Optical Effects in Gems: Birefringence
Optical Birefringence in Gemstones & Minerals
The term "birefringence" describes the optical phenomenon of double refraction as a single beam of light travels through a transparent, molecularly ordered material, and is split into two separate beams. The amount of birefringence in a given material is directly linked to the orientation-dependent differences in its dual refractive indices. The term "intrinsic birefringence" is used to describe any naturally occurring mineral's asymmetry with respect to its refractive indices which are inherently direction-dependent.
The optical characteristics of a given transparent material is categorized as being either anisotropic or isotropic. Most transparent solid minerals are optically isotropic, meaning that their index of refraction is equal in all directions throughout their crystalline lattice structure. Simple glass is an example of a material that is isotropic. Materials that exhibit no birefringence are also referred to as being "singly refractive."
Isotropic mineral crystals that belong to very symmetrical crystal systems (ie. cubic or hexagonal) are singly refractive, and these isotropic gems include: diamond, cubic zirconia, garnet and spinel.
Double Refraction in Anisotropic Gems
Certain anisotropic crystals exhibit the optical phenomenon known as "double refraction," where the incident light is split into two separate rays, each with different refractive indices and velocities, and their refractive indices will typically vary between two extreme values. The term "anisotropic" or "anisotropism" is not limited to optical phenomenon, but also describes minerals that exhibit other physical properties with multiple/variable values. For instance, the Mohs hardness rating of the mineral kyanite has two values when the hardness is measured in different crystallographic directions (i.e., along the a/b-axis or along the c-axis).
Crystals belonging to asymmetrical crystal systems (ie. monoclinic, triclinic) tend to have a higher occurrence of double refraction [2]. Gemstones that are "doubly refractive" can exhibit pleochroism, dichroism or trichroism, all of which can alter the apparent color of the gemstone through pseudochromatic coloration.
Birefringence in Calcite |
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The mineral calcite (above, left) has two different refractive indices of 1.490 and 1.660 exhibiting strong double refraction and therefore, birefringence. Calcite's rhombohedral cleavage block produces two distinct images (double vision) when it is placed over an object.
This splitting of light gives a double-vision effect. Anisotropic crystals such as calcite, alexandrite, amethyst (quartz) or tourmaline have crystallographically distinct axes, and interacting with the light traveling through them by a mechanism which is dependent upon the orientation of their crystalline lattice with respect to the angle of incident light.
When a beam of incident light enters the "optical axis" of these anisotropic crystals, it behaves in a manner similar to the interaction with isotropic crystals, and passes through at a single velocity. But when the beam of light enters a "non-equivalent" axis, it is refracted (split) into two separate rays, each polarized with their vibration directions oriented at right angles to one another (mutually perpendicular), exhibiting birefringence. Each separate beam is now traveling at different velocities (speeds), and therefore, their frequencies (colors) are also now different.
Uniaxial Minerals
Anisotropic minerals that have a single optic axis and crystallize in the hexagonal and tetragonal crystal systems are called "uniaxial minerals." In these minerals, when light travels along the direction of their single "optic axis" they exhibit the same optical properties as isotropic materials; meaning that the polarization direction of the light is not changed by its passage through the material [4].
This single "optic axis" is coincident with the c-axis in hexagonal and tetragonal minerals, so if the light travels parallel to the c-axis it will behave as if it were traveling through an isotropic material. As is the case with all anisotropic minerals, a uniaxial mineral's refractive indices will typically vary between two values which are defined as "w" (or No) and "e" (or Ne).
Interference Colors in Anisotropic Minerals
When the "ordinary" and "extraordinary" rays emerge from a birefringent crystal (above, left), they are still vibrating at right angles with respect to one another. Because one wave is retarded (delayed) with respect to the other, interference (either constructive or destructive) occurs between the waves as they pass through the crystal, the result being that some birefringent crystal acquires a spectrum of color when observed in white light [5]. Such "interference color" effects are often mistakenly referred to as a "rainbow" or solar "spectral colors," and are commonly seen in soap bubbles, or in oil slicks on the surface of water.
The effect of interference color is observed and quantified using a polarized-light microscope, and quantitative analysis of the interference colors observed in an anisotropic crystal is accomplished by using a Michel-Lévy "interference color chart" (Tableau Des Biréfringences). This chart was created in 1888, for a book on rock-forming minerals titled Les Minéraux des Roches.
If you were to take any transparent mineral and view it between crossed "polars" (lower polarizer) using a polarizing microscope, viewing it in all possible orientations, the mineral would either show interference colors, and appear bright and colored against a black background, or it will not be seen at all and the field would remain black. Any mineral that would remain dark at all orientations between crossed polars would therefore be isotropic [1].
Bibliography on Birefringence in Gemstones
1. John G. Delly, Michel-Lévy Interference Color Chart  . www.modernmicroscopy.com
2. Stanford University, Refraction in Gems . www.stanford.edu
3. Wuerzburg Uniaxial Minerals . www.geographie.uni-wuerzburg.de
4. Stephen A. Nelson Introduction to Uniaxial Minerals . www.tulane.edu
5. Douglas B. Murphy Optical Birefringence . www.micro.magnet.fsu.edu
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