1. Optical Mineralogy WS 2008/2009

2. Last week…. Indicatrix - 3-d representation of changing n in minerals (Z = biggest = slowest, X = smallest = fastest) Uniaxial indicatrix - ellipsoid of rotation  tetragonal, hexagonal and trigonal crystal systems Uniaxial indicatrix can be positive (prolate or ‘rugby ball’) or negative (oblate or ‘smartie’) Basal section  circular  o-ray (n  ) only  isotropic Random section  ellipse  o-ray and e’-ray (n    n  '  )  intermediate polarisation colour Principal section  ellipse  o-ray and e-ray (n    n  )  maximum birefringence (  n)  highest polarisation colour

3. Uniaxial indicatrix – ellipsoid of rotation optic axis ≡ c-axis n e n o b=Y=X c=Z a=X n e b=Y=X c=X n o a=X n e > n o uniaxial positive (+) PROLATE or ‘RUGBY BALL‘ n e < n o uniaxial negative (-) OBLATE or ‘SMARTIE‘ NOTE: n o = n  n e  n 

4. Last week…. Polarisation colours - result of retardation (  v) between o- and e-rays  = retardation = d ∙  n  = retardation = d ∙  n Michel-Levy colour chart  find maximum polarisation colour  25  m sections  measure birefringence (  n)  CHARACTERISTIC OF MINERAL Colours reported by order and colour ….fringe counting….

5. The Biaxial Indicatrix (….the potato….) For orthorhombic, monoclinic and triclinic crystal systems: The indicatrix is a triaxial ellipsoid with the axes X, Y, Z The indicatrix has 3 principal refractive indices - n  < n  < n  The XZ plane (maximum  n) is the OPTIC AXIAL PLANE  n  = smallest n  n  = intermediate n  n  = largest n Possible vibration directions = XYZ X, Y and Z  X || n , Y || n , Z || n     ' <    ' <  n   n  ' < n   n  ' < n 

6. Biaxial indicatrix - principal section (XZ) As n  < n  < n , there must be a point between n  und n  with n = n  This gives a circular section (= isotropic) The OPTIC AXIS is perpendicular to the circular section There must be 2 circular sections  optically BIAXIAL The optic axes lie in the XZ plane and are perpendicular to n   OPTIC AXIAL PLANE (max  n) OAOA Cut ^ n  nn nn = n 

7. The Bisectrix & 2V Angle between the optic axes  2V angle  2V X and 2V Z Bisector of this angle  Bisectrix  B X or B Z If the angle is acute  acute bisectrix (2V < 90°) If the angle is obtuse  obtuse bisectrix (2V > 90°) 2V X 2V Z OA BXBX BZBZ

8. Optical Sign (+ or -) Biaxial positive (+) Biaxial positive (+) defined as 2V Z < 90° …or… n  closer to n  than to n  ‘RUGBY BALL’ like Biaxial negative (-) Biaxial negative (-) defined as 2V Z > 90° …or… n  closer to n  than to n  ‘SMARTIE’ like

9. Biaxial indicatrix - summary

10. How do we know? We use CONOSCOPIC light to see whether a crystal is uniaxial or biaxial, positive or negative…. ….next two weeks….

11. Vibration directions & EXTINCTION In any random cut through an anistropic indicatrix, the privileged vibration directions are the long and short axis of the ellipse. We know where these are from the extinction positions….

12. Extinction Angle The EXTINCTION ANGLE is the angle between a linear feature in the crystal (a crystal edge, a cleavage plane, a twin plane) and the extinction position. The EXTINCTION ANGLE is (surprise, surprise) directly related to the CRYSTAL SYSTEM…. …more specifically, the angular relationship with the c-axis and the other crystallographic axes….

13. Symmetry and extinction angles In cubic minerals and those in the tetragonal, hexagonal and trigonal systems (= uniaxial minerals), the c-axis is at 90° to the other crystallographic axes….  STRAIGHT EXTINCTION

14. Symmetry and extinction angles This is also true of orthorhombic minerals  STRAIGHT EXTINCTION For minerals in the monoclinic and triclinic systems (= biaxial), the c- axis is NOT at 90° to all the other crystallographic axes….  INCLINED EXTINCTION

15. Extinction Angle Extinction angle  = I – II = 29,5° I = 153,0° II = 182,5° Only the MAXIMUM extinction angle is diagnostic of a mineral  measure lots of grains

16. Extinction Angle Only the MAXIMUM extinction angle is diagnostic of a mineral  measure lots of grains The maximum is the angle between the c-axis (crystallographic) and the Z-axis ( biaxial indicatrix)

17. Troeger….

18. Troeger Tables

19. Extinction Angle - Plagioclase