A time crystal was a crystal with a non-equilibrium matter state. Time crystals might be identified by their orthogonal indices.
By the mid-23rd century, the Vulcan Academy taught about time crystals, but no Federation-aligned species had been able to stabilize them, as the decay rate of the lattice was too unpredictable. However, it was theorized that four-dimensional races might be able to perfect the technology.
Harcourt Fenton Mudd at some point acquired a time crystal device capable of creating chronal displacements. This technology consisted of two components, a wrist-mounted crystal with controls in an unknown script, and a much larger one on his ship capable of generating the required energy for chronal displacements.
It was suspected that he used this device to rob a Betazoid bank, and during the Federation-Klingon War of 2256 he used it to attempt to steal the USS Discovery and sell it to the Klingons. The crystal on Mudd's wrist disintegrated after he allowed the Discovery to rejoin the time stream. (DIS: "Magic to Make the Sanest Man Go Mad")