If you remember, we orient the light coming out of the lower polarizer E-W. Unless the light split within the mineral, it will continue to be oriented E-W and when it reaches the inserted N-S polarizer (also referred to as the “analyzer”), nothing will pass through and all the petrographer will see is black. There are two cases when this will happen:
- isotropic minerals, where light is not split into two rays because of high symmetry
- circular sections of anisotropic minerals, which are a special case; in uniaxial minerals, there is one circular section that is perpendicular to the c-axis, and in biaxial minerals, there are two circular sections perpendicular to the two optic axes; we’ll get back how to distinguish between between uniaxial & biaxial minerals and why circular sections are important in next week’s installment on interference figures
Isotropic minerals are not the most fascinating things to look at in crossed polars, which is why this blog is entitled “Life in Plane Light” and not… “The analyzer is in”? “Light Interference”? “Maximum birefringence”?
Anisotropic minerals, in contrast, are quite interesting in XPL. When light enters most orientations of an anisotropic mineral, its split into two rays that have different speeds. When the light exits the crystal, it has to condense back down one ray. So, let’s talk for a second about light addition / subtraction. In 2D, we simply take the two rays and add them together:
There are two special cases to consider: when the two light rays are exactly in sync with each other they will add to give the maximum value (“in phase”); when 1/2 a length “out of phase” from each other, they will cancel out each other to give the minimum value.
In 3D, we have to do a bit of vector math in order to add the two waves together. Since light is divided into two waves mutually perpendicular to each other, the following is true:
As the crystal is rotated, the orientation of the crystal varies and the light entering will vary in speed, which means that the sum of light will vary as you rotate the stage. There will be two end-members: one oriented perpendicular to the upper polarizer (minimum light) & one parallel to the analyzer (maximum light).
Turns out that every 90 degrees rotation of the stage, every mineral will go through both the maximum and minimum. We call the minimum “extinction.”
We can have a variety of types of extinction (EA):
- parallel: when the crystal / cleavage is oriented N-S or E-W, the mineral is extinct
- inclined: when the crystal / cleavage is NOT N-S or E-W when extinct; we record this including the acute angle between when the mineral is extinct & oriented N-S
- symmetrical: mineral goes extinct at the same angle to two sides of a mineral / cleavage planes
- other: if the mineral isn’t elongate or has cleavage, you will not be able to record an EA; minerals that have undergone deformation may have undulatory extinction
The maximum color will depend on the thickness of the crystal (it can vary somewhat depending on how well your thin section is made) as well as what the difference between the refractive indices of the two rays. The color we see in crossed polars, is called the “interference color” and is varies through a sequence of ever more pastel sequence of rainbow colors on a “Michel-Levy chart.” If you look at the photomicrograph above, you can see that the non-garnet minerals vary from quartzes & plagioclases that are 1st order greys to white to muscovite & biotite that are 2nd to 3rd order.
to find the birefringence, we determine the interference color of the mineral at the maximum light (45 degrees from extinction) and go up to the thickness of the mineral (usually 0.3 mm). Follow the inclined line up to the top or to the right side to read off what the birefringence is.
Another property we can specify for elongate minerals is the sign of elongation (stop sniggering). The property depends on whether the fast or slow light ray is parallel to the elongate direction of the crystal. However, to test for this one, we need to use one more component on the microscope: the “quartz wedge” or “accessory plate” or “gypsum plate” or “the psychedelic color thingy” (my students occasionally get creative with their naming).
The accessory plate is labeled with the slow vibration direction & the wave length of light that it will add. The vibration direction is usually oriented SW-NE. When the slow ray of the mineral is oriented in the same direction, we get addition and the interference color will increase by whatever the specified wave length is. If the fast direction is NE-SW, the interference color will decrease by the wave length.
If the slow light path is parallel to the elongate direction of the mineral, the mineral will be called “length slow” or “positive elongation.” The opposite will be “length fast” or “negative elongation.”
The last property we’re going to talk about is the more formal pleochroic scheme (we did informal last week). In plane light, the absorbed color of the mineral will vary depending on the orientation of the crystal. In the formal scheme, we assign specific colors to specific orientations.
- For uniaxial minerals, there are two end-member colors: the “omega” or “w” or “ordinary” direction, which is the only light direction in the circular section; the “epsilon” or “E” or “extraordinary” direction, which is the maximum difference in refractive indices from the ordinary direction & is perpendicular to the circular section (also called the “principal section”). The ordinary direction will always be present when the crystal is oriented with the circular section parallel to the stage (e.g. when the mineral acts isotropicly).
- For biaxial minerals, we need to assign three colors: “alpha” or “X” & “beta” or “Y” and “omega” or “Z” which correspond to the smallest, moderate, and largest refractive indices; you can only see a maximum of two of the colors for any given orientation of the mineral, so you’ll need 2 different cuts (circular & principal section) through the mineral to describe the whole pleochroic scheme; beta can be seen in the circular section, while alpha & omega will be found in the principal section (use the accessory plate to determine which one is the alpha = fast and omega = slow directions).
Dave Hirsch has some great pleochroism movies on his website.
Next week, we’re going to go to structure for a post & discuss Mohr circles, but then we’ll be back to mineralogy & optic axis figures.