A facile thermodynamic model for grain boundaries in dilute alloys was developed. The macroscopic analysis was based upon known descriptions of metallic solutions and the universal equation of state. The thermodynamic variable free energy was derived as a function of composition and excess volume. Employing Guggenheim’s condition for equilibrium between bulk and grain boundaries, the segregation behaviour and the interface free energy of two model systems, copper–silver and copper–bismuth, were calculated. The results showed good agreement with experimental data. This coarse-grained approach appeared to be especially attractive for the calculation of phase diagrams of nanocrystalline materials.

Thermodynamic Model of Alloy Grain Boundaries. A.Kirchner, B.Kieback: Scripta Materialia, 2011, 64[5], 406-9