Structural and mechanical properties of predicted vacancy ordered tantalum carbide phases

ABSTRACT A search for ordered TanCm phases in nonstoichiometric tantalum carbide has been performed with the use of an evolutionary algorithm. Three thermodynamically stable phases Ta2C, Ta6C5, and TaC with trigonal, monoclinic and cubic symmetry as well as metastable Ta3C2, Ta4C3, Ta7C5, Ta9C7, Ta10C7, Ta5C4, Ta7C6, Ta8C7, Ta10C9, and Ta9C8 phases have been predicted in the composition range TaC0.5 - TaC1.0. The disorder-order phase transition channels Ta2Cy → Ta2C and TaCy → Ta6C5 associated with the formation of stable trigonal and monoclinic superstructures have been determined for the first time. The distribution functions of carbon atoms over the sites of these trigonal Ta2C and monoclinic Ta6C5 superstructures have been calculated. The elastic stiffness constants cij of all the predicted TanCm phases have been also calculated. All the predicted TanCm tantalum carbides are mechanically stable. The calculated values of inverse Pugh's ratio k = G/B values for all the predicted TanCm carbides (except Ta2C) are greater than 0.57 indicating that the considered materials are brittle. The calculated Debye temperatures θD of all TanCm phases grow almost monotonically with decreasing concentration of vacancies in TanCm (TaCy with y = m/n) carbides. The calculated heat capacity of all TanCm phases (except the trigonal Ta3C2 phase) decrease almost monotonically when the concentration of vacancies in TanCm carbides lowers.