Modeling solute segregation in grain boundaries of binary substitutional alloys: Effect of excess volume

The effect of excess volume in grain boundary (GB) on GB solute segregation was quantitatively evaluated by means of thermodynamic modeling. Helmholtz free energies of bulk (grain interior) and GBs in binary substitutional systems with fcc (face centered cubic) and bcc (body centered cubic) crystal structures were derived as functions of composition, temperature and atomic volume by applying Embedded-atom-method (EAM) to standard thermodynamic relations under random site occupation assumption. The equilibrium solute distribution between GBs and bulk was then obtained in terms of the parallel tangent construction between bulk and GB phases' Helmholtz free energy curves. By modeling the Cu-Ag (fcc) and W-Nb (bcc) systems, an enhanced GB segregation with increased GB excess volume was predicted. The segregation enthalpy and the solute enrichment ratio were further calculated, showing good agreements with the experimental and simulated results.