Open BCC · Ridges and troughs

BCC(210)

BCC(210) exposes pronounced ridges separated by deep channels. Low-coordinate ridge atoms and mixed-height pockets make it a useful contrast to the flatter (110) face.

Plane: (210)
Layer character: Stepped · very open
ASE slab builder: surface

From bulk to facet

How BCC(210) is cut

(210) plane cutting through a Body-centred cubic bulk unit cell — The coloured sheet is one translated member of the (210) plane family; translating it along its normal gives an equivalent termination.

(210)

Tilting the normal from [100] towards [110] forces the cut through alternating corner and body-centred rows, creating a short-period staircase.

Bulk lattice: Body-centred cubic
Plane normal: [210]
What remains: Ridges and troughs

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 BCC(210) with numbered adsorption sites — The outlined reference cell has |a₁| = 6.4175 Å, |a₂| = 2.8700 Å, and γ = 90.00° for the Fe slab used in the drawing. Fractional coordinates mean r_∥ = ua₁ + va₂.

ridge ontop1-fold
Above an atom on the upper ridge.
(u,v) = (7/10, 1/2)s = s₁ · support shell: mean Δz = +0.000 Å from L1
Projection of the L1 atom at (7/10, 1/2).
Not named in ASE
lower-row ontop1-fold
Above an exposed atom below the ridge.
(u,v) = (2/5, 0)s = s₁ · support shell: mean Δz = -0.642 Å from L1
Projection of the L2 atom at (2/5, 0).
Not named in ASE
ridge bridge2-fold
Between adjacent atoms along the ridge.
(u,v) = (7/10, 0)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1
Periodic midpoint of L1 (17/10, 1/2) and L1 (17/10, -1/2).
Not named in ASE
ridge-to-trough bridge2-fold
Between a ridge atom and a lower trough atom.
(u,v) = (11/20, 1/4)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.321 Å from L1
Periodic midpoint of L1 (17/10, -1/2) and L2 (7/5, -1).
Not named in ASE
mixed-layer trough pocket4-fold
A four-atom pocket assembled from different heights.
(u,v) = (11/20, 3/4)s = (Σᵢ sᵢ) / 4 · support shell: mean Δz = -0.321 Å from L1
Least-squares centroid of the 4-atom projected shell: L1 (-3/10, 1/2), L1 (-3/10, -1/2), L2 (-3/5, 0), L2 (-3/5, -1).
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 projected trough contains neighbours from several heights, so lateral coordination alone understates the local environment.

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 the cubic lattice, \(d_{210}=a/\sqrt{5}\), and [210] is \(\cos^{-1}(2/\sqrt{5})\approx26.6^\circ\) from [100].

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

fe = bulk("Fe", "bcc", a=2.87, cubic=True)
slab = surface(fe, (2, 1, 0), 10, vacuum=10)

Things that are easy to misread

Reading trough atoms as coplanar with the ridge.
Reusing FCC high-index site names without recalculating the neighbours.