Stepped FCC · (111)-like terraces

FCC(331)

FCC(331) is vicinal to (111): close-packed terrace motifs are interrupted at regular intervals by straight ledges, creating terrace and step hollows in one repeat.

Plane: (331)
Layer character: Stepped · close-packed rows
ASE slab builder: surface

From bulk to facet

How FCC(331) is cut

(331) plane cutting through a Face-centred cubic bulk unit cell — The coloured sheet is one translated member of the (331) plane family; translating it along its normal gives an equivalent termination.

(331)

The [331] normal sits close to [111]. The modest tilt interrupts the close-packed plane every few rows, producing regular straight ledges.

Bulk lattice: Face-centred cubic
Plane normal: [331]
What remains: (111)-like terraces

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 FCC(331) with numbered adsorption sites — The outlined reference cell has |a₁| = 5.1053 Å, |a₂| = 11.4158 Å, and γ = 102.92° for the Cu slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

terrace ontop1-fold
Above an atom within the close-packed terrace.
(u,v) = (15/38, 11/38)s = s₁ · support shell: mean Δz = -1.656 Å from L1
Projection of the L3 atom at (15/38, 11/38).
Not named in ASE
ledge ontop1-fold
Above a low-coordinate atom on the ledge.
(u,v) = (3/38, 3/19)s = s₁ · support shell: mean Δz = +0.000 Å from L1
Projection of the L1 atom at (3/38, 3/19).
Not named in ASE
lower-step ontop1-fold
Above the exposed atom below the ledge.
(u,v) = (9/38, 9/19)s = s₁ · support shell: mean Δz = -0.828 Å from L1
Projection of the L2 atom at (9/38, 9/19).
Not named in ASE
terrace bridge2-fold
Between neighbours within the terrace.
(u,v) = (0.4868, 9/19)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.828 Å from L1
Periodic midpoint of L2 (-5/19, 9/19) and L2 (-29/38, 9/19).
Not named in ASE
ledge bridge2-fold
Between adjacent atoms along the ledge.
(u,v) = (0.8289, 3/19)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1
Periodic midpoint of L1 (3/38, 3/19) and L1 (-8/19, 3/19).
Not named in ASE
cross-step bridge2-fold
Between atoms on opposite step levels.
(u,v) = (3/19, 0.5658)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.414 Å from L1
Periodic midpoint of L1 (3/38, 25/38) and L2 (9/38, 9/19).
Not named in ASE
terrace threefold hollow3-fold
A terrace hollow whose registry must be checked below.
(u,v) = (9/38, 0.807)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -0.828 Å from L1
Least-squares centroid of the 3-atom projected shell: L2 (9/38, 9/19), L2 (14/19, 37/38), L2 (-5/19, 37/38).
Not named in ASE
mixed-layer step pocket3-fold
A pocket coordinated by atoms from multiple layers.
(u,v) = (9/38, 0.1404)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -0.828 Å from L1
Least-squares centroid of the 3-atom projected shell: L1 (3/38, 3/19), L2 (9/38, -1/38), L3 (15/38, 11/38).
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 triangular terrace pattern remains visible, but the ABC stacking is interrupted at each ledge. Hollow labels must therefore be tied to a specific local registry.

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 \(d_{331}=a/\sqrt{19}\); [331] is \(\cos^{-1}(7/\sqrt{57})\approx22.0^\circ\) from [111].

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

cu = bulk("Cu", "fcc", a=3.61, cubic=True)
slab = surface(cu, (3, 3, 1), layers=8, vacuum=10)

Things that are easy to misread

Carrying FCC/HCP labels across a step without rechecking the local stacking.
Treating the macroscopic (331) plane as one geometrically flat atomic layer.