Stepped FCC · (111) terraces

FCC(211)

FCC(211) is commonly read as narrow (111)-like terraces separated by monatomic (100)-type steps. Terrace and step atoms therefore offer clearly different local coordination.

Plane: (211)
Layer character: Stepped · kink-free
ASE slab builder: fcc211

From bulk to facet

How FCC(211) is cut

(211) plane cutting through a Face-centred 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 [211] normal tilts the cut away from (111). At atomic scale the plane becomes three-row (111)-like terraces separated by single-height steps.

Bulk lattice: Face-centred cubic
Plane normal: [211]
What remains: (111) 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(211) with numbered adsorption sites — The outlined reference cell has |a₁| = 6.2527 Å, |a₂| = 5.1053 Å, and γ = 90.00° for the Cu slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

terrace ontop1-fold
Above an atom within the narrow (111)-like terrace.
(u,v) = (2/3, 1/4)s = s₁ · support shell: mean Δz = -1.474 Å from L1
Projection of the L3 atom at (2/3, 1/4).
Not named in ASE
step-edge ontop1-fold
Above a low-coordinate atom at the upper step edge.
(u,v) = (1/3, 1/4)s = s₁ · support shell: mean Δz = +0.000 Å from L1
Projection of the L1 atom at (1/3, 1/4).
Not named in ASE
lower-step ontop1-fold
Above the exposed atom immediately below the step.
(u,v) = (0, 0)s = s₁ · support shell: mean Δz = -0.737 Å from L1
Projection of the L2 atom at (0, 0).
Not named in ASE
terrace bridge2-fold
Between nearest neighbours within the terrace.
(u,v) = (0, 3/4)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.737 Å from L1
Periodic midpoint of L2 (0, 0) and L2 (0, -1/2).
Not named in ASE
step-edge bridge2-fold
Between adjacent atoms along the upper ledge.
(u,v) = (1/3, 0)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1
Periodic midpoint of L1 (1/3, 1/4) and L1 (1/3, -1/4).
Not named in ASE
cross-step bridge2-fold
Between atoms on opposite sides of the step.
(u,v) = (1/6, 5/8)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.368 Å from L1
Periodic midpoint of L1 (4/3, 3/4) and L2 (1, 1/2).
Not named in ASE
terrace threefold hollow3-fold
Within a three-atom opening on the terrace.
(u,v) = (1/3, 1/2)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -0.737 Å from L1
Least-squares centroid of the 3-atom projected shell: L2 (0, 0), L2 (0, 1), L2 (1, 1/2).
Not named in ASE
step threefold hollow3-fold
A mixed-height threefold pocket beside the step.
(u,v) = (2/3, 2/3)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -0.737 Å from L1
Least-squares centroid of the 3-atom projected shell: L1 (-2/3, 3/4), L2 (0, 1), L3 (-1/3, 1/4).
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

Rows at the upper ledge have fewer substrate neighbours than atoms inside a terrace. This under-coordination often makes the step edge more reactive than the terrace.

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 reciprocal normal is \([211]\) and \(d_{211}=a/\sqrt{6}\). The periodic surface cell contains the distinct projected rows used in the site constructions.

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 fcc211

# fcc211() builds the slab, but exposes no named adsorption sites.
slab = fcc211("Cu", size=(3, 2, 8), a=3.61, vacuum=10)

Things that are easy to misread

Describing the entire facet as a flat (111) plane and omitting the steps.
Comparing terrace and ledge sites using only their lateral coordination.