interference figures interference figures
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ERSC 2P22 – Brock University Greg Finn
Interference Figures
Uniaxial Minerals
ERSC 2P22 – Brock University Greg Finn
Interference FiguresUses:• Means by which uniaxial and biaxial
minerals can be _____________ from each other, and
• For determining the ___________ of a mineral, specifically for uniaxialminerals whether:– nω > nε
– nω < nε
Optically Negative, orOptically Positive
ERSC 2P22 – Brock University Greg Finn
Interference FiguresTo obtain and observe an interference figure:
1. With high power, focus on a mineral grain free of cracks and inclusions
2. Flip in the auxiliary condensor and refocus, open aperture diaphragm to its maximum
3. Cross the polars4. Insert the Bertrand lens, look down the
microscope tube• Will not see the grain, but the interference
figure, which appears on the top surface of the objective lense
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ERSC 2P22 – Brock University Greg Finn
UniaxialInterference
Figure
Nature and pattern of the figure is dependant on the orientation of the
grain and its corresponding indicatrix
Pattern of Interference
Colours
Black band, which may or may not display a cross
shape
ERSC 2P22 – Brock University Greg Finn
Uniaxial Interference Figure• For Uniaxial minerals three types of
interference figures are produced:1. Centred Optic Axis Figure (OA vertical)2. Off Centred OA Figure (OA) inclined)3. Flash Figure (OA horizontal)
• Each figure reflects the orientation of the indicatrix within the mineral grain
ERSC 2P22 – Brock University Greg Finn
Optic Axis Figure• If the optic axis is ________, the
mineral grain will exhibit 0 birefringence and remain black, or nearly black, on rotating the stage
• Resulting figure produced is a ______ ______________________________
• Consists of a centred black ______ superimposed on _______ bands of __________________
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ERSC 2P22 – Brock University Greg Finn
Anatomy of a UniaxialOptic Axis
Interference Figure
ISOGYRE
Two arms of the cross form the
isogyre
MELATOPE
The point where the optic axis emerges in the interference figure, corresponds to 0
retardation
If the Optic Axis is exactly
vertical, then on rotating
the stage the interference figure does not move
ISOCHROMES
Interference colours are identical to those on the colour chart, increase in order from the melatope
ERSC 2P22 – Brock University Greg Finn
Formation of Isochromes
All other light rays traveling through the mineral
experiences a variable degree of retardation,
reflecting the path it follows
Optic Axis is vertical and the optic properties vary
symmetrically about the OA
Number of Isochromesdepends on the retardation and thickness of the sample
Simplified, ignored the splitting of light into its two component rays
SamplePrincipal
Section of Indicatrix
Optic Axis
1
1
Auxiliary Condensor
ObjectiveLense
2
2
4
4
35
3 5
IncreasingRetardation
Isochromes in theInterference Figure(Isogyres removed for clarity)
Ray 1 travels along the Optic Axis and experiences 0
retardation
ERSC 2P22 – Brock University Greg Finn
Formation of Isogyres• Isogyres form when the _________
directions in the interference figure are _______ to the _______ directions of the upper and lower _______
• Results in areas of __________ in the interference figure, as no component of light can be resolved into the vibration direction of the upper polar
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ERSC 2P22 – Brock University Greg Finn
Formation of Isogyres
ω ωε ε
Vibration Directions on the Indicatrix Surface
Vibration directions for each ray of light passing through the mineral can be determined
(we did this earlier)
If we do this for an infinite number of rays then:
All Ordinary Rays vibrate parallel to lines analogous to
lines of latitude
All Extraordinary Rays vibrate parallel to lines analogous to
lines of longitude
ω
ε
ERSC 2P22 – Brock University Greg Finn
ω
ε
Formation of Isogyres
Vibration Directions in the Interference Figure
The mineral, with its indicatrixoriented such that the Optic
Axis is vertical, with a convergent cone of light
Light rays, each of which is split into ε and ω rays, pass
through the objective lenseand the vibration directions
for each ray can be projected onto the upper surface of the objective
lense
ERSC 2P22 – Brock University Greg Finn
Formation of Isogyres
Vibration Directions in the Interference Figure
Extraordinary Ray
___________________
Ordinary Ray
___________________
ω
ε
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ERSC 2P22 – Brock University Greg Finn
Biaxial Interference FigureFor comparison
ERSC 2P22 – Brock University Greg Finn
Determining the Optic Sign• Once the interference figure has been:
1. Obtained2. Identified as to whether it is uniaxial vs.
biaxial, and3. The orientation of the optic axis in the
figure is determined then4. The optic sign can be determined using
the accessory plate(s)• Why determine the optic sign?
