Tutorial 5 · Slabs & Strain¶

What you'll learn: how to build bare crystalline slabs (without adsorbates) using named facets or arbitrary Miller indices, and how to apply mechanical strain and other geometric transforms.

Prerequisites: Tutorial 4. No extra dependencies.

The standalone slab builder¶

The slab builder creates a clean crystalline surface model — no adsorbate. All atoms are tagged as framework (tc_fragment == -1), meaning they're treated as immobile substrate atoms by the MC sampler. You would then use strain or supercell transforms, or switch to surface_adsorbate to put something on top.

examples/13_slab_strain_md.toml

[run]
name = "cu111_strained"
seed = 13

[geometry.builder]
type    = "slab"
element = "Cu"
facet   = "fcc111"    # (1)
size    = [3, 3, 4]   # (2)
vacuum  = 12.0        # (3)

[[geometry.transforms]]
type  = "strain"
voigt = [0.02, 0.02, 0.0, 0.0, 0.0, 0.0]  # (4)

[calculator]
type = "emt"

[sampling]
type        = "md"
temperature = 400.0
steps       = 200
interval    = 20

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

[dataset]
path = "dataset"

pixi run example-13

facet — named low-index facets: fcc111, fcc100, fcc110, bcc110, bcc100, bcc111, hcp0001.
size — [nx, ny, nz]. For a slab: nx and ny repeat the surface unit cell in-plane; nz (or layers) sets the slab thickness.
vacuum — total vacuum gap in Å (added above and below the slab).
Biaxial strain via the Voigt notation — see below.

Miller index slabs¶

For any surface orientation, specify Miller indices directly:

[geometry.builder]
type             = "slab"
element          = "Fe"
miller           = [1, 1, 0]    # (1)
crystalstructure = "bcc"        # (2)
a                = 2.87         # (3)
layers           = 8            # (4)
size             = [2, 2, 0]    # (5)
vacuum           = 15.0

miller — the surface Miller indices as a list of 3 integers. When miller is set, facet is ignored.
crystalstructure — needed to construct the bulk cell to cleave.
a — lattice constant. If omitted, ASE uses its tabulated value.
layers — number of atomic layers (used in Miller mode; nz from size is used in named-facet mode).
size — [nx, ny, 0] in Miller mode; the third element is ignored.

Why does Miller mode give fewer atoms?

The surface unit cell for a high-index surface is often smaller than for a named facet. Use a larger size to get a reasonable supercell.

Transforms¶

Transforms are composable post-processing steps applied after the builder. They're specified as an array of [[geometry.transforms]] sections.

`strain` — elastic deformation¶

Deforms the cell and scales atom positions with it (fractional coordinates are preserved — this is a proper elastic deformation, not just repositioning).

Hydrostatic (isotropic) strain:

[[geometry.transforms]]
type        = "strain"
hydrostatic = 0.02     # +2% in all three directions

Voigt notation — (e_xx, e_yy, e_zz, e_yz, e_xz, e_xy):

[[geometry.transforms]]
type  = "strain"
voigt = [0.02, 0.02, 0.0, 0.0, 0.0, 0.0]   # biaxial in-plane tensile

[[geometry.transforms]]
type  = "strain"
voigt = [0.0, 0.0, -0.01, 0.0, 0.0, 0.0]   # 1% uniaxial compression along z

Sign convention

Positive strain = expansion. Negative strain = compression. A hydrostatic strain of 0.02 increases each lattice parameter by 2%.

`rotate` — rigid rotation¶

[[geometry.transforms]]
type        = "rotate"
angle       = 45.0      # degrees
axis        = "z"       # "x", "y", "z" or a 3-vector [x, y, z]
rotate_cell = false     # (1)

rotate_cell — if true, also rotates the periodic cell vectors (a rigid reorientation of the whole system). If false, atoms rotate within the existing cell box.

`set_pbc` — change periodicity flags¶

[[geometry.transforms]]
type = "set_pbc"
pbc  = [true, true, true]   # make fully periodic

Or to remove all periodicity (cluster/molecule):

[[geometry.transforms]]
type = "set_pbc"
pbc  = false

Combining transforms¶

Transforms are applied left-to-right (top to bottom in the TOML):

[[geometry.transforms]]
type   = "supercell"
repeat = [2, 2, 1]        # 1. double in-plane

[[geometry.transforms]]
type        = "strain"
hydrostatic = -0.01       # 2. compress 1% hydrostatically

[[geometry.transforms]]
type   = "perturb"
stddev = 0.03             # 3. add thermal-like noise

Generating a strain dataset¶

A common workflow in computational materials science is to compute energies and forces at several strain values to fit an equation of state or elastic constants.

[run]
name = "cu_eos_point"    # change this for each strain value in a scan
seed = 42

[geometry.builder]
type             = "crystal"
name             = "Cu"
crystalstructure = "fcc"
a                = 3.61
cubic            = true
supercell        = [2, 2, 2]

[[geometry.transforms]]
type        = "strain"
hydrostatic = 0.02         # vary this from -0.05 to +0.05

[calculator]
type = "emt"

[sampling]
type        = "rattle"
n_structures = 5
std          = 0.03

[selection]
steps  = ["physicality", "dedup"]
budget = 5

[dataset]
path = "dataset"

Summary¶

Transform	Effect	Key parameters
`strain`	Elastic deformation	`hydrostatic` or `voigt` (6-vector)
`rotate`	Rigid rotation	`angle`, `axis`, `rotate_cell`
`set_pbc`	Change boundary conditions	`pbc` (bool or 3-bool)
`supercell`	Tile the cell	`repeat` (3-int)
`vacuum`	Add vacuum padding	`amount` (Å)
`perturb`	Random displacements	`stddev` (Å)

Next: Tutorial 6 — layered 2D materials and moiré stacks.