A computational framework for quantifying the contributions of individual atomic motions to self-diffusion in liquid metals

This study aims to quantify the contributions of atomic motion in jump, gradual-motion, and stay sections to the self-diffusion coefficient in liquid metals. A computational framework is proposed to reconstruct the self-diffusion coefficient from the average squared displacement and frequency of each section type. Molecular dynamics simulations of liquid Pb at 773 K were performed using a polynomial machine-learning potential. The trajectory of each atom was classified into the three section types. A correction derived from localized oscillatory motion was introduced to relate the calculated section displacements to the effective translational displacements. The self-diffusion coefficient reconstructed from the classified atomic motions differed by less than 1 % from that independently obtained from the long-time mean-squared displacement. At 773 K, gradual motion contributed approximately 65 % of the reconstructed self-diffusion coefficient, while jump and stay motions contributed approximately 25 % and 10 %, respectively. These results demonstrate that the framework can quantitatively relate classified microscopic atomic motions to macroscopic self-diffusion. An exact decomposition of the calculated displacement vectors further revealed a net negative contribution from correlations among these vectors. Analysis of temporally adjacent displacement vectors belonging to the same atom showed that shared section boundaries generate negative correlations through local oscillatory fluctuations. An important part of this correlation effect is therefore approximately incorporated into the oscillation correction rather than being simply neglected in the motion-resolved formulation. At 773 K, the scalar oscillation correction was close to the magnitude of the negative calculated-vector cross contribution. The framework thus provides a quantitative connection between macroscopic self-diffusion and classified microscopic atomic motions while allowing the assumptions and applicability of the motion-resolved representation to be examined from the calculated trajectories.