Open SC · Oblique ledges

SC(211)

SC(211) adds a finite third index to the (210)-type tilt. The surface becomes a corrugated sequence of oblique ledges with several projected height levels.

Plane: (211)
Layer character: Stepped · corrugated
ASE slab builder: surface

From bulk to facet

How SC(211) is cut

(211) plane cutting through a Simple cubic bulk unit cell — The coloured sheet is one translated member of the (211) plane family; translating it along its normal gives an equivalent termination.

(211)

The plane cuts all three cubic axes with unequal intercepts, producing an oblique in-plane cell rather than the rectangular repeat of SC(210).

Bulk lattice: Simple cubic
Plane normal: [211]
What remains: Oblique ledges

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 SC(211) with numbered adsorption sites — The outlined reference cell has |a₁| = 5.8024 Å, |a₂| = 4.7376 Å, and γ = 90.00° for the Po slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

ledge ontop1-fold
Above an atom on the highest oblique ledge.
(u,v) = (0, 1/2)s = s₁ · support shell: mean Δz = +0.000 Å from L1
Projection of the L1 atom at (0, 1/2).
Not named in ASE
lower-row ontop1-fold
Above an exposed atom below the ledge.
(u,v) = (1/3, 0)s = s₁ · support shell: mean Δz = -1.368 Å from L1
Projection of the L2 atom at (1/3, 0).
Not named in ASE
ledge bridge2-fold
Between nearest atoms along the ledge.
(u,v) = (0, 0)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1
Periodic midpoint of L1 (0, 1/2) and L1 (0, -1/2).
Not named in ASE
cross-ledge bridge2-fold
Between atoms on adjacent height levels.
(u,v) = (1/6, 3/4)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.684 Å from L1
Periodic midpoint of L1 (-1, 1/2) and L2 (-2/3, 1).
Not named in ASE
mixed-height pocket3-fold
A three-atom pocket assembled from successive exposed rows.
(u,v) = (1/3, 1/3)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -1.368 Å from L1
Least-squares centroid of the 3-atom projected shell: L1 (0, 1/2), L2 (1/3, 0), L3 (2/3, 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

Ledge, lower-row, and deeper atoms occupy different lateral registries, so apparent neighbours in projection can be separated vertically.

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 plane spacing is \(d_{211}=a/\sqrt{6}\). Both in-plane translations combine multiple cubic axes.

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 bulk, surface

po = bulk("Po", "sc", a=3.35, cubic=True)
slab = surface(po, (2, 1, 1), 10, vacuum=10)

Things that are easy to misread

Treating SC(211) as a rectangular terrace merely because its parent lattice is cubic.
Counting projected coordination without retaining atom heights.