The science of crystallography at first thought may seem to be esoteric and a dusty old endeavor of limited practical use. Not so! Without crystallography, the whole world would come to a grinding halt, being composed of useless amorphous particles.
Almost everything is composed of crystals of a particular chemical compound, or natural mineral, or man-made material, which are identified either visually, or by X-ray diffraction, to be shown what they actually are, from one crystal compound to another, just like fingerprints. The research chemist, the research physicist, the gem cutter, the rock hound, in fact nearly everybody needs to have a basic understanding of crystallography, except perhaps politicians and used car salesmen.
Let’s start by examining a lovely quartz crystal. Quartz is the second most common mineral on earth. Therefore I expect every household to have at least one quartz crystal on show, and beloved, like having a pet cat or dog, or goldfish (and you don’t have to feed them). I have many beautiful quartz crystals scattered around my apartment. Now and then I handle them and peer through inside to look at the feather inclusions, and admire their crystal faces and symmetry.
Quartz crystals, or any crystal really, are found in one or more typical habits, or to have a favored appearance, like you wearing your only suit to work. Quartz crystals have hexagonal prism faces usually horizontally striated, capped by sloping faces all coming to a point. Usually there are 3 big sloping faces alternating with 3 littler ones. This observation shows that the terminal faces of a quartz crystal are rhombohedral faces, like you get with calcite, and not pyramid faces sometimes found on beryl crystals. Actually, quartz belongs to the trigonal crystal system, as does several other well-known minerals, such as tourmaline, ruby, sapphire and calcite.
There are 7 crystal systems to which all crystals belong. Each has its distinctive array of crystal axes, exhibiting 2, 3, 4 and 6-fold rotation, plus various mirror planes of symmetry, and possibly a center of symmetry.
The simplest crystal system is the isometric or cubic system, having 3 axes of equal length, arranged perpendicular to one another. Common forms encountered are the cube, octahedron and dodecahedrons. Diamond, spinel and magnetite have the habit of crystallizing as octahedra. Common salt, or sodium chloride, whose mineral name is halite, always likes to form cubes, as does fluorite, the calcium fluoride mineral. In shales one sometimes sees little cubes of pyrite, but that found in metalliferous veins, where it crystallizes at high temperatures, may show the more complicated pentagonal dodecahedron, or pyritohedron.
Garnets are cubic too and love to grow as dodecahedra, usually at high temperatures in mica schists, gneisses, pegmatites and contact metamorphic zones. Red almandine garnet dodecahedra an inch or two in size make nice collectors items. Tiny water-worn garnets, when found in the heavy residue of a stream bed, or larger when set as a gemstone, are isotropic to light which helps in its identification. Some crystals may show a combination of forms, such as a cube with corners truncated by octahedral, or dodecahedral faces, (and vice versa), which does complicates things.
The hexagonal crystal system has a vertical axis of 6-fold symmetry and in the plane perpendicular to it are 3 axes of equal length intersecting at 60 degrees. The mineral beryl (and emerald) and apatite, show normal hexagonal symmetry. Typical habit is of the hexagonal prism face, capped by the flat basal pinacoid. In Nature they may be stumpy prisms or sometimes elongated along the c-axis with aquamarine. The prism corners and edges may be clipped off by the presence of small pyramid faces. What can we learn from this?
Beryl and emeralds are noticeably dichroic, meaning that the color differs slightly depending on whether you view the crystal down the c-axis or across it, through the prism faces. This is important to the gem cutter who always likes to present the best color, after avoiding any obvious flaws. It is also important to the commercial crystal grower of emeralds and to those jewelers who have to identify synthetic emeralds, and to the customer’s preference of green color.
Light transmitted along the c-axis is called the o-ray (grass green to yellowish green) whereas that transmitted across the prism is a combination of the o-ray and the e-ray and tends towards a bluish green color. A polaroid filter can be used to isolate the e-ray to see its true color, which is a stronger bluish green. The green color is due to a trace of chromium in the structure, and is modified by the presence of iron, both ferrous and ferric ions, and by the rare presence of vanadium, although vanadium emeralds are known having little if any chromium.
When a natural or synthetic emerald is faceted into a gemstone, the resultant green color depends on how it is orientated with regard to the crystal axes. Much of the original Chatham synthetic emeralds were flux grown spontaneous nucleated .prisms and were cut rectangular shape with the table facet parallel to the prism, and therefore had a bluish tint to them. Later, the Gilson flux emeralds were grown on seed plates sawn parallel to the basal plane, so the gemstones were cut with the table facet parallel to the basal plane and so showed the more desired grass-green color without the blue tint.
Next on the market were the hydrothermally grown emeralds produced by the Linde Company and others. Experimental research demonstrated that in order to get acceptably fast growth rates it was best to orientate the seed plate (from a clear beryl or aquamarine) parallel to a pyramid face, which produced a comparatively weird shaped crystal but acceptable for gem cutting. A rule of thumb is that the largest crystal faces present have the slowest growth rates, and vice versa.
For example, in the industrial hydrothermal growth of quartz crystals, the seed plates used are sawn parallel to the basal plane, to produce hexagonal shaped tabular crystals, since the c-axis is the fastest growing direction, and the basal pinacoid as a face doesn't exist, unlike beryl.
Study of crystals is fascinating for the gem collector and rock hound. Here is a puzzle, tell me how do doubly terminated quartz crystals grow, like the prized “Herkimer Diamonds”? What holds them up so that both ends and sides may grow freely?
Ruby and sapphire crystals have trigonal symmetry. Sapphire crystals are often found as cigar-shaped hexagonal crystals with horizontal striations, with pyramidal and rhombohedral faces, whereas rubies sometimes form hexagonal tablets with the basal pinacoid predominate. Star rubies and sapphires must be cut with their base perpendicular to the c-axis to get the perfect star effect.
In conclusion, a knowledge of crystallography is important to the prospector, gem cutter, crystal grower and the aficionado of minerals, just like numbers and arithmetic are important to accountants. Crystallography is great stuff and should be studied at your leisure.