Stepped FCC · Close-packed ledges
FCC(221)
The (221) orientation lies near (111) but resolves into closely spaced ledges. The short repeat makes subsurface registry especially important when naming hollows.
- Plane
- (221)
- Layer character
- Stepped · narrow terraces
- ASE slab builder
surface
From bulk to facet
How FCC(221) is cut
(221)
Equal h and k keep a mirror direction in the plane, while the smaller l component tilts the cut away from (111) and introduces closely spaced ledges.
- Bulk lattice
- Face-centred cubic
- Plane normal
- [221]
- What remains
- Close-packed 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
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.
- ledge ontop1-fold
Above an atom at the upper ledge.
(u,v) = (7/18, 5/18)s = s₁ · support shell: mean Δz = +0.000 Å from L1Projection of the L1 atom at (7/18, 5/18).
Not named in ASE - lower-row ontop1-fold
Above an exposed atom below the ledge.
(u,v) = (0, 0)s = s₁ · support shell: mean Δz = -0.602 Å from L1Projection of the L2 atom at (0, 0).
Not named in ASE - ledge bridge2-fold
Between neighbouring atoms along the ledge.
(u,v) = (23/36, 5/18)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1Periodic midpoint of L1 (-1/9, -13/18) and L1 (-11/18, -13/18).
Not named in ASE - terrace bridge2-fold
Between neighbours in the narrow terrace.
(u,v) = (1/4, 0)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.602 Å from L1Periodic midpoint of L2 (-1/2, 0) and L2 (-1, 0).
Not named in ASE - cross-step bridge2-fold
Between atoms on different step levels.
(u,v) = (25/36, 5/36)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.301 Å from L1Periodic midpoint of L1 (8/9, 23/18) and L2 (1/2, 1).
Not named in ASE - lower threefold hollow3-fold
A three-atom opening in the lower row.
(u,v) = (5/18, 1/18)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -1.203 Å from L1Least-squares centroid of the 3-atom projected shell: L3 (-7/18, 13/18), L3 (11/18, 13/18), L3 (11/18, 31/18).
Not named in ASE - mixed-height step pocket3-fold
A pocket coordinated by atoms at different heights.
(u,v) = (5/6, 0)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -0.602 Å from L1Least-squares centroid of the 3-atom projected shell: L1 (8/9, 23/18), L2 (1, 1), L3 (11/18, 13/18).
Not named in ASE
Interactive model
Rotate the slab
Sites share a schematic display height · drag to rotate · hover for names
Below the top layer
Why the sites are different
Several apparent openings overlap atoms in lower layers. Reading the pale registry together with the profile prevents an empty-looking top view from being mistaken for a simple hollow.
Cell
Geometry at a glance
The normal is \([221]\), giving \(d_{221}=a/3\). Equal h and k preserve a mirror direction in the surface plane.
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, (2, 2, 1), layers=8, vacuum=10)
Things that are easy to misread
- Assuming every triangular opening has the same subsurface registry.
- Ignoring that the two sides of a step can expose different local environments.