Interference Figures. Biaxial Interference Figures. Acute Bisectrix Figure. Biaxial Minerals

Transcription

1 Interference Figures Biaxial inerals 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 () Biaxial Axis () Obtuse Bisectricx () Biaxial Normal or Flash Figure () Random Orientation Acute Bisectrix Figure Normal Plane Isochromes Isogyre 1

2 Acute Bisectrix Figure The Acute Bisectrix () figure results when the is perpendicular to the microscope stage. If the 2V angle is < 60, both elatopes (), marking the point of emergence of the Axes, lie within the FOV. The Isochromes form a tear drop or figure 8 shape about the melatopes. The Isochromes are assymmetrically arranged about the. Normal Isogyre At Extinction the Isogyre cross forms. The arm parallel to the Plane contains the elatopes () and is the thinner arm. Plane The arm parallel to the Normal is the fatter arm. Isochromes The two arms intersect at the. Acute Bisectrix Figure On rotating the stage, the Isogyre cross splits into two identical hyperbolae. Each arm is centered on and rotates about the elatopes (), which in turn rotate around the. The Isogyre arms are curved, with the convex side pointing towards the. The Isochromes also rotate with the figure, but maintain their symmetrical arrangment about the elatopes. Normal 45 Rotation Normal Plane Plane At extinction 45 from extinction Acute Bisectrix Figure Formation of Isochromes I Retardation increases outwards from the. Towards the 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 1-4 experience ~600 nm of retardation and when this light exits the mineral grain defines the 600 nm isochrome Y Convergent cone of light from Auxillary Condensor Z 2

3 Acute Bisectrix Figure Formation of Isochromes II Light traveling along each experiences 0 retardation = d(n s -n f ) Light traveling along any other path experiences varying degrees of retardation, depending on the distance through the mineral and the corresponding birefringence nm nm 900 nm The Isochromes are developed along lines of equal retardation Y Convergent cone of light from Auxillary Condensor Z Acute Bisectrix Figure The vibration directions on the biaxial indicatrix can be derived in a similar manner to that used for Uniaxial inerals Principal Sections through the indicatrix contain the indicatrix axes X, Y and Z XZ plane = al Axial Plane () Axis Z 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. X Y Normal Vibration directions of light rays emerging from the biaxial indicatrix, projected onto the indicatrix surface Axis Vibration Directions Isogyre cross forms where the vibration directions of the light rays passing through the mineral are parallel to the vibration directions of the Polars Vibration Directions of light, within the interference figure Vibration directions for a number of wave paths through the mineral, projected onto the top surface of the mineral FOV Vibration Directions of light, on the surface of the indicatrix, exiting the mineral 3

4 Isogyre Rotation If the 2V < 60, both elatopes will remain within the FOV on rotation At Extinction 45 from Extinction With the Axial Plane () oriented EW, the isogyre forms a cross a that: 1) Narrows at the elatopes (), and 2) Widens along the trace of the Normal () With a rotation of the stage the cross splits into two segments that pivot about the position of the elatopes (). Again the isogyre is narrowest at the elatope. With the in the 45 position the isogyres form hyperbole centred on the elatopes (). Light vibrating along the has an RI=n, light vibrating along the trace of the has an RI=n β. Isogyre Rotation If the 2V > 60, both elatopes will remain outside the FOV on rotation At Extinction 45 from Extinction for a mineral with a 2V > 60. Both elatopes lie outside the FOV, along the thinner arm of the cross. The Isochromes are oriented about the elatopes. The is oriented parallel to the EW crosshair. On rotation (30-45 ) the Isogyre cross splits and the arms leave the FOV in the quadrants into which the 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 is oriented NE-SW and the Isogyres lie entirely outside the FOV. The Isochromes occupy the FOV 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 4

