Optical Mineralogy

WS 2012/2013

The week before last….

BIAXIAL INDICATRIX

EXTINCTION ANGLES

Biaxial indicatrix - summary

Extinction Angle

Extinction anglee = 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)

Vibration direction of the higher n ray (slow ray) is NE-SW

Vibration direction of the lower n ray (fast ray) is NW-SE

Retardation = 550nm (= 1 order)

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 (1o Grey) in diagonal position:

With analyser only

With analyser and compensator

1o Grey 2o Blue

GMineral = 100 nm (1o Grey)

GGips = 550 nm (1o Red)

Gobs = GMineral + GGyps

Gobs = 650 nm (2o Blue)

When the interference colour is 1o 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)

GMineral = 100 nm (1o Grey)

GGips = 550 nm (1o Red)

Gobs = |GMineral – GGips|

Gobs = 450 nm (1o Orange)

When the interference colour is 1o lower (subtraction), then the NE-

SW direction is the lower n - fast ray.

With analyser only

With analyser and compensator

1o Grey 1o 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 g

If slow ray (n) of compensator is parallel to the slow ray of the mineral (higher n) (Addition)

Length slow

ngna

If slow ray (n) of compensator is perpendicular to slow ray of the mineral (lower n) (Subtraction)

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

Polarisedlight (E_W)

Fast wavewith vf

(lower nf)Slow wave with vs

(higher ns)

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/vs

Fast wave: t = d/vf + /vair

…and so d/vs = d/vf + /vair

= d(vair/vs - vair/vf)

= d(ns - nf)

= d ∙ Δn

Retardation, = d ∙ Δn (in nm)

Interference

Polariser forces light to vibrate E–W Light split into two perpendicular rays Analyser forces rays to vibrate in the N-

S plane and interfere.

Destructive interference (extinction):

= k∙k = 0, 1, 2, 3, …

Constructive interference (maximum intensity):

= (2k+1) ∙ /2k = 0, 1, 2, 3, …

Retardation, 550 550 550 550 550 550Wavelength, 400 440 489 550 629 733

13/8 l 11/4 l 11/8 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, 800 800 800 800 800 800 800Wavelength, 400 426 457 550 581 711 800

2 l 17/8 l 13/4 l 11/2 l 13/8 l 1 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 Crystal shape/form Transparent or opaque Colour and pleochroism Relief and (variable) refractive index Cleavage, fracture

Orthoscopic, XN (in the diagonal position) Isotropic or anisotropic Maximum polarisation colour birefringence (n) Extinction angle crystal system Length fast or slow Zoning (normal, oscillatory, etc.) Twinning (simple, polysynthetic, sector)