A nuclear-quantum-corrected machine-learning potential reveals quantum-enhanced hydrogen segregation at general grain boundaries in α-iron

Understanding hydrogen embrittlement in high-strength steels requires precise atomistic descriptions of how hydrogen diffuses, interacts with defects, and segregates at grain boundaries. Because hydrogen is the lightest solute in metals, its behavior is heavily influenced by nuclear quantum effects—such as zero-point motion and spatial nuclear delocalisation—even at room temperature. However, explicitly simulating these quantum effects using path-integral molecular dynamics (PIMD) is computationally prohibitive for large-scale systems like general grain boundaries. This study aims to overcome this limitation by developing a nuclear-quantum-corrected machine-learning interatomic potential (NQC-PACE) that incorporates 300 K nuclear quantum effects at the computational cost of classical molecular dynamics.

The authors constructed NQC-PACE by taking an existing high-performance atomic cluster expansion (PACE) potential for the Fe-H system and relabeling its comprehensive training configurations with quantum mean forces. These forces were obtained from 300 K centroid-constrained PIMD simulations while holding the Fe atoms fixed and treating the hydrogen nuclei as quantum ring polymers. By retraining only the hydrogen-related interaction terms without adding new density functional theory calculations, the resulting potential accurately reproduces 300 K nuclear quantum corrections across a wide range of defect environments, including vacancies, dislocations, surfaces, and grain boundaries.

Using grand-canonical Monte Carlo and molecular dynamics simulations powered by NQC-PACE, the study demonstrates that nuclear quantum effects markedly enhance hydrogen segregation and trapping at general grain boundaries in alpha-iron. Compared to classical potentials that treat hydrogen nuclei as classical particles, NQC-PACE yields hydrogen diffusion coefficients and trapping energies that match experimental trends much more closely. Structural analysis reveals that this enhanced segregation stems from selective quantum stabilisation of hydrogen in open, anisotropically soft local environments where zero-point motion provides a significant energetic advantage.