Optical Mineralogy WS 2012/2013

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

Biaxial indicatrix - summary

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

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)

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). ?

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 ?

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 ….

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 -

Hauptzone + or -?

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….

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

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

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

Zoning (XN) Reflects compositional differences in solid solution minerals

Zoning

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

So why do we see polarisation colours?

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)

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, …

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

 Retardation,  Wavelength, / / / / 8 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

 Retardation,  Wavelength, / / / 2 3 / / 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

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)