Correlation between stabilizing and strengthening effects due to grain boundary segregation in iron-based alloys: Theoretical models and first-principles calculations

Grain boundary (GB) segregation can drastically affect both the thermal stability and fracture strength of nanocrystalline metals. Underlying physics of the correlation between the above two aspects, however, remains unclear, since a comprehensive study addressing a variety of properties and involving a wide range of solute types seems not available. In this work, we theoretically modeled the GB segregation and strengthening energies considering both the chemical and elastic contributions of segregated solutes. Then using first-principles method, the GB segregation behaviors of twenty-six 3d, 4d and 5d transition metal atoms at three typically symmetrical tilt GBs (∑3(112), ∑5(210) and ∑5(310)), with iron as representative, were studied, where the GB segregation and strengthening energies of solutes were calculated, thus revealing their dependence on GB structures, group number and solute parameters (such as atomic radius and electronegativity). Arising from the competition between the chemical (related to the electronegativity) and the elastic (related to the atomic radius) contributions from solutes, a concave-down (concave-up) parabolic-like dependency of the GB segregation (strengthening) energy on the group number has been discovered. Furthermore, the stabilizing and the strengthening mechanisms of the segregants were revealed by analyses of bond length and charge density. The strengthening energy generally decreases with increasing the GB segregation energy, as reflected by a so-called trade-off relationship between the strengthening effect and the stabilizing effect. This work could be beneficial for understanding the GB segregation and the strengthening behaviors of the segregants in iron-based alloys and designing the iron-based alloys with comprehensively desired performances.