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Tutorial 6 · 2D Materials

What you'll learn: how to build graphene, hexagonal boron nitride (hBN), MX₂ transition-metal dichalcogenides, and vertically stacked bilayers — including twisted moiré geometries.

Prerequisites: Tutorial 4. No extra dependencies.

The layered builder

examples/14_graphene_bilayer_md.toml
[run]
name = "graphene_bilayer"
seed = 14

[geometry.builder]
type                = "layered"
material            = "graphene"    # (1)
size                = [3, 3]        # (2)
n_layers            = 2             # (3)
stacking            = "AB"          # (4)
interlayer_spacing  = 3.35          # (5)
vacuum              = 15.0          # (6)

[calculator]
type = "emt"

[sampling]
type        = "md"
temperature = 300.0
steps       = 200
interval    = 20

[selection]
steps  = ["physicality", "dedup", "diversity"]
budget = 8

[dataset]
path = "dataset"

pixi run example-14

Parameters explained

  1. material — the 2D crystal type:

    Value Description Default a (Å)
    graphene Carbon honeycomb 2.46
    hbn Hexagonal boron nitride 2.50
    mx2 Transition-metal dichalcogenide 3.18

  2. size — [nx, ny] in-plane repetitions of the primitive monolayer cell. [3, 3] → 9 primitive cells in the layer = 18 C atoms per graphene layer.

  3. n_layers — number of layers to stack.

  4. stacking — how layers are stacked:

  5. "AA" — atoms sit directly on top of each other.

  6. "AB" — Bernal stacking (the physical ground state of graphite). Alternate layers are shifted by one NN vector, (a₁ + a₂) / 3.

  7. interlayer_spacing — vertical distance between consecutive layers (Å). Graphite: 3.35 Å. MoS₂ bulk: ~6.15 Å.

  8. vacuum — total vacuum above and below the stack (Å). 15 Å avoids interaction with periodic images along z.

Material-specific examples

[geometry.builder]
type     = "layered"
material = "graphene"
size     = [4, 4]
n_layers = 1
vacuum   = 15.0

hBN naturally stacks in AA' order (B over N). Use AB stacking to approximate the experimental structure:

[geometry.builder]
type               = "layered"
material           = "hbn"
a                  = 2.504
size               = [3, 3]
n_layers           = 2
stacking           = "AB"
interlayer_spacing = 3.30
vacuum             = 15.0

Molybdenum disulfide — each layer is 3 atoms thick (S–Mo–S sandwich):

[geometry.builder]
type               = "layered"
material           = "mx2"
formula            = "MoS2"    # or "WS2", "WSe2", "MoSe2", "MoTe2"
a                  = 3.18
size               = [2, 2]
n_layers           = 2
interlayer_spacing = 6.15
vacuum             = 15.0

[geometry.builder]
type               = "layered"
material           = "mx2"
formula            = "WSe2"
a                  = 3.28
size               = [2, 2]
n_layers           = 3
interlayer_spacing = 6.48
vacuum             = 15.0

Moiré stacks via twist angle

When you specify a non-zero twist, each layer is rotated by an additional twist degrees relative to the previous one. Because moiré supercells are generally incommensurate with any small periodic cell, TrainCraft returns a finite, non-periodic flake padded with vacuum:

[geometry.builder]
type    = "layered"
material = "graphene"
size    = [6, 6]        # (1)
n_layers = 2
twist   = 21.787        # (2)
vacuum  = 15.0

  1. size controls the flake size. Larger size → more atoms → larger moiré period.

  2. twist — the twist angle in degrees. For graphene, magic angles occur near 1.08°, 1.74°, … but small angles require enormous supercells. Use larger angles (e.g. 21.8°, 38.2°) for feasible training-set generation.

from traincraft.config.models import LayeredBuilder, GeometryConfig
from traincraft.geometry import build_geometry

s = build_geometry(GeometryConfig(builder=LayeredBuilder(
    material="graphene", size=(6, 6), n_layers=2, twist=21.787
)))
print(s.atoms.get_pbc())            # [False False False] — non-periodic flake
print(s.provenance.extra["twist"])  # 21.787
print(len(s.atoms))                 # 144 atoms (6×6×2×2 C atoms, before vacuum)

Non-periodic structures and EMT/tblite

EMT works fine for non-periodic flakes. tblite also handles them. MACE-MP0 is designed for periodic systems — for large non-periodic flakes, use MACE-OFF23 instead.

Controlling the lattice constant

Use a to override the default lattice constant:

[geometry.builder]
type     = "layered"
material = "graphene"
a        = 2.46          # Å — close to DFT-PBE value; ASE default is also 2.46
size     = [4, 4]
n_layers = 2
stacking = "AB"

This is useful when you want to match an experimentally measured or DFT-relaxed lattice constant.

Summary

material Species Available formulas
graphene C —
hbn B, N —
mx2 M, X₂ MoS2, WS2, WSe2, MoSe2, MoTe2, …

Next: Tutorial 7 — using MACE-MP0 as the energy/force engine.