Low-index SC · Triangular net

SC(111)

SC(111) produces a triangular outermost net even though simple cubic is not a close-packed structure. Subsurface registry distinguishes the two orientations of threefold hollow.

Plane: (111)
Layer character: Flat · threefold symmetry
ASE slab builder: surface

From bulk to facet

How SC(111) is cut

(111) plane cutting through a Simple 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 orient the plane normal along the cube body diagonal. Each translated plane selects one triangular registry from a three-layer sequence.

Bulk lattice: Simple cubic
Plane normal: [111]
What remains: Triangular 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 SC(111) with numbered adsorption sites — The outlined reference cell has |a₁| = 4.7376 Å, |a₂| = 4.7376 Å, and γ = 60.00° for the Po slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

ontop1-fold
Directly above an atom in the triangular outermost layer.
(u,v) = (0, 0)s = s₁ · support shell: mean Δz = +0.000 Å from L1
Projection of the L1 atom at (0, 0).
Not named in ASE
bridge2-fold
Midpoint of a nearest in-plane connection.
(u,v) = (1/2, 0)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1
Periodic midpoint of L1 (0, 0) and L1 (1, 0).
Not named in ASE
L2-registry hollow3-fold
Threefold opening whose lateral coordinate coincides with a second-layer atom.
(u,v) = (1/3, 1/3)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = +0.000 Å from L1
Least-squares centroid of the 3-atom projected shell: L1 (0, 0), L1 (1, 0), L1 (0, 1).
Not named in ASE
L3-registry hollow3-fold
The other threefold opening
(u,v) = (2/3, 2/3)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = +0.000 Å from L1
Least-squares centroid of the 3-atom projected shell: L1 (1, 0), L1 (0, 1), L1 (1, 1).
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

The projected layers cycle through three registries. One hollow lies above L2 and the other above L3, so their top-layer coordination is identical but their subsurface support differs.

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 spacing is \(d_{111}=a/\sqrt{3}\), and the triangular surface vectors have length \(a\sqrt{2}\) with a 60° angle.

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, (1, 1, 1), 9, vacuum=10)

Things that are easy to misread

Calling SC(111) close packed because its top view is triangular.
Treating the two hollow orientations as identical without checking lower layers.