Atomic-vacancy ordering in the lowest tungsten carbide W₂C

Abstract

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 ɛ-W₂C phase (space group P $\overline 3$ 1m). This trigonal ɛ-W₂C phase is found to form via a disorder-order phase transition channel, which includes three superstructure vectors (k ⁽¹⁾₁₅ , k ⁽²⁾₁₅ , k ⁽¹⁾₁₇ ) of two Lifshitz stars ({k ₁₅}, {k ₁₇}, and to be described by two long-range order parameters (η₁₅, η₁₇). The distribution function of carbon atoms in the trigonal ɛ-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.