13 Biaxial Interference Figures I - Brock University...Isogyre arms are curved, with the convex side...
Transcript of 13 Biaxial Interference Figures I - Brock University...Isogyre arms are curved, with the convex side...
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ERSC 2P22 – Brock University Greg Finn
Interference Figures
Biaxial Minerals
ERSC 2P22 – Brock University Greg Finn
Biaxial Interference Figures• Figures are obtained the same way as
uniaxial figures• The appearance of the figure is dependant on
the orientation of the mineral grain and its corresponding indicatrix
• Figures to be examined:– Acute Bisectrix (Bxa)– Biaxial Optic Axis (OA)– Obtuse Bisectricx (Bxo)– Biaxial Optic Normal or Flash Figure (ON)– Random Orientation
ERSC 2P22 – Brock University Greg Finn
Acute Bisectrix Figure
M MOpticPlane
OpticNormal
Bxa
Isochromes
Isogyre
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ERSC 2P22 – Brock University Greg Finn
Acute Bisectrix FigureThe Acute Bisectrix (Bxa) figure results when the Bxa is perpendicular to the microscope stage. If the 2V angle is < 60°, both Melatopes (M), marking the point of emergence of the Optic Axes, lie within the FOV.
Bxa
M MAt Extinction the Isogyre cross forms. The arm parallel to the Optic Plane contains the Melatopes (M) and is the thinner arm.
The arm parallel to the Optic Normal is the fatter arm.
The two arms intersect at the Bxa.
OpticPlane
OpticNormal
Isogyre
Isochromes
The Isochromes form a tear drop or figure ‘8’shape about the melatopes.
The Isochromes are assymmetrically arranged about the M.
ERSC 2P22 – Brock University Greg Finn
Acute Bisectrix FigureOn rotating the stage, the Isogyre cross splits into two identical hyperbolae. Each arm is centered on and rotates about the Melatopes (M), which in turn rotate around the Bxa. The Isogyre arms are curved, with the convex side pointing towards the Bxa. The Isochromesalso rotate with the figure, but maintain their symmetrical arrangment about the Melatopes.
BxaM M
OpticPlane
OpticNormal
At extinction 45° from extinction
M
M
Bxa
OpticPlane
OpticNormal45°
Rotation
ERSC 2P22 – Brock University Greg Finn
Acute Bisectrix FigureFormation of Isochromes I
BxaOA OA
Z
YConvergent cone of light from Auxillary Condensor
OAOA Bxa
Retardation increases outwards from the OA. Towards the Bxa the retardation increases at a slower rate than in the opposite direction. This is a function of lower birefringence and the length of the path the light follows.
Light following paths 1 - 4experience ~600 nm of retardation and when this light exits the mineral grain defines the 600 nm isochrome
1
2
3
4
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ERSC 2P22 – Brock University Greg Finn
Acute Bisectrix FigureFormation of Isochromes II
BxaOA OA
Z
YConvergent cone of light from Auxillary Condensor
OAOA Bxa
Light traveling along any other path experiences varying degrees of retardation, depending on the distance through the mineral and the corresponding birefringence
1
2
3
4
The Isochromes are developed along lines of equal retardation
MM1
2
3
4
Bxa
300 nm
600 nm900 nm
Light traveling along each OAexperiences 0 retardation
∆ = d(ns-nf)
ERSC 2P22 – Brock University Greg Finn
Acute Bisectrix FigureThe vibration directions on the biaxial indicatrix can be derived in a similar manner to that used for UniaxialMinerals
X
Y
Z
OpticNormal
Principal Sections through the indicatrix contain the indicatrix axes X, Y and Z
XZ plane =Optical Axial Plane
(OAP)
OpticAxis
OpticAxis
Vibration directionsVibration directions of light rays emerging from the biaxial indicatrix, projected onto the indicatrix surface
By taking a series of slices through the indicatrix, at right angles to the wave normals, the vibration directions for all paths of light emerging from the indicatrix can be determined.
