicated…

Biaxial indicatrix(triaxial ellipsoid)

OA OA2Vz

YX

Z

nβ

nγ

nαnβ

nβ

nγ

nα

nγ

nβ

nα

nβ

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

c olivine augite(cpx)

… 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 RIsto describe a biaxial mineral

X direction = nα (lowest)Y direction = nβ (intermed; radius of circ. section)Z direction = nγ (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 OA2Vz

YX

Z

nβ

nγ

nα

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 polarizer What do we see??

Effects of multiple cuts thru indicatrix

εω

εω

εω

ε

ω

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°

See Nesse or handout

determine sign w/ gypsum plate(+) (-)

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 δ.

Biaxial interference figures

Use this figure to get sign and 2V:

(+) 2V=20° 2V=40° 2V=60°See handout/Nesse

OA OA2Vz

YX

Z

nβ

nγ

nα

Quick review of why we use indicatrix:

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 OA2Vz

YX

Z

nβ

nγ

nα

hi δ

OA OA2Vz

YX

Z

nβ

nγ

nα

lo δ

Isotropic? Uniaxial? Biaxial? Sign? 2V?All of these help us to uniquely identify unknown minerals.