The surface of the workpiece is saturated with either carbon atoms (carburising plasma) or nitrogen atoms (nitriding plasma). Carburising, carried out at high temperatures, involves bombarding the surface to be coated with the plasma. The workpiece is held under vacuum until carbon atoms have diffused into the heated surface, to form hardened surface layers on quenching. Nitriding is carried out under vacuum, but without external heat. The heat to diffuse the nitrogen into the surface is provided by kinetic energy, produced when the atoms hit the surface. Hardened surface layers are formed on cooling of the workpiece in situ.