First-principles calculations of elastic moduli of Ti–Mo–Nb alloys using a cluster-plus-glue-atom model for stable solid solutions

Using the first-principles calculations, a cluster-plus-glue-atom model was employed to investigate the elastic and electronic properties of Ti–Mo–Nb alloys with cluster formula of [MoTi₁₄] (glue atom) _x (glue atom = Ti, Mo, Nb, x = 1 or 3) for a theoretical guidance in composition design of β titanium alloys. The bulk modulus, shear modulus, Young’s modulus, and Poisson ratio were evaluated from the calculated elastic constants using Voigt–Reuss–Hill average scheme on the periodic supercell model of cluster packing. The electronic properties of the Ti–Mo–Nb alloys were discussed by analyzing the electron density of state and Mulliken population. Meanwhile, we designed two series of Ti–Mo–Nb alloys, i.e., [MoTi₁₄]X₁ (X = Ti, Mo, Nb) and [YTi₁₄]Nb₃ (Y = Ti, Mo), and experimentally measured their mechanical properties. Our theoretical results (including mass density, Young’s modulus, ductility) based on our cluster packing model agreed well with the experimental data, especially for [TiMo₁₄]X₁ (X = Ti, Mo, Nb) alloy series. On the contrary, the random solid solution structures were mechanically unstable and the calculated values significantly deviated from the experiments. Based on the cluster-plus-glue-atom model, an Ashby map of E/ρ versus B/G was constructed and indicated the inverse correlation between stiffness and ductility, for which the random solid solution model was unable to reflect. The Mo/Ti = 1/14 rule derived from the cluster model may serve as an important guideline for composition design of Ti–Mo based systems to achieve low elastic modulus alloys with stable β phase.