Prismatic HCP · Rectangular rows

HCP(10-10)

The first-order prism face runs parallel to the c axis. It exposes rectangular atomic rows and makes the difference between basal and axial directions explicit.

Plane: (10-10)
Layer character: Prism · nonpolar
ASE slab builder: hcp10m10

From bulk to facet

How HCP(10-10) is cut

The coloured sheet is one translated member of the (10-10) plane family; translating it along its normal gives an equivalent termination.

(10-10)

The plane is parallel to c and cuts one pair of basal axes. In the bulk prism it appears as a vertical sheet through the hexagonal column.

Bulk lattice: Hexagonal close packed
Plane normal: reciprocal vector G(10-10)
What remains: Rectangular rows

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 HCP(10-10) with numbered adsorption sites — The outlined reference cell has |a₁| = 3.2100 Å, |a₂| = 5.2100 Å, and γ = 90.00° for the Mg slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

raised-row ontop1-fold
Above an outermost prism-row atom.
(u,v) = (0, 1/2)s = s₁ · support shell: mean Δz = +0.000 Å from L1
Projection of the L1 atom at (0, 1/2).
ASE keywordontop
lower-row ontop1-fold
Above an exposed atom in the lower prism row.
(u,v) = (1/2, 0)s = s₁ · support shell: mean Δz = -0.927 Å from L1
Projection of the L2 atom at (1/2, 0).
Not named in ASE
row bridge2-fold
Between nearest neighbours along the raised row.
(u,v) = (1/2, 1/2)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1
Periodic midpoint of L1 (0, 1/2) and L1 (-1, 1/2).
Not named in ASE
axial bridge / channel pocket4-fold
The axial midpoint is also surrounded by the lower row
(u,v) = (0, 0)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1
Periodic midpoint of L1 (0, 1/2) and L1 (0, 3/2).
Not named in ASE
cross-row bridge2-fold
Between atoms in adjacent prism rows.
(u,v) = (1/4, 1/4)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.463 Å from L1
Periodic midpoint of L1 (0, 1/2) and L2 (1/2, 0).
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

Alternating rows originate from the two-atom HCP basis, so equal-looking gaps can have different atoms immediately underneath.

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 HCP spacing formula gives \(d_{10\bar{1}0}=\sqrt{3}a/2\). The outlined rectangle uses one basal translation and one [0001] 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 ase.build import hcp10m10

slab = hcp10m10("Mg", size=(3, 4, 6), a=3.21, c=5.21,
                vacuum=10)

Things that are easy to misread

Dropping the redundant i index without stating the three-index conversion.
Treating the basal and c-axis directions as equivalent.