Extinction Angle and Sign of Elongation
The extinction angle is the angle between the length or a prominent cleavage direction in a mineral and a vibration direction of the polarized light passing through it. It is measured with crossed polarizers and is a diagnostic property because its value and category - parallel, inclined, symmetrical, or absent - are controlled by the orientation of the optical indicatrix relative to the crystal axes, which varies systematically with crystal system and mineral species. [1]
Quick Revision
- Extinction angle is measured as the stage rotation needed to go from cleavage/length aligned N-S to the extinction position. [1]
- Parallel extinction (EA = 0°) → length or cleavage is parallel to a crosshair at extinction. [1]
- Inclined extinction (EA > 0°) → diagnostic for monoclinic and triclinic minerals. [1]
- Symmetrical extinction → equal angles to two cleavages; common in orthorhombic minerals. [1]
- Length slow = positive elongation; length fast = negative elongation. [1]
- Undulatory extinction → wavy pattern caused by grain deformation. [1]
- Diagnostic extinction angles are always reported for grains at maximum retardation (optic axes horizontal). [1]
Measuring the Extinction Angle
The measurement is made in grain mount or thin section with crossed polarizers. The procedure is straightforward. First, rotate the stage until the length of the mineral grain or the trace of a prominent cleavage is aligned parallel to the north-south crosshair, and record the stage goniometer reading (g1). Then rotate the stage - either clockwise or counterclockwise - until the grain goes extinct. This extinction position places one vibration direction parallel to the N-S crosshair. Record the new goniometer reading (g2). The extinction angle is the difference between g1 and g2. If the angle measured with clockwise rotation is EA, then the angle obtained by counterclockwise rotation is 90° - EA. Normally the smaller of these two angles is reported, though in some minerals it is necessary to measure the angle specifically to the slow or fast vibration direction. [1]
Because the measured extinction angle depends on the exact orientation of the grain in the section, the value is only diagnostic when measured on grains in a specific orientation. In most cases, the diagnostic measurement is made on grains that show maximum retardation - that is, grains with their optic axes horizontal - because this orientation places the X and Z indicatrix axes in the plane of the stage where their relationship to the crystal axes is geometrically defined. [1]
Sign of Elongation
Many minerals are elongated in one direction - either because they are prismatic crystals or because they display a prominent cleavage that defines a linear direction in the grain. The sign of elongation records whether the slow ray or the fast ray vibrates approximately parallel to that length. Length slow means the slow ray vibrates more or less parallel to the mineral’s long axis; it is also called positive elongation. Length fast means the fast ray vibrates more or less parallel to the length; it is also called negative elongation. Sign of elongation is a separate property from optic sign - the two should not be confused. [1]
Measuring Sign of Elongation
The determination follows directly from the extinction angle measurement. Start with the grain at extinction and its length (or cleavage trace) less than 45° from the N-S crosshair - this is typically the position just reached after measuring the extinction angle. Rotate the stage 45° clockwise, which swings the vibration direction closest to the mineral length into the NE-SW diagonal. Insert an accessory plate whose slow ray is NE-SW. If the retardations of the grain and the plate add, the ray vibrating closest to the mineral length is the slow ray, so the mineral is length slow. If the retardations subtract, that ray is the fast ray and the mineral is length fast. [1]
Categories of Extinction
The source distinguishes four categories of extinction based on the geometric relationship between the grain’s length or cleavage and its vibration directions at the extinction point. [1]
Parallel Extinction
With parallel extinction, the grain is extinct precisely when its cleavage or length is aligned parallel to one of the crosshairs. The extinction angle is 0°. Either the slow or fast vibration direction may be parallel to the cleavage trace or mineral length - parallel extinction does not specify which. Parallel extinction is characteristic of many uniaxial minerals and of orthorhombic minerals viewed in sections parallel to their principal planes. [1]
Inclined Extinction
With inclined extinction, the grain is extinct when its cleavage or length is at a non-zero angle to the crosshairs. Neither vibration direction is aligned parallel to the cleavage trace or mineral length. If the slow ray vibration direction is closer to the length or cleavage, the mineral is length slow; if the fast ray is closer, it is length fast. Inclined extinction is the expected result for most orientations of monoclinic and triclinic minerals, and it is particularly diagnostic because the specific angle value, measured on grains at maximum retardation, is a species-level property in those crystal systems. [1]
