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