Conoscopic interference pattern: Difference between revisions

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== Characteristic figures of uniaxial and biaxial minerals ==

[[File:Uniaxial interference figures.jpg|thumb|center|upright=2.5|Sketches of uniaxial interference figures, viewed along the optic axis of each mineral. The colours approximate [[birefringence]] colours which might be seen if this were a mineral with second order maximum birefringence. The dark "maltese cross" pattern is characteristic of uniaxial minerals, and will not vary as the microscope stage is turned. Also shown are schematics of the shape of a cross section through the mineral's optical indicatrix (recording its refractive index in 3D) that would be seen at each position. The elongated direction could be distinguished by adding a [[sensitive tint plate]] to the microscope, letting the user discriminate between "uniaxial positive" (left) and "uniaxial negative" (right) minerals.]]

An interference figure produced looking straight down or close to the optic axis of a uniaxial mineral will show a characteristic 'Maltese' cross shape to its isogyres. If you are looking perfectly down the optic axis, the pattern will remain completely unchanging as the stage is rotated. However, if the viewing angle is slightly away from the optic axis, the centre of the cross will revolve/orbit around the central point as the stage is rotated. However, the form of the cross will stay constant as it moves.

[[File:Biaxial interference figures.jpg|thumb|center|upright=2.5|Possible interference figures for a biaxial mineral with a fairly large 2V, viewed along one of its two optic axes. The curved shape of the dark arc (the "isogyre") is characteristic of biaxial minerals - though the degree of curvature will change as the microscope stage is rotated, and at some orientations the pattern will resemble the "maltese cross" pattern of a uniaxial mineral. The left hand image illustrates the figure alone; the grey patch at the centre indicates the low first order (grey) birefringence colours seen here (the order of the colours seen would in reality increase away from the center, but these colours are not shown). The two right hand figures show the effect of adding a sensitive tint plate to the setup, replacing the grey at the centre with second order blue and first yellow birefringence colours. The polarity of the yellow and blue reveals whether the mineral being viewed is optically "biaxial positive" (top) or "biaxial negative" (bottom), which can be a key property in identifying the mineral (or investigating its composition).]]

[[File:Biaxial interference figures.jpg|thumb|center|upright=2.5|Possible interference figures for a biaxial mineral with a fairly large 2V, viewed along one of its two optic axes. The curved shape of the dark arc (the "isogyre") is characteristic of biaxial minerals - though the degree of curvature will change as the microscope stage is rotated, and at some orientations the pattern will resemble the "maltese cross" pattern of a uniaxial mineral. The left hand image illustrates the figure alone; the grey patch at the centre indicates the low first order (grey) birefringence colours seen here (the order of the colours seen would in reality increase away from the center, but these colours are not shown). The two right hand figures show the effect of adding a sensitive tint plate to the setup, replacing the grey at the centre with second order blue and first yellow birefringence colours. The polarity of the yellow and blue reveals whether the mineral being viewed is optically "biaxial positive" (top) or "biaxial negative" (bottom), which can be a key property in identifying the mineral (or investigating its composition).]]

The optic axis figure of a biaxial mineral is more complex. It will typically show a saddle-shaped figure (with one isogyre thicker than the other, typically) that will often morph into two curved isogyres (called brushes) with rotation of the stage. The difference in these curved isogyres is known as the ''optic angle'', or"2V". In minerals that have far-off-center optic axes, only one part of the above sequence may be seen. On either side of the saddle the interferences rings surround two eye like shapes called melanotopes. The closest bands are circles, but further out they become pear shaped with the narrow part pointing to the saddle. The larger bands surrounding the saddle and both melanotopes are figure 8 shaped.<ref name="hartshorne">{{cite book|last1=Hartshorne|first1=N. H.|last2=Stuart|first2=A.|title=Practical Optical Crystallography|year=1964|publisher=Edward Arnold|___location=London|pages=210–211}}</ref> By combining interference pattern microscopy with use of a [[sensitive tint plate]], the optic sign and optic angle can be determined together. This information can help both with mineral identification, and with interpreting the chemical composition of some minerals (for example, feldspars).

The optic axis figure of a biaxial mineral is more complex. One or two curved isogyres (called "brushes") will be visible, one of which will have its point of maximum curvature perfectly centred. (The figure shows an example with a single isogyre visible.) If two isogyres are visible, they will be positioned back-to-back. Rotating the stage will cause the isogyres to move and change shape strikingly - moving from a position where the isogyres curve smoothly and are widely separated at their closest point, then gradually becoming more tightly curved/squarer at their midpoints as they approach each other (a second isogyre appearing from out of the field of view if it was absent before), then merging to form a maltese cross pattern very much like that of a uniaxial mineral. Continuing to rotate the stage will cause the isogyres to separate again - but into the opposite quadrants to where they were previously - then meet again, then separate again into their original quadrants, and so on. The isogyres will touch each other four times in one 360 degree revolution, with each time corresponding to one of the [[extinction position]]s seen in normal cross polarised light.

The maximum separation between isogyres occurs when the slide is rotated exactly 45 degrees from one of the points where the isogyres come together. The point where the isogyres is most tightly curved represents the position of each of the two optic axes present for a biaxial mineral, and thus the maximum separation between the two curves is diagnostic of the angle between the two optic axes for the mineral. This angle is called the '''optic angle''' and often notated as '''"2V"'''. In some cases, knowing the optic angle can be a useful diagnostic tool to discriminate between two minerals which otherwise look very similar. In other cases, 2V varies with chemical composition in a known way for a given mineral, and its measured value can be used to estimate ratios between elements in the crystal structure - for example, Fe/Mg in olivines. However, in these cases it becomes important to also be sure of the ''optic sign'' of the mineral (essentially, this tells you how the optic angle is orientated with respect to the whole [[optical indicatrix]] describing the refractive indices of the mineral in 3D). The optic sign and optic angle can be determined together by combining interference pattern microscopy with use of a [[sensitive tint plate]].

On either side of the "saddle" formed by the isogyres, birefringent rings of colour run concentrically around two eye like shapes called ''melanotopes''. The closest bands are circles, but further out they become pear shaped with the narrow part pointing to the saddle. The larger bands surrounding the saddle and both melanotopes are figure 8 shaped.<ref name="hartshorne">{{cite book|last1=Hartshorne|first1=N. H.|last2=Stuart|first2=A.|title=Practical Optical Crystallography|year=1964|publisher=Edward Arnold|___location=London|pages=210–211}}</ref>

A [[Interference colour chart|Michel-Levy Chart]] is often used in conjunction with the interference pattern to determine useful information that aids in the identification of minerals.