Nanocrystalline Materials at Equilibrium: A Thermodynamic Review

The instability of nanocrystalline materials against both grain growth and bulk phase separation is a principal challenge in their production and usage. This article reviews the thermodynamic stabilization of nanocrystalline structures by alloying, where a nanocrystalline state is considered to be stable if the nanostructure has the lowest free energy available to the alloy system, such that it is stable both against grain growth and the formation of bulk second phases. The thermodynamic accessibility of nanocrystalline structures in the alloy phase space introduces configurational degrees of freedom both at the atomic scale of the grain boundary structure and at the mesoscale level of the grains and grain boundary topology, which should be considered when identifying the equilibrium state. This article presents a survey of the kinds of thermodynamic models and simulations that have been developed to search for equilibrium nanocrystalline states. The review emphasizes the utility of Monte Carlo simulations to assess the thermodynamic stability of nanocrystalline states, including methods that have been proposed to account for degrees of freedom at both the atomic and grain scales. Although atomic scale simulations provide detailed segregation energetic information, the topological degrees of freedom in nanoscale polycrystals seem to be more critical considerations in the free energy description for identifying whether a nanocrystalline state is stable, and these are better addressed with mesoscale lattice-based simulation methods. A variety of interesting new nanostructural alloy states awaits further exploration by computational methods.