ERSC 2P22 – Brock University Greg Finn
Determining the Optic Sign• The Optic Sign tells whether the
Ordinary Ray is the ____ or ____ ray exiting the mineral
• Optically Positive– ω = fast ray– ε = slow ray
• Optically Negative– ω = slow ray– ε = fast ray
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ERSC 2P22 – Brock University Greg Finn
Determining the Optic SignTo determine the optic sign:1. Obtain an optic axis interference figure, (Look for a
grain that exhibits the lowest interference colour for the mineral)
2. Note the interference colour of the mineral3. Insert the accessory plate (become familiar with the
gypsum plate)4. Observe the change in interference colours
• In two quadrants the colours increase• Colours move up the colour chart
• In two quadrants the colours decrease• Colours move down the colour chart
5. Look in the NE quadrant of the interference figure
ERSC 2P22 – Brock University Greg Finn
CLARIFICATION!!!!!Quadrants of the Field of
ViewQuadrants of the
Interference Figure
NW
SW SE
NENE
ERSC 2P22 – Brock University Greg Finn
Uniaxial Optic Axis Figure –
Optic Sign Determination
Few to no isochromes
ε
ω
SLOW
Case I
In the NE quadrant of the Interference Figure the interference colours increaseincrease,
move up the colour chart, from greygrey to blueblue
Overall this is an increase in total retardation, as the slow ray of the
mineral is parallel to the slow ray in the accessory.
Therefore the ε ray is the slow ray
Using the Gypsum Plate
Optically Positive
ε ray = slow ray
ε
ω
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ERSC 2P22 – Brock University Greg Finn
Uniaxial Optic Axis Figure –
Optic Sign Determination
Few to no isochromes
ε
ω
Case II
In the NE quadrant of the Interference Figure the interference colours decreasedecrease, move down the colour chart, from greygrey to
yellowyellow
Overall this is a decrease in total retardation, as the fast ray of the mineral
is parallel to the slow ray in the accessory.
Therefore the ε ray is the fast ray
Using the Gypsum Plate
Optically Negative
ε ray = fast raySLOW
ε
ω
ERSC 2P22 – Brock University Greg Finn
Uniaxial Optic Axis Figure –
Optic Sign Determination
ε
ω
Case II
Using the Gypsum Plate
Optically Negative
ε ray = fast ray
SLOW
ε
ω
SLOW
Case I
ε ray = slow ray
ε
ω
Optically Positive
ERSC 2P22 – Brock University Greg Finn
Optic Sign Determination• If the interference figure exhibits few to
no _________, the gypsum plate is used to determine the sign,
• Insert the plate and note the change in colour in the NE quadrant, of the figure, from grey to:
•• BlueBlue (positive) or•• YellowYellow (negative)
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ERSC 2P22 – Brock University Greg Finn
Uniaxial Optic Axis Figure –
Optic Sign Determination
ε
ω
Case II
Using the Gypsum Plate
Optically Negative
ε ray = fast ray
SLOW
ε
ω
SLOW
Case I
ε ray = slow ray
ε
ω
Optically Positive
ERSC 2P22 – Brock University Greg Finn
Quartz Wedge• If the interference figure exhibits
_________ isochromes then the quartz wedge is used to determine the optic sign
• Inserting the quartz wedge results in the _________ of the isochromes about the isogyre
• The direction of movement assists in determining the optic sign
ERSC 2P22 – Brock University Greg Finn
Quartz Wedge• In quadrants where the fast ray of the mineral
is parallel to the slow ray of the wedge, the isochromes move ___, as ____ order coloursform at the melatope and displace ______ order colours
• ε = fast ray• In quadrants where the slow ray of the
mineral is parallel to the slow ray of the wedge, the isochromes move _______, as ______ order colours replace ______ order colours
• ε = slow ray
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ERSC 2P22 – Brock University Greg Finn
Quartz WedgeOptically Positive
ε
ω
In the NE and SW quadrants of the figure the isochromes move in
In the NW and SE quadrants of the figure the isochromes move out
ε ray = slow ray
Direction of movement of the isochromes as the wedge is
inserted
SLOW
Numerous Isochromes
Uniaxial Optic Axis Figure – Optic Sign
Determination
ERSC 2P22 – Brock University Greg Finn
In the NE and SW quadrants of the figure the isochromes move out
In the NW and SE quadrants of the figure the isochromes move in
Direction of movement of the isochromes as the wedge is
inserted
ε
ω
SLOW
Quartz WedgeOptically Negative
ε ray = fast ray
Numerous Isochromes
Uniaxial Optic Axis Figure – Optic Sign
Determination
ERSC 2P22 – Brock University Greg Finn
