Atomic-vacancy ordering in the lowest tungsten carbide W2C

Atomic-vacancy ordering in the lowest tungsten carbide W2C with an L'3-type basic hexagonal structure has been studied by neutron diffraction and X-ray diffraction. In the temperature range 2700-1370 K, the only ordered phase of the lowest tungsten carbide is shown to be the trigonal ε-W2C phase (space group P Σ 3-bar1m). This trigonal ε-W2C phase is found to form via a disorder-order phase transition channel, which includes three superstructure vectors (k15(1), k15(2), k17(1)) of two Lifshitz stars ({k15}, {k17}, and to be described by two long-range order parameters (η15, η17). The distribution function of carbon atoms in the trigonal ε-W2C superstructure is calculated, and the corresponding region of the allowable values of the long-range order parameters η15 and η17 is found. Symmetry analysis of other possible superstructures of the lowest tungsten carbide W2C is performed, and the physically acceptable sequence of phase transformations in W2C is determined