Analytic model for grain-boundary segregation ener-gies in metal polycrystal

Solute segregation at grain boundaries (GBs) of polycrystals strongly impacts the mechanical properties of metals including strength, fracture, embrittlement, and corrosion. However, the complexity of GB structures and the large chemical space of solutes and matrices impede the understanding of segregation. Herein, we identify a physical-based determinant, by unifying the effects of plastic strain and bonding breaking, for determining the segregation energies at GBs. By further combining with the usual coordination number, atomic radius of solutes and matrices, and cohesive energy of matrices, we build an analytic framework to predict segregation energies of polycrystal GBs across various solutes and matrices. These findings indicate an unusual Coulombic-like and localized nature of the bonding at polycrystal GBs and bulk metallic glasses (BMGs). Our scheme not only uncovers the coupling rule of solutes and matrices for GB segregation in polycrystals, but also provides an effective tool for the design of high-performance alloys.