The Case for Phase-Field Crystal Simulations of Grain Boundary Migration
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Grain boundaries (GBs), interfaces between crystalline domains with different orientations, play a central role in the mechanical, transport, and functional properties of polycrystalline materials. Their migration, interactions with other defects, and responses to internal and external driving forces are mediated by microscopic processes and collectively govern microstructural evolution. Capturing this multiscale nature requires models that preserve microscopic physics while remaining tractable at the scale of microstructures and over long timescales. The Phase-Field Crystal (PFC) model [1] describes crystalline systems evolving over long, diffusive timescales while retaining essential microscopic detail. It is based on a smooth, periodic order parameter that represents the atomic density field averaged over fast vibrational timescales, with energetics governed by coarse-grained free-energy functionals. Despite relevant underlying approximations, it uniquely incorporates lattice symmetry, elasticity, and defects. Recent developments further extended the model’s capabilities by explicitly treating elastic relaxation timescales and mechanics [2]. In this presentation, we showcase the relevance and versatility of state-of-the-art PFC simulations for the study of GB kinetics by discussing recent applications. After introducing the model and its recent developments, we demonstrate that GBs can behave as Brownian ratchets, i.e. exhibit directional migration under oscillatory driving forces and, uniquely accessible through PFC simulations, under thermal cycling, with direct consequences for manipulating the coarsening of microstructures [3]. We then discuss insights from PFC simulations into the role of plastic deformation within grains in governing GB migration and stability. Finally, we demonstrate how the PFC framework can be extended to account for additional physical effects, and in particular present an extension describing the impact of vacancy diffusion on defect migration and microstructural evolution. [1] H. Emmerich, H. Löwen, R. Wittkowski et al, Advances in Physics, 61, 665, 2012. [2] V. Skogvoll, M. Salvalaglio, L. Angheluta, Model. Simul. Mater. Sci. Eng. 30, 084002, 2022. [3] C. Qiu, M. Punke, Y. Tian et al, Science 385, 980, 2024.