Symmetrical Extinction
Symmetrical extinction is observed in minerals that display two cleavages or two distinct crystal faces. If the extinction angles measured from each of the two cleavage directions to the same vibration direction are equal, extinction is symmetrical. The practical measurement requires rotating the grain to extinction and then measuring the stage rotation to each cleavage in turn - first clockwise, then returning to extinction and measuring counterclockwise. Equal angles confirm symmetrical extinction. Symmetrical extinction is common in orthorhombic minerals viewed in certain orientations and in some monoclinic minerals when the {010} section is in view. [1]
No Extinction Angle
Many minerals lack distinct cleavages and show neither an elongation nor prominent crystal faces. Although these grains go extinct every 90° of stage rotation like any anisotropic mineral, there is no reference direction - no cleavage, edge, or crystal face - from which to measure the extinction angle. Such minerals have no extinction angle. The category is not a defect in the mineral; it simply means the grain lacks a geometric reference for the measurement. [1]
Anomalous Extinction Patterns
Beyond the four main categories, some grains exhibit irregular extinction behavior caused by grain deformation or chemical zoning. [1]
Undulatory extinction occurs in deformed rocks where mineral grains have been bent or otherwise strained. Different parts of the same grain go extinct at different stage rotation angles because the crystallographic orientation varies across the grain. The extinction position sweeps across the grain in an irregular or wavy pattern as the stage is rotated, rather than the whole grain extinguishing at once. Undulatory extinction is a useful strain indicator in rocks such as quartz-bearing tectonites. [1]
Zoned extinction is seen in chemically zoned minerals, such as plagioclase. In monoclinic and triclinic minerals the extinction angle is controlled partly by chemical composition, so a grain whose composition changes from core to rim will display one extinction angle in the center and a different angle at the rim. The variation is systematic rather than wavy. No special term is applied to this pattern, but the mineral is simply described as zoned. [1]
Extinction by Crystal System
Uniaxial Minerals
Tetragonal and hexagonal minerals tend to be prismatic with their elongation parallel to the c axis. The common crystal forms - prisms parallel to c, pinacoids perpendicular to c, pyramids - and the cleavages parallel to these forms are all either parallel or perpendicular to the optic axis. As a result, tetragonal minerals display parallel extinction to prismatic cleavage when their c axis is in the plane of the stage (the highest-birefringence orientation). They display inclined or symmetrical extinction relative to rhombohedral or pyramidal cleavages. The {001} pinacoid cleavage yields parallel extinction in all grain orientations because the indicatrix section perpendicular to the c axis is always the circular section. Trigonal minerals that crystallize in the rhombohedral habit are common in hexagonal minerals. [1]
Biaxial Minerals
Extinction behavior in biaxial minerals is controlled by the relationship between the indicatrix axes and the crystallographic axes, which is symmetry-constrained. [1]
Orthorhombic minerals display parallel or symmetrical extinction in sections cut parallel to (100), (010), and (001), because in each of these principal cuts the indicatrix axes and crystal axes coincide. All other cuts - at random angles - produce inclined extinction. Grains at maximum retardation (optic axes horizontal) always show parallel or symmetrical extinction. [1]
Monoclinic minerals display parallel or symmetrical extinction only when the {010} plane happens to be vertical. Most other orientations yield inclined extinction. A common indicatrix geometry in monoclinic minerals is Y parallel to b; in monoclinic pyroxenes and amphiboles with this geometry, grains at maximum retardation display inclined extinction angles that directly reflect the relationship between the X and Z indicatrix axes and the a and c crystal axes. This extinction angle is one of the most useful diagnostic measurements for distinguishing these minerals. [1]
Triclinic minerals display inclined extinction in almost all sections because no indicatrix axis is constrained to be parallel to any crystal axis. This means that even in the highest-birefringence orientation, the vibration directions are at angles to all cleavages and crystal edges. [1]
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References & Citations
- 1.Introduction to Mineralogy Nesse, W. D.
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