Pyramidal HCP · Oblique ridges

HCP(10-11)

The first-order pyramidal face cuts both the basal plane and c axis. Its oblique rows contain atoms at several heights and lack the simple symmetry of basal or prism faces.

Plane: (10-11)
Layer character: Pyramidal · stepped
ASE slab builder: surface

From bulk to facet

How HCP(10-11) is cut

The coloured sheet is one translated member of the (10-11) plane family; translating it along its normal gives an equivalent termination.

(10-11)

Adding a nonzero l index tilts the (10-10) prism plane towards the basal plane. The cut crosses both the side and end of the hexagonal bulk cell.

Bulk lattice: Hexagonal close packed
Plane normal: reciprocal vector G(10-11)
What remains: Oblique ridges

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(10-11) with numbered adsorption sites — The outlined reference cell has |a₁| = 6.1195 Å, |a₂| = 3.2100 Å, and γ = 74.79° for the Mg slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

ridge ontop1-fold
Above an atom on the upper oblique ridge.
(u,v) = (0.6792, 0.1604)s = s₁ · support shell: mean Δz = +0.000 Å from L1
Projection of the L1 atom at (0.6792, 0.1604).
Not named in ASE
lower-row ontop1-fold
Above an exposed atom below the ridge.
(u,v) = (0.9945, 0.5027)s = s₁ · support shell: mean Δz = -2.044 Å from L1
Projection of the L2 atom at (0.9945, 0.5027).
Not named in ASE
ridge bridge2-fold
Between neighbours along the upper ridge.
(u,v) = (0.6792, 0.6604)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1
Periodic midpoint of L1 (0.6792, 0.1604) and L1 (0.6792, -0.8396).
Not named in ASE
cross-ridge bridge2-fold
Between atoms on opposite sides of the ridge.
(u,v) = (0.8368, 0.8316)s = (s₁ + s₂) / 2 · support shell: mean Δz = -1.022 Å from L1
Periodic midpoint of L1 (0.6792, 0.1604) and L2 (0.9945, -0.4973).
Not named in ASE
lower threefold pocket3-fold
A mixed-height pocket below the ridge.
(u,v) = (0.7909, 0.1045)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -2.453 Å from L1
Least-squares centroid of the 3-atom projected shell: L3 (0.4576, 0.7712), L3 (0.4576, 1.7712), L3 (1.4576, 0.7712).
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

The two-atom HCP basis appears as alternating-height ridges; rotating the model is essential for separating projected neighbours.

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 this pyramidal plane, \(d_{10\bar{1}1}^{-2}=4/(3a^2)+1/c^2\); both basal and c-axis reciprocal components are nonzero.

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 bulk, surface

mg = bulk("Mg", "hcp", a=3.21, c=5.21)
slab = surface(mg, (1, 0, 1), 10, vacuum=10)

Things that are easy to misread

Flattening all projected rows into one atomic layer.
Omitting the c/a ratio when comparing pyramidal surfaces.