Nanocrystalline SiO₂

A 30 Å cubic SiO₂ supercell (2052 atoms) built with the nanocrystalline regime (grain_size = 22 Å — closer to the standard 35 Å preset, fits cleanly inside the 30 Å cell with ~4 Å of amorphous boundary on each face). This is the realistic “large-interior-crystal + amorphous-boundary” scenario; the earlier 15 Å / 20 Å examples used a 13 Å grain to fit smaller cells and filled essentially the whole cell with one grain.

To re-generate:

python scripts/regen_dftb_examples.py --regime nanocrystalline --box 30.0

g(r) per stage

Si–O bond length distribution

stage	Si–O peak (Å)	⟨r⟩ (Å)	σ (Å)	# Si–O bonds
Voronoi	1.61	1.61	0.052	2409
after orient	1.61	1.61	0.052	2409
after FIRE	1.69	1.70	0.069	2546
after DFTB+ (60 steps)	1.65	1.71	0.066	2502

DFTB+ pulls the peak back from the FIRE-broadened 1.69 Å to 1.65 Å and slightly narrows σ. Residual fmax at step 60 is 8.65 eV/Å — the 60-step cap stops the relax short of the 1.0 eV/Å target, but the energy descent across all 60 steps is monotonic.

Angle distributions

Energy ladder

stage	E_total (eV)	ΔE vs previous
Voronoi	-142619.07	—
after orient	-142619.07	0
after FIRE	-145906.27	-3287
after DFTB+ relax	-146096.28	-190 (≈ -0.09 eV/atom)

Cell volume change Voronoi → DFTB+: +0.1 %. DFTB+ total at 60 steps is -71.2 eV/atom, matching the smaller-cell results.

DFTB+ relax wallclock: 13,689 s = 3.8 hr for the seed SP (~48 min) + 60 FIRE+UCF steps (~2 min/step average).

Note

The after orient row is identical to Voronoi because the Voronoi tile in tricor already assigns each grain an orientation that locally minimises the pair-distance score at grain boundaries. A swept SO(3) coordinate search over 4400 trial rotations (11 grains × 4 amplitudes × 2 rounds × 50 trials/grain) finds zero improvements: every perturbation worsens the score. The step still runs (~12 s); it just produces no change. This was confirmed to hold across grain_size ∈ {16, 17, 18, 22} Å, displacement_sigma ∈ {0.004, 0.008, 0.012}, and 7 RNG seeds.

Reproduction summary

knob	value
cell side	30 Å
atoms	2052
grain_size	22 Å
FIRE steps (tricor stage 3)	200
pre-DFTB cleanup	bond_relax(20) + enforce_hard_core(40)
DFTB+ optimizer	ASE FIRE, maxstep = 0.03 Å
DFTB+ cell DOFs	volume only (hydrostatic_strain=True)
DFTB+ fmax target	1.0 eV/Å, 60-step cap
charge restart	seed SP + ReadInitialCharges=Yes
SK set	matsci-0-3
k-points	(1, 1, 1) Γ-only

Per-stage trajectory (extxyz): docs/_static/dftb/nanocrystalline_traj.xyz