Re: Optical Mineralogy Paul F Kerr.pdf
Annice Hemmerling
The Michel-Lvy interference color chart has been in continuous use by analytical microscopists for more than 100 years. Why such endurance? Because this chart, also known as the Michel-Lvy Table of Birefringence, is just as useful today as it was over a century ago in unlocking the many mysteries of microscopic particle analysis and identification. This extraordinarily valuable aid to the polarized-light microscopist graphically relates the thickness, retardation (optical path difference), and birefringence (numerical difference between the principal refractive indices) for particular views of transparent, colorless or colored substances. These characteristics allow unknown materials to be identified; additionally, they provide important optical information about those materials whose identity is known.
The early applications of the Michel-Lvy interference color chart were in the fields of mineralogy and petrology, for the identification of mineral grains in rock thin-sections, and also for comminuted, free mineral grains. The general utility of the chart, however, is such that today it is used as an aid not only for the identification of minerals, but synthetic textile fibers, chemicals, food and food-processing ingredients, biologicals, drugs, catalysts, ores, fertilizers, explosives, etc., etc. In fact, the chart is today used routinely by analytical microscopists in the identification of almost all dust-size particles regardless of nature or origin; it is fundamental to the use of The Particle Atlas (2). Some specific fields of application include criminalistics (trace evidence analysis), air pollution, pharmaceuticals, aerospace, papermaking, microelectronics, fibers, polymers, explosives, manufacturing, graphic arts, and brewing!
If you were to take all transparent substances in the world, natural or man-made, and view them between crossed polars using a polarizing microscope, and then view them in all possible orientations, you would observe one of two effects: either the specimen will show interference colors, and appear bright and colored against a black background, or it will not be seen at all; i.e., the field remains black.
Anisotropic substances having two principal refractive indices, epsilon (ε) and omega (ω) belong to the tetragonal or hexagonal crystal systems. Crystals in these two systems have one unique view, along which they appear isotropic; thus they are termed uniaxial. Examples of substances having two principal refractive indices include quartz, calcite, silicon carbide, and man-made polymer fibers.
Substances having three principal refractive indices, alpha (α), beta (β), and gamma (γ), belong to the orthorhombic, monoclinic, or triclinic crystal systems. Crystals in these three systems have two views along which they appear isotropic; thus they are termed biaxial. Examples of biaxial substances include borax, talc, sucrose, mica, gypsum and oriented polymer films.
The refractive indices are characteristic identifying properties of transparent substances. It is these anisotropic substances which can be identified with the aid of the Michel-Lvy interference color chart, often without having to determine each principal refractive index individually.
Retardation, r, increases linearly with both the thickness, t, of a specimen and with the birefringence, n2-n1: the greater the thickness, the greater the retardation (the thicker the crystal, the farther behind the slow ray gets from the fast ray); the greater the difference between the refractive indices (birefringence) to begin with, the greater the retardation (or higher the interference color). That is,
where r is the retardation expressed in nanometers, nm; t is the thickness, which we measure with our eyepiece micrometer, and express in micrometers, m; and B is the birefringence (the numerical difference between the principal refractive indices), which is unitless. It will be seen immediately that, in order to achieve equality of units, the thickness, t, must be multiplied by 1000 (1000 nm/m) in order to express retardation in nanometers,
Since the Michel-Lvy chart shows the interrelationships between thickness, birefringence, and interference color, the microscopists can, as suggested earlier, determine any one from the chart if they know the other two. Several examples will illustrate this:
Example 1: Suppose a cylindrical synthetic fiber 15 m in diameter shows a maximum interference color corresponding to about 900 nm. This is determined by orienting the length of the fiber at 45 degrees to the vibration directions of the crossed polars, and comparing the color running down the center of the fiber to the colors in the chart. The order is found by noting the number of reds between the center and either edge of the fiber. One must be very careful here because the colors are very, very close together at the edge of a cylindrical fiber. It is often better to count orders on a taper-cut end of a fiber. In the present example, we pass through only first-order red, indicating the yellow at the center is second order.
