An analytic descriptor for determining the effect of grain-boundary structures of metals on solute segregation

The structure of grain boundaries (GBs) of metals is essential in determining the solute segregation at GBs; however, its complexity prohibits the understanding of the underlying mechanism. We propose a geometric descriptor of GB segregation based on the non-local coordination number of cut surfaces from GBs, which determines the segregation energies of solutes at the grain boundaries of metals across multidimensional GB space, different solutes, and different matrices. The effectiveness of the descriptor originates from the correlation between bonding strength, d-band width, and coordination number. This descriptor only depends on the bond length and angle of pre-segregation sites at GBs and can be readily used for description and prediction. Our scheme builds a novel picture for understanding the role of GB structures in segregation and provides a useful tool for the design of advanced alloys.