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Gemstones
The traditional classification in the West, which goes back to the Ancient Greeks, begins with a distinction between precious and semi-precious stones; similar distinctions are made in other cultures. The precious stones are diamond, ruby, emerald and sapphire, with all other gemstones being semi-precious.
This distinction is unscientific and reflects the rarity of the respective stones in ancient times, as well as their quality – all are translucent with fine color in their purest forms, except for the colorless diamond, and very hard, with hardnesses of 8-10 on the Mohs scale. Other stones are classified by their color, translucency and hardness.

Precious Gemstones
The traditional distinction does not necessarily reflect modern values, for example, while garnets are relatively inexpensive, a green garnet called Tsavorite, can be far more valuable than an mid-quality emerald.
Next, many gems are crystals which are classified by their crystal system such as cubic or trigonal or monoclinic. Another term used is habit, the form the gem is usually found in. For example diamonds, which have a cubic crystal system, are often found as octahedrons.
Gemstones are classified into different groups, species, and varieties. For example, ruby is the red variety of the species corundum, while any other color of corundum is considered sapphire. Emerald (green), aquamarine (blue), bixbite (red), goshenite (colorless), heliodor (yellow), and morganite (pink) are all varieties of the mineral species beryl.
Gems are characterized in terms of refractive index, dispersion, specific gravity, hardness, cleavage, fracture, and luster. They may exhibit pleochroism or double refraction. They may have luminescence and a distinctive absorption spectrum.
Material or flaws within a stone may be present as inclusions.

