Glossary

Disorder regimes¶

Liquid: A structure with only nearest-neighbour correlations enforced. No grain construction; atoms are placed randomly and relaxed with weak angle springs.
Amorphous: Short-range order limited to the first nearest-neighbour shell. Constructed from very small grains (~6 Å) with heavy broadening.
Short-range order (SRO): Correlations extend out to ~3 visible maxima in the pair correlation function. Constructed from small grains (~10 Å).
Medium-range order (MRO): Correlations extend to 4-5 visible maxima. Constructed from grains of ~13 Å.
Long-range order (LRO): Larger grains (~18 Å) extend correlations further (8-10 Å range).
Nanocrystalline: Grains filling the box with sharp crystalline peaks. Grain size determines the crystallite domain size (e.g. 10 Å, 20 Å nanocrystalline).

g3: Rooted three-body distribution. A 4D histogram g3[type, r01, r02, phi] counting triplets of atoms (centre and two neighbours) by their two radial distances and bond angle.
Triplet type: Species combination of a rooted triplet, written as centre | neigh1 neigh2. For SiC: Si | Si Si, Si | Si C, Si | C C, C | C C, C | C Si, C | Si Si.
g2: Pair distribution. A 2D histogram g2[species_pair, r] counting all atomic pairs by their interatomic distance.
Reduced g3: Density-normalised g3, approaching 1.0 in the random limit. Computed as g3 / (A * r01^2 * r02^2 * sin(phi)).

pair_peak: Mean nearest-neighbour distance for each species pair, extracted from the reference crystal.
pair_inner, pair_outer: Inner and outer radial boundaries of the first coordination shell.
pair_hard_min: Absolute minimum distance (hard-core overlap prevention).
coordination_target (K): Expected number of neighbours of a given species around each centre species. For Si diamond: K_Si-Si = 4. For SiC zincblende: K_Si-C = K_C-Si = 4, K_Si-Si = K_C-C = 0.
angle_mode_deg: Most probable bond angle for each triplet type in the reference crystal.
angle_enabled_mask: Per-triplet bool array that controls whether shell_relax installs an angle spring for that triplet type. Bond-distance springs are always installed (independent of this mask). Used to silence multi-modal cases (cuboctahedral SrO₁₂ in SrTiO₃, whose O-Sr-O distribution is spread over 60°/90°/120°/180° so picking one mode distorts the others). Toggled via ~atomode.CoordinationShellTarget.with_angle_triplets / ~atomode.CoordinationShellTarget.without_angle_triplets.

grain_size: Diameter of crystalline grains in Å. Smaller grains give fewer visible shells in g3.
crystalline_fraction: Volume fraction filled by crystalline grains. The rest is amorphous fill. 1.0 = all grains, 0.0 = all random.
Voronoi cell: Region of space closer to one grain seed than any other. The supercell box is partitioned into one Voronoi cell per seed.
Grain boundary: Region between adjacent grains where atoms belong to different rotations of the reference crystal. Overlaps occur here and are removed.

bond_weight: Spring strength for bond distances in the relaxation.
angle_weight: Spring strength for bond angles.
repulsion_weight: Strength of the short-range repulsive force.
hard_core_scale: Multiplier for the minimum bond distance wall. Values below 1.0 allow shorter bonds (softer wall).
nonbond_push_scale: Multiplier for the non-bonded clearance distance. Values below 1.0 give broader 2nd shells.
displacement_sigma: Gaussian displacement (Å) applied to grain atoms before relaxation.
k_restraint: Spring constant of the optional position-restraint term $\tfrac{1}{2} k_\text{restraint} \sum_i \lVert \mathbf r_i - \mathbf r_i^{(0)} \rVert^2$ that tethers atoms to their starting positions during shell_relax. 0 disables the term and reproduces unrestrained relaxation; large values pin the structure.

amplitudes_deg: Schedule of rotation amplitudes (degrees) the SO(3) coordinate search walks through. Default (30, 15, 5, 2): the largest step lets a misaligned grain escape its starting basin, the smallest step locks in the chosen orientation.
trials_per_amplitude_per_grain: Number of random rotations sampled per (amplitude, grain). Default 50. The best-scoring trial is accepted if it beats the current orientation by more than score_cutoff_factor.
cost_function: "pair_distance" (default, topology-free, sub-millisecond per trial) or "bond_angle" (rebuilds bond + triplet topology per trial; usually not worth the slowdown).
score_cutoff_factor: Acceptance threshold for the per-trial score relative to the current baseline. Higher values accept more aggressively.

Composite shell target: A single CoordinationShellTarget produced by CoordinationShellTarget.from_targets({key: target, ...}) that stacks two or more per-chemistry targets into one object with a widened species axis. Used for phase blends (sp²/sp³ carbon, potential SiO₂/Si₃N₄ mixes) where atoms share an atomic number but want different local coordination.
Virtual species: A species slot in a composite shell target. Each virtual species carries its own row of coordination_target, pair_peak, angle_mode_deg, etc. Multiple virtual species can share an atomic number (e.g. sp²_C and sp³_C both have Z=6).
grain_sources: The generate(..., grain_sources=[{atoms, species_offset, weight}, ...]) kwarg that assigns each Voronoi grain a reference crystal by weight. species_offset is the virtual-species index each atom from that grain receives; the relaxer consults it via Supercell._atom_shell_species_index.
atom_species_index: Optional generate(atom_species_index=...) override; a (num_atoms,) array of virtual-species indices. Used when the caller wants to assign virtual species directly rather than letting grain_sources do it.