Optical Mineralogy WS 2008/2009

Next week ….

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

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 n at that point.

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

Sphere n 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

Beobachtungen unter gekreuzten Polarisatoren (gekreuzte Nicols) XPL = crossed nicols (crossed polars) West (links) Ost (rechts) Süden (vorne) Norden (hinten) Schwarz!! z.B. Granat PolarisatorAnalysator Isotropic minerals and polarized light

Anisotropic minerals – Double refraction Example: Calcite The incident ray is split into 2 rays that vibrate perpendicular to each other. v n These rays have variable v (and therefore variable n)  fast and slow rays One of the rays (the fast ray for calcite) obeys Snell’s Law - ordinary ray (n o ) The other ray does not obey Snell’s law - extraordinary ray (n e )  Birefringence = Δn = n e − n o

Optic axis O E However, there is always a direction in which a ray of transmitted light suffers no double refraction - this is the OPTIC AXIS = c-axis Ordinary ray vibrates perpedicular to the optic axis (= c-axis) Extraordinary ray vibrates parallel to the optic axis (= c- axis)

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

Uniaxial indicatrix – ellipsoid of rotation optic axis ≡ c-axis n e n o b=Y=X c=Z a=X n e b=Y c=X n o a=X n e > n o uniaxial positive (+) PROLATE or ‘RUGBY BALL‘ n e < n o uniaxial negative (-) OBLATE or ‘SMARTIE‘ NOTE: n o = n  n e  n 

Quartz n e > n o uniaxial positive Calcite n e < n o uniaxial negative

Uniaxial 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 section Basal section Cut perpendicular to the optic axis: only n o  No birefringence (isotropic section) Principal section Principal section Parallel to the optic axis: n o & n e  Maximum birefringence Random section Random section  n e' and n o  n e' is between n e and n o  Intermediate birefringence All sections contain n o ! Different slices through the indicatrix (+)

Isotropic section (remains black in XN) Cut PERPENDICULAR to the c- axis, Contains only n o (n  ) Basal Section

The principal section shows MAXIMUM birefringence and the HIGHEST polarisation colour  DIAGNOSTIC PROPERTY OF MINERAL n  > n  Principal Section Cut PARALLEL to the c-axis, contains n o (n  ) und n e (n  )

A random section shows an intermediate polarisation colour  no use for identification purposes Random Section Cut at an angle to the c-axis, contains n o (n  ) und n e‘ (n  ‘ )

Double 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 n e :  only the extraordinary ray is transmitted BLACK inserting the analyser  BLACK = EXTINCTION POSITION Polariser parallel to n o :  only the ordinary ray is transmitted BLACK inserting the analyser  BLACK = EXTINCTION POSITION Polariser nene nono Parallel position nono nene

As both rays are forced to vibrate in the N-S direction, they INTERFERE Split into perpendicular two rays (vectors) : 1) ordinary ray where n = n o 2) extraordinary ray where n = n e  Each ray has a N-S component, which are able to pass through the analyser.  Maximum brightness is in the diagonal position. nenenene nononono Polariser Diagonal position

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) ….and we know d (= 30  m)….

Interference 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, …

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

Explanation of interference colours Example: a mineral with retardation of 550 nm in the diagonal position  Retardation,  Wavelength, / / / / 8 3 / / 8 l1 1 / 4 l1 1 / 8 l 1 l 7 / 8 l 3 / 4 l  550 nm is lost, other wavelengths will be partly or fully transmitted.

 Retardation,  Wavelength, / / / / 8 3 / / 8 l 1 1 / 4 l 1 1 / 8 l 1 l 7 / 8 l 3 / 4 l No green (absorbed)  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 (absorbed)  green interference colour Fig 7-7 Bloss, Optical Crystallography, MSA

Michel-Lévy colour chart

thickness of section birefringence (  ) 30  m (0.03 mm)  =  = first ordersecond orderthird order lines of constant  Michel-Lévy colour chart retardation (  ) ….orders separated by red colour bands….

Uniaxial 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 n w ; 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 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….. 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….