Appearance of crystals in microscope
• Crystal shape – how well defined the crystal
shape is
– Euhedral – sharp edges, well- defined crystal
shape
– Anhedral – rounded edges, poorly defined shape
– Subhedral – in between anhedral and euhedral
• Cleavage – just as in hand samples!
• Physical character – often note evidence of
strain, breaking, etching on crystals – you will
notice some crystals show those features
better than others…
Cleavage
Most easily observed in PPL (upper polarizer out),
but visible in XPL as well
• No cleavages:
quartz, olivine
• 1 good cleavage: micas
• 2 good cleavages: pyroxenes, amphiboles
Cleavage
2 cleavages
intersecting
at ~90°
pyroxene
2 cleavages
intersecting
at 60°/120°:
amphibole
120°
60°
Cleavage
random fractures,
no cleavage:
olivine
Twinning
Presence and style of twinning can be diagnostic
Twins are usually most obvious in XPL (upper polarizer in)
Twinning - some examples
Clinopyroxene (augite)
• Simple twin on {100}
Plagioclase
• Simple (Carlsbad) twin on (010)
• Polysynthetic albite twins on (010)
• Pericline twin on (h01)
Twinning and Extinction Angle
• Twinning is characteristic in thin section for
several common minerals – especially
feldspars
• The twins will go from light to dark over
some angle
• This is characteristic of the composition
• Stage of the petrographic microscope is
graduated in degrees with a vernier scale to
measure the angle of extinction precisely
Extinction angle – parallel extinction
• All uniaxial minerals show parallel extinction
• Orthorhombic minerals show parallel extinction
(this is because the crystal axes and indicatrix axes coincide)
orthopyroxene
PPL
XPL
Extinction angle - inclined extinction
Monoclinic and triclinic minerals:
indicatrix axes do not coincide with crystallographic axes
These minerals have inclined extinction
(and extinction angle helps to identify them)
extinction
angle
clinopyroxene
Habit or form
acicular
anhedral/irregular
bladed
blocky
elongate
euhedral
fibrous
prismatic
rounded
tabular
Habit or form
acicular
anhedral/irregular
bladed
blocky
elongate
euhedral
fibrous
prismatic
rounded
tabular
Michel-Lévy Color Chart – Plate 4.11
What interference color is this?
So far, all of this has been orthoscopic (the normal way)
All light rays are ~ parallel and vertical as they pass through
the crystal
• xl has particular interference color
Orthoscopic
viewing
Fig 7-11 Bloss, Optical
Crystallography, MSA
= f(biref, t, orientation)
• Points of equal thickness will have
the same color
• isochromes = lines connecting
points of equal interference color
• At thinner spots and toward edges
will show a lower color
• Count isochromes (inward from
thin edge) to determine order
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 d = nhi-nlo = 0 = black
anisotropic minerals - uniaxial indicatrix
c-axis
c-axis
calcite
quartz
Let’s perform the same thought experiment…
Uniaxial indicatrix
c-axis
c-axis
tangerine = uniaxial (-)
Spaghetti squash = uniaxial (+)
quartz
calcite
Uniaxial indicatrix
Circular section is perpendicular to the stem (c-axis)
Uniaxial indicatrix
(biaxial ellipsoid)
c=Z
c=Z
n
n
b=Y
n
a=X
b=Y
n
a=X
What can the indicatrix tell us about
optical properties of individual grains?
Propagate light along the c-axis, note what
happens to it in plane of thin section
n
c=Z
n
n
n

a=X
b=Y
n - n = 0
therefore, d=0: grain stays black
(same as the isotropic case)
Now propagate light perpendicular to c-axis
n - n > 0
N
therefore, d > 0
n

n
n

W
E
n
S
Grain changes color upon rotation.
Grain will go black whenever indicatrix
axis is E-W or N-S
This orientation will show the maximum d of the mineral
Conoscopic Viewing
A condensing lens below the stage and a
Bertrand lens above it
Arrangement essentially folds planes  cone
Fig 7-13 Bloss, Optical
Crystallography, MSA
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 Figures Very
useful for determining
optical properties of xl
How interference figures work (uniaxial example)
What do we see??
Bertrand
lens
N-S polarizer
Sample
(looking down OA)
sub-stage
condenser
W
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!!
E-W polarizer
© Jane Selverstone, University of New Mexico, 2003
Uniaxial Interference
Figure
O
E
• Circles of isochromes
Fig. 7-14
• Black cross (isogyres) results from
locus of extinction directions
• Center of cross (melatope)
represents optic axis
• Approx 30o inclination of OA will
put it at margin of field of view
Uniaxial Figure
– Centered axis figure as 7-14: when
rotate stage cross does not rotate
– Off center: cross still E-W and N-S, but
melatope rotates around center
Fig. 7-14
– Melatope outside field: bars sweep
through, but always N-S or E-W at
center
– Flash Figure: OA in plane of stage
Diffuse black fills field brief time as
rotate
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 -)
anisotropic minerals - biaxial indicatrix
clinopyroxene
feldspar
Now things get a lot more complicated…
Biaxial indicatrix
2Vz
(triaxial ellipsoid)
Z
OA
OA
2Vz
n
n
n
Y
n
n
The potato!
X
n
n
n
n
n
n
There are 2 different ways to cut this and get a circle…
Alas, the potato (indicatrix) can have any orientation
within a biaxial mineral…
Y c
a
Z
c
olivine
Z
augite
b
Y
b
X
a
X
… 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
2V: a diagnostic property of biaxial minerals
Z
OA
OA
• When 2V is acute about Z: (+)
2Vz
• When 2V is acute about X: (-)
• When 2V=90°, sign is indeterminate
n
• When 2V=0°, mineral is uniaxial
n
Y
n
X
2V is measured using an interference figure…
More in a few minutes
How interference figures work (uniaxial example)
Converging lenses force light
rays to follow different paths
through the indicatrix
Bertrand
lens
N-S polarizer
What do we see??
Sample
(looking down OA)
substage
condensor
Effects of multiple cuts thru indicatrix
W
E
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 sign w/ gyps
(+)
determine 2V from curvature of isogyre
90°
60°
40°
(-)
Biaxial interference figures
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
Z
intermediate d.
OA
OA
2Vz
n
n
Y
n
Use this figure to get sign and 2V:
(+)
2V=20°
2V=40°
2V=60°
X
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
Z
OA
OA
hi d
2Vz
n
n
X
n
Y
Z
OA
OA
lo d
2Vz
n
n
Y
n
X
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 angle
And Confocal lense:
• Uniaxial or biaxial?
• 2V if biaxial
• Positive or negative?
Go to your book…
•
•
•
•
•
•
Chemical formula
Symmetry
Uniaxial or biaxial, (+) or (-)
RIs: lengths of indicatrix axes
Birefringence (d) = N-n
2V if biaxial
Diagrams:
* Crystallographic axes
* Indicatrix axes
* Optic axes
* Cleavages
* Extinction angles