Basal BCT · Square net

BCT(001)

BCT(001) exposes a square basal net like BCC(100), but the separation between alternating corner and body-centred layers is controlled independently by c.

Plane: (001)
Layer character: Basal · fourfold symmetry
ASE slab builder: surface

From bulk to facet

How BCT(001) is cut

(001) plane cutting through a Body-centred tetragonal bulk unit cell — The coloured sheet is one translated member of the (001) plane family; translating it along its normal gives an equivalent termination.

(001)

The plane is perpendicular to the tetragonal c axis. Translating it by c/2 alternates between corner and body-centred square registries.

Bulk lattice: Body-centred tetragonal
Plane normal: reciprocal vector G(001)
What remains: Square net

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 BCT(001) with numbered adsorption sites — The outlined reference cell has |a₁| = 3.2500 Å, |a₂| = 3.2500 Å, and γ = 90.00° for the In slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

ontop1-fold
Directly above an outermost basal atom.
(u,v) = (1/2, 1/2)s = s₁ · support shell: mean Δz = +0.000 Å from L1
Projection of the L1 atom at (1/2, 1/2).
Not named in ASE
bridge2-fold
Halfway between nearest surface atoms along a square edge.
(u,v) = (0, 1/2)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1
Periodic midpoint of L1 (1/2, 1/2) and L1 (3/2, 1/2).
Not named in ASE
fourfold hollow4-fold
Centre of the top-layer square
(u,v) = (0, 0)s = (Σᵢ sᵢ) / 4 · support shell: mean Δz = +0.000 Å from L1
Least-squares centroid of the 4-atom projected shell: L1 (1/2, 1/2), L1 (-1/2, 1/2), L1 (1/2, -1/2), L1 (-1/2, -1/2).
Not named in ASE

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

L1 and L2 are square nets shifted by half a surface diagonal. The fourfold hollow of one layer lies above an atom in the next.

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

For tetragonal metrics, \(d_{001}=c\); the body-centred basis inserts atom-bearing planes every \(c/2\). The surface square has side \(a\).

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 import Atoms
from ase.build import surface

a, c = 3.25, 4.95
indium = Atoms("In2", scaled_positions=[(0, 0, 0), (.5, .5, .5)],
               cell=[(a, 0, 0), (0, a, 0), (0, 0, c)], pbc=True)
slab = surface(indium, (0, 0, 1), 6, vacuum=10)

Things that are easy to misread

Replacing c with a in the layer spacing.
Passing a primitive BCT cell to ASE surface while interpreting the indices as conventional tetragonal indices.