1. Biaxial Crystals
Orthorhombic, Monoclinic, and Triclinic crystals don't have 2 or more identical crystallographic axes
The indicatrix is a triaxial 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 < a' < b < g '< g

2. Biaxial Crystals
If a < b < 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

3. Biaxial Crystals Perpendicular is by definition the optic axis;
Looking down b (  to g- a plane)
Biaxial Crystals g
If a < b < g then there must be some point between a & g with n = b OA OA
Perpendicular is by definition
the optic axis;
and there must be two!  Biaxial
Hexagonal and tetragonal are Uniaxial
= b a
= b

4. Biaxial Crystals Looking down true b g
Has all of the properties of a circular section!
all rays = b
no preferred vibration direction
polarized incoming light will remain so
unpolarized “ “ “ “
thus appear isotropic as rotate stage
= b a

5. 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
Acute angle between OA's = 2V
The axis that bisects the acute angle = acute bisectrix = Bxa
The axis that bisects the obtuse angle = obtuse bisectrix = Bxo

6. Biaxial Crystals B(+) defined as Z (g) = Bxa
Looking down true b
Biaxial Crystals g
B(+) defined as Z (g) = Bxa
described by the 2Vz angle
Thus b is closer to a than to g OA OA
= b a
= b

7. Biaxial Crystals B(-) defined as X (a) = Bxa
Looking down true b
Biaxial Crystals g
B(-) defined as X (a) = Bxa
described by the 2Vx angle
Thus b is closer to g than to a
= b OA a OA
= b

8. Biaxial Interference Figures
Bxa figure (Bxa is vertical on stage)
As in uniaxial, condensing lens causes rays to emanate out from O
OX ® OS ® OA
results in decreasing
retardation (color) as
g ® b
OA ® OT ® OU
Increase again, but
now because b ® a
OX ® OQ ® OP
 increase retardation
(interference colors)
OR is random with a' and g'
black
Fig Bloss, Optical Crystallography, MSA

9. Biaxial Interference Figures
Fig Bloss, Optical Crystallography, MSA
Bxa figure
Result is this pattern of isochromes for biaxial crystals

10. Biaxial Interference Figures
Application of B-F rule to conoscopic view Bxa figure
+ = bisectrices of optic axis planes
Isogyres are locus of all N-S (& E-W) vibration directions
Since incoming light vibrates E-W, there will be no N-S component ® extinct
Fig Bloss, Optical Crystallography, MSA

11. black

12. Biaxial Interference Figures
Centered Bxa Figure
Fig Bloss, Optical Crystallography, MSA

13. Biaxial Interference Figures
Same figure rotated 45o
Optic axes are now E-W
Fig 10-16B Bloss, Optical Crystallography, MSA

14. Centered Optic Axis Figure Large 2V:
As rotate
Centered Optic Axis Figure Large 2V:
Bxa Figure with Small 2V:
Not much curvature
Makes use of Bxa tricky

15. Biaxial Optic Sign B(-) a = Bxa thus b closer to g add subtract add
100 gray ® 650 blue
Fig. 11-1A
add
subtract
add
100 gray ® 450 yellow

16. Biaxial Optic Sign B(-) a = Bxa thus b closer to g (in stage) add
subtract
Centered Bxa 2V = 35o
Centered Bxa 2V = 35o
With accessory plate

17. Biaxial Optic Sign B(+) g = Bxa thus b closer to a (in stage) sub add
Fig. 11-1A
sub
add
sub

18. Always use Optic Axis Figure & curvature of isogyre to determine optic sign
How find a crystal for this?
Blue in NW is (-) still works

19. Estimating 2V
Fig 11-5A Bloss, Optical Crystallography, MSA
OAP

20. 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

21. Tourmaline

22. Sign of Elongation If g || elongation will always add ® length slow
If a || elongation will always subtract ® length fast g a N
U(-) will also ® length fast
U(+) will also ® length slow

23. Sign of Elongation If b || elongation Sometimes will add ® length slow
Sometimes will subtract ® length fast g b b a N

24. Sign of Elongation If b || elongation Sometimes will add ® length slow
Sometimes will subtract ® length fast g b b a N
Platy minerals may appear elongated too
Can still use sign of elongation on edges

25. Sign of Elongation

26. Cleavage Tendency of minerals to break parallel to atomic planes
Octahedral
Cubic
Dodecahedral
(12)
Prismatic
Basal
Rhombohedral

27. Extinction (symmetrical)

28. Extinction (symmetrical and parallel)

29. Extinction

30. Extinction (inclined)

31. Extinction Angles
Extinction angle is taken as the acute angle between a crystallographic direction (as seen by a crystal edge or cleavage direction) and a vibration direction. The extinctin angle is generally indicated e.g. Z^c where Z is the vibration direction and c is the crystallographic direction.
Extinction angles are taken as positive or negative with respect to a slow or fast vibration direction One source considers that a counter-clockwise rotation from a crystallographic direction to the slow vibration direction is a positive extinction angle, and a clockwise rotation is negative.

32. Extinction Angle Trace of a {110} cleavage Fast vibration direction
Slow vibration direction
-60º
+20º
Trace of a {110}
cleavage