Surface Atlas
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Basal SH · Triangular net

SH(0001)

The simple-hexagonal basal face is a triangular net repeated in AA registry. Its top view resembles HCP(0001), but it has no shifted second atom in the bulk basis.

Plane
(0001)
Layer character
Basal · sixfold symmetry
ASE slab builder
surface

From bulk to facet

How SH(0001) is cut

(0001) plane cutting through a Simple hexagonal bulk unit cell
The coloured sheet is one translated member of the (0001) plane family; translating it along its normal gives an equivalent termination.

(0001)

The basal plane is perpendicular to c and parallel to all three basal axes. Translating it by c reaches the next identical one-site layer.

Bulk lattice
Simple hexagonal
Plane normal
reciprocal vector G(0001)
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 SH(0001) with numbered adsorption sites
The outlined reference cell has |a1| = 2.7000 Å, |a2| = 2.7000 Å, and γ = 60.00° for the X slab used in the drawing. Fractional coordinates mean r∥ = ua1 + va2.
  1. ontop1-fold

    Directly above a basal-plane atom.

    (u,v) = (0, 0)s = s₁ · support shell: mean Δz = +0.000 Å from L1

    Projection of the L1 atom at (0, 0).

    Not named in ASE
  2. bridge2-fold

    Halfway between nearest basal neighbours.

    (u,v) = (1/2, 0)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1

    Periodic midpoint of L1 (0, 0) and L1 (1, 0).

    Not named in ASE
  3. threefold hollow3-fold

    Centre of a triangular opening; the opposite orientation is symmetry equivalent.

    (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 (0, 0), L1 (1, 0), L1 (0, 1).

    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

Every deeper layer projects onto the outermost atoms. The two triangular hollow orientations are symmetry equivalent and neither lies above a shifted HCP-like sublayer.

Side profile of SH(0001) showing its first repeating atomic layers
Side profile showing one compact stacking repeat. The dashed line follows the macroscopic surface plane.
Layer registry of SH(0001)
Layer registry viewed from above; opacity increases towards the surface.

Cell

Geometry at a glance

For a simple hexagonal lattice, \(d_{0001}=c\). The primitive basal cell has side \(a\), a 60° angle, and one lattice site.

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 math import sqrt
from ase import Atoms
from ase.build import surface

a, c = 2.70, 4.40
# X is ASE's dummy atom; replace it with the species being modelled.
sh = Atoms("X", cell=[(a, 0, 0), (-a/2, sqrt(3)*a/2, 0),
                      (0, 0, c)], pbc=True)
slab = surface(sh, (0, 0, 1), 6, vacuum=10)
Things that are easy to misread
  • Equating simple hexagonal AA stacking with the two-atom AB stacking of HCP.
  • Assigning FCC and HCP names to symmetry-equivalent SH hollows.