Low-index BCC · Triangular rows

BCC(111)

BCC(111) is an open, strongly layered face. Its apparent triangular symmetry spans several closely spaced heights rather than one close-packed atomic sheet.

Plane: (111)
Layer character: Flat · open and corrugated
ASE slab builder: bcc111

From bulk to facet

How BCC(111) is cut

(111) plane cutting through a Body-centred cubic bulk unit cell — The coloured sheet is one translated member of the (111) plane family; translating it along its normal gives an equivalent termination.

(111)

Equal intercepts give a plane normal to the cube body diagonal. In BCC this direction runs through the central atom, creating a sequence of corrugated triangular layers.

Bulk lattice: Body-centred cubic
Plane normal: [111]
What remains: Triangular rows

The plane is drawn through the centre so high-index cuts remain legible. Its orientation is what the indices specify, not its absolute position inside one cell.

Surface geometry

Read the surface from above

surface second layer third layer

L1 is the highest atom-bearing plane, followed by L2 and L3. Support coordinates outside 0–1 are periodic images. The listed Δz describes the supporting atoms, not the marker height. In the interactive model, every numbered site is placed on the same schematic guide plane above the slab; no adsorption distance or energetic ordering is implied.

Top view of BCC(111) with numbered adsorption sites — The outlined reference cell has |a₁| = 4.0588 Å, |a₂| = 4.0588 Å, and γ = 60.00° for the Fe slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

outermost ontop1-fold
Above an atom in the highest corrugated row.
(u,v) = (1/3, 1/3)s = s₁ · support shell: mean Δz = +0.000 Å from L1
Projection of the L1 atom at (1/3, 1/3).
ASE keywordontop
lower-row ontop1-fold
Above an exposed atom in the lower projected row.
(u,v) = (0, 0)s = s₁ · support shell: mean Δz = -0.828 Å from L1
Projection of the L2 atom at (0, 0).
Not named in ASE
row bridge2-fold
Between atoms in neighbouring projected rows.
(u,v) = (1/6, 1/6)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.414 Å from L1
Periodic midpoint of L1 (1/3, 1/3) and L2 (0, 0).
Not named in ASE
mixed-height hollow3-fold
The source-defined hollow; verify its actual coordinating shell.
(u,v) = (2/3, 2/3)exact ASE affine transform · support shell: mean Δz = +0.000 Å from L1
Current ASE bcc111 hollow offset (1/3, 1/3) added to the outermost atom at (1/3, 1/3).
ASE sourcehollow

Interactive model

Rotate the slab

Sites share a schematic display height · drag to rotate · hover for names

Building the model…

Below the top layer

Why the sites are different

Three-layer registry is essential here because the topmost plane alone contains comparatively few atoms.

Side profile showing one compact stacking repeat. The dashed line follows the macroscopic surface plane.

Layer registry viewed from above; opacity increases towards the surface.

Cell

Geometry at a glance

The crystallographic spacing is \(d_{111}=a/\sqrt{3}\). The body-centred basis inserts atom-bearing sublayers at half that distance, which produces the strong corrugation.

A site name describes the ideal starting geometry. Relaxation can move an adsorbate away from it.

Practical model

Build it with ASE

The builder creates the slab. Sites marked ASE keyword can be passed directly as a named position; ASE source marks current but inconsistently documented support. Other sites require explicit Cartesian coordinates converted from the fractional construction above.

from ase.build import bcc111

slab = bcc111("Fe", size=(3, 4, 9), a=2.87, vacuum=10,
              orthogonal=True)

Things that are easy to misread

Treating BCC(111) as the analogue of close-packed FCC(111).
Assigning a hollow from top-view symmetry without checking atom heights.