Elastic tensor-derived properties of composition-dependent disordered refractory binary alloys using DFPT

The elastic tensor provides valuable insight into the mechanical behavior of a material with lattice strain, such as disordered binary alloys. Traditional stress-strain methods have made it possible to compute elastic constants for ordered structures and individually tailored alloy compositions. However, this approach depends on predetermined or iteratively-chosen strain tensors. This poses a significant challenge for systematic, composition-dependent studies of disordered materials with low symmetry. DFPT provides a compelling alternative to stress-strain methods: it allows for an unbiased determination of the elastic tensor, as well as access to local field data derived from the underlying general response function framework. Despite its intrinsic flexibility and efficiency, DFPT has seen limited application to the study of disordered systems. At the same time, there is a growing need for expanded quantum mechanical data to improve predictive modeling of complex disordered material properties. Here we present results for the rigid-ion and relaxed-ion elastic tensors computed using DFPT, for a comprehensive set of structural refractory BCC binary alloys of Mo, Nb, Ta, and W. We map the quantum-driven heterogeneity in elastic properties, and associated relaxation fields at each disordered structure lattice site, by computing the force response internal strain tensor and displacement response internal strain tensors. Derived properties -- the bulk modulus ($B$), shear modulus ($G$), Young's modulus ($E$), Poisson's ratio ($\nu$), Pugh's ratio ($B/G$), Cauchy pressure and elastic anisotropy -- are reported as a function of composition for all refractory binaries. The DFPT-computed mechanical properties data for the refractory binary alloys at systematically-varied Mo, Nb, Ta, and W compositions are in excellent agreement with available experimental data.