Interface migration governs microstructural evolution during phase transformations and grain growth, thereby dictating those material properties that depend on microstructure. Recent work continues to highlight the rich range of behaviors exhibited by migrating interfaces, and the complex connection between these behaviors and the underlying atomistic processes that determine coarse-grained interfacial mobility. For interfaces moving at low homologous temperatures and small driving forces, we show that significant non-Markovian effects can arise that invalidate commonly used analysis methods. Specifically, we demonstrate that solute can act as a source of such non-Markovian motion. In turn, we introduce a time-local or time convolutionless propagator approach to account for memory-dominated short and intermediate time interface dynamics. This approach extrapolates to the long-time diffusive limit, enabling robust mobility estimates from molecular simulation time windows far shorter than those required to directly observe linear mean-square displacement scaling. Comparison with solute-free boundaries validates the method and quantifies solute drag in the Cahn-Hillert sense, providing a route to extract drag coefficients and effective mobilities across a range of solute concentrations. Our results demonstrate that analysis including memory is essential for connecting atomistic simulations to continuum models and offer a practical framework for studying interface kinetics in systems with slow internal processes.

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• Collective effects in atomic physics
• Materials
• Random walks
• Alloys
• Atoms
• Interfaces
• Metals
• Polycrystalline materials
• Surfaces
• Monte Carlo methods