Optical MineralogyOptical Mineralogy

WS 2008/2009WS 2008/2009

Next week ….Next week ….

So far ….So far ….

• Light - properties and behaviour;

• Refraction - the refractive index (n) of minerals leads to many of their optical properties Snell’s law - learn it!;

• Double refraction;

• Polarization and the polarizing microscope;

• Plane polarised light observations (PPL):• crystal shape/habit• colour/pleochroism• cleavage/fracture• relief, Becke test refractive index estimation

Crystal systems and symmetryCrystal systems and symmetry

The crystal systems are sub-divided by their degree of symmetry….

CUBIC > TETRAGONAL, HEXAGONAL, TRIGONAL > ORTHORHOMBIC, MONOCLINIC, TRICLINIC

The Optical IndicatrixThe 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 n at that point.

The simplest case - cubic minerals (e.g. garnet)

The Optical IndicatrixThe Optical Indicatrix

• 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?

Spheren is constant is every direction -isotropic minerals do not change the vibration direction of the light - no polarisation

Indicatrix = Indicatrix = 3-d representation of refractive index

Isotropic indicatrix (= cubic)Isotropic indicatrix (= cubic)

Isotropic indicatrixIsotropic indicatrix

Beobachtungen unter gekreuzten Polarisatoren(gekreuzte Nicols)

XPL = crossed nicols (crossed polars)

West (links)

Ost (rechts)

Süden (vorne)

Norden (hinten)

Schwarz!!

z.B. Granat

Polarisator Analysator

Isotropic minerals and polarized lightIsotropic minerals and polarized light

Anisotropic minerals – Double refractionAnisotropic minerals – Double refraction

Example: Calcite

The incident ray is split into 2 rays that vibrate perpendicular to each other.

These rays have variable vv (and therefore variable nn) fast and slow rays

One of the rays (the fast ray for calcite) obeys Snell’s Law - ordinary ray (no)

The other ray does not obey Snell’s law - extraordinary ray (ne)

Birefringence = ΔBirefringence = Δnn = = nnee − − nnoo

QuartzQuartz CalciteCalcite

c-axis

Anisotropic Minerals – The Uniaxial IndicatrixAnisotropic Minerals – The Uniaxial Indicatrix

c-axis

What does the indicatrix for each mineral look like?

Uniaxial indicatrix – ellipsoid of rotationUniaxial indicatrix – ellipsoid of rotation

optic axis ≡ c-axis

ne

no b=Y=X

c=Z

a=X

ne

b=Y

c=X

no

a=X

ne > no

uniaxial positive (+)

PROLATE or ‘RUGBY BALL‘

ne < no

uniaxial negative (-)

OBLATE or ‘SMARTIE‘

NOTE:no = n

nen

Quartzne > no

uniaxial positive

Calcitene < no

uniaxial negative

Uniaxial IndicatrixUniaxial Indicatrix

All minerals belonging to the TRIGONAL, TETRAGONAL and HEXAGONAL crystal 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)….

Basal sectionBasal sectionCut perpendicular to the optic axis:

only no

No birefringence (isotropic section)

Principal sectionPrincipal section Parallel to the optic axis: no & ne

Maximum birefringence

Random sectionRandom section ne' and no

ne' is between ne and no

Intermediate birefringence

All sections contain no!

Different slices through the indicatrix (+)Different slices through the indicatrix (+)

Isotropic sectionIsotropic section(remains black in XN)

n

n =a X

=c Z

=b Y

Cut PERPENDICULAR to the c-axis,Contains only no (n)

Basal SectionBasal Section

The principal section shows MAXIMUM The principal section shows MAXIMUM birefringence and the HIGHEST polarisation birefringence and the HIGHEST polarisation colourcolour

DIAGNOSTIC PROPERTY OF MINERAL

n > n

Principal SectionPrincipal SectionCut PARALLEL to the c-axis,contains no (n) und ne (n)

A random section shows an intermediate A random section shows an intermediate polarisation colourpolarisation colour

no use for identification purposes

Random SectionRandom SectionCut at an angle to the c-axis,contains no (n) und ne‘ (n‘)

Double RefractionDouble Refraction

Privileged Vibration directions

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….

Polariser parallel to ne:

only the extraordinary ray is transmitted inserting the analyser BLACKBLACK

= = EXTINCTION POSITIONEXTINCTION POSITION

Polariser parallel to no:

only the ordinary ray is transmitted inserting the analyser BLACKBLACK

= = EXTINCTION POSITIONEXTINCTION POSITION

Polariser

ne

no

Parallel positionParallel position

no

ne

As both rays are forcedto vibrate in the N-S direction,

they INTERFERE

Split into perpendicular two rays (vectors) :

1) ordinary ray where n = no

2) extraordinary ray where n = ne

Each ray has a N-S component, which are able to pass through the analyser.

Maximum brightness is in the diagonal position.

nneennoo

Polariser

Diagonal positionDiagonal position

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 (Retardation (GangunterschiedGangunterschied))

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 ∙ ΔnRetardation, = d ∙ Δn (in nm)

….and we know d (= 30m)….

InterferenceInterference

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) ∙ /2

k = 0, 1, 2, 3, …

Explanation of interference coloursExplanation of interference colours

Example: a mineral with retardation of 550 nm in the diagonal position

Retardation, 550 550 550 550 550 550Wavelength, 400400 440440 489489 550550 629629 733733

1133//88 l 1111//44 l 1111//88 l 11 l 77//88 l 33//44 l

550 nm is lost, other wavelengths will be partly or fully transmitted.

Retardation, 550 550 550 550 550 550Wavelength, 400400 440440 489489 550550 629629 733733

1133//88 l 1111//44 l 1111//88 l 11 l 77//88 l 33//44 l

No green (absorbed) red + violet purple interference colour

Fig 7-7 Bloss, Optical Crystallography, MSA

Retardation, 800 800 800 800 800 800 800Wavelength, 400400 426426 457457 550550 581581 711 800711 800

22 l 1177//88 l 1133//44 l 1111//22 l 133//88 l 1 1 11//88 l 11 l

No red or violet(absorbed) green interference colour

Fig 7-7 Bloss, Optical Crystallography, MSA

Michel-Lévy colour chartMichel-Lévy colour chart

thic

knes

s of

sec

tion

birefringence ()

30 m (0.03 mm)

= 0.009 = 0.025

first order second order third order

lines of constant

Michel-Lévy colour chartMichel-Lévy colour chart

retardation ()

….orders separated by red colour bands….

Uniaxial indicatrix - summaryUniaxial indicatrix - summary

Can be positive or negative;

Mierals of the tetragonal, 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 nw;

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.

Polarisation coloursPolarisation 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.).

Todays practical…..Todays practical…..

Making the PPL observations you made in the previous 2 weeks;

Putting a scale on your sketches to estimate grain sizes;

Distinguishing isotropic from anisotropic minerals;

Calculating retardation;

Calculating and reporting birefringence - fringe counting.

Thinking about vibration directions….