Surface Atlas
← Common surfaces

Prismatic SH · Wide rectangular net

SH(11-20)

SH(11-20) rotates the prism normal by 30 degrees in the basal plane. It remains parallel to c but changes the cross-row repeat and surface density.

Plane
(11-20)
Layer character
Prism · rotated basal cut
ASE slab builder
surface

From bulk to facet

How SH(11-20) is cut

(11-20) plane cutting through a Simple hexagonal bulk unit cell
The coloured sheet is one translated member of the (11-20) plane family; translating it along its normal gives an equivalent termination.

(11-20)

The cut is vertical like (10-10), but it meets a different pair of basal directions in the hexagonal prism.

Bulk lattice
Simple hexagonal
Plane normal
reciprocal vector G(11-20)
What remains
Wide rectangular 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(11-20) with numbered adsorption sites
The outlined reference cell has |a1| = 4.6765 Å, |a2| = 4.4000 Å, and γ = 90.00° for the X slab used in the drawing. Fractional coordinates mean r∥ = ua1 + va2.
  1. ontop1-fold

    Above an atom in the outermost prism row.

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

    Projection of the L1 atom at (1/2, 0).

    Not named in ASE
  2. axial bridge2-fold

    Midpoint between neighbours parallel to c.

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

    Periodic midpoint of L1 (1/2, 0) and L1 (1/2, 1).

    Not named in ASE
  3. cross-row bridge2-fold

    Midpoint across the wider basal surface repeat.

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

    Periodic midpoint of L1 (1/2, 0) and L1 (3/2, 0).

    Not named in ASE
  4. rectangular hollow4-fold

    Centre of the four-atom rectangular opening.

    (u,v) = (0, 1/2)s = (Σᵢ sᵢ) / 4 · support shell: mean Δz = +0.000 Å from L1

    Least-squares centroid of the 4-atom projected shell: L1 (1/2, 0), L1 (3/2, 0), L1 (1/2, 1), L1 (3/2, 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

Atom-bearing planes alternate across the wide basal repeat; the unchanged axial rows make the contrast with SH(10-10) easy to isolate.

Side profile of SH(11-20) 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(11-20)
Layer registry viewed from above; opacity increases towards the surface.

Cell

Geometry at a glance

The spacing is \(d_{11\bar{2}0}=a/2\). One surface vector remains the c-axis translation of length \(c\).

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, (1, 1, 0), 8, vacuum=10)
Things that are easy to misread
  • Treating the two prism orientations as the same surface cell.
  • Confusing the four-index label with four independent Miller indices.