Carbon

This example models carbon along the sp² ↔ sp³ coordination axis. Graphite stacks planar 3-coordinated (sp²) sheets; diamond is the 4-coordinated (sp³) tetrahedral network; ta-C (tetrahedral amorphous carbon), DLC coatings, glassy carbon, and nanocrystalline diamond all sit at controlled points along that axis. The crystalline ↔ amorphous disorder axis (the one the Si / Cu / SiO₂ / SrTiO₃ examples walk) is another sensible way to explore carbon; we hold it roughly fixed here (every regime is nanocrystalline) so the sp²/sp³ mix is the only variable.

The pipeline builds six regimes by mixing Voronoi grains: each grain is either a rotated graphite tile (sp², 3 neighbours, 120°) or a rotated diamond tile (sp³, 4 neighbours, 109.5°), and the mix fraction controls where on the sp²/sp³ axis the cell sits.

Overview

All six regimes at 40 × 40 × 40 Å, rotating in sync. Green triangles decorate every sp² atom whose three neighbours form a 120° trigonal planar motif; navy tetrahedra decorate every sp³ atom whose four neighbours form a 109.5° tetrahedron. Drag any panel to orbit manually.

Stacked g(r) per regime, most sp²-dominant curve at the bottom, most sp³-dominant at the top. Only one pair appears in the dropdown (C-C) because the g(r) measurement uses atomic numbers and both virtual species (sp2_C, sp3_C) share atomic number 6. The two characteristic bond lengths still split the first peak: a sharp contribution at 1.42 Å (sp² in-plane) and a sharper one at 1.54 Å (sp³ tetrahedral), with the relative peak heights tracking the (w_graphite, w_diamond) regime weights.

Reference crystals

from ase.io import read

atoms_graphite = read("docs/structures/C_graphite.cif")  # P6₃/mmc, a=2.467 Å, c=6.708 Å
atoms_diamond  = read("docs/structures/C_diamond.cif")   # Fd-3m,  a=3.561 Å

Composite shell target

Carbon uses a composite shell target: one CoordinationShellTarget per chemistry, stacked into a single object with two virtual species (sp2_C and sp3_C) that share atomic number 6 but carry distinct coordination + bond-angle targets:

import tricor as tc

shell_sp2 = tc.CoordinationShellTarget.from_atoms(atoms_graphite, phi_num_bins=90)
shell_sp3 = tc.CoordinationShellTarget.from_atoms(atoms_diamond,  phi_num_bins=90)
shell_target = tc.CoordinationShellTarget.from_targets(
    {"sp2": shell_sp2, "sp3": shell_sp3}
)

The relaxer consults each atom’s virtual species index (assigned per grain during construction) so sp² atoms develop 3 bonds at 120° and sp³ atoms develop 4 bonds at 109.5°, inside the same cell.

Grain-level sp²/sp³ mixing

Every regime is nanocrystalline (multi-grain Voronoi). Each grain is sampled from graphite or diamond by the regime’s (w_graphite, w_diamond) weights:

cell.generate(
    shell_target,
    grain_size=10.0,
    grain_sources=[
        {"atoms": atoms_graphite, "species_offset": 0, "weight": 0.4},
        {"atoms": atoms_diamond,  "species_offset": 1, "weight": 0.6},
    ],
    num_steps=120,
    bond_weight=2.0, angle_weight=1.0, repulsion_weight=2.0,
    hard_core_scale=0.9, nonbond_push_scale=0.8,
    displacement_sigma=0.03,
)

Atom count scales naturally with the regime’s phase mix; diamond is denser than graphite (0.177 vs 0.098 atoms/ų), so diamond-dominant regimes carry more atoms at the same box size.

Disorder regimes

Click any regime for the full interactive trajectory viewer and g3 distribution.

• Graphite (nanocrystalline)
• sp²-rich mixed
• sp²-leaning mixed
• sp³-leaning mixed
• sp³-rich mixed
• Diamond (nanocrystalline)

Preset summary

Regime	w_graphite	w_diamond	grain_size (Å)	num_steps
graphite_nc	1.00	0.00	18.0	250
sp2_rich	0.80	0.20	18.0	250
sp2_leaning	0.60	0.40	18.0	250
sp3_leaning	0.40	0.60	18.0	250
sp3_rich	0.20	0.80	18.0	250
diamond_nc	0.00	1.00	18.0	250

Shell-relax weights are identical across regimes: bond_weight=2.5, angle_weight=1.2, repulsion_weight=2.0, hard_core_scale=0.92, nonbond_push_scale=0.85, displacement_sigma=0.02.

All regimes use 18 Å grains with num_steps = 250 to limit the fraction of atoms at sp²/sp³ grain boundaries — those boundary atoms cannot pass either the triangle (3-coord, 120°) or the tetrahedron (4-coord, 109.5°) detector regardless of relaxation, so a large crystalline interior is the only lever for visible ordering in the mixed regimes.