Optical Mineralogy

1
Optical Mineralogy

• Wave Theory
• 2 X Amplitude
• Frequency of waves/sec to pass a given point
  (hz)
• f v/l v velocity

2

• Electromagnetic spectrum visible portion
• Violet (400 nm) ? Red (700 nm)
• White ROYGBV
• (can be separated by dispersion)

3

• Refraction
• Incident ray and reflected ray
• 1) ? of incidence i ? of reflection r'
• 2) coplanar plane of incidence
• (in plane interface)
• Refracted ray
• 1) Slower in water (or glass)
• 2) ? r ? ? I
• Depends on D v

Incident
Reflected
i
r
air
water
r
Refracted
4
Index of refraction For a substance xnx
vair/vxnair ?? light is slower in water,
glass, crystalsIs nwater greater or less than
1??Larger n associated with slower V !!Snells
Law ni sin i nr sin rfor 2 known media
(air/water) sin i/sin r nr / ni const So can
predict angle change!
5
Polarization

• Non-polarized (usual) light
• Each photon vibrates as a wave form in a single
  plane
• Light beam numerous photons, each vibrating in
  a different plane
• Vibration in all directions perpendicular to
  propagation direction

6
Polarization
incoming ray is non-polarized
reflected and refracted rays both become polarized
7
Polarization

• Microscopes have two polarizers
• polarizer (below stage) is E-W
• analyzer (above stage) is N-S

8
The Optical Indicatrix

• Shows how ni varies with vibration direction.
• Vectors radiating from center
• Length of each proportional to ni for light
  vibrating in the direction of the vector
• Indicatrix surface connecting tips of vectors
• (a shape to represent changes in n with
  direction)
• Isotropic media have all ni the same (by
  definition)
• What is the shape of an isotropic indicatrix?
• a spherical indicatrix

9
The Optical Indicatrix
North
A
South
P
P

• For isotropic minerals
• When analyzer inserted crossed-nicols or XPL
  shorthand (vs PPL) no light passes
• ? extinct, even when the stage is rotated

Fig. 6-6
A
Fig 6-6 Bloss, Optical Crystallography, MSA
P
West
P
East
10
Anisotropic crystals

• Calcite experiment and double refraction

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Anisotropic crystals

• Calcite experiment and double refraction

Double images Ray ? 2 rays with different
propagation and vibration directions Each is
polarized ( each other)
Fig 6-7 Bloss, Optical Crystallography, MSA
12
Anisotropic crystals

• Calcite experiment and double refraction

O-ray (Ordinary) Obeys Snell's Law and goes
straight Vibrates plane containing ray and
c-axis (optic axis) E-ray (Extraordinary) deflec
ted Vibrates in plane containing ray and
c-axis ..also doesn't vibrate propagation, but
we'll ignore this as we said earlier
Fig 6-7 Bloss, Optical Crystallography, MSA
13

IMPORTANT A given ray of incoming light is
restricted to only 2 (mutually perpendicular)
vibration directions once it enters an
anisotropic crystal Called privileged
directions Each ray has a different n w no e
nE w lt e (in the case of calcite)
Fig 6-7 Bloss, Optical Crystallography, MSA
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n gt 1 for all anisotropic substances n
f(vibration direction) Indicatrix no longer a
sphere Indicatrix ellipsoid Hexagonal and
tetragonal xls have one unique xl axis (c axis)
2 identical ones --UNIAXIAL MINERALS The optical
properties reflect this as well ellipsoid of
rotation about c
15
Fig 6-10 Bloss, Optical Crystallography, MSA

• For light travelling parallel c, all vibration
  directions c are the same

• circular section of indicatrix ( c)
• thus behaves as isotropic
• (no unique plane containing ray and c-axis)
• only one ray (O-ray) with n w (doesnt split
  to two rays)
• extinct with analyzer in and stays that way as
  rotate stage