ERSC 2P22 – Brock University Greg Finn
BxaVibrationDirections
M MBxa
FOV
Vibration Directions of light, on the surface of
the indicatrix, exiting the mineral
Vibration directions for a number of wave paths through the mineral,
projected onto the top surface of the mineral
Vibration Directions of light, within the
interference figure
Isogyre cross forms where the vibration directions of
the light rays passing through the mineral are parallel to the vibration directions of the Polars
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ERSC 2P22 – Brock University Greg Finn
Isogyre RotationIf the 2V < 60°, both Melatopes will remain within the FOV on rotation
Bxa MM
ON
OAP
With the Optic Axial Plane (OAP) oriented EW, the isogyre forms a cross a that:
1) Narrows at the Melatopes (M), and
2) Widens along the trace of the Optic Normal (ON)
With a rotation of the stage the cross splits into two segments that pivot about the position of the Melatopes (M). Again the isogyre is narrowest at the Melatope.
M
MBxa
OAP
ON
OAP
ON
With the OAP in the 45° position the isogyres form hyperbole centred on the Melatopes (M). Light vibrating along the OAPhas an RI=nBxo, light vibrating along the trace of the ON has an RI=nβ.
M
M
Bxa
At Extinction 45° from Extinction
ERSC 2P22 – Brock University Greg Finn
Isogyre RotationIf the 2V > 60°, both Melatopes will remain outside the FOV on rotation
Bxa
ON
OAP
Bxa for a mineral with a 2V > 60°. Both Melatopeslie outside the FOV, along the thinner arm of the cross. The Isochromesare oriented about the Melatopes. The OAP is oriented parallel to the EW crosshair.
MM
OAPON
Bxa
M
M
OAPON
Bxa
M
M
On rotation (30-45°) the Isogyre cross splits and the arms leave the FOV in the quadrants into which the OAP is being rotated. The Larger the 2V, the lower the angle of rotation for the Isogyres to exit. Isochrome shape is preserved.
Following a rotation of 45°, the OAP is oriented NE-SW and the Isogyreslie entirely outside the FOV. The Isochromesoccupy the FOV
At Extinction 45° from Extinction
ERSC 2P22 – Brock University Greg Finn
Bxa Figure• For minerals with a 2V < 60°, the
melatopes and Isogyres will remain in the FOV as the stage is rotated
• For minerals with a 2V > 60°, the melatopes will lie outside the FOV
• And the isogyres will leave the FOV and are not visible in the 45° position
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ERSC 2P22 – Brock University Greg Finn
Estimating the 2V Angle• A reliable estimate of the 2V angle,
based on the separation of the isogyres, can be obtained with the BxaFigure in the 45° position, with the OAPoriented NE-SW
ERSC 2P22 – Brock University Greg Finn
Estimate of 2V based on the separation of the isogyres in the Bxa Figure
2V = 15° 2V = 30°
2V = 45°2V = 60°
ERSC 2P22 – Brock University Greg Finn
Optic Axis FigureFor Biaxial Minerals with 2V < 30°
• An Optic Axis Figure results when one Optic Axis (OA) is vertical
• The figure may be centred or off-centred, depending on how close to vertical the OA is
• For a Centred Optic Axis Figure, the melatope for that OA, is positioned directly under the crosshairs
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ERSC 2P22 – Brock University Greg Finn
Centred Optic Axis FigureFor Biaxial Minerals with 2V < 30°ON
OAPBxa MM
OAP
ON
Bxa
M
M
One Melatope (M) lies at the intersection of the crosshairs. The thin arm of the Isogyre marks the position of the OAPand contains the melatopes and the Bxa.
With a low 2V the figure resembles an off-centred Bxa Figure
With a rotation of 45°, the Isogyre splits into two hyperbolae, centred on the Melatopes. The Isochromes are rotated, yet retain their tear-drop/Figure ‘8’ shape
At Extinction 45° from Extinction
ERSC 2P22 – Brock University Greg Finn
OA
OA
Bxo
Bxa
BxaM
OAP
OAP
ON
ON
Centred Optic Axis FigureFor Biaxial Minerals with 2V > 45°
IndicatrixIndicatrix is oriented such that one OA is vertical
At extinction one arm of the Isogyre cross will be visible. This arm will narrow at the Melatopeand be parallel to the OAP. This arm will be oriented parallel to
one of the crosshairs.
Principal sections and Vibration directionsVibration directions of light are shown on the indicatrix
surface.
