Prismatic HCP · Rectangular zig-zag rows
HCP(11-20)
HCP(11-20), the second common prism orientation, is rotated by 30 degrees in the basal plane relative to (10-10). That rotation changes which HCP rows terminate at the surface.
- Plane
- (11-20)
- Layer character
- Prism · rotated basal cut
- ASE slab builder
surface
From bulk to facet
How HCP(11-20) is cut
(11-20)
Like (10-10), this plane is parallel to c, but its basal normal is rotated. The hexagonal bulk diagram makes the two inequivalent prism cuts visible.
- Bulk lattice
- Hexagonal close packed
- Plane normal
- reciprocal vector G(11-20)
- What remains
- Rectangular zig-zag 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
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.
- outer-row ontop1-fold
Above an atom in the outer zig-zag row.
(u,v) = (1/2, 0)s = s₁ · support shell: mean Δz = +0.000 Å from L1Projection of the L1 atom at (1/2, 0).
Not named in ASE - lower-row ontop1-fold
Above an exposed atom in the lower row.
(u,v) = (0, 0)s = s₁ · support shell: mean Δz = -1.605 Å from L1Projection of the L2 atom at (0, 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 L1Periodic midpoint of L1 (1/2, 0) and L1 (1/2, 1).
Not named in ASE - zig-zag row bridge2-fold
Between neighbours following the outer row.
(u,v) = (2/3, 1/4)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1Periodic midpoint of L1 (5/6, -1/2) and L1 (1/2, -1).
Not named in ASE - cross-row bridge2-fold
Between atoms in adjacent projected rows.
(u,v) = (5/12, 1/4)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.803 Å from L1Periodic midpoint of L1 (1/2, -1) and L2 (1/3, -1/2).
Not named in ASE - threefold row pocket3-fold
A pocket between three atoms in neighbouring rows.
(u,v) = (7/9, 1/6)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -1.605 Å from L1Least-squares centroid of the 3-atom projected shell: L1 (-1/2, 0), L2 (0, 0), L3 (-1/6, 1/2).
Not named in ASE
Interactive model
Rotate the slab
Sites share a schematic display height · drag to rotate · hover for names
Below the top layer
Why the sites are different
The axial periodicity is unchanged, while the cross-row spacing and exposed two-atom registry differ from the first-order prism.
Cell
Geometry at a glance
The HCP spacing formula gives \(d_{11\bar{2}0}=a/2\). The plane contains [0001], so one in-plane repeat has 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 bulk, surface
mg = bulk("Mg", "hcp", a=3.21, c=5.21)
slab = surface(mg, (1, 1, 0), 10, vacuum=10)
Things that are easy to misread
- Treating the two prism families as the same cut.
- Confusing Miller-Bravais (11-20) with a cubic four-index notation.