16

• For light travelling c get elliptical principal
  section of indicatrix
• get 2 rays
• O-ray with n w
• E-ray with n e
• this e (parallel c) is the maximum possible
  deviation in n from w (true e)

For random vibration direction ? same situation
as above Except that E-ray has some n between e
and w All intermediate values are called e (a
variable value between e and w)
17

• ellipsoid and conventions
• () crystal prolate e gt w
• (-) crystal oblate e lt w

Fig 6-11 Bloss, Optical Crystallography, MSA
18
Summary

• Circular Section
• ( optic axis all w's)
• extinct
• Principal Sections
• (have w and true e max min n's) largest
  birefringence!
• Random Sections (e' and w)
• always have w!!
• Any cut through center of a uniaxial indicatrix
  will have w as one semiaxis

19
Color chart

• Shows the relationship between retardation,
  crystal thickness, and interference color
• 550 mm red violet
• 800 mm green
• 1100 mm red-violet again (note repeat
  ?)
• 0-550 mm 1st order 550-1100 mm 2nd
  order 1100-1650 mm 3rd order...
• Higher orders are more pastel

20
Example Quartz w 1.544 e 1.553
Data from Deer et al Rock Forming Minerals John
Wiley Sons
21

• Example Quartz w 1.544 e 1.553

• Sign??
• () because e gt w
• e - w 0.009 and is called the birefringence (d)
  maximum interference color
• What color is this??
• 1) Follow line 0.009 in toward origin
• 2) Where it crosses 30 micron thickness (the
  standard for thin sections) we get a yellowish
  tan (see when quartz oriented with OA in plane of
  stage)
• For other orientations get e' - w progressively
  lower color
• Extinct when priv. direction N-S (every 90o)
• 360o rotation 4 extinction positions exactly
  90o apart

22
Conoscopic Viewing

• A condensing lens below the stage and a Bertrand
  lens above it
• Arrangement essentially folds planes of Fig 7-11
  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 Figures Very useful for
determining optical properties of xl
Fig 7-13 Bloss, Optical Crystallography, MSA
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Uniaxial Figure

• Circles of isochromes
• Note vibration directions
• w tangential
• e' radial variable magnitude
• 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

24
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
• 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

25
Accessory Plates
Fig 8-1 Bloss, Optical Crystallography, MSA

• Use a 1st-order red (gypsum) plate
• Slow direction is marked N on plate
• Fast direction (n) axis of plate
• The gypsum crystal is oriented and cut so that D
  (N-n) 550nm retardation
• ? thus it has the effect of retarding the N ray
  550 nm behind the n ray
• If insert with no crystal on the stage 1-order
  red in whole field of view

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Accessory Plates
N

• Suppose we view an anisotropic crystal with
  D 100 nm (1-order gray) at 45o from
  extinction

n

• If Ngyp Nxl Addition
• Addition since ray in xl Ngyp
• already behind by 100nm it gets further
  retarded by 550nm in the gypsum plate
• 100 550 650nm
• On your color chart what will result?
• Original 1o grey 2o blue

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Optic Sign Determination

• For all xls remember e' vibrates in plane of ray
  and OA, w vibr normal to plane of ray and OA

1) Find a uniaxial crystal in which the optic
axis (OA) is vertical (normal to the stage)
How? 2) Go to high power, insert condensing and
Bertrand lenses to optic axis interference
figure
() crystals e gt w so w faster
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Fig 7-13 Bloss, Optical Crystallography, MSA
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Optic Sign Determination

