1. Optical Mineralogy WS 2012/2013

2. The week before last…. l BIAXIAL INDICATRIX l EXTINCTION ANGLES

3. Biaxial indicatrix - summary

4. Extinction Angle Extinction angle  = I – II = 29,5° I = 153,0° II = 182,5° For MONOCLINIC and TRICLINIC crystals…. Only the MAXIMUM extinction angle is diagnostic of a mineral  measure lots of grains

5. Compensator (Gypsum plate) l Vibration direction of the higher n ray (slow ray) is NE-SW l Vibration direction of the lower n ray (fast ray) is NW-SE = 550nm l Retardation  = 550nm (= 1 order) l Observed retardation (in diagonal position):  Addition  obs =  Mineral +  Gyps  Subtraction  obs =  Mineral -  Gyps Gypsum plate ( -plate) = helps in measuring the relative size of n (e.g. allows identification of fast and slow rays)

6. Addition Example: Minerals with small birefringence (e.g. Quartz, Feldspar)  Mineral = 100 nm (1 o Grey) in diagonal position: With analyser only With analyser and compensator 1 o Grey2 o Blue  Mineral = 100 nm (1 o Grey)  Gips = 550 nm (1 o Red)  obs =  Mineral +  Gyps   obs = 650 nm (2 o Blue) When the interference colour is 1 o higher (addition), then the NE- SW direction is the higher n - slow ray (parallel to n  of the gypsum plate). ?

7. Subtraction Turn the stage through 90° (  Mineral stays at 100 nm )  Mineral = 100 nm (1 o Grey)  Gips = 550 nm (1 o Red)  obs = |  Mineral –  Gips |   obs = 450 nm (1 o Orange) When the interference colour is 1 o lower (subtraction), then the NE- SW direction is the lower n - fast ray. With analyser only With analyser and compensator 1 o Grey1 o Orange ?

8. Marking on vibration directions 1 – Rotate into extinction and draw the grain and its privileged vibration directions 2 – Rotate 45° until the polarisation colour is brightest Note the interference colour 3 – insert the gypsum plate Note the interference colour (addition or subtraction) 4 – rotate the mineral 90º Note the interference colour (addition or subtraction) 5 – Mark the fast (short line) and slow (long line) rays How do these relate to pleochroic scheme? Also a helpful way to tell the order of the polarisation colour ….

9. Length fast or length slow? nnnn If slow ray (n   of compensator is parallel to the slow ray of the mineral (higher n) (Addition) Length slow  Length slow nn nn If slow ray (n   of compensator is perpendicular to slow ray of the mineral (lower n) (Subtraction) Length fast  Length fast ALWAYS align length of mineral NE-SW = Hauptzone + = Hauptzone -

10. Hauptzone + or -?

11. Optical character and Hauptzone Prismatic crystal: If HZ + and Optically + If HZ - and Optically - Tabular crystal: If HZ + and Optically - If HZ - and Optically + Uniaxial minerals….

12. Long dimension of mineral is parallel to the slow ray (n  ) = LENGTH SLOW (HZ +) = PRISMATIC CRYSTAL Long dimension of mineral is parallel to the slow ray (n  ) = LENGTH SLOW (HZ +) = TABULAR CRYSTAL Sillimanite (+) Muscovite (-) Optical character and HZ

13. Exsolution (XN) Exsolution lamellae of orthopyroxene in augite Exsolution lamellae albite in K-feldspar (perthite)

14. Undulose extinction (XN) Undulose extinction in quartz, the result of strain

15. Zoning (XN) Reflects compositional differences in solid solution minerals

16. Zoning

17. Twinning (XN) simple (K-feldspar) polysynthetic (plagioclase) cross-hatched or ‘tartan‘ (microcline) sector (cordierite)

18. So why do we see polarisation colours?

19. Mineral Polarised light (E_W) Fast wave with v f (lower n f ) Slow wave with v s (higher n s ) Polariser (E-W)   = retardation d Retardation (Gangunterschied) After time, t, when the slow ray is about to emerge from the mineral: The slow ray has travelled distance d…..  The fast ray has travelled the distance d +  ….. Slow wave:t = d/v s  Fast wave: t = d/v f +  /v air  …and so d/v s = d/v f +  /v air   = d(v air /v s - v air /v f )   = d(n s - n f )   = d ∙ Δn  Retardation,  = d ∙ Δn (in nm)

20. Interference l Polariser forces light to vibrate E–W l Light split into two perpendicular rays l Analyser forces rays to vibrate in the N- S plane and interfere. l Destructive interference (extinction):   = k∙ k = 0, 1, 2, 3, … l Constructive interference (maximum intensity):   = (2k+1) ∙ /2 k = 0, 1, 2, 3, …

21. Transmission through the analyser  = retardation = d ∙  n   d ∙  n = 1  0% Transmission   d ∙  n = 1.5  100% Transmission Fig 7-6 Bloss, Optical Crystallography, MSA

22.  Retardation,  550550550550550550 400440489550629733 Wavelength, 400440489550629733 1 3 / 8 1 1 / 4 1 1 / 8 1 7 / 8 3 / 4 1 3 / 8 l 1 1 / 4 l 1 1 / 8 l 1 l 7 / 8 l 3 / 4 l No green (eliminated)  red + violet  purple interference colour Fig 7-7 Bloss, Optical Crystallography, MSA

23.  Retardation,  800800800800800800 800 400426457550581711 800 Wavelength, 400426457550581711 800 21 7 / 8 1 3 / 4 1 1 / 2 3 / 8 1 1 / 8 1 2 l1 7 / 8 l 1 3 / 4 l 1 1 / 2 l 1 3 / 8 l1 1 / 8 l 1 l No red or violet (eliminated)  green interference colour Fig 7-7 Bloss, Optical Crystallography, MSA

24. Orthoscopic properties - summary Orthoscopic, PPL FCrystal shape/form FTransparent or opaque FColour and pleochroism FRelief and (variable) refractive index FCleavage, fracture Orthoscopic, XN (in the diagonal position) FIsotropic or anisotropic  Maximum polarisation colour  birefringence (  n) FExtinction angle  crystal system FLength fast or slow FZoning (normal, oscillatory, etc.) FTwinning (simple, polysynthetic, sector)