Analytic description of grain boundary segregation, tension, and formation energy in the copper–nickel system

Abstract

In this theoretical study, a recently proposed segregation model is applied to segregation data of an exemplary Σ5 grain boundary (GB), which is investigated using a copper–nickel embedded-atom method potential. Segregation in the semi-grandcanonical ensemble is systematically studied by varying the chemical potential in order to explore the full composition range for temperatures from 500 K to 1000 K. As a major thermodynamic feature, the mentioned segregation model avoids the usage of interface compositions, for which an arbitrary volume must be defined, but rather models the thermodynamically unambiguous solute excess. It was shown that the solute excess and the interface formation energy could be described very accurately over a wide range of temperatures and over the entire composition range based on a composition-dependent, but temperature-independent effective energy of segregation. However, the model was initially derived for systems without lattice mismatch so that interface tensions were neglected. Since the copper–nickel system exhibits a moderate lattice mismatch of roughly 2.7%, the copper–nickel system is chosen in this study to further extend the segregation model by a linear-elastic theory to also account for the interface tensions. Using this extended model, it will be shown that the solute excess, GB tensions, and GB formation energies can be derived from the effective energy of segregation for all temperatures and over the whole composition range. As in principle only one single segregation isotherm is sufficient to determine the effective energy of segregation and derived thermodynamic interface quantities, the application of this model is especially interesting for experimental evaluations.