Nanocrystalline Materials at Equilibrium: A Thermodynamic Review

Abstract

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.

A new approach to grain boundary engineering for nanocrystalline materials

“…This is often associated with the nonequilibrium deformation of microstructures introduced by severe plastic deformation (SPD) with less thermal stability, excess structural defects and chemical composition by segregation to grain boundaries and interfaces [12,15,24–29]. Since the concept of grain boundary design and control was first proposed by Watanabe [30], an increasing number of researchers have been involved in the development of high performance polycrystalline materials, including nanocrystalline or nanostructured materials.…”

“…More recently, Raabe et al [27–28] proposed grain boundary segregation engineering for improvement of material properties, such as the stabilization of grains in nanocrystalline steel by carbon and solute element segregation. Kalidindi et al [29] have suggested that the stability of the nanocrystalline structure is improved by preferential segregation of solute atoms to grain boundaries because their excess free energy can be reduced. Therefore, it is very likely that the grain boundary microstructure characterized by appropriate microstructural parameters (e.g., grain boundary character distribution (GBCD) [30], grain boundary connectivity [30] and triple junction character distribution (TJCD)) may dominantly affect and control the bulk mechanical, physicochemical, electro-magnetic and other grain-boundary-related properties in nanocrystalline materials, as well as ordinary polycrystalline materials.…”

Phase transitions in stable nanocrystalline alloys

“…are surveyed in search of the minimum free energy configuration. 27 The equilibrium state from these simulations matches a bulk phase diagram when the enthalpy of grain boundary segregation is low, but when the enthalpy of grain boundary segregation is large enough to offset the pure solvent grain boundary energy, nanocrystalline configurations with solute decorated grain boundaries emerge as stable states.…”

A compound unit method for incorporating ordered compounds into lattice models of alloys

“…In such cases, while using a cluster expansion to define the interatomic potential may still be feasible, it is not optimal because (i) the stability of compounds in bulk systems is already known [30], and thus ''predicting" the stable compounds through simulation is unnecessary and (ii) the multi-body terms are calculated for each alloy system and thus too specific to probe a large number of alloy combinations and often not easily extendable to non-bulk environments. In some of our group's work on nanostructured alloys we have found a need for a lattice-based method that can be rapidly calibrated to known bulk thermodynamics and then used to explore, e.g., driven processing through ballistic mixing [34] or deposition [35], or simply to explore the space of accessible structures in nanostructured systems [18,[36][37][38]. It is our purpose in this paper to present such a method that overcomes the limitations of the pairwise model in describing negative enthalpy of mixing systems, specifically for cases where the structure and formation energy of equilibrium compounds are already known, and a full cluster expansion would be redundant.…”