Scaling laws for lattice distortions: Application to high entropy alloys

Lattice distortions are intrinsic features of all solid solution alloys associated with varying atomic radii; this phenomenon facilitates the formation of single-phase solid solutions. Using high-entropy alloys (HEAs), as an example, we investigate the influence of variations in inter-atomic separations for stabilizing and controlling their structural, mechanical, and thermodynamic properties. This is done through a combination of statistical mechanics analysis and molecular dynamics simulations on simplified 2D systems, as well as a 3D crystals with harmonic and anharmonic inter-atomic bonds with varying natural inter-atomic separations. We demonstrate that the impact of this inter-atomic length disorder (representing static lattice distortion) and temperature fluctuations (representing dynamic lattice distortion) on fundamental and universal thermodynamic, structural, and elastic characteristics are similar and can be unified through effective temperature; i.e. a scaling law for HEAs that establishes a relationship between these factors. This scaling law reveals that different HEAs (i.e. varying degrees of local lattice distortions) collapse onto a single curve when plotted against the effective temperature. We demonstrate that lattice distortion significantly enhances the stability of solid solution alloys (relative to phase separation or ordering by effectively increasing the temperature of the system; this stabilization effect is particularly pronounced in HEAs).