Stepped FCC · (100) terraces
FCC(311)
The (311) surface combines short (100)-like terraces with close-packed step edges. Square-like terrace pockets sit next to lower-coordinate ledge atoms.
- Plane
- (311)
- Layer character
- Stepped · compact
- ASE slab builder
surface
From bulk to facet
How FCC(311) is cut
(311)
The [311] cut lies between the (100) and (111) orientations. Its repeated intersection with the FCC lattice creates compact terraces and close-packed step rims.
- Bulk lattice
- Face-centred cubic
- Plane normal
- [311]
- What remains
- (100) 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
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.
- terrace ontop1-fold
Above an atom within the terrace.
(u,v) = (1/11, 21/22)s = s₁ · support shell: mean Δz = -2.177 Å from L1Projection of the L3 atom at (1/11, 21/22).
Not named in ASE - step-edge ontop1-fold
Above an atom at the upper step edge.
(u,v) = (1/22, 5/22)s = s₁ · support shell: mean Δz = +0.000 Å from L1Projection of the L1 atom at (1/22, 5/22).
Not named in ASE - lower-row ontop1-fold
Above the exposed row below the step.
(u,v) = (7/22, 1/11)s = s₁ · support shell: mean Δz = -1.088 Å from L1Projection of the L2 atom at (7/22, 1/11).
Not named in ASE - terrace bridge2-fold
Between neighbours within the terrace.
(u,v) = (9/11, 37/44)s = (s₁ + s₂) / 2 · support shell: mean Δz = -1.088 Å from L1Periodic midpoint of L2 (9/11, -9/22) and L2 (9/11, 1/11).
Not named in ASE - step bridge2-fold
Between adjacent atoms along the step.
(u,v) = (6/11, 43/44)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1Periodic midpoint of L1 (-5/11, 8/11) and L1 (-5/11, 27/22).
Not named in ASE - cross-step bridge2-fold
Between atoms on different step levels.
(u,v) = (19/44, 7/44)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.544 Å from L1Periodic midpoint of L1 (6/11, 5/22) and L2 (7/22, 1/11).
Not named in ASE - terrace fourfold hollow4-fold
At a four-atom opening on the terrace.
(u,v) = (25/44, 37/44)s = (Σᵢ sᵢ) / 4 · support shell: mean Δz = -1.088 Å from L1Least-squares centroid of the 4-atom projected shell: L2 (7/22, 1/11), L2 (7/22, -9/22), L2 (9/11, -9/22), L2 (9/11, 1/11).
Not named in ASE - mixed-height ledge hollow3-fold
A threefold pocket coordinated across the ledge.
(u,v) = (16/33, 13/22)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -1.088 Å from L1Least-squares centroid of the 3-atom projected shell: L1 (6/11, -3/11), L2 (7/22, -9/22), L3 (13/22, -6/11).
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
The top view mixes square terrace motifs with step pockets. The side profile identifies which apparent neighbours actually lie one atomic level lower.
Cell
Geometry at a glance
The reciprocal normal is \([311]\), so \(d_{311}=a/\sqrt{11}\). The equal minor indices retain a mirror-related in-plane geometry.
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, 1, 1), layers=8, vacuum=10)
Things that are easy to misread
- Calling the mixed-height ledge pocket a flat fourfold hollow.
- Comparing coverages without accounting for the larger high-index repeat cell.