To determine the birefringence, we look for 900 nm on the abscissa and move vertically until we reach a horizontal line corresponding to a thickness of 15 m on the ordinate. There will be a diagonal line where the two lines intersect. We now follow the diagonal line to the upper right to read the birefringence, 0.060, at the top of the chart. Looking up this value in a birefringence table for synthetic fibers, we learn that a cylindrical fiber having this birefringence is nylon. We could also have calculated birefringence from (n2-n1) = r/1000t:
Some non-cylindrical fibers and polymer films can be cut with a razor at a precise 45 degree angle and the thickness measured as the horizontal projection of the cut. Polymer films can be measured directly, using a thickness gauge before mounting.
Example 2: Suppose now, we wish to predict what interference colors would be observed on a sieved sample of the mineral wollastonite, randomly oriented in a viscous medium in which the maximum vertical dimension is 40 m. The known birefringence of wollastonite from analytical tables is 0.014. On the chart, we look along the top until we come to 0.014, where we find a diagonal line. We follow this line down to the lower left until it intersects a line corresponding to a thickness of 40 m. Reading downward at the point where these lines cross, we find the maximum interference color to be slightly more purple than first-order red. Thus, wollastonite particles 0 to 40 m thick will show first-order interference colors of black, gray, white, yellow, orange, red and purplish red depending on their thickness and orientation.
Example 3: Finally, suppose we have a rock thin-section containing the mineral augite (birefringence 0.024) showing an optic normal interference figure and a first-order red interference color (550 nm). It is desired to know the thickness of the section. At the top of the chart, we find the birefringence 0.024 and follow the diagonal line until it intersects the 550 nm line on the abscissa. From the coordinates, we go directly left to the thickness on the ordinate and find 23 m. Once again, we can find the solution from the equation:
The original chart was used for aiding in the identification of minerals that make up rocks. The standard rock thin-section is 30 m thick; thus, the chart, which is applicable up to 50 m, is more than adequate for rock thin-section work. A rock section is determined to be 30 m thick by grinding it down while periodically stopping to observe the decreasing interference colors of ubiquitous quartz (birefringence 0.009) until they show a maximum interference color of pale straw-yellow. Many industrial specimens, soil minerals, etc. are larger (thicker) than 50 m. For these specimens, one can simply extrapolate. For example, if a comminuted quartz grain shows second-order blue colors, how thick is it? Extend the 0.009 diagonal birefringence line beyond the top of the chart until it intersects a vertical line at, say 650 nm (blue), also extended beyond the top of the chart. At the point where the two lines intersect, come straight left to an extended thickness line, and estimate the thickness to be about 70 m (it calculates to 72.2 m).
For the Olympus BX-51 polarizing microscope I am using for the Atlas of Microscopic Particles, I have two rotary Berek compensators; one measures very accurately within the range 0-3 orders, and the other measures within the range 0-20 orders. The Snarmont compensator measures very accurately retardations within 1 order, using monochromatic light and the rotating graduated analyzer. The entire subject of compensation is deserving of treatment, and an article in this series on Snarmont compensation will appear shortly.
Michel-Lvy charts are included in almost all textbooks on optical crystallography, although they are not always in color. We will consider here only the colored ones. Besides the color charts in optical crystallography textbooks, most manufacturers of polarized-light microscopes supply full-color Michel-Lvy charts, including Olympus, Nikon, Zeiss, Leitz, and, formerly, Vickers. Typically, the polarized-light microscopist has the interference color chart framed, laminated, or otherwise mounted on a wall next to the microscope where it can be conveniently and quickly consulted. The more one uses the interference color chart, the more useful and familiar it becomes; its potential application to the analysis of transparent substances is virtually unlimited.
Over the last 75 years or so, the Michel-Lvy interference color chart appears in virtually all optical crystallography textbooks, or the chart has been supplied by the manufacturers of polarizing microscopes. Let us look at some of these.
Over the next seven years, the authors would learn that their text found application in other forms of mineral identification, e.g., comminuted, in addition to thin-section. Thus, the title of the 1942 second edition was changed to Optical Mineralogy (24). The interference color chart in the eighth impression of this edition is identical to the first edition; only its location within the text is different.
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