First-principles calculations were carried out to study the hypothetical MoC, Mo₂C, Mo₃C₂ and random MoC_x, 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 Ti_0.75Mo_0.25C (27.2 GPa) and orthorhombic Ti_0.5Mo_1.5C (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.

进行第一性原理计算以研究假设的 MoC、Mo ₂ C、Mo ₃ C ₂和随机 MoC _x、x = 1.0、0.875、0.75 和 0.5 相，以及经过实验验证的相，以及随机立方和六方 TiC-MoC 和立方和正交 Ti ₂ C-Mo ₂C 固溶体（合金）。计算了这些结构的电子和声子结构、形成能、弹性常数和模量、硬度、德拜温度、断裂韧性和应力应变关系，以了解相稳定性的差异；解释它们的特性；并预测可能的新稳定相。三种成分的 Mo-C 系统的相图，67 at.% Mo + 33 at.% C，60 at.% Mo + 40 at.% C 和 50 at.% Mo + 50 at.% C，是建在温度范围内的0-4000 K.第一原理分子动力学模拟和基团的理论分析被用于识别在α-由温度引起的结构转变的似是而非的机制，γ-和γ ^'- MoC 阶段。发现固溶体的机械特性的组成依赖性具有极值特性，尤其是立方 Ti _0.75 Mo _0.25 C (27.2 GPa) 和正交 Ti _0.5 Mo _1.5 C (14.6 GPa) 合金的最大硬度。Mo-C 系统和 Ti-Mo-C 合金的理论相稳定性图不仅包含实验观察到的结构，还包含假设的相，并且再现和解释了可用的实验特性。