6 anisitropic mineralsho - brock university...anisitropic minerals i 6 ersc 2p22 – brock...
TRANSCRIPT
Anisitropic Minerals I
1
ERSC 2P22 – Brock University Greg Finn
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 Single row of dots on paper
Calcite Rhomb
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
Anisitropic Minerals I
2
ERSC 2P22 – Brock University Greg Finn
Each row of dots corresponds to one ray, each with its own ________________ and ____.
Double Refraction
Calcite - What happens?
ERSC 2P22 – Brock University Greg Finn
The Vibration Direction can be determined using a __________ _________.The two rays are _____ ________(have a single vibration direction) and _______ __ ___ to each other.
Double Refraction
Calcite – Vibration Direction
ERSC 2P22 – Brock University Greg Finn
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.
Double Refraction
Calcite – Refractive Index
Anisitropic Minerals I
3
ERSC 2P22 – Brock University Greg Finn
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 MineralsCAUTIONARY 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
Anisitropic Minerals I
4
ERSC 2P22 – Brock University Greg Finn
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
Close
Packin
g
X
ModeratePacking Y
Wid
ePa
ckin
g
Z
Atomic Packing
ERSC 2P22 – Brock University Greg Finn
Maxim
um
X
Intermediate Y
Min
imum
Z
Electric Field Strength
Direction of Propagation
Random Wavefront
Ellipse on wavefront defined by the electric field strength
Vibration Directions of light, parallel the axes of ellipse
Anisitropic Minerals I
5
ERSC 2P22 – Brock University Greg Finn
Anisotropic Minerals • The resulting two rays encounter
different electronic configurations therefore their velocities and indices of refraction must be different
medium
vac
vvn =
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
Anisitropic Minerals I
6
ERSC 2P22 – Brock University Greg Finn
∆
Fast RaySlow Ray
PlanePolarizedLight
Mineral fragment of thickness (d)
Plane Polarized light-passed through the lower polar and has a single vibration direction
Retardation (∆) –the amount that the Slow Ray lags behind the Fast Ray upon existing the mineral
Developmentof Retardation
Fast Ray
Slow Ray
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
∆
d
FastRay
SlowRay
ss V
dt = Time it takes for the slow ray to pass through the mineral
airinvelocityVwhereVV
dtf
s =∆
+=Time for the fast ray to pass through the mineral
VVd
Vd
fs
∆+= s
sfs
nVVSince
VV
VVd =⎟
⎟⎠
⎞⎜⎜⎝
⎛−=∆
( )fs nnd −=∆
Anisitropic Minerals I
7
ERSC 2P22 – Brock University Greg Finn
Development of Retardation
• 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
( )fs nnd −=∆
ERSC 2P22 – Brock University Greg Finn
QUESTIONWe 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
PPL
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
Lower Polar
Mineral(constant d)
Upper Polar
∆ = 1 λ
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 polarsvibration direction.
No Light passes the Upper Polar
S
Fast Ray
Anisitropic Minerals I
8
ERSC 2P22 – Brock University Greg Finn
Interference at the Upper Polar II
PPL
Fast Ray
The fast and slow rays on exiting the mineral are OUT OF PHASE, with the slow ray lagging behind the fastray by ½ wavelength
Lower Polar
Mineral(constant d)
Upper Polar
∆ = ½ λ
Vector components of the slowand 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
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 ==
ERSC 2P22 – Brock University Greg Finn
0λ 1λ 2λ 3λ 4λ
2λ 12λ 22λ 32λ
Dark areas where ∆ = 0λ, 1λ, 2λ, etc. Light areas where ∆ = 2λ, 12λ, 22λ, etc.
Quartz Wedge viewed between crossed polars under Red Light
Increasing Retardation
Anisitropic Minerals I
9
ERSC 2P22 – Brock University Greg Finn
0λ 1λ 2λ 3λ 4λ
2λ 12λ 22λ 32λ
0λ 1λ 2λ 3λ 4λ2λ 12λ 22λ 32λ
Retardation
100
50
Percentage of Light Transmitted by the Upper Polar
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
Anisitropic Minerals I
10
ERSC 2P22 – Brock University Greg Finn
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 yellowyellow to red and then a repeating sequence from blue to green to yellowyellowto red
– With each repetition the colours become paler
ERSC 2P22 – Brock University Greg Finn
Michel-Levy Colour ChartQuartz wedge viewed between crossed polars
Anisitropic Minerals I
11
ERSC 2P22 – Brock University Greg Finn
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
200 600400 1000800 1200 1400 1600 1800 2000
Retardation ∆ (nm)
Retardation (∆)
1652 220311015510 First Order Second Order Third Order Fourth Order
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
Anisitropic Minerals I
12
ERSC 2P22 – Brock University Greg Finn
xpl
AnomalousInterference
Colours
All images from D. Schulze, 2003
chlorite
ppl
xpl
hbl
hbl
hbl
hbl
ERSC 2P22 – Brock University Greg Finn
Michel-Levy Colour ChartRelates:
Thic
knes
s (d
) in
mic
rons
10
20
30
40
Thickness (d)
200 600400 1000800 1200 1400 1600 1800 2000
Retardation ∆ (nm)
Retardation (∆)
0.00
0
0.00
5
0.01
5
0.01
0
0.02
0
0.02
5
0.03
0
0.03
5
0.04
0
0.04
5
0.05
0
0.05
5
0.065
0.075
0.090
0.110
0.135
0.225
Birefringence (δ)
Birefringence (δ)
1652 220311015510 First Order Second Order Third Order Fourth Order
( )fs nnd −=∆
ERSC 2P22 – Brock University Greg Finn
Thic
knes
s (d
)in
mic
rons
Retardation (nm)∆
First Order Second Order Third Order Fourth Order
Birefringence (n - n )δ = s f
0.000 0.005 0.010 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055
0.065
0.015
0.075
0.090
0.110
0.135
0.2250.170
275 nm
0.009
30 microns
Determining Thicknessof a known mineral (Quartz)
1st order grey, just a hint of yellow
Mineral is Quartz
Anisitropic Minerals I
13
ERSC 2P22 – Brock University Greg Finn
Thic
knes
s (d
)in
mic
rons
Retardation (nm)∆
First Order Second Order Third Order Fourth Order
Birefringence (n - n )δ = s f
0.000 0.005 0.010 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055
0.065
0.015
0.075
0.090
0.110
0.135
0.2250.170
750 nm
30 microns
0.025
Determining Birefringenceof an unknown mineral
Max Birefringence - 2nd order yellow, with a hint of green
Unknown mineral birefringence
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