Near-equilibrium solubility of nanocrystalline alloys

Grain boundaries are the dominating type of defect in nanocrystalline materials. Understanding their properties is crucial to the comprehension of nanocrystalline materials behavior. A facile thermodynamic model for alloy grain boundaries is developed. The macroscopic analysis is based on established descriptions of metallic solutions and the universal equation of state at negative pressure, using mainly parameters obtainable from measurements on macroscopic samples. The free energy of atoms in grain boundaries is derived as a function of excess volume, composition, and temperature. Interfacial enrichment is computed using equilibrium conditions between bulk phase and grain boundaries. The excess volume of symmetric '100' tilt grain boundaries in Cu as a common system is obtained by atomistic computer simulation. In a general case the predictions of the proposed model are compared to experimental grain boundary segregation data, yielding a good match. The near-equilibrium solubility of Ag in nanocrystalline Cu and of Cu in nanocrystalline Fe is calculated.