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Dilithium was an element primarily occurring as a crystalline mineral. It could be found on only a few planets in the galaxy, and was therefore a rare and valuable substance.
In Starfleet starships, dilithium was used to regulate the matter/antimatter reaction. Injectors would feed matter and antimatter into the dilithium chamber, where the two substances would mix and react, with the dilithium crystals used to control the reaction.
In or around 2257, Me Hani Ika Hali Ka Po, a member of the Xahean royal family, built an incubator to recrystallize dilithium. However, Starfleet did not have this ability until at least the 2280s.
By the 2360s, Starfleet had the ability to synthesize dilithium via recrystallization while it was still enclosed in the warp core's dilithium articulation frame using a theta-matrix compositor. This was done by recompositing fractured crystals.
In 2372, the USS Voyager discovered a new form of dilithium in the Delta Quadrant that remained stable at much higher reaction rates, thus allowing a vessel to travel more efficiently at much higher speeds. This dilithium was installed aboard the shuttlecraft Cochrane to test an experimental warp 10 flight.
By the late 31st century, the dilithium supply in the galaxy began to dry up. This caused the Federation to start trials on alternate warp drive designs but none proved reliable. In roughly 3069, refined dilithium across the galaxy suddenly became inert, resulting in an uncontrolled mixing of matter and antimatter which destroyed all ships that had an active warp core. This disastrous event was known as "the Burn". This event lead to the near-collapse of the Federation.
In 3189, the USS Discovery discovered Theta Zeta, a planet composed of dilithium, in the Verubin Nebula while investigating the cause of the Burn. The large repository gave Starfleet a means to distribute dilithium to planets and systems around the galaxy.