Pleochroism and biaxial indicatrix

1. Pleochroism and biaxial indicatrix

2. Pleochroism • Seen in plane polarized light or x-polars? • Tourmaline • Uniaxial negative • E-ray is fast ray, what color is associated with it? • O-ray is slow ray, what color is associated with it?

3. Pleochroism • When a ray is vibrating parallel to lower polarizer, you see the associated color • 1) Cross polars, find grain with lowest interference colors (optic axis vertical or all o-ray), uncross polars, note color

4. Pleochroism • 2) cross polars, find grain with highest interference colors (optic axis horizontal, o and e-rays in stage) • Orient at extinction, rotate 45°clockwise from here • Slide in accessory plate, if addition you have slow ray • Uncross polars, remove plate, rotate 45° clockwise and note color for slow ray color • Rotate another 90° and note fast ray color

5. Isometric a=b=c Hexagonal a=b=c Tetragonal a=b=c Orthorhombic a=b=c Monoclinic a=b=c Triclinic a=b=c Isotropic Uniaxial Uniaxial Biaxial Biaxial biaxial Crystal systems

6. Biaxial minerals • 2 optical axis • Indices of refraction n, n, n • nnn so is slow ALWAYS • What is max. birefringence? • 3 indices, only 2 light rays in mineral • Both are e-rays

7. Biaxial Crystals Orthorhombic, Monoclinic, and Triclinic crystals don't have 2 or more identical crystal 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) • Theprincipal vibration directionsare x, y, and z ( x || a, y || b, z || g) • By definitiona < a' < b < g '< g

8. Which plane has max birefringence? • Which plane has min birefringence?

9. Biaxial Crystals g 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 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

10. Biaxial Crystals g If a < b < g then there must be some point between a & g with n = b OA ^ optic axis by definition = b a Looking down true b

11. g OA OA = b a = b Looking down true b Biaxial Crystals If a < b < g then there must be some point between a & g with n = b ^ optic axis by definition And there must be two! Biaxial Orthorhombic, Monoclinic, and Triclinic minerals are thus biaxial and Hexagonal and tetragonal minerals are uniaxial

12. 2 circular sections with radius n

13. Perpendicular to the circular section is the optic axis

14. X-Z plane is the optic plane

15. Optic plane contains optic axes

16. Angle between optic axes is the 2V • Acute angle between optic axes is the acute bisectrix or Bxa

17. Angle between optic axes is the 2V • obtuse angle between optic axes is the obtuse bisectrix or Bxo

18. Optic sign determined if Z or X axis is Bxa

21. Optic orientation linked to symmetry!

22. Optic orientation linked to symmetry!

23. Optic orientation linked to symmetry!

24. Possible orientations • Light passes parallel to y-axis • X and Z in plane of stage • How do you ID a grain in this orientation?

25. Possible orientations • Light passes parallel to optic axis • How do you ID a grain in this orientation?

26. Possible orientations • Random orientation • How do you ID a grain in this orientation?