Direction of movement of the isochromes as the wedge is
inserted
ε
ω
SLOW
Quartz Wedge
Optically Negative
Numerous Isochromes
Uniaxial Optic Axis Figure – Optic Sign
Determination
SLOW
Optically Positive
ε ray = fast ray
ε ray = slow ray
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ERSC 2P22 – Brock University Greg Finn
Off Centred Optic Axis• Produced when the optic axis is ____
_______, and results in the interference figure no longer ________ in the field of view (FOV)
• Isogyres still form a cross, which will lie outside the FOV with the melatope at the centre
ERSC 2P22 – Brock University Greg Finn
Off Centred Optic Axis(at extinction)
Mineral, with its indicatrixoriented such that the Optic Axis is inclined to vertical, with a convergent cone of
light
Melatope (point where the Optic Axis emerges, the centre of the cross) lies
outside the FOV. Will only see a single isogyre in the
FOV
The isogyre fattens as the distance from the melatope increasesThe vibration direction of the:
Ordinary ray is tangential to the isochromes,
Extraordinary ray is radial, from the melatope
Optic Axis
MFOV
M
Vibration Directions on indicatrix surface
ERSC 2P22 – Brock University Greg Finn
Off Centred Optic Axis(on rotation)
Can now determine the optic sign in the same way
as with a centred Optic Axis Figure:
Is the ε ray the fast or slow ray?
Only one isogyre will be visible in the FOV at any time. As the stage is rotated the isogyre will sweep across the FOV, in the direction indicated, to be replaced by
another arm of the cross
Identify the NE quadrant of the figure, no part of the isogyre will be in the FOV
NW NE
SESW
NW NE
SESW
NW NE
SESW
NW NE
SESW
NW NE
SESW
ε
ω
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ERSC 2P22 – Brock University Greg Finn
Uniaxial Flash Figure• Mineral grain is oriented with the optic
axis ________• Grain will exhibit its ___________
interference colour• Interference figure is a broad, fuzzy
cross
ERSC 2P22 – Brock University Greg Finn
Centred Uniaxial Flash Figure(at extinction)
Mineral, with its indicatrixoriented such that the Optic
Axis is horizontal, in this case EW in the FOV
In this orientation the mineral will exhibit its maximum
interference colour
The resulting isogyre is a broad, fuzzy cross which
nearly fills the FOV, because the vibration directions in all
but the outermost parts of the FOV are parallel to the
vibrations directions of the polars
Optic Axis
FOV
Vibration Directions on indicatrix surface
ERSC 2P22 – Brock University Greg Finn
Centred Uniaxial Flash Figure(on rotation)
0° at Extinction
A broad fuzzy cross that fills the
FOV
With a minor clockwise rotation (<5°), the isogyre splits and
rapidly leaves the FOV, moving out into the
quadrants of the FOV into which the Optic Axis (OA) is being
rotated
With a rotation of 45°, the isogyres lie well
outside the FOV and the OA is oriented either NE-SW or NW-SE, depending on the
direction of rotation
OA
OA
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ERSC 2P22 – Brock University Greg Finn
Uniaxial Figures - Summary• Optic Axis Figure
– Section perpendicular to the c-axis (Optic Axis)– Lowest interference colour– Appears isotropic or nearly isotropic under crossed polars
• Off-Centred Optic Axis Figure– c-axis (Optic Axis) inclined to vertical– Only see one isogyre arm at a time, will sweep through the
field of view– Intermediate birefringence therefore intermediate
interference colour• Flash Figure
– c-axis (Optic Axis) is horizontal, parallel to the stage– Maximum interference colour
ERSC 2P22 – Brock University Greg Finn
Interpretation of Interference Figures
Type of Figure Interference Colour
Accessory effect for a positive mineral
These are distinguished from biaxial minerals by the failure of the centre of the isogyre cross to break as the stage is rotated, or if the centre of the cross is not visible, by the isogyres remaining parallel to the crosshairs. This distinction does not apply to the flash figure.
UNIAXIAL MINERALS
Optic axis is vertical
Extinction
Off Centred Optic Axis Centre of cross dis- placed from centre of field. Vertical and horizontal isogyres alternately sweep across field, parallel to crosshairs.
Optic axis is inclined to vertical
fast
Not definitive to determine sign, however interference figure and accessory plate may be used to determine whether e ray is fast or slow.
Optic axis is parallel to microscope stage
Low to moderate
Maximum colour for that grain
Yellow
Yellow
GCF '98