Optical MineralogyOptical Mineralogy

WS 2008/2009WS 2008/2009

Last week….Last week…. Indicatrix - 3-d representation of changing n in minerals

(Z = biggest = slowest, X = smallest = fastest)

Uniaxial indicatrix - ellipsoid of rotation tetragonal, hexagonal and trigonal crystal systems

Uniaxial indicatrix can be positive (prolate or ‘rugby ball’) or negative (oblate or ‘smartie’)

Basal section circular o-ray (n) only isotropic

Random section ellipse o-ray and e’-ray (nn') intermediate polarisation colour

Principal section ellipse o-ray and e-ray (nn) maximum birefringence (n) highest polarisation colour

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=X

c=X

no

a=X

ne > no

uniaxial positive (+)

PROLATE or ‘RUGBY BALL‘

ne < no

uniaxial negative (-)

OBLATE or ‘SMARTIE‘

NOTE:no = n

nen

Last week….Last week…. Polarisation colours - result of retardation (v) between o- and e-rays

= retardation = d ∙ = retardation = d ∙ nn

Michel-Levy colour chart find maximum polarisation colour 25 m sections measure birefringence (n) CHARACTERISTIC OF MINERAL

Colours reported by order and colour

….fringe counting….

The Biaxial Indicatrix (….the potato….)The Biaxial Indicatrix (….the potato….)

For orthorhombic, monoclinic and triclinic crystal systems: The indicatrix is a triaxial ellipsoid with the axes X, Y, Z The indicatrix has 3 principal refractive indices - n < n < n

The XZ plane (maximum n) is the OPTIC AXIAL PLANE

n = smallest n

n = intermediate n

n = largest n

Possible vibration directions = XX, YY and ZZ

X || n , Y || n , Z || n

nn'' < < nn'' < < n

Biaxial indicatrix - principal section (XZ)Biaxial indicatrix - principal section (XZ)

As n < n < n, there must be a point between n und n with n = n

• This gives a circular section (= isotropic)

• The OPTIC AXIS is perpendicular to the circular section

• There must be 2 circular sections optically BIAXIALoptically BIAXIAL

The optic axes lie in the XZ plane and are perpendicular to n

OPTIC AXIAL PLANE (max OPTIC AXIAL PLANE (max nn))

OAOA OAOA

Cut ^ n

n

n

= n

= n

The Bisectrix & 2VThe Bisectrix & 2V

Angle between the optic axes 2V angle 2VX and 2VZ

Bisector of this angle Bisectrix BX or BZ

If the angle is acute acute bisectrix (2V < 90°)If the angle is obtuse obtuse bisectrix (2V > 90°)

2VX

2VZ

OAOA

BX

BZ

Optical Sign (+ or -)Optical Sign (+ or -)

Biaxial positive (+)Biaxial positive (+) defined as 2VZ < 90°

…or… n closer to n than to n

‘RUGBY BALL’ like

Biaxial negative (-)Biaxial negative (-) defined as 2VZ > 90°

…or… n closer to n than to n

‘SMARTIE’ like

Biaxial indicatrix - summary

How do we know?

We use CONOSCOPIC light to see whether a crystal is uniaxial or biaxial, positive or negative….

….next two weeks….

Vibration directions & EXTINCTION

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….

Extinction AngleExtinction Angle

The EXTINCTION ANGLE is the angle between a linear feature in the crystal (a crystal edge, a cleavage plane, a twin plane) and the extinction position.

The EXTINCTION ANGLE is (surprise, surprise) directly related to the CRYSTAL SYSTEM….

…more specifically, the angular relationship with the c-axis and the other crystallographic axes….

Symmetry and extinction anglesSymmetry and extinction angles

In cubic minerals and those in the tetragonal, hexagonal and trigonal systems (= uniaxial minerals), the c-axis is at 90° to the other crystallographic axes….

STRAIGHT EXTINCTION

Symmetry and extinction anglesSymmetry and extinction angles

This is also true of orthorhombic minerals STRAIGHT EXTINCTION

For minerals in the monoclinic and triclinic systems (= biaxial), the c-axis is NOT at 90° to all the other crystallographic axes….

INCLINED EXTINCTION

Extinction AngleExtinction Angle

Extinction angle = I – II = 29,5°

I = 153,0°

II = 182,5°

Only the MAXIMUM extinction angle is diagnostic of a mineral measure lots of grains

Extinction AngleExtinction Angle

Only the MAXIMUM extinction angle is diagnostic of a mineral measure lots of grains

The maximum is the angle between the c-axis (crystallographic) and the Z-axis ( biaxial indicatrix)

Troeger….Troeger….

Troeger TablesTroeger Tables

Extinction Angle - PlagioclaseExtinction Angle - Plagioclase