optical mineralogy interference figures 1. uniaxial figures interference figures 1. uniaxial figures

Optical MineralogyOptical Mineralogy

Interference Figures1. Uniaxial Figures

Interference Figures1. Uniaxial Figures

Optical Indicatrix and Interference Figures:

LAB TS-3:Uniaxial mineralsInterference figuresOptic signPleochroic scheme

LAB TS-4:Biaxial mineralsInterference figuresOptic signPleochroic scheme

Optical Indicatrix and Interference Figures:

1. Optical Indicatrix

2. Uniaxial Interference Figures

3. Biaxial Interference Figures

Polarisation in the petrographic microscope

lower polarising filter (polariser)

mineral sample (thin section)

light source

unpolarised light

upper polarising filter (analyser)

plane polarised light (PPL)

what happenshere???

LAB TS-1

what happenshere???

LAB TS-2

condenser lens

conoscopic light what happens here???

LAB TS-3,4

sensitive tint plate

Optical Indicatrix

constructed as a sphere or ellipsoid with radii parallel to the principal vibration directions and lengths of axes proportional to refractive index

in 2D:

nmin

nmin = nmax

nmax

(slow)

nmin

(fast)

nmax

circle:isotropic nmin < nmax

ellipse:anisotropic

in 3D: indicatrix for isotropic mineral is a sphere (of no further interest)

indicatrix for anisotropic mineral is an ellipsoid 2 cases: uniaxial and biaxial

Nesse, 2000; Fig. 7.23

X-Y plane: circular section(all planes perpendicular to Z)Z = optic axis (c-axis = slow)

ne > nw +ve

X = Y < Z X < Y = Z

Y-Z plane: circular section(all planes perpendicular to X)X = optic axis (c-axis = fast)

ne < nw -ve

Case 1: Uniaxial minerals (hexagonal, tetragonal: a1 = a2 = c)

principal axes: ne // c nw // a

e: “extraordinary” ray w: “ordinary” ray

Nesse, 2000; Fig. 7.25

optic axis // plane of sectionplane of section contains

both nw and n e : maximum d

optic axis I plane of sectionplane of section contains

only nw : minimum d (extinct!)

random section:contains nw and

ne’ < neintermediate d

Case 1: Uniaxial minerals (hexagonal, tetragonal: a1 = a2 = c)

principal axes: ne // c nw // a

e: “extraordinary” ray w: “ordinary” ray

Case 1: Uniaxial minerals:

Z = optic axis (c-axis = slow)

ne > nw +ve

X = optic axis (c-axis = fast)

ne < nw -ve

Case 2: Biaxial minerals:

+ ve where Bxa // Z

-ve where Bxa // X

+ve -ve+ve -ve

Z Z

X X

c = OA = Z

c = OA = X

a a

Optic Signhow do we figure this out???

Optic Signhow do we figure this out???

Requires: conoscopic light (condenser lens in place)interference figures (viewed with Bertrand lens)use of STP to determine fast and slow directions

Nesse, Ch. 7, p. 139 -143 (uniaxial) p. 143 - 151 (biaxial)

Extinction Angles:where optic axis is normal to plane of thin sectionmineral will appear extinct for full stage rotation!

applies to both uniaxial and biaxial mineralshow distinguished from isotropic minerals?

(also requires interference figures: stay tuned.....)

Optical Indicatrix and Symmetry

isometric system: a1 = a2 = a3; all angles = 90o

indicatrix is a sphere; minerals extinct in XN

hexagonal, trigonal, tetragonal systems: a1 = a2 (= a3) = call angles either 90o or 120o

uniaxial: indicatrix is ellipsoid; X < Y < Z c-axis = optic axis = e (either X or Z) parallel extinction

orthorhombic system: a = b = c; all angles = 90o

biaxial: indicatrix is ellipsoid; X < Y < Z X, Y, Z // crystallographic axes 2 circular sections I 2 optic axes parallel extinction

2. Uniaxial Interference Figures(Nesse Ch. 7 p. 139-143)

optic axis = c crystallographic axis

ne // c; nw // a

e can be either fast or slow

Interference Figures

require conoscopic light

condenser lens(sub-stage)

Bertrand lens(on eyepiece tube)

rays focused throughcentre of sample:

concentric interference ringswhen viewed through Bertrand lens

result:interference

figure

Nesse Fig. 7.36

Interference Figures result:interference

figure uniaxial optic axis figure

isochrome

melatope

isogyre

sample orientedwith optic axis normal

to plane of section(in XN, grain appears extinct

through 360o rotation)

number of rings (isochromes)

birefringence

OA

OA

Nesse Fig. 7.36

Interference Figures

uniaxial optic axis figure

isochrome

melatope

isogyre

sample orientedwith optic axis normal

to plane of section(in Xn, grain appears extinct

through 360o rotation)

number of rings (isochromes) birefringence

what it really looks like:

optic axis figure (OAF)for high d mineral

(e.g., calcite)

isogyre

isochromesmelatope

cross-hairs

Interference Figures

uniaxial optic axis figure

isochrome

melatope

isogyre

sample orientedwith optic axis normal

to plane of section(in XN, grain appears extinct

through 360o rotation)

e oriented radially

w oriented tangentially

ew

Nesse Fig. 7.35

number of rings (isochromes) birefringence

Interference Figures:Determining Optic Sign

uniaxial optic axis figure

if e slow: mineral is +ve

if e fast: mineral is -ve

ew

insert tint plate!

observe colourchange in

SE-NWquadrants

?

