Prismatic SH · Rectangular net

SH(10-10)

SH(10-10) is a first-order prism face with independent basal and c-axis repeats. Those unequal directions create basal and axial bridge sites around a rectangular hollow.

Plane: (10-10)
Layer character: Prism · anisotropic
ASE slab builder: surface

From bulk to facet

How SH(10-10) is cut

(10-10)

The plane is parallel to c and cuts one pair of basal axes, appearing as a vertical sheet through the simple hexagonal prism.

Bulk lattice: Simple hexagonal
Plane normal: reciprocal vector G(10-10)
What remains: 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(10-10) with numbered adsorption sites — The outlined reference cell has |a₁| = 2.7000 Å, |a₂| = 4.4000 Å, and γ = 90.00° for the X slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

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
basal bridge2-fold
Between neighbours along the 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
axial bridge2-fold
Between neighbours parallel to the c axis.
(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
rectangular hollow4-fold
Centre of the rectangle bounded by two basal and two axial rows.
(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

Adjacent atom-bearing planes alternate laterally by half the basal surface repeat, while the c-axis rows remain straight.

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 spacing is \(d_{10\bar{1}0}=\sqrt{3}a/2\). The rectangular surface repeats are \(a\) and \(c\).

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, 0, 0), 8, vacuum=10)

Things that are easy to misread

Treating the basal and axial bridge directions as equivalent when a and c differ.
Forgetting that (10-10) is written as (100) in the three-index ASE cell.