A phase transition coil was the component in the transporter device that converted a person or object from matter to energy and back again.
The transition coils of the USS Enterprise-D's transporter system were ruled out as having caused the transporter malfunction resulting in Ambassador T'Pel's apparent death shortly after stardate 44390.1, as they had been replaced only a week earlier. (TNG: "Data's Day")
When weapons were beamed to a rebel camp on Krios from a cargo transporter of the Enterprise-D, Geordi La Forge ordered to run a level-1 diagnostic of the phase transition coil. (TNG: "The Mind's Eye")
When the USS Voyager achieved contact with a Romulan science vessel via a micro-wormhole in 2371, they attempted to transport a test cylinder to the ship. Due to the complexity of the transport and a phase variance, power to the phase transition coils had to be increased. (VOY: "Eye of the Needle")
Later that year, Kathryn Janeway set the phase transition coils to maximum in preparation for rematerializing a victim of the metreon cascade whose bodily fragments were widely scattered. (VOY: "Jetrel")