A metallurgical analysis was a thorough sensor scan of a metal. Metallurgical scans could detect microfractures. (TNG: "Phantasms")
In 2369, Captain Jean-Luc Picard ordered a metallurgical scan of the hull of the USS Enterprise-D to see if subspace field incursions by the solanogen-based lifeform had left a trace. (TNG: "Schisms")
The same year, Dr. Julian Bashir ran a metallurgical analysis of one of Quark's holosuites for DNA or skin fragments, hoping to discover who Ibudan's murderer was. (DS9: "A Man Alone")
In 2373, the USS Voyager conducted a metallurgic analysis of the Takarian planet, ascertaining that the Takarians were at a Bronze Age level of development. (VOY: "False Profits")