Grain size dependencies of intergranular solute segregation in nanocrystalline materials

Grain boundary segregation is of increasing importance for stabilizing nanocrystalline alloys, and while segregation is typically modeled as a scale-independent phenomenon, at the finest nanocrystalline grain sizes there are several sources of grain size dependence. Here we provide quantitative detail on two grain size dependencies not previously elaborated, both of which arise from the spectrality of intergranular segregation sites. The first of these arises because a change in grain size affects which portions of the segregation spectrum are occupied by the solutes, with no change in the shape or nature of the spectrum itself. The second of these arises from the presence of higher-order grain junctions, which have unique segregation behaviors and an increasing relative presence at finer grain sizes. This paper uses molecular statics to quantify these size dependencies in detail for the case of an Al(Mg) binary alloy. Together, these two effects combined have a significant effect on the effective McLean segregation energy of more than 6 kJ/mol (from approximately -18.5 kJ/mol at 5 nm to -12.5 kJ/mol at more than 40 nm), with the majority of grain size dependence arising from the spectrality of segregation sites.