5 Estimating the 2V Angle A reliable estimate of the 2V angle, based on the separation of the isogyres, can be obtained with the Figure in the 45 position, with the oriented NE-SW Estimate of 2V based on the separation of the isogyres in the Figure 2V = 15 2V = 30 2V = 45 2V = 60 Axis Figure For Biaxial inerals with 2V < 30 An Axis Figure results when one Axis () is vertical The figure may be centred or offcentred, depending on how close to vertical the is For a Centred Axis Figure, the melatope for that, is positioned directly under the crosshairs 5

6 Centred Axis Figure For Biaxial inerals with 2V < 30 At Extinction One elatope () lies at the intersection of the crosshairs. The thin arm of the Isogyre marks the position of the and contains the melatopes and the. With a low 2V the figure resembles an offcentred Figure 45 from Extinction With a rotation of 45, the Isogyre splits into two hyperbolae, centred on the elatopes. The Isochromes are rotated, yet retain their tear-drop/figure 8 shape Centred Axis Figure For Biaxial inerals with 2V > 45 At extinction one arm of the Isogyre cross will be visible. This arm will narrow at the elatope and be parallel to the. This arm will be oriented parallel to one of the crosshairs. Indicatrix is oriented such that one is vertical Principal sections and Vibration directions of light are shown on the indicatrix surface. Centred Axis Figure For Biaxial inerals with 2V > 30 With a counterclockwise rotation the isogyre arm rotates clockwise, pivoting around the With the optic plane in the 45 position the Isogyre will show its maximum curvature and the position of the lies on the convex side of the Isogyre 6

7 Estimate of 2V based on the curvature of the Isogyre in the Axis Figure 2V = 5 2V = 15 2V = 30 2V = 45 2V = 60 2V = 75 Axis Figure 2V=90 Isogyre is straight, no curvature lies at 45, passing through the elatope Cannot determine the position of the Obtuse Bisectrix () Figure Results when Obtuse Bisectrix () is perpendicular to microscope stage As the angle between and Axes > 45, elatopes will always lie outside FOV The pattern of the Isochromes and vibration directions are similar to those of figure The isogyre cross is generally fuzzier than figure, but Plane will still parallel EW or NS crosshair 7

8 Obtuse Bisectrix () Figure On rotating the stage the Isogyre cross will split and leave the field of view in the quadrants into which the Plane is being rotated, as with figure Isogyres split and leave FOV, usually with a rotation of 5 to 15 For a figure the Isogyres, when they split, will not be in the field of view If 2V = 90, and Figures are identical If 2V is small, figure resembles an Normal (Biaxial Flash) Figure Obtuse Bisectrix () Figure In the interference figure the two elatopes () lie outside the FOV. The Isogyre cross has a broad fuzzy appearance, with the thinner arm lying along the Indicatrix is oriented such that the is vertical The is vertical, containing the, and s Obtuse Bisectrix () Figure With a rotation of 5 to 15 the Isogyre cross splits and leaves the FOV in the quadrants into which the is being rotated 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 8

9 Normal Figure AKA Biaxial Flash Figure Similar to Uniaxial Flash Figure Results when the Normal is vertical and the Plane is horizontal A grain that will produce an Normal Figure will display the maximum interference colours The vibration directions in figure are similar to those for a uniaxial flash figure 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 <5 causes the isogyres to split and leave the field of view from the quadrants into which the is being rotated If 2V = 90 the cross - shaped isogyre does not split as the stage is rotated, it simply dissolves away with a 5-10 rotation or Normal Figure or With the and parallel to the polarization directions the Isogyres form a broad fuzzy cross, with only the outer edges of each quadrant allowing any light to pass FOV The Indicatrix is oriented such that the Normal () is vertical. The Plane, containing the, and s, is horizontal and lies in the plane of the section 9

10 or Normal Figure or At Extinction 5 Rotation With the and parallel to the polarization directions the Isogyres form a broad fuzzy cross The Indicatrix is oriented such that the Normal () is vertical. The Plane, containing the, and s, is horizontal and lies in the plane of the section 45 from Extinction Off-Centred Figures ost interference figures examined during routine microscope work are offcentred figures. In these instances none of the indicatrix or optic axes is vertical. Any combination of orientations are possible for off-centred figures 10