Theoretical study of the M7X6 type of vacancy ordered phases in nonstoichiometric hafnium and tantalum carbides

Carbides of IV and V group transitional metals with B1 structure contain large amounts of vacancies in the carbon sublattice. Ordering of the vacancies leads to formation of new phases with various stoichiometry. Ordered structures were discovered and studied for all the IV and V group transitional metal carbides except carbides of hafnium and tantalum. Nevertheless, recent theoretical works have predicted large variety of ordered structures in non-stoichiometric HfCy and TaCy including unusual Hf7C6 and Ta7C6. Such a stoichiometry is not typical for the ordered carbides. In this work, we study in detail the new M7X6 type of vacancy ordered structures using ab initio methods. For both compounds Hf7C6 and Ta7C6, we have found two B1-derived vacancy-ordered phases: trigonal (space group R3¯) and monoclinic (space group C2/m). The comparison of their formation enthalpies with the disordered B1 structure has showed that the only ordered phase Hf7C6 can be trigonal phase while in Ta7C6 both trigonal and monoclinic structures are possible. Using the predicted monoclinic superstructure, we explain some peculiarities of the neutron diffraction pattern of the annealed partially ordered samples of TaC0.83–0.85. The theoretical and experimental data on the short range structural order in superstructures is discussed. We also study the influence of the M7X6 type of ordered structure on mechanical properties. The highest Vickers hardness ∼27.1 GPa is expected for the trigonal ordered Hf7C6 phase. © 2022 Elsevier Ltd