• Inserting plate for a () crystal
• subtraction in NW SE where nN
• addition in NE SW where NN
• Whole NE ( SW) quads add 550nm
• isochromes shift up 1 order
• Isogyre adds red
• In NW SE where subtract
• Each isochrome loses an order
• Near isogyre (100nm)
• get yellow in NW SE
• and blue in NE SW

add
sub
add
sub
() crystals e gt w so w faster
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() OA Figure without plate
() OA Figure with plate Yellow in NW is ()
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(-) OA Figure without plate (same as () figure)
(-) OA Figure with plate Blue in NW is (-)
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Estimating birefringence
1) Find the crystal of interest showing the
highest colors (D depends on orientation) 2) Go
to color chart thickness 30 microns (but slides
can be thick!) use 30 micron line color, follow
radial line through intersection to margin read
birefringence Suppose you have a mineral with
second-order green What about third order yellow?
33
Pleochroism

• Changes in absorption color in PPL as rotate
  stage (common in biotite, amphibole)
• Pleochroic formula
• Tourmaline e dark green to bluish
  w colorless to tan
• Can determine this as just described by isolating
  first w and then e E-W and observing the color

34
Biaxial Crystals

• Orthorhombic, Monoclinic, and Triclinic xls don't
  have 2 or more identical crystallographic axes
• The indicatrix is a general ellipsoid with three
  unequal, mutually perpendicular axes
• One is the smallest possible n and one the largest

Fig 10-1 Bloss, Optical Crystallography, MSA
a smallest n (fastest) b intermediate n g
largest n (slowest) The principal vibration
directions are x, y, and z ( x a, y b, z
g) By definition a lt a' lt b lt g 'lt g
35
Biaxial Crystals
g

• If a lt b lt g then there must be some point
  between a g with n b
• Because b in plane, and true b is normal to
  plane, then the section containing both is a
  circular section
• Has all of the properties of a circular section!
  If look down it
• all rays b
• no preferred vibration direction
• polarized incoming light will remain so
• thus appear isotropic as rotate stage

b
a
Looking down true b
36
Biaxial Crystals
g

• If a lt b lt g then there must be some point
  between a g with n b

OA
optic axis by definition
b
a
Looking down true b
37
Biaxial Crystals
g

• If a lt b lt g then there must be some point
  between a g with n b

OA
OA
optic axis by definition And there must be two!
? Biaxial Hexagonal and tetragonal are Uniaxial
b
a
b
Looking down true b
38
Biaxial Crystals

• Nomenclature
• 2 circular sections 2 optic axes Must be in
  a-g plane Optic Axial Plane (OAP)
• Y b direction OAP optic normal

Fig 10-2 Bloss, Optical Crystallography, MSA

• Acute angle between OA's 2V
• The axis that bisects acute angle acute
  bisectrix Bxa
• The axis that bisects obtuse angle obtuse
  bisectrix Bxo

39
Biaxial Crystals
g

• B() defined as Z (g) Bxa
• Thus b closer to a than to g

OA
OA
b
a
b
Looking down true b
40
Biaxial Crystals
g

• B(-) defined as X (a) Bxa
• Thus b closer to g than to a

b
OA
a
OA
b
Looking down true b
41
Biaxial Interference Figures
Fig 10-15 Bloss, Optical Crystallography, MSA

• Bxa figure
• Result is this pattern of isochromes for biaxial
  crystals

42
Biaxial Interference Figures
Centered Bxa Figure
Fig 10-16 Bloss, Optical Crystallography, MSA
43
Biaxial Interference Figures
Same figure rotated 45o Optic axes are now
E-W Clearly isogyres must swing
44
As rotate Centered Optic Axis Figure Large
2V Bxa Figure with Small 2V
Not much curvature
45
Biaxial Optic Sign

• B(-) a Bxa thus b closer to g

100 gray 550 650 blue
add
subtract
add
100 gray - 550 450 yellow
46
Biaxial Optic Sign

• B(-) a Bxa thus b closer to g (in stage)

Centered Bxa 2V 35o
Centered Bxa 2V 35o With accessory plate
47
Biaxial Optic Sign

• B() g Bxa thus b closer to a (in stage)

sub
add
sub
48
Estimating 2V
Fig 11-5A Bloss, Optical Crystallography, MSA
OAP