Stability and mechanical properties of molybdenum carbides and the Ti–Mo–C solid solutions: A first-principles study

Abstract

First-principles calculations were carried out to study the hypothetical MoC, Mo2C, Mo3C2 and random MoCx, x = 1.0, 0.875, 0.75 and 0.5 phases, and those that were experimentally verified, as well as the random cubic and hexagonal TiC–MoC and cubic and orthorhombic Ti2C–Mo2C solid solutions (alloys). The electronic and phonon structures, formation energy, elastic constants and moduli, hardness, Debye temperature, fracture toughness and stress-strain relation for these structures were calculated in order to understand the differences in phase stability; to explain their properties; and to predict possible new stable phases. The phase diagrams of the Mo–C system for three compositions, 67 at.% Mo + 33 at.% C, 60 at.% Mo + 40 at.% C and 50 at.% Mo + 50 at.% C, were built in the temperature range of 0–4000 K. First-principles molecular dynamics simulations and the group-theoretical analysis are used to identify the plausible mechanisms of the temperature-induced structural transformations in the α-, γ- and γ’-phases of MoC. The composition dependence of the mechanical characteristics of the solid solutions was found to have an extremal character, and in particular a maximum hardness for the cubic Ti0.75Mo0.25C (27.2 GPa) and orthorhombic Ti0.5Mo1.5C (14.6 GPa) alloys. The theoretical phase stability diagrams for the Mo–C system and Ti–Mo–C alloys contain not only the structures experimentally observed but also hypothetical phases, and the available experimental properties were reproduced and explained.