Silicon dioxide

Silicon dioxide is a two-species network-former. Each Si sits at the centre of a tetrahedron of four O neighbours (Si-O ≈ 1.61 Å), and each O bridges two Si atoms. The reference here is α-quartz (trigonal P3₁21, a = 4.9134 Å, c = 5.4052 Å) tiled into an orthogonal 40 × 40 × 40 Å supercell by tricor.Supercell.

Instead of drawing pairwise bonds, each panel renders a translucent polyhedron around every Si whose four nearest O neighbours form a near-ideal tetrahedron (bond length within ±15 % of 1.61 Å, all six O-Si-O angles within ±25° of 109.47°).

Overview

All six regimes at an orthogonal 40 × 40 × 40 Å supercell, rotating in sync. Drag any panel to orbit manually.

g(r) per regime overlaid on a single axis (most disordered curve at the bottom, most ordered at the top). The dropdown below the plot switches between the three species pairs in alphabetical order (O-O, O-Si, Si-Si); only O-Si is a real chemical bond, the other two peaks are lattice separations through a bridging atom. The Si-O peak at 1.61 Å sharpens monotonically up the ladder; the Si-Si and O-O second-shell peaks at 2.64 / 3.06 Å develop crystalline fine structure (split shells) only at LRO / NC.

Reference crystal

from ase.io import read
atoms_ref = read('structures/SiO2.cif')   # 3 Si + 6 O

Supercell

tricor.Supercell tiles the α-quartz primitive into a Cartesian 40 × 40 × 40 Å box. The algorithm seeds Voronoi cells, tiles the reference out to a sphere that covers the largest cell, rotates the tile per grain (identity rotation when grain_size=None), and filters atoms by exact convex-hull membership against each Voronoi cell. Per-species atom counts are then pinned to the reference stoichiometry scaled by V_box / V_ref × relative_density so every regime has identical Si and O counts, and grain-boundary overlaps are culled at 0.9 × hard_min.

import tricor as tc

# Only Si-O is a real chemical bond in SiO2.  The second-shell
# Si-Si (3.06 Å) and O-O (2.64 Å) peaks are lattice separations
# through a bridging atom; ``from_atoms`` zeroes their coordination
# targets automatically (``auto_filter_lattice_artifacts=True``), so
# they install no bond springs.
shell_target = tc.CoordinationShellTarget.from_atoms(atoms_ref, phi_num_bins=90)

cell = tc.Supercell.from_atoms(
    atoms_ref,
    cell_dim_angstroms=(40, 40, 40),
    r_max=10, r_step=0.1, phi_num_bins=90,
    rng_seed=42,
)
cell.generate(shell_target, grain_size=None)  # liquid; see regime pages

Disorder regimes

• Liquid
• Amorphous
• Short-range order
• Medium-range order
• Long-range order
• Nanocrystalline

Preset summary

Regime	num_steps	grain_size (Å)	bond_weight	angle_weight	repulsion_weight	hard_core_scale	nonbond_push_scale	displacement_sigma
liquid	120	-	0.50	0.0	1.5	1.05	0.60	0.010
amorphous	250	12.0	1.55	1.25	1.25	0.81	0.70	0.012
short-range order	250	15.0	1.65	1.35	1.30	0.82	0.72	0.010
medium-range order	300	20.0	1.65	1.35	1.30	0.82	0.72	0.008
long-range order	350	26.0	1.65	1.35	1.30	0.82	0.72	0.006
nanocrystalline	400	35.0	1.65	1.35	1.30	0.82	0.72	0.003

The liquid panel uses angle_weight=0 so the random starting positions aren’t pulled into tetrahedral coordination by the angle spring; every other regime keeps the angle spring on so SiO₄ tetrahedra form.

SRO through NC share the same bond + angle weights (1.65 / 1.35). The order ladder is built by progressively growing the grain (15 → 20 → 26 → 35 Å) and the relaxation budget (250 → 300 → 350 → 400 steps) while tightening displacement_sigma (0.010 → 0.008 → 0.006 → 0.003). Larger crystalline grain interiors and longer FIRE budgets give the boundary atoms more time to settle into tetrahedral coordination. Larger weights saturate at the same number of detected SiO₄ tetrahedra while distorting boundary atoms past the 0.10 / 18° detector tolerance.

The benchmark ladder (rng seed 42, 40 Å cell, 0.10 / 18° detector) walks ≈ 668 (amorphous) → 788 (SRO) → 895 (MRO) → 1022 (LRO) → 1141 (NC) clean SiO₄ tetrahedra out of 1622 Si atoms, a monotonic 41 % → 70 % progression.