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Neutronium is a dense material found naturally in the cores of neutron stars. It was impossible to scan inside neutronium. (TNG: "Evolution"; TOS: "The Doomsday Machine") Despite many readings and theories, the Federation was never able to produce neutronium artificially as of 2375. (VOY: "Think Tank")

In 2267, the sensors of the USS Enterprise recorded a pure neutronium hull on the extra-galactic planet killer prior to its destruction. According to Spock, there is no known way of penetrating neutronium. (TOS: "The Doomsday Machine")

In 2366, Doctor Paul Stubbs studied the cyclical decay of trace amounts of neutronium in the Kavis Alpha sector through the use of the probe "The Egg." (TNG: "Evolution")

In 2369, the USS Enterprise-D encountered the only known Dyson sphere. The structure was composed of a carbon-neutronium alloy and was impervious to phaser fire. (TNG: "Relics")

The Iconians had mastered the use of neutronium, and used it on a ziggurat containing a gateway on the planet Vandros IV. This was discovered by the Dominion in 2372 and was destroyed by a joint Starfleet-Jem'Hadar team before a group of rogue Jem'Hadar could use the gateway. (DS9: "To the Death")

The Dominion had begun using neutronium by 2375 and used it to protect the entranceways on Dominion Headquarters from weapons fire. (DS9: "What You Leave Behind")

By 3189, Starfleet had the ability to produce neutronium alloy. (DIS: "Die Trying")

It is assumed, though unclear, that neutronium is a harder substance than rodinium since neutronium seems to be impervious to weapons fire while rodinium can be destroyed by Romulan plasma torpedoes. However, according to Spock, rodinium was the hardest substance known to Federation science as of 2266. (TOS: "Balance of Terror") Neutronium was mentioned in 2267 during the confrontation with the Doomsday Machine. So, it is possible that neutronium was first discovered by the Federation sometime between those two incidents. In DIS: "Die Trying", a bridge officer on the Discovery, which disappeared in 2258, was familiar with neutronium, implying it was discovered before that date.
Neutronium was also mentioned in a joke in TOS: "A Piece of the Action" equating it to steel.
The term was coined in 1926 for a hypothesized element with the atomic number 0 and currently is used for a degenerate form of matter which cannot exist outside neutron stars. Since 1942, it has been used in various science fiction material to refer to a super-dense alloy or a trans-uranic element on the periodic table.

Neutronium in the Delta Quadrant[]

The crew of the USS Voyager learned that the Borg never assimilated the knowledge to collect or create neutronium. (VOY: "Think Tank")

Separated from the Alpha Quadrant in 2371 Voyager encountered neutronium several times while stranded in the Delta Quadrant.

In 2371, Voyager encountered an artificial asteroid composed of a neutronium alloy created by the Vidiian Sodality. (VOY: "Phage")

According to an Alpha Hirogen hunter, at least one collapsed star in the Delta Quadrant had a neutronium mantle. The hunter claimed to the crew of Voyager that he tracked a silicon-based lifeform through this mantle. (VOY: "Prey")

In 2375, Voyager encounter the Think Tank, who traveled aboard a vessel composed of a neutronium alloy. This impressed the crew, who had rarely encountered it before. (VOY: "Think Tank")

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