Pyramidal HCP · Broad oblique terraces
HCP(10-12)
HCP(10-12) has a stronger c-axis index than (10-11), changing the inclination and spacing of the exposed ridges. It is a useful visual example of how l controls pyramidal tilt.
- Plane
- (10-12)
- Layer character
- Pyramidal · lower tilt
- ASE slab builder
surface
From bulk to facet
How HCP(10-12) is cut
(10-12)
Doubling l moves the plane's c-axis intercept closer to the origin. The coloured cut therefore rotates relative to (10-11) while keeping the same basal orientation.
- Bulk lattice
- Hexagonal close packed
- Plane normal
- reciprocal vector G(10-12)
- What remains
- Broad oblique terraces
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.
- terrace ontop1-fold
Above an atom within the terrace.
(u,v) = (0.7186, 0)s = s₁ · support shell: mean Δz = -1.901 Å from L1Projection of the L3 atom at (0.7186, 0).
Not named in ASE - ridge ontop1-fold
Above an atom on the upper ridge.
(u,v) = (0.9848, 1/2)s = s₁ · support shell: mean Δz = +0.000 Å from L1Projection of the L1 atom at (0.9848, 1/2).
Not named in ASE - lower-row ontop1-fold
Above an exposed atom below the ridge.
(u,v) = (0.396, 1/2)s = s₁ · support shell: mean Δz = -0.634 Å from L1Projection of the L2 atom at (0.396, 1/2).
Not named in ASE - terrace bridge2-fold
Between neighbours within the terrace.
(u,v) = (0.396, 0)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.634 Å from L1Periodic midpoint of L2 (0.396, 1/2) and L2 (0.396, 3/2).
Not named in ASE - ridge bridge2-fold
Between adjacent atoms along the ridge.
(u,v) = (0.9848, 0)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1Periodic midpoint of L1 (0.9848, 1/2) and L1 (0.9848, -1/2).
Not named in ASE - cross-step bridge2-fold
Between atoms on different step levels.
(u,v) = (0.1904, 1/2)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.317 Å from L1Periodic midpoint of L1 (0.9848, 3/2) and L2 (1.396, 3/2).
Not named in ASE - mixed-layer step pocket3-fold
A pocket coordinated by atoms from multiple layers.
(u,v) = (0.6998, 2/3)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -0.845 Å from L1Least-squares centroid of the 3-atom projected shell: L1 (1.9848, 1/2), L2 (1.396, 1/2), L3 (1.7186, 1).
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 terrace width and layer sequence differ from (10-11), even though both share the same basal indices.
Cell
Geometry at a glance
Here \(d_{10\bar{1}2}^{-2}=4/(3a^2)+4/c^2\). Relative to (10-11), doubling l increases the c-axis reciprocal component.
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, 2), 10, vacuum=10)
Things that are easy to misread
- Assuming the second pyramidal index changes only the cell label.
- Comparing geometry without holding the c/a ratio fixed.