Star Trek Expanded Universe
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Dilithium is a rare transperiodic element in the hypersonic series, usually found in crystalline form throughout the galaxy. It is one of the key components of warp drive, regulating the flow of matter and antimatter.

Dilithium had an atomic number of 119 and was first identified in 2049 on Amalthea, one of Jupiter's moons. (Star Fleet Medical Reference Manual, Federation Spaceflight Chronology, vol. 3) However, soon after this, it was found that 2-3 percent of Earth quartz was, in fact, dilithium. This fostered a "gold rush" mentality as many museums dug through their collections and identified dilithium via a test for the mineral's extension into the fourth dimension. (TOS novel: Prime Directive)

Politics and economics of dilithium

Planets rich in dilithium were of very high strategic importance. Some of those worlds included Coridan, Elas, and Halka. (TOS: "Journey to Babel", "Elaan of Troyius", "Mirror, Mirror")

The Klingon and Romulan Star Empires both used prisoners to mine dilithium from Rura Penthe and Remus, respectively. (Star Trek VI: The Undiscovered Country, Star Trek Nemesis)

Dilithium-rich planets near the borders between galactic powers were often sources of contention. Ghioghe, in the Triangle between Federation, Klingon and Romulan space was one, as was Pharos in the Marrat Nebula. (Yesterday's Heroes; Star Trek: Early Voyages comic: "The Fires of Pharos")

In the 24th century, Coleman Dynamic Industries and the Dytallix Mining Corporation were leading civilian firms in the Federation dilithium industry. (Star Trek: Pendragon)

Urie gave what was then dubbed by her as "the most expensive dance lesson ever" for the cost of a container full of dilithium crystals. (Star Trek: The Stoneship Files: "Dilithium Dance")

Recrystallization

Dilithium crystals were fragile things, and could crack under severe strain, such as ship-to-ship combat, or a temporal breakaway maneuver. However, Captains Spock and Montgomery Scott devised a method of recrystallizing dilithium while stranded on Earth in 1986 and by the 24th century, dilithium recrystallization had become commonplace aboard Federation starships. (TOS: "Elaan of Troyius"; Star Trek IV: The Voyage Home; TNG: "Family")

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