Anisitropic Minerals I
Anisotropic Minerals
Chapter 5 or Nesse
ERSC 2P22 – Brock University Greg Finn
Anisotropic Minerals
• Differ from Isotropic Minerals because:
– The velocity of light ______ depending on
the direction through the mineral, and
– They exhibit ____________________
ERSC 2P22 – Brock University Greg Finn
Anisotropic Minerals
• On entering an
anisotropic mineral
light is ____ into two
rays that;
– Have different
________ (and RI’s)
– Vibrate at _____ to
each other
Two rows of dots, with each row corresponding to
one of the two light rays formed as the light is
split upon entering the calcite
Calcite Rhomb
Single row of
dots on paper
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1
Anisitropic Minerals I
Double
Refraction
Calcite - What happens?
Each row of dots corresponds
to one ray, each with its own
________________ and ____.
ERSC 2P22 – Brock University Greg Finn
Double
Refraction
Calcite – Vibration Direction
The Vibration Direction can be
determined using a __________
_________.
The two rays are _____ ________
(have a single vibration direction)
and _______ __ ___ to each
other.
ERSC 2P22 – Brock University Greg Finn
Double
Refraction
Calcite – Refractive Index
The RI of each ray can be
measured, using _________ ___.
One will be higher than the other.
The ray with the _____ index is
called the ____ ray.
The ray with the ______ index is
called the _____ ray.
ERSC 2P22 – Brock University Greg Finn
2
Anisitropic Minerals I
Anisitropic Minerals
• There are one or two _________ through an
anisotropic mineral along which light behaves
as though the mineral were isotropic. This
direction or directions are called the _____
______
• Hexagonal and Tetragonal minerals have ___
optic axis and are termed Uniaxial
• Orthorhombic, monoclinic and triclinic
minerals have ___ optic axes and are termed
Biaxial
ERSC 2P22 – Brock University Greg Finn
Anisitropic Minerals
CAUTIONARY NOTE
• Remember the difference between:
• Vibration direction – side to side
oscillation of the electric vector of the
plane light, and;
• Propagation direction – the direction the
light is travelling
ERSC 2P22 – Brock University Greg Finn
Why is Light Split?
• Electromagnetic theory provides insight
as to why light is split and why the
velocity of the light varies with direction
through the anisotropic mineral
• Strength of chemical bonds and atom density
are different in different directions
• A light ray will ‘see’ different electronic
configuration depending on direction
• The electron clouds around each atom vibrate
with different frequencies in different directions
ERSC 2P22 – Brock University Greg Finn
3
Anisitropic Minerals I
Why is Light Split?
•
Velocity of light in an anisotropic mineral is
dependant on:
1. the interaction between the ______________ of
the electric vector of the light, and;
2. the ______________ of the electron clouds.
•
Resulting in a variation in ________ with
direction.
_________________ theory can explain
why light is split into two rays, each with a
different velocity, which vibrate at 90°
•
ERSC 2P22 – Brock University Greg Finn
Atomic Packing
Wide
Packing
Z
Moderate
e
Packing
os ng
Cl cki
a
P
X
Y
ERSC 2P22 – Brock University Greg Finn
Electric Field Strength
Random
Wavefront
Direction of
Propagation
Vibration
Directions of
light, parallel
the axes of
ellipse
Minimum
Z
X
M
im
ax
um
Intermediate
Y
Ellipse on
wavefront defined
by the electric field
strength
ERSC 2P22 – Brock University Greg Finn
4
Anisitropic Minerals I
Anisotropic Minerals
• The resulting two rays encounter
different electronic configurations
therefore their velocities and indices of
refraction must be different
n=
vvac
vmedium
ERSC 2P22 – Brock University Greg Finn
Anisotropic Minerals
• There will be one or two _____ in anisotropic
minerals which show uniform electron
configurations, resulting in the EFS plotting as
