Low-index FCC · Triangular net

FCC(111)

The (111) plane is the close-packed FCC face. Every surface atom has six neighbours in a triangular net, and two visually similar threefold hollows are distinguished by the stacking below.

Plane: (111)
Layer character: Flat · close packed
ASE slab builder: fcc111

From bulk to facet

How FCC(111) is cut

(111) plane cutting through a Face-centred 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)

The plane meets x, y, and z at equal intercepts. It slices across the cube corner-to-corner and selects one close-packed layer from the ABC sequence.

Bulk lattice: Face-centred 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 FCC(111) with numbered adsorption sites — The outlined reference cell has |a₁| = 5.1053 Å, |a₂| = 5.1053 Å, and γ = 60.00° for the Cu slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

ontop1-fold
Directly above one atom in the triangular net.
(u,v) = (0, 0)s = s₁ · support shell: mean Δz = +0.000 Å from L1
Projection of the L1 atom at (0, 0).
ASE keywordontop
bridge2-fold
Halfway along a nearest-neighbour bond.
(u,v) = (1/4, 0)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1
Periodic midpoint of L1 (0, 0) and L1 (1/2, 0).
ASE keywordbridge
FCC hollow3-fold
Threefold opening above a third-layer atom.
(u,v) = (1/6, 1/6)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 (1/2, 0), L1 (0, 1/2).
ASE keywordfcc
HCP hollow3-fold
Threefold opening above 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 (1/2, 0), L1 (0, 1/2), L1 (1/2, 1/2).
ASE keywordhcp

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

FCC layers follow an ABC sequence. An HCP hollow lies above a second-layer atom; an FCC hollow lies above a third-layer atom and continues the ABC sequence.

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 plane spacing is \(d_{111}=a/\sqrt{3}\). Primitive surface vectors have length \(a/\sqrt{2}\) at \(60^\circ\); the outlined cell is a \(2\times2\) repeat of that primitive net.

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 add_adsorbate, fcc111

slab = fcc111("Cu", size=(3, 3, 4), a=3.61, vacuum=10)
add_adsorbate(slab, "H", 1.2, position="fcc")

Things that are easy to misread

Calling the triangular atomic net a honeycomb lattice.
Identifying FCC and HCP hollows without looking below the top layer.