Optical Mineralogy WS 2012/2013. Crystal systems and symmetry The crystal systems are sub-divided by...
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Transcript of Optical Mineralogy WS 2012/2013. Crystal systems and symmetry The crystal systems are sub-divided by...
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 the refractive index (n) at that point;
• Smallest n = X, intermediate n = Y, largest n = Z
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?
Spheren is constant is every direction -isotropic minerals do not change the vibration direction of the light - no polarisation
Indicatrix = 3-d representation of refractive index
Isotropic indicatrix
Anisotropic minerals – Double refraction
Example: Calcite
The incident ray is split into 2 rays that vibrate perpendicular to each other.
These rays have variable v (and therefore variable n) fast and slow rays
As n ∞ 1/v, fast = small n, slow = big n One of the rays (the slow ray for calcite)
obeys Snell’s Law - ordinary ray (no) The other ray does not obey Snell’s law -
extraordinary ray (ne)
Birefringence = Δn = ne − no
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
ne
no b=X
c=Z
a=X
ne
b=Z
c=X
no
a=Z
n > n
uniaxial positive (+)
PROLATE or ‘RUGBY BALL‘
n < n
uniaxial negative (-)
OBLATE or ‘SMARTIE‘
NOTE:no = n
nen
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 sectionCut perpendicular to the optic axis: only n
No birefringence (isotropic section)
Principal section Parallel to the optic axis: n & n
Maximum birefringence
Random section n' and n
n' is between n and n
Intermediate birefringence
All sections contain n!
Different slices through the indicatrix
Isotropic section(remains black in XPL)
Cut PERPENDICULAR to the c-axis,
Contains only no (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 no (n) und ne (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 no (n) and ne‘ (n‘)
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 BLACK
= EXTINCTION POSITION
Polariser parallel to no:
only the ordinary ray is transmitted inserting the analyser BLACK
= EXTINCTION POSITION
Polariser
ne
no
Parallel 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.ne
no
Polariser
Diagonal position
Mineral
Polarisedlight (E–W)
Fast wave with 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)
thic
knes
s of
sec
tion
birefringence (d)
30 mm (0.03 mm)
d = 0.009 d = 0.025
first order second order third order
lines of constant d
Michel-Lévy colour chart
retardation ()
….orders separated by red colour bands….
birefringence (d)
30 mm (0.03 mm)
d = 0.009 d = 0.025
lines of constant d
Which order? - Fringe counting….
retardation ()
Uniaxial indicatrix - summary
Can be positive or negative;
Mierals of the tertragonal, 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;
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.).