Fig. 6: N diffusion pathway on Fe(111) surface and corresponding potential energy profiles determined by reinforcement learning.

The identified N diffusion path on the bare Fe(111) surface as determined by reinforcement learning (RL): (a, c) The diffusion path for the N atom from one bridge site to the other bridge site. The N atom in the initial and final state is represented by blue sphere, while the small blue spheres represent its positions along the diffusion path as identified by RL. The Fe atoms in the top, sublayer, deep-layer, and 4th–6th layers are represented by light blue, orange, purple, and bronze spheres, respectively. The RL with no relaxation in DFT is displayed in a and the RL with relaxation in density functional theory (DFT) is in c. b, d The potential energy profile for the snapshots taken along the diffusion path of N atom. The RL with no relaxation in DFT is shown in b and the RL with relaxation in DFT is in d. The arrows in a, c represent the diffusion path of N atom on Fe(111) surface. Source data for b, d are provided as a Source Data file. The structure files in a, c are provided in Supplementary Data 1.