ERSC 2P22 – Brock University Greg Finn
BxaMOAP
ON
Centred Optic Axis FigureFor Biaxial Minerals with 2V > 30°
With a counterclockwise rotation the isogyre arm rotates
clockwise, pivoting around the M
Bxa
OAP
M
Bxa
OAP
M
With the optic plane in the 45° position the Isogyre will show its maximum curvature
and the position of the Bxa lies on the convex side of the Isogyre
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ERSC 2P22 – Brock University Greg Finn
Estimate of 2V based on the curvature of the Isogyre in the Optic Axis Figure
2V = 5°
2V = 75°2V = 60°2V = 45°
2V = 30°2V = 15°
OAP
ERSC 2P22 – Brock University Greg Finn
Optic Axis Figure 2V=90°Isogyre is straight, no curvatureOAP lies at 45°, passing through the MelatopeCannot determine the position of the Bxa
OAP
M
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Obtuse Bisectrix (Bxo) Figure• Results when Obtuse Bisectrix (Bxo) is
perpendicular to microscope stage• As the angle between Bxo and Optic Axes >
45°, Melatopes will always lie outside FOV• The pattern of the Isochromes and vibration
directions are similar to those of Bxa figure• The isogyre cross is generally fuzzier than
Bxa figure, but Optic Plane will still parallel EW or NS crosshair
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ERSC 2P22 – Brock University Greg Finn
Obtuse Bisectrix (Bxo) Figure• On rotating the stage the Isogyre cross will
split and leave the field of view in the quadrants into which the Optic Plane is being rotated, as with Bxa figure
• Isogyres split and leave FOV, usually with a rotation of 5° to 15°
• For a Bxo figure the Isogyres, when they split, will not be in the field of view
• If 2V = 90°, Bxa and Bxo Figures are identical
• If 2V is small, Bxo figure resembles an Optic Normal (Biaxial Flash) Figure
ERSC 2P22 – Brock University Greg Finn
Bxo
OAOA
Bxa
ON
BxoM M
Obtuse Bisectrix (Bxo) Figure
IndicatrixIndicatrix is oriented such that the Bxo is vertical
The OAP is vertical, containing the Bxo, Bxa and OAs
In the interference figure the two Melatopes (M) lie outside the
FOV.
The Isogyre cross has a broad fuzzy appearance, with the
thinner arm lying along the OAP
OAP
ERSC 2P22 – Brock University Greg Finn
BxoM M
Obtuse Bisectrix (Bxo) Figure
With a 45° rotation the arms of the Isogyre lie well outside the FOV and
the pattern of the Isochromes, if present will be visible
With a rotation of 5° to 15° the Isogyre cross splits and leaves the FOV in the quadrants into
which the OAP is being rotated
OAPOAP
Bxo
Bxo
OAP
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ERSC 2P22 – Brock University Greg Finn
Optic Normal Figure
• AKA Biaxial Flash Figure• Similar to Uniaxial Flash Figure• Results when the Optic Normal is vertical
and the Optic Plane is horizontal• A grain that will produce an Optic Normal
Figure will display the maximum interference colours
• The vibration directions in figure are similar to those for a uniaxial flash figure
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Optic Normal Figure
• When X & Z indicatrix axes parallel the polarization directions, figure is a broad fuzzy cross with only the outer edges of each quadrant allowing any light to pass.
• Very small degree of rotation
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ERSC 2P22 – Brock University Greg Finn
Optic Normal Figure
The Indicatrix is oriented such that the Optic Normal (ON) is vertical. The Optic Plane, containing the Bxa, Bxo and OAs, is horizontal
and lies in the plane of the section
With the Bxa and Bxo parallel to the polarization directions the Isogyres
form a broad fuzzy cross
ON Bxa or
Bxo
Bxa or Bxo
At Extinction
5° Rotation
45° from Extinction
Bxo
Bxa
Bxo
Bxa
ON
ON
ERSC 2P22 – Brock University Greg Finn
Off-Centred Figures• Most interference figures examined
during routine microscope work are off-centred figures.
• In these instances none of the indicatrixor optic axes is vertical.
• Any combination of orientations are possible for off-centred figures