Institute of High Pressure Physics

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 is an unusual manifestation of quantum mechanics in macroscopic objects. This crystal behavior cannot be explained within the framework of classical physics. This phenomenon is closely related to the balancing of internal forces resulting from Coulomb interactions, Pauli repulsion, and band overlap under the influence of stress on the crystal.

In the recent paper by C. Sobczak, P. Kwasniak, P. Strak, M. Muzyk, and S. Krukowski, "Elastic Anisotropy in BCC Ti-X Alloys (X = V, Nb, Ta) Determined from First Principles," published in Materials, 2025, 18(18), 4294, our PhD student Cyprian Sobczak described the anisotropy of titanium alloy crystals. This work was developed in collaboration between a group of theoreticians from our Institute and from the Cardinal Stefan Wyszyński University in Warsaw.

Authors identificatied a new titanium-niobium alloy with a 53% niobium content, Ti-53Nb, exhibiting elastic isotropy. Calculations also showed that this phenomenon cannot occur in the case of titanium-tantalum alloys, Ti-Ta, regarding the mechanical stability of these alloys. The publication summarizes the main trends exhibited by the elastic constants, Young's modulus, and bulk modulus of the Ti-based alloys discussed, based on ab initio methods. See more details here.

Figure. A comparison of trends observed in Ti-X alloys (X = V, Nb, Ta, Mo): (a) C11 elastic constant, (b) C12 elastic constant, (c) C44 elastic constant, (d) C′ = (C11 − C12)/2, (e) bulk modulus B, and (f) Young’s modulus E, determined using PBE.