Thermodynamic stability of binary nanocrystalline alloys: Analysis of solute and excess vacancy

Regarding that the excess volume in grain boundaries (GBs) is released as the vacancies which are accommodated by the crystal bulk during grain growth, a free-energy function for binary nanocrystalline solid solution is proposed, based on the pairwise nearest-neighbor interactions. The model, for the given composition and temperature, predicts an equilibrium grain size, subjected to a mixed effect due to solute segregation and due to excess vacancies. Furthermore, excess-vacancy-inhibited grain coarsening can be attained, which plays a minor role in holding the thermal stability of nanocrystalline alloys, as compared to the effect of solute segregation.