a _____ rather than an _______
• Lines at _________ to this plane or planes
are called the Optic Axis –
– __________________________________
__________________________________ (the
mineral behaves as an isotropic mineral)
ERSC 2P22 – Brock University Greg Finn
Interference Phenomena
• Under crossed polars anisotropic
minerals display a variety of colours –
_____________________ which are
produced as a consequence of the light
being _______ into two rays on passing
through the mineral
• Examine interference phenomena using
monochromatic light and apply the
concepts to polychromatic (white) light
ERSC 2P22 – Brock University Greg Finn
5
Anisitropic Minerals I
Development
of Retardation
Retardation (∆) –
the amount that the
Slow Ray lags
behind the Fast
Ray upon existing
the mineral
∆
Fast Ray
Slow Ray
Mineral fragment
of thickness (d)
Fast Ray
Slow Ray
Plane Polarized lightpassed through the lower
polar and has a single
vibration direction
Plane
Polarized
Light
ERSC 2P22 – Brock University Greg Finn
Development of Retardation
• Magnitude of the retardation is
dependant on:
– The ________ of the sample (d)
– The ________ in velocity of the slow (Vs)
and fast (Vf) rays
ERSC 2P22 – Brock University Greg Finn
Development of Retardation
ts =
d
Vs
ts =
d ∆
+
Vf V
Time it takes for the slow ray to pass
through the mineral
d
d
∆
=
+
Vs V f V
Fast
Ray
∆
where V = velocity in air
Slow
Ray
Time for the fast ray to
pass through the
mineral
⎛V V
∆ = d⎜ −
⎜V V
f
⎝ s
d
⎞
⎟
⎟
⎠
Since
∆ = d (ns − n f )
V
= ns
Vs
ERSC 2P22 – Brock University Greg Finn
6
Anisitropic Minerals I
Development of Retardation
∆ = d (ns − n f )
• Relationship (ns – nf) is termed
____________ (δ) and represents the
difference in the indices of refraction of the
slow and fast rays
• In anisotropic minerals one path, along the
optic axis, exhibits ____ birefringence, others
show a __________, but most show an
____________ value
• Maximum Birefringence is characteristic for
each mineral
• Birefringence ______ with wavelength of light
ERSC 2P22 – Brock University Greg Finn
QUESTION
We have just observed that upon
entering a mineral, light is split into two
rays - Fast and Slow
What happens to the two rays of
light (Slow and Fast rays) after they
have exited the mineral grain?
ERSC 2P22 – Brock University Greg Finn
Interference at the
Upper Polar I
When vector components of the
slow and fast rays are resolved
into the vibration direction of
the upper polar they are in
opposite directions and cancel,
so no light passes. The vector
S, the sum of the two waves, is
at right angles to the polars
vibration direction.
No Light
passes the
Upper Polar
Upper Polar
Fast Ray
S
∆=1λ
Mineral
The fast and slow rays
on exiting the mineral
are IN PHASE, with the
slow ray lagging
behind the fast ray by
1 whole wavelength
(constant d)
PPL
Lower Polar
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7
Anisitropic Minerals I
Interference at the
Upper Polar II
Vector components of the slow
and fast rays resolved into the
vibration direction of the upper
polar are in the same direction,
so they constructively interfere
to yield R, which passes the
upper polar and the mineral
appears bright.
Resultant –
some light
passes
Fast Ray
Upper Polar
∆=½λ
Mineral
(constant d)
The fast and slow rays
on exiting the mineral
are OUT OF PHASE,
with the slow ray
lagging behind the fast
ray by ½ wavelength
PPL
Lower Polar
ERSC 2P22 – Brock University Greg Finn
Interference at the Upper Polar
• In the two cases examined, the sample was a
constant thickness and exhibited a constant
retardation
• If our sample is ________ shaped, the
thickness and therefore the retardation will
______ along the length
∆ – Varies along the length ==Î
ERSC 2P22 – Brock University Greg Finn
0λ
1λ
2λ
2λ
12λ
3λ
22λ
4λ
32λ
Increasing Retardation Î
Quartz Wedge viewed between crossed polars under Red Light
Dark areas where ∆ = 0λ, 1λ, 2λ, etc.
