Brookite is a rare mineral, typically brown in color, but sometimes yellowish or reddish, or black. Brookite is one of four minerals with the chemical formula TiO2, titanium dioxide. It occurs in the orthorhombic crystal structure. 
(Faceted. From Pakistan. Weight: 0.05 carats)
Image © supplied by Woodmansee* Gems
The other titanium minerals are Anatase (tetragonal), akaogiite (monoclinic) and Rutile (tetragonal) . Brookite is said to be polymorphous with these minerals. Brookite has the interesting property that at temperatures over 750ºC it will revert to rutile. 
Brookite was discovered in 1825 and named after the English mineralogist and crystallographer Henry James Brook. Brookite crystals have been graded as facet grade crystals by the International Mineralogical Association. Facet grade crystals are the rarest among the rare gemstones. The facet grading makes the crystals of Brookite extremely rare and stunningly attractive.
Though Brookite is not used to adorn jewelry it does feature in any serious mineral collector's cabinet. It has occasionally been faceted, as can be seen in the example in the image top left.
Brookite - Properties:
Brookite is composed of Titanium Oxide and have a molecular weight of almost 80 grams. The Brookite crystals contain the highest percentage of Titanium among the gemstones known to contain Titanium. The Brookite crystals contain almost 60 percent of Titanium and 40 percent of oxygen. The most common impurities to occur in brookite are iron, tantalum and niobium. 
The crystals of Brookite display orthorhombic and dipyramidal crystallography properties. The crystals are found in their natural form as 12 cm long tabular crystals with massive striations. Brookite is quite brittle and also displays irregular and uneven fracturing, also sometimes sub-conchoidal fracturing.
Brookite occurs naturally in light brown or dark brown coloring and very rarely in reddish brown, orange and red coloring. Brookite is not radioactive but displays luminescence properties ranging from white to yellowish white and grayish white. Brookite crystals are rarely transparent and display transparency only in very small fragments. Usually Brookite crystals are opaque and sometimes translucent.
The Brookite crystals display various optical properties of very strong dispersion and weak pleochroism. Brookite has a higher refractive index even than diamond, at over 2.5 (diamond is 2.42).  Brookite crystals are relatively dense at 4 g/cm3. The hardness of Brookite is between 5.5 and 6.0 (Moh). The twinning properties of Brookite crystals are unclear but till date no twinning has been found in any of the crystals of Brookite.
Brookite - Occurrence:
Despite being extremely rare the crystal of Brookite are found in many localities but only about 1 or 2 percent of these localities produce usable and quality facet grade crystals of Brookite. Brookite is mainly found in Wales, England, Switzerland, France and Austria. Trace amounts of quality facet grade Brookite crystals have also been found in Norway and Russia. The largest crystals of Brookite have been found in the Southern Ural Mountains in Russia. The Dodo mines in the Ural Mountains in Russia have produced the largest and best quality facet grade crystals of Brookite. Trace amounts of low quality Brookite have also been mined in Italy, Brazil and USA.
The largest crystals of Brookite have recently been found in the Balochistan province of Pakistan. The Brookite crystals are sought after for their unique and rare orangish red color - as seen beautifully in the image below.
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Brookite - Sources Referenced:
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