Optical Mineralogy

1. Optical Mineralogy WS 2012/2013

2. Crystal systems and symmetry The crystal systems are sub-divided by their degree of symmetry…. CUBIC >TETRAGONAL, HEXAGONAL, TRIGONAL>ORTHORHOMBIC, MONOCLINIC, TRICLINIC

3. The Optical Indicatrix • The optical indicatrix is a 3-dimensional graphical representation of the changing refractive index of a mineral; • The shape of the indicatrix reflects the crystal system to which the mineral belongs; • The distance from the centre to a point on the surface of the indicatrix is a direct measure of the refractive index (n) at that point; • Smallest n = X, intermediate n = Y, largest n = Z

4. The Optical Indicatrix The simplestcase - cubicminerals (e.g. garnet) • Cubic minerals have highest symmetry (a=a=a); • If this symmetry is reflected in the changing refractive index of the mineral, what 3-d shape will the indicatrix be?

5. Isotropic indicatrix nisconstantiseverydirection - isotropic minerals do not change the vibration direction of the light - no polarisation Sphere Indicatrix = 3-d representation of refractive index

6. Isotropic indicatrix

7. Anisotropic minerals – Double refraction Example: Calcite • The incident ray is split into 2 rays that vibrate perpendicular to each other. • These rays have variable v (and therefore variable n)  fast and slow rays • As n ∞ 1/v, fast = small n, slow =big n • One of the rays (the slow ray for calcite) obeys Snell’s Law - ordinary ray (no) • The other ray does not obey Snell’s law - extraordinary ray (ne) • Birefringence = Δn = ne− no

8. Anisotropic Minerals – The Uniaxial Indicatrix c-axis c-axis Quartz Calcite What does the indicatrix for each mineral look like?

9. Uniaxialindicatrix – ellipsoid ofrotation c=Z c=X n e n e n n o o b=X b=Z a=Z a=X opticaxis ≡ c-axis NOTE: no = n nen n > n uniaxial positive (+) PROLATE or ‘RUGBY BALL‘ n < n uniaxial negative (-) OBLATE or ‘SMARTIE‘

10. Calcite n < n uniaxial negative Quartz n > n uniaxial positive

11. Uniaxial Indicatrix All minerals belonging to theTRIGONAL, TETRAGONALand HEXAGONALcrystal systems have a uniaxial indicatrix…. This reflects the dominance of the axis of symmetry (= c-axis) in each system (3-, 4- and 6-fold respectively)….

12. Different slicesthroughtheindicatrix • Basal section Cut perpendicular to the optic axis: only n  No birefringence (isotropic section) • Principal section Parallel to the optic axis: n & n  Maximum birefringence • Random section  n' and n  n' is between n and n  Intermediate birefringence • All sections contain n!

13. Basal Section Cut PERPENDICULARtothe c-axis, Containsonlyno (n) Isotropicsection (remainsblack in XPL)

14. Principal Section Cut PARALLELtothe c-axis, containsno (n) und ne (n) n > n The principalsectionshows MAXIMUM birefringenceandthe HIGHEST polarisationcolour  DIAGNOSTIC PROPERTY OF MINERAL

15. Random Section Cut at an angletothe c-axis, containsno (n) andne‘ (n‘) A randomsectionshows an intermediate polarisationcolour  no use for identification purposes

16. Double Refraction

17. Privileged Vibration directions In any random cut through an anistropicindicatrix, the privileged vibration directions are the long and short axis of the ellipse. We know where these are from the extinction positions….

18. Parallel position Polariser parallel to ne: onlytheextraordinaryrayistransmitted insertingtheanalyserBLACK = EXTINCTION POSITION Polariser parallel tono: onlytheordinaryrayistransmitted insertingtheanalyserBLACK = EXTINCTION POSITION ne no Polariser no ne

19. Diagonal position • Split intoperpendiculartworays (vectors) : • 1) ordinaryraywheren = no • 2) extraordinaryraywheren = ne • Eachrayhas a N-S component, whichareableto pass throughtheanalyser. • Maximum brightnessis in the diagonal position. no ne Polariser As bothraysareforced tovibrate in the N-S direction, theyINTERFERE

20. Retardation (Gangunterschied) • After time, t, whentheslowrayisabouttoemergefromthemineral: • The slowrayhastravelleddistance d….. • The fast rayhastravelledthedistanced+…..  = retardation Fast wavewithvf (lowernf) Slow wavewithvs (higherns) Slow wave: t = d/vs Fast wave: t = d/vf + /vair …and so d/vs = d/vf + /vair  = d(vair/vs - vair/vf)  = d(ns - nf)  = d ∙ Δn d Mineral Polarised light (E–W) Retardation,  = d ∙ Δn (in nm) Polariser (E-W)

21. Michel-Lévy colour chart

22. Michel-Lévy colour chart birefringence(d) d = 0.009 d = 0.025 30 mm (0.03 mm) thickness of section lines of constant d retardation() first order second order third order ….orders separated by red colour bands….

23. Which order? - Fringe counting…. birefringence(d) d = 0.009 d = 0.025 30 mm (0.03 mm) lines of constant d retardation()

24. Uniaxial indicatrix - summary • Can be positive or negative; • Mierals of the tertragonal, trigonal and hexagonal crystal systems have a uniaxial indicatrix; • All sections apart from the basal section show a polarisation colour; • All sections through the indicatrix contain n; • The basal section is isotropic and means you are looking down the c-axis of the crystal; • The principal section shows the maximum polarisation colour characteristic for that mineral.

25. Polarisation colours • Isotropic (cubic) minerals show no birefringence and remain black in XN; • Anisotropic minerals have variable n and therefore show polarisation colours; • The larger n is, the higher the polarisation colour; • The polarisation colour is due to interference of rays of different velocities; • THE MAXIMUM POLARISATION COLOUR IS THE CHARACTERISTIC FEATURE OF A MINERAL (i.e., look at lots of grains); • Polarisation colours should be reported with both ORDER and COLOUR (e.g., second order blue, etc.).

26. Todays practical….. • Making the PPL observations you made last week; • Distinguishing isotropic from anisotropic minerals; • Calculating retardation; • Calculating and reporting birefringence - fringe counting. • Thinking about vibration directions….