1. GEOL 3055 Morphological and Optical Crystallography JHSchellekens
Biaxial optics
Nesse, 1991
Chapter 7, page 77 to 108
13 Biaxial Optics

2. Optics Crystal system Unit cell Isotropic minerals a1=a2=a3
Indices of refraction
Isotropic minerals
Isometric
Highly symmetric
a1=a2=a3
One index of refraction
Uniaxial minerals
Tetragonal hexagonal
Less symmetric
a1=a2=c
Two indices of refraction
Biaxial minerals
Orthorhombic
Monoclinic
Triclinic
Even less symmetry
a=b=c
Three indices of refraction

3. 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 < nb < ng
so maximum birefringence is ng- na

4. Biaxial minerals 3 indices of refraction: na < nb < ng
Light still broken into two rays, one fast & one slow
Both rays are extraordinary
Slow ray is always ng’, with ng > ng’ > nb
Fast ray is always na’, with na < na’< nb

5. 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)

6. Biaxial Minerals X-Y, X-Z, and Y-Z plane 3 Principal sections na nb ng

7. 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

8. 2V 2Vx Optic Sign? Obtuse bisectrix Acute bisectrix
Z=acute bxa = optically positive
Z=obtuse bxo = optically negative 2V
Obtuse bisectrix Z Z
2Vx
Acute bisectrix

9. Example: Normal incidence parallel to an optic axis
Produces isotropic section (remains dark on rotation between crossed polars)

10. Random section
Indicatrix section is an ellipse with R.I. values of n’ & n’
Section - Partial birefringence

11. Example: Normal incidence parallel to an indicatrix axis
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

12. Relationship between crystallographic axes and indicatrix axes
Orthorhombic minerals
Crystallographic axes and indicatrix axes coincide

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

14. Triclinic minerals
None of crystal axes coincides with indicatrix axes

15. 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

16. 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
0 degree position
45 degree position
melatopes

17. Optic plane
Optic Normal
isochrome
isogyre

18. Use change of isogyres of acute bisectrix with rotation of the stage
2V>60
7.17
Use change of isogyres of acute bisectrix with rotation of the stage
NOTE: If melatopes rotate out ~ 30º of rotation THEN 2V > 60o

19. 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 < 30º
Optic plane in 45° position

20. 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

21. 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.

22. 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

23. Sign of elongation Length fast or length slow? Elongate minerals
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

24. Determining the optical properties of an oriented mineral
Determining the optical properties of an oriented mineral. Section (100), (010), and (001)

25. (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

26. (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

27. (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

28. 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