We present an extension of the semi-grand-canonical (SGC) ensemble that we refer to as the variance-constrained semi-grand-canonical (VC-SGC) ensemble. It allows for transmutation Monte Carlo simulations of multicomponent systems in multiphase regions of the phase diagram and lends itself to scalable simulations on massively parallel platforms. By combining transmutation moves with molecular dynamics steps, structural relaxations and thermal vibrations in realistic alloys can be taken into account. In this way, we construct a robust and efficient simulation technique that is ideally suited for large-scale simulations of precipitation in multicomponent systems in the presence of structural disorder. To illustrate the algorithm introduced in this work, we study the precipitation of Cu in nanocrystalline Fe.
Nanocrystalline materials have received great attention due to their potential for improved functionality and have been proposed for extreme environments where the interfaces are expected to promote radiation tolerance. However, the precise role of the interfaces in modifying defect behavior is unclear. Using long-time simulations methods, we determine the mobility of defects and defect clusters at grain boundaries in Cu. We find that mobilities vary significantly with boundary structure and cluster size, with larger clusters exhibiting reduced mobility and that interface sink efficiency depends on the kinetics of defects within the interface via the in-boundary annihilation rate of defects. Thus, sink efficiency is a strong function of defect mobility, which depends on boundary structure, a property that evolves with time. Further, defect mobility at boundaries can be slower than in the bulk, which has general implications for the properties of polycrystalline materials. Finally, we correlate defect energetics with the volumes of atomic sites at the boundary.
The decomposition of Fe-Cr solid solutions during thermal aging is modeled by atomistic kinetic Monte Carlo simulations, using a rigid lattice approximation with pair interactions that depend on the local composition and temperature. The pair interactions are fitted on ab initio calculations of mixing energies and vacancy migration barriers at 0 K. The entropic contributions to the mixing of Fe-Cr alloys and to the vacancy formation and migration free energies are taken into account. The model reproduces the change in sign of the mixing energy with the alloy composition and gives realistic thermodynamic and kinetic properties, including an asymmetrical miscibility gap at low temperature and diffusion coefficients in good agreement with available experimental data. Simulations of short-range ordering and $\alpha${}-$\alpha${}$'${} decomposition are performed at 773 and 813 K for Cr concentrations between 10% and 50%. They are compared with experimental kinetics based on three-dimensional atom probe and neutron scattering measurements. The possible effect of magnetic properties on diffusion in the $\alpha${} and $\alpha${}$'${} phases, and therefore on the decomposition kinetics, is emphasized.