?

Nesse Fig. 7.40

Interference Figures:Determining Optic Sign

uniaxial optic axis figure

if e slow: mineral is +ve

if e fast: mineral is -ve

ew

coloursgo down

(subtraction)w = fast

e = slow

+ ve

coloursgo up

(addition)w = slow

e = fast

- ve

down

down

up

up

Interference Colour Chart

30 mm

low d optic axis figure

addition:grey blue

subtraction:grey yellow

what do addition and subtraction look like?

Interference Colour Chart

30 mm

low d optic axis figure

addition:grey blue

subtraction:grey yellow

what do addition and subtraction look like?

high d optic axis figure

addition:2nd order red 3rd order red

subtraction:2nd order red 1st order red

Interference Figures:Determining Optic Sign

uniaxial optic axis figure

coloursgo down

(subtraction)w = fast

e = slow

+ ve

coloursgo up

(addition)w = slow

e = fast

- ve

SE-NW quadrant:if colours go from grey-white to yellow

(subtraction; “down”)

mineral is +ve (YAY!)

Y

Y

Interference Figures:Determining Optic Sign

uniaxial optic axis figure

coloursgo down

(subtraction)w = fast

e = slow

+ ve

coloursgo up

(addition)w = slow

e = fast

- ve

SE-NW quadrant:if colours go from grey-white to blue

(addition; “up”)

mineral is -ve (BOO!)

B

B

Interference Figures:Determining Optic Sign

coloursgo down

(subtraction)w = fast

e = slow

+ ve

coloursgo up

(addition)w = slow

e = fast

- ve

high d mineral (many isochromes)

notint plate

low order colours (grey-white)

near centre of figure

Interference Figures:Determining Optic Sign

coloursgo down

(subtraction)w = fast

e = slow

+ ve

coloursgo up

(addition)w = slow

e = fast

- ve

high d mineral (many isochromes)

notint plate

tint plate in

+(rings

move in)

-(rings

move out)

Interference Figures:Determining Optic Sign

coloursgo down

(subtraction)w = fast

e = slow

+ ve

coloursgo up

(addition)w = slow

e = fast

- ve

high d mineral (many isochromes)

notint plate

tint plate in

+(rings

move in)

-(rings

move out)

mineral isuniaxial -ve

Interference Figures

Practical problem(s):

1. How to find a grain with optic axis normal to plane ofthin section?

2. What if you can’t find a suitably oriented grain?

Interference Figures

Practical problem(s):

1. How to find a grain with optic axis normal to plane ofthin section?

2. What if you can’t find a suitably oriented grain?

look for grain that is extinct for full rotation of stage (opaque? isotropic? hole in slide? optic axis grain?)

Interference Figures

Practical problem(s):

1. How to find a grain with optic axis normal to plane ofthin section?

2. What if you can’t find a suitably oriented grain?

look for grain that is extinct for full rotation of stage (opaque? isotropic? hole in slide? optic axis grain?)

look for low d grain with minimum change during rotation“off-centre” figure:

not ideal, but may be best possible in your section

Interference Figures

“off-centre” uniaxial figure:

obtained from low d grain withminimum colour change

during rotation

not ideal, but may be best possible in your section

slightlyoff-centre(melatope

visible)

OK to use

wayoff-centre(melatopenot visible)

best avoided

Nesse Fig. 7.38

Interference Figures

Flash Figures:

both e and w in plane of section(maximum d)

useless fordetermining

optic sign

very similar for bothuniaxial and biaxial

field of viewlight darkvery quickly

as stagerotated

Nesse Fig. 7.39

Uniaxial Minerals: Pleochroic Scheme

Nesse, 2000; Fig. 7.30

1. In PPL, find grain with minimum colour change as stage rotated(w in plane of section); observed colour = w (= a)

2. In PPL, find grain with maximum colour change as stage rotated(both w and e in plane of section); w colour already determined

other colour = e (= c)3. Can also be determined by finding fast and slow rays + optic sign

Optic Sign: Summary

Case 1: Uniaxial minerals:

Z = optic axis (c-axis = slow)

ne > nw +ve

X = optic axis (c-axis = fast)

ne < nw -ve

Case 2: Biaxial minerals:

+ ve where Bxa // Z

-ve where Bxa // X

+ve -ve+ve -ve

Z Z

X X

c = OA = Z

c = OA = X

a a

determined from OA figure determined from Bxa or OA figure

Bxa

Bxa