BlueTiger Eye is a chatoyant gemstone that is variety of Quartz.
 
It's chatoyancy is naturally created from sub-parallel intergrowth of Quartz crystals and altered amphibole fibers that have mostly turned into Limonite.
 
The original, Crocidolite, is a bluish-gray color, and sometimes the pseudomorphism to Quartz is incomplete resulting in a stone with a bluish-gray color with chatoyant effect. This is considered Hawk's Eye.
 
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* Sizes, shapes and colors my vary due to being a natural stone, being hand-carved and/or difference in computer monitors