Biaxial optics

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Biaxial optics

• Nesse, 1991
• Chapter 7, page 77 to 108

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Biaxial Minerals

• Minerals in orthorhombic, monoclinic and
  triclinic
• specify length of unit cell along all three
  crystallographic axes
• Also specify three indices of refraction
• named a, b, and g (in book called na, nb and
  ng)
• Where na lt nb lt ng
• so maximum birefringence is ng- na

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Biaxial minerals

• 3 indices of refraction na lt nb lt ng
• Light still broken into two rays, one fast one
  slow
• Both rays are extraordinary
• Slow ray is always ng, with ng gt ng gt nb
• Fast ray is always na, with na lt nalt nb

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Biaxial Indicatrix
Similar to uniaxial indicatrix Main difference -
3 principal indices instead of 2 The 3 indices
are plotted on 3 mutually perpendicular axes n?
is always plotted on X-axis n? plotted on
Y-axis n? plotted on Z-axis The Biaxial
indicatrix is a Triaxial Ellipsoid (elongate
along the Z-axis)
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Biaxial Minerals
3 Principal sections

• X-Y,
• X-Z, and
• Y-Z plane

na
nb
ng
na
ng
nb
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Biaxial Minerals

• The biaxial indicatrix has 2 circular sections
  with radius nb
• The 2 optic axes (O.A.) are perpendicular to
  these circular sections
• The angle between the 2 O.A.s is called 2V
• Axis bisecting acute angle is acute bisectrix or
  Bxa
• Axis bisecting obtuse angle is obtuse bisectrix
  or Bxo

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Optic Sign?
Zacute bxa optically positive
Zobtuse bxo optically negative
2V
Obtuse bisectrix
Z
Z
2Vx
Acute bisectrix
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Example Normal incidence parallel to an optic
axis
Produces isotropic section (remains dark on
rotation between crossed polars)
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• Random section

Indicatrix section is an ellipse with R.I. values
of n? n?? Section - Partial birefringence
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Fig 7.7
REMEMBER The axes of the biaxial indicatrix
indicate the refractive indices and the vibration
directions
Example Normal incidence parallel to an
indicatrix axis
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Relationship between crystallographic axes and
indicatrix axes

• Orthorhombic minerals
• Crystallographic axes and indicatrix axes coincide

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• Monoclinic minerals
• b-axis coincides with one of the indicatrix axes

b
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• Triclinic minerals
• None of crystal axes coincides with indicatrix
  axes

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Biaxial Interference Figures
Interference figures obtained in same manner as
uniaxial ones Conoscopic light High power
objective Condenser lens Bertrand lens Cross
polars Biaxial interference figures are
distinctly different from uniaxial figures Can be
used to distinguish biaxial or uniaxial mineral
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Biaxial acute bisectrix figure - when acute
bisectrix oriented perpendicular to the
microscope stage
isochrome
Optic plane oriented E-W
Optic plane in 45º position
7.12
45 degree position
0 degree position
melatopes
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Optic plane
Optic Normal
isochrome
isogyre
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2Vgt60
7.17
Use change of isogyres of acute bisectrix with
rotation of the stage NOTE If melatopes rotate
out 30º of rotation THEN 2V gt 60o
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Centered Optic Axis Figure

• when one of the optic axes is vertical, the
  melatope will be under the cross-hair
• other melatope in field of view if 2V lt 30º

Optic plane in 45 position
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• Estimating 2V on the basis of the curvature of
  the isogyre in a centered optic axis figure
• If both melatopes in field of view, the 2V can be
  estimated. When 2V is zero, figure is a uniaxial
  cross

Both melatopes in FOV
Fig 7.32
One melatope in FOV
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Extinction in orthorhombic minerals
REMEMBER Extinction angle is the angle between a
cleavage trace extinction position. This angle
varies depending on crystal orientation.
Fig 7.33
parallel extinction
Cut parallel to c-axis-prismatic cleavage
random section - inclined extinction
symmetrical extinction - cut parallel to (001)
NOTE Usually, cleavages are parallel to 3
crystallographic axes (100)(010) (001) are
pinacoidal cleavages - common in Biaxial minerals.
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Extinction in monoclinic minerals
For Monoclinic minerals, 1 axis of indicatrix is
parallel to the b crystallographic axis
Fig 7.34
parallel extinction - prismatic cleavage
inclined extinction
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Sign of elongation
Length fast or negative elongation
Length slow or positive elongation

• Length fast or length slow?
• Elongate minerals
• When z-axis is parallel to the length - length
  slow (ve)
• When X-axis is parallel to the length - length
  fast (-ve)

or -
or -
positive
Platy minerals
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Determining the optical properties of an oriented
mineral.Section (100), (010), and (001)
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• (100) perpendicular to a-axis so b and c-axis in
  field of view
• Draw grain and determine color and relief
• Cross polars and determine fast and slow
  direction
• Make interference figure

One ray is fast and other slow
The optic direction towards you is // to a-axis,
bxa, bxo or ON
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• (010) perpendicular to b-axis, so a and c-axis
  in field of view
• Draw grain and determine color and relief
• Cross polars and determine fast and slow
  direction
• Make interference figure

One ray is fast and other slow
The optic direction towards you is // to a-axis,
bxa, bxo or ON
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• (001) perpendicular to b-axis, so a and c-axis
  in field of view
• Draw grain and determine color and relief
• Cross polars and determine fast and slow
  direction
• Make interference figure

One ray is fast and other slow
The optic direction towards you is // to a-axis,
bxa, bxo or ON
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• Now you know which optical direction is parallel
  to the a, b, and c-axis
• With your interference figure you can estimate
  the 2V.
• Draw all the information on a block diagram