Basal HCP · Triangular net

HCP(0001)

HCP(0001) is the close-packed basal face. Its triangular top layer resembles FCC(111), but the stacking repeats AB rather than ABC.

Plane: (0001)
Layer character: Basal · close packed
ASE slab builder: hcp0001

From bulk to facet

How HCP(0001) is cut

The coloured sheet is one translated member of the (0001) plane family; translating it along its normal gives an equivalent termination.

(0001)

The (0001) plane is perpendicular to the hexagonal c axis and parallel to all basal axes. It selects one close-packed sheet from the ABAB sequence.

Bulk lattice: Hexagonal close packed
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 HCP(0001) with numbered adsorption sites — The outlined reference cell has |a₁| = 3.2100 Å, |a₂| = 3.2100 Å, and γ = 60.00° for the Mg slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

ontop1-fold
Directly above one basal-plane atom.
(u,v) = (1/3, 1/3)s = s₁ · support shell: mean Δz = +0.000 Å from L1
Projection of the L1 atom at (1/3, 1/3).
ASE keywordontop
bridge2-fold
Halfway along a nearest-neighbour bond.
(u,v) = (5/6, 1/3)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1
Periodic midpoint of L1 (1/3, 1/3) and L1 (4/3, 1/3).
ASE keywordbridge
FCC hollow3-fold
Threefold opening that would continue ABC stacking.
(u,v) = (2/3, 2/3)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = +0.000 Å from L1
Least-squares centroid of the 3-atom projected shell: L1 (1/3, 1/3), L1 (4/3, 1/3), L1 (1/3, 4/3).
ASE keywordfcc
HCP hollow3-fold
Threefold opening above the second-layer registry.
(u,v) = (0, 0)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = +0.000 Å from L1
Least-squares centroid of the 3-atom projected shell: L1 (4/3, 1/3), L1 (1/3, 4/3), L1 (4/3, 4/3).
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

HCP and FCC hollows look identical in one layer; the ABAB stacking below distinguishes them from the ABC sequence on FCC(111).

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

For HCP, \(d_{hkil}^{-2}=\frac{4}{3}(h^2+hk+k^2)/a^2+l^2/c^2\). Thus \(d_{0001}=c\), with the AB basis producing atomic layers separated by \(c/2\).

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 hcp0001

slab = hcp0001("Mg", size=(3, 3, 6), a=3.21, c=5.21,
               vacuum=10)

Things that are easy to misread

Treating HCP(0001) and FCC(111) as identical beyond the top layer.
Forgetting to report the c/a ratio used for the slab.