A roadmap from the bond strength to the grain-boundary energies and macro strength of metals.

Correlating the bond strength with the macro strength of metals is crucial for understanding mechanical properties and designing multi-principal-element alloys (MPEAs). Motivated by the role of grain boundaries in the strength of metals, we introduce a predictive model to determine the grain-boundary energies and strength of metals from the cohesive energy and atomic radius. This scheme originates from the d-band characteristics and broken-bond spirit of tight-binding models, and demonstrates that the repulsive/attractive effects play different roles in the variation of bond strength for different metals. Importantly, our framework not only applies to both pure metals and MPEAs, but also unravels the distinction of the bond strength caused by elemental compositions, lattice structures, high-entropy, and amorphous effects. These findings build a physical picture across bond strength, grain-boundary energies and strength of metals by using easily accessible material properties and provide a robust method for the design of high-strength alloys.