A free-energy function for binary polycrystalline solid solutions is developed based on pairwise nearestneighbor interactions. The model permits intergranular regions to exhibit unique energetics and compositions from grain interiors, under the assumption of random site occupation in each region. For a given composition, there is an equilibrium grain size, and the alloy configuration in equilibrium generally involves solute segregation. The present approach reduces to a standard model of grain boundary segregation in the limit of infinite grain size, but substantially generalizes prior thermodynamic models for nanoscale alloy systems. In particular, the present model allows consideration of weakly segregating systems, systems away from the dilute limit, and is derived for structures of arbitrary dimensionality. A series of solutions for the equilibrium alloy configuration and grain size are also presented as a function of simple input parameters, including temperature, alloy interaction energies, and component grain boundary energies.

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The hardening effect caused by the relaxation of nonequilibrium grain boundary structure has been explored in nanocrystalline Ni-W alloys. First, the kinetics of relaxation hardening are studied, showing that higher annealing temperatures result in faster, more pronounced strengthening. Based on the temperature dependence of relaxation strengthening kinetics, triple junction diffusion is suggested as a plausible kinetic rate limiter for the removal of excess grain boundary defects in these materials. Second, the magnitude of relaxation strengthening is explored over a wide range of grain sizes spanning the Hall-Petch breakdown, with an apparent maximum hardening effect found at a grain size below 10 nm. The apparent activation volume for plastic deformation is unaffected by annealing for grain sizes down to ;10 nm, but increases with annealing for the finest grain sizes, suggesting a change in the dominant deformation mechanism for these structures.

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