Modulated and Incommensurate Superstructures of Atomic–Vacancy Ordering in Refractory Transition Metal Carbides

Abstract

The formation of partially disordered modifications in refractory nonstoichiometric carbides prone to M₆X₅-type ordering is considered. In M₆X₅ superstructures the ray ${\mathbf{k}}_{9}^{{(3)}}$ of the Lifshitz star {k₉} with a current parameter μ₉ = 1/2 in the disorder–order phase transition channel is replaced by the rays ${\mathbf{k}}_{5}^{{(6)}}$ and ${\mathbf{k}}_{5}^{{(5)}}$ of the non-Lifshitz star {k₅} with a variable current parameter 0 < μ₅ < 1/2. Depending on the specific value of the index μ₅, this replacement leads to various modulated structures that differ by the concentration of vacancies in the defective ($1\bar {1}1$) planes of the carbon fcc sublattice and by the modulation period. In the diffraction spectra the positions of the superstructure reflections due to the star {k₅} at μ₅ ≈ 0.473 correspond to the incommensurate ordered phase experimentally detected in a nonstoichiometric tantalum carbide. The incommensurate phase is close in short-range order in the first coordination sphere to the initial M₆X₅ superstructures with a reduced long-range order parameter η ≈ 0.6.