time for some new tricks: the optical indicatrix thought experiment: consider an isotropic mineral...
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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
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
Optic Sign
• Find NE-SW quadrants of the field
• Slide the full wave (550nm) plate (aka gypusm plate) in
• This slows the ray aligned NE-SW relative to the retardation - if that ray is more retarded it turns blue (adds 550 nm of retardation)
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
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 -)
… 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
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?