Mathematical details of atomode’s structure-generation pipeline, ordered to match the natural flow of a build: measure the reference crystal, lay down a Voronoi-tiled initial cell, optionally walk grain orientations into a better-aligned basin, clean up grain-boundary overlaps, relax (with the built-in FIRE spring network, or hand off to the MACE-MP0 potential), and optionally synthesise a target g3 distribution against which the supercell can be compared.
| Stage | Page | What it covers |
|---|---|---|
| 1. Measure | Three-body distribution | g3 + g2 histogram, reduced coordinates, CoordinationShellTarget extraction. |
| 2. Build | Supercell generation | Voronoi grain construction: seeds → tessellation → master block tiling → cell filling → overlap removal → close-pair push → optional thermal jitter. |
| 3. Align grains | Orientation refinement | Per-grain SO(3) coordinate search that re-runs the full grain assembly per trial and keeps rotations that lower a global pair-distance cost, before the final relaxation (FIRE or MACE) runs. |
| 4. Cleanup | Cleanup sweeps | cKDTree bond_relax + enforce_hard_core sweeps that remove grain-boundary overlaps before the relaxer starts. O(N log N) per iteration. |
| 5. Relax | FIRE relaxation | Bond + angle + repulsion (+ restraint) springs minimised with a simplified FIRE integrator. This is what Supercell.generate() calls internally. |
| 5’. ML relax | MACE-MP0 potential | The machine-learning Hamiltonian and the LBFGS / Langevin update strategies used by the MACE refinement examples. |
| — | FIRE vs MACE-MP0 | Term-by-term comparison of the two energy models, and the strategy for calibrating FIRE’s spring weights against MACE from a single reference crystal. |
| 6. Compare | Target g3 construction | Blur + blend a measured crystalline g3 toward the random limit to produce a comparison target. |
| Reference | Glossary | Disorder regimes, shell-target fields, force-term nomenclature. |