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

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.