Optical Mineralogy
Interference Figures
1. Uniaxial Figures
Optical Indicatrix and Interference Figures:
LAB TS-3:
Uniaxial minerals
Interference figures
Optic sign
Pleochroic scheme
LAB TS-4:
Biaxial minerals
Interference figures
Optic sign
Pleochroic scheme
Optical Indicatrix and Interference Figures:
1. Optical Indicatrix
2. Uniaxial Interference Figures
3. Biaxial Interference Figures
Polarisation in the petrographic microscope
upper polarising filter (analyser) what happens
here???
sensitive tint plate
LAB TS-2
what happens
mineral sample (thin section)
here???
conoscopic light what happens here???
LAB TS-1
LAB TS-3,4
condenser lens
plane polarised light (PPL)
lower polarising filter (polariser)
unpolarised light
light source
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:
nmax
(slow)
nmin = nmax
circle:
isotropic
nmin
nmin
(fast)
nmin < nmax
ellipse:
anisotropic
nmax
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
Case 1: Uniaxial minerals (hexagonal, tetragonal: a1 = a2 = c)
principal axes: ne // c
nw // a
e: “extraordinary” ray
w: “ordinary” ray
X=Y<Z
X<Y=Z
Nesse, 2000; Fig. 7.23
X-Y plane: circular section
(all planes perpendicular to Z)
Z = optic axis (c-axis = slow)
Y-Z plane: circular section
(all planes perpendicular to X)
X = optic axis (c-axis = fast)
ne > nw +ve
ne < nw -ve
Case 1: Uniaxial minerals (hexagonal, tetragonal: a1 = a2 = c)
principal axes: ne // c
nw // a
e: “extraordinary” ray
w: “ordinary” ray
optic axis // plane of section
plane of section contains
optic axis I plane of section
both nw and ne :
plane of section contains
maximum d
only nw :
minimum d (extinct!)
random section:
contains nw and
ne’ < ne
intermediate d
Nesse, 2000; Fig. 7.25
Optic Sign
how do we figure this out???
Case 1: Uniaxial minerals:
Case 2: Biaxial minerals:
Z = optic axis (c-axis = slow)
ne > nw +ve
+ ve where Bxa // Z
-ve where Bxa // X
X = optic axis (c-axis = fast)
ne < nw -ve
c = OA = Z
Z
Z
+ve
-ve
c = OA = X
a +ve
X
a
-ve
X
Optic Sign
how 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 section
mineral will appear extinct for full stage rotation!
applies to both uniaxial and biaxial minerals
how 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) = c
all 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
result:
interference
figure
Bertrand lens
(on eyepiece tube)
rays focused through
centre of sample:
concentric interference rings
when viewed through Bertrand lens
condenser lens
(sub-stage)
Nesse Fig. 7.36
Interference Figures
uniaxial optic axis figure
result:
interference
figure
isochrome
OA
melatope
isogyre
number of rings
(isochromes)
 birefringence
OA
sample oriented
with optic axis normal
to plane of section
(in XN, grain appears extinct
through 360o rotation)
Nesse Fig. 7.36
Interference Figures
uniaxial optic axis figure
isochrome
what it really looks like:
melatope
isochromes
melatope
isogyre
isogyre
number of rings
(isochromes)
 birefringence
sample oriented
with optic axis normal
to plane of section
(in Xn, grain appears extinct
through 360o rotation)
cross-hairs
optic axis figure (OAF)
for high d mineral
(e.g., calcite)
Interference Figures
uniaxial optic axis figure
isochrome
melatope
isogyre
number of rings
(isochromes)
 birefringence
sample oriented
with optic axis normal
to plane of section
(in XN, grain appears extinct
through 360o rotation)
w
e
Nesse Fig. 7.35
e oriented radially
w oriented tangentially
insert
tint plate!
Interference Figures:
Determining Optic Sign
uniaxial optic axis figure
w
e
if e slow: mineral is +ve
if e fast: mineral is -ve
observe colour
change in
SE-NW
quadrants
?
?
Nesse Fig. 7.40
Interference Figures:
Determining Optic Sign
down
uniaxial optic axis figure
down
colours
go down
(subtraction)
w = fast
e = slow
+ ve
w
e
if e slow: mineral is +ve
if e fast: mineral is -ve
up
up
- ve
colours
go up
(addition)
w = slow
e = fast
Interference Colour Chart
low d optic axis figure
addition:
grey  blue
30 mm
subtraction:
grey  yellow
what do addition and subtraction look like?
Interference Colour Chart
low d optic axis figure
addition:
grey  blue
high d optic axis figure
addition:
2nd order red  3rd order red
30 mm
subtraction:
grey  yellow
subtraction:
2nd order red  1st order red
what do addition and subtraction look like?
colours
go down
(subtraction)
w = fast
e = slow
Interference Figures:
Determining Optic Sign
uniaxial optic axis figure
Y
+ ve
colours
go up
(addition)
w = slow
e = fast
Y
SE-NW quadrant:
if colours go from grey-white to yellow
(subtraction; “down”)
mineral is +ve (YAY!)
- ve
colours
go down
(subtraction)
w = fast
e = slow
Interference Figures:
Determining Optic Sign
uniaxial optic axis figure
B
+ ve
colours
go up
(addition)
w = slow
e = fast
B
SE-NW quadrant:
if colours go from grey-white to blue
(addition; “up”)
mineral is -ve (BOO!)
- ve
colours
go down
(subtraction)
w = fast
e = slow
Interference Figures:
Determining Optic Sign
high d mineral (many isochromes)
no
tint
plate
+ ve
colours
go up
(addition)
w = slow
e = fast
low order colours (grey-white)
near centre of figure
- ve
colours
go down
(subtraction)
w = fast
e = slow
Interference Figures:
Determining Optic Sign
high d mineral (many isochromes)
no
tint
plate
+ ve
colours
go up
(addition)
w = slow
e = fast
tint plate in
+
(rings
move in)
(rings
move out)
- ve
colours
go down
(subtraction)
w = fast
e = slow
Interference Figures:
Determining Optic Sign
high d mineral (many isochromes)
no
tint
plate
+ ve
colours
go up
(addition)
w = slow
e = fast
tint plate in
+
(rings
move in)
(rings
move out)
mineral is
uniaxial -ve
- ve
Interference Figures
Practical problem(s):
1. How to find a grain with optic axis normal to plane of
thin 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 of
thin section?
look for grain that is extinct for full rotation of stage
(opaque? isotropic? hole in slide? optic axis grain?)
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 of
thin section?
look for grain that is extinct for full rotation of stage
(opaque? isotropic? hole in slide? optic axis grain?)
2. What if you can’t find a suitably oriented 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 with
minimum colour change
during rotation
not ideal, but may be best
possible in your section
slightly
off-centre
(melatope
visible)
OK to use
way
off-centre
(melatope
not visible)
best
avoided
Nesse Fig. 7.38
Interference Figures
Flash Figures:
both e and w in
plane of section
(maximum d)
useless for
determining
optic sign
field of view
light  dark
very quickly
as stage
rotated
very similar for both
uniaxial and biaxial
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:
Case 2: Biaxial minerals:
Z = optic axis (c-axis = slow)
ne > nw +ve
+ ve where Bxa // Z
-ve where Bxa // X
X = optic axis (c-axis = fast)
ne < nw -ve
Z
c = OA = Z
Z
c = OA = X
a +ve
X
a
+ve
Bxa
-ve
X
-ve
Bxa
determined from OA figure
determined from Bxa or OA figure