Well formed crystals are very rare as stishovite does not get much time to form crystal faces. It forms quickly at very high pressures but not necessarily at high temperatures. Where on Earth do you find such an environment? At a meteor impact site! Where the pressures are great but the overall temperature is not that high. And indeed it was at the meteorite crater in Arizona, called Meteor Crater, one of the most well studied meteor impact sites in the world, that the first tiny crystals of stishovite to be found in nature were identified. Stishovite was actually first synthesized in 1961 before the discovery at Meteor Crater. Now the presence of stishovite is diagnostic evidence of a meteor impact when craters of unknown origin are examined.
Stishovite's basic structural unit is an SiO6 octahedron. This is a much more compact arrangement than the SiO4 tetrahedron of quartz and the other Quartz Group members. Because of this compactness stishovite is the densest member of the Quartz Group and has the highest index of refraction. Comparing stishovite's density and index of refraction to that of quartz's, 4.28 to 2.65 and 1.81 to 1.55 respectively, it is hard to believe that they are both composed of the same elements and in the same proportions.
Stishovite's structure is made of parallel chains of single octahedrons composed of a silicon ion surrounded by six oxygens. It is the parallel chain structure that produces the prismatic crystal habit typical of the Rutile Group. The octahedron chains are arranged with the octahedrons on their "sides" and sharing opposing edges with other octahedrons. The four fold symmetry is the result of the square void created between the chains.
Stishovite is classified as an oxide instead of a silicate like quartz because the structure of stishovite is identical to other oxide minerals. Quartz's structure is the foundation of many tectosilicate minerals and therefore the similarity of quartz's structure to other silicates is justification for its classification, although many mineralogists classify quartz as an oxide.
Stishovite is only metastable at normal surface pressures; meaning that, if it could, it would slowly convert to the quartz structure. But this is a slow and complicated process taking thousands of years if it happens at all. It is so slow a process mostly because the transformation involves the breaking of bonds and the rearrangement of atoms.
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