Reducing grain boundary, dislocation line and vacancy formation energies by solute segregation

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Design of Stable Nanocrystalline Alloys (2012, background): “Whereas one approach to the problem is a classical kinetic strategy, that is, including alloying elements to slow grain growth, there is increasing interest in the notion of genuine thermodynamic stabilization of grain boundaries (12-18).”
Thermal stability of nanocrystalline materials: thermodynamics and kinetics (2017, background): “If the solute distribution in the bulk and GBs follows the Langmuir–McLean segregation equation, as suggested by Weissmüller [30] and Liu and Kirchheim [32], a quantitative relationship between xbulkA and x GB A can be expressed as [104] xGBA xGBA0 − xGBA = x bulk A 1− xbulkA exp Hseg RT ( ) (28) wh”