Elastic Anisotropy in BCC Ti-X Alloys (X = V, Nb, Ta) Determined from First Principles

Elastic isotropy is a phenomenon in which a material responds uniformly to stress, regardless of its direction. In the case of cubic crystals, which possess distinct crystallographic directions, this represents a remarkable manifestation of quantum mechanics in macroscopic objects. Such behavior of a crystal cannot be explained within the framework of classical physics. The phenomenon is closely related to the balancing of internal forces resulting from Coulomb interactions, Pauli repulsion, and the overlap in the bands when stress is applied to the crystal. On the macroscopic level, this corresponds to the relationship between elastic constants given by 2 C₄₄/(C₁₁ - C₁₂) = 1. The subject of the present work is to demonstrate the influence of the number of valence electrons per atom in binary titanium alloys with vanadium, niobium, and tantalum on the shape of the anisotropy curve. The result of the work is the identification of a new Ti-53Nb alloy exhibiting elastic isotropy, and the demonstration that this phenomenon cannot occur for TiTa alloys, in the range of mechanical stability of these alloys. This study includes a summary of the main trends exhibited by the elastic constants, Young's modulus, and bulk modulus of the discussed Ti-based alloys, based on ab initio methods. Additionally, the work addresses the well-known difficulty in determining the elastic constants of vanadium and niobium, along with a proposed solution that offers significant improvement in reproducing experimental results compared to the conventional use of the PBE (Perdew-Burke-Ernzerhof) functional.