Light areas where ∆ERSC
= 2λ,
etc.Greg Finn
2P2212λ,
– Brock22λ,
University
8
Anisitropic Minerals I
0λ
1λ
2λ
12λ
2λ
3λ
22λ
4λ
32λ
Percentage of Light Transmitted by the Upper Polar
100
50
0λ
2λ
1λ
12λ
2λ
22λ
Retardation
3λ
32λ
4λ
ERSC 2P22 – Brock University Greg Finn
Polychromatic or White Light
• Light of a variety of wavelengths, each of
which is split into a slow and fast ray, the
retardation is the same for all wavelengths
• Due to different wavelengths, some reach the
upper polar ________ and are cancelled,
while others are __________ and are
transmitted through the upper polar
• The combination of wavelengths that pass
the upper polar produces the __________
__________
ERSC 2P22 – Brock University Greg Finn
Polychromatic or White Light
• Interference colours depend on the
retardation of the slow and fast ray,
which reflects:
• ____________, and
• _____________
• Samples of the same mineral will
display different interference colours,
depending on thickness and the
orientation of the sample
ERSC 2P22 – Brock University Greg Finn
9
Anisitropic Minerals I
Polychromatic or White Light
• Examining the quartz wedge between
crossed polars produces a range of colours
From: D. Schulze, 2003
ERSC 2P22 – Brock University Greg Finn
Polychromatic or White Light
• At the thin edge , thickness and retardation
are ~ 0, all wavelengths of light are cancelled
at the upper polar, so colour is black
• With increasing thickness colour changes
from:
black to grey to yellow to red and then a
repeating sequence from blue to green to yellow
to red
– With each repetition the colours become paler
ERSC 2P22 – Brock University Greg Finn
Michel-Levy Colour Chart
Quartz wedge viewed between crossed polars
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10
Anisitropic Minerals I
Order of Interference Colours
• On the colour chart, the repetition of
interference colours, from red to blue occurs
at retardations of 550, 1100, 1650 and 2200
nm
• Boundaries are used to separate the colour
sequence into orders
• 1st and 2nd order colours are vivid
• Higher order colours become progressively
more washed out, beyond 4th order the
colours become a creamy white
ERSC 2P22 – Brock University Greg Finn
Michel-Levy Colour Chart
Retardation (∆)
200
0
400
First Order
600
800
551 Second
1000
1200
1400
1600
Order 1101 Third Order
Retardation ∆ (nm)
1800
1652 Fourth
2000
Order 2203
ERSC 2P22 – Brock University Greg Finn
Anamolous Interference Colours
• Colours under crossed polars that ________
appear on the colour chart
• Colours result when birefringence and
retardation are significantly __________ for
different wavelengths of light, resulting in a
different complement of wavelengths passing
the upper polar, which is perceived as a
different interference colour
• Mineral colour also influences interference
colour as some wavelengths of light are
selectively absorbed by the mineral
– Green minerals transmit green light, absorb
others, resulting in interference colours with a
greenish tint
ERSC 2P22 – Brock University Greg Finn
11
Anisitropic Minerals I
Anomalous
Interference
Colours
hbl
hbl
ppl
chlorite
hbl
hbl
xpl
All images from D. Schulze, 2003
xpl
ERSC 2P22 – Brock University Greg Finn
Michel-Levy Colour Chart
Thickness (d) Retardation (∆)
Birefringence (δ)
∆ = d(n − n )
0.055
0.050
0.035
0.030
0.025
0.020
0.015
0.010
0.005
0.000
Thickness (d) in microns
f
0.045
s
Birefringence (δ)
0.040
Relates:
40
0.065
0.075
30
0.090
0.110
20
0.135
0.225
10
200
0
400
800
600
First Order
551 Second
1000
1400
1200
1600
Order1101 Third Order
Retardation ∆ (nm)
1800
1652 Fourth
2000
Order 2203
ERSC 2P22 – Brock University Greg Finn
Determining Thickness
of a known mineral (Quartz)
Birefringence δ = (ns - nf)
Mineral is Quartz
0.000
0.005
0.010
0.009
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
30 microns
0.055
Thickness
(d)
in microns
0.065
0.075
0.090
0.110
0.135
0.170
0.225
First Order
275 nm
Second Order
Third Order
Fourth Order
Retardation ∆ (nm)
1st order grey, just a hint of yellow
ERSC 2P22 – Brock University Greg Finn
12
Anisitropic Minerals I
Determining Birefringence
of an unknown mineral
Birefringence δ = (ns - nf)
0.000
0.005
0.010
0.015
0.020
0.025
0.025
Unknown
mineral
0.050
0.045 birefringence
0.055
0.040
0.035
0.030
30 microns
Thickness
(d)
in microns
0.065
0.075
0.090
0.110
0.135
0.170
0.225
First Order
Second Order
Third Order
750 nm
Fourth Order
Retardation ∆ (nm)
Max Birefringence - 2nd order yellow, with a hint of green
ERSC 2P22 – Brock University Greg Finn
Recognizing the Order of the
Interference Colour
• Becomes easier with practice and
familiarity
– eg. Distinguishing 2nd order red from 4th
order red
• Coloured grains may mask the
interference colour
• Look at grain edges vs centres
• 1st order white vs high-order white
ERSC 2P22 – Brock University Greg Finn
13