Mixed-index BCT · Distorted triangular rows
BCT(111)
BCT(111) is a tetragonally distorted counterpart of BCC(111). Its three-index label does not imply three equal Cartesian intercept lengths because c differs from a.
- Plane
- (111)
- Layer character
- Mixed basal–axial · open
- ASE slab builder
surface
From bulk to facet
How BCT(111) is cut
(111)
The plane meets both basal axes after a and the c axis after c. The body-centred basis inserts a second registry halfway between equivalent planes.
- Bulk lattice
- Body-centred tetragonal
- Plane normal
- reciprocal vector G(111)
- What remains
- Distorted triangular 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.
- outermost ontop1-fold
Above an atom in the highest distorted row.
(u,v) = (0.5923, 0.1845)s = s₁ · support shell: mean Δz = +0.000 Å from L1Projection of the L1 atom at (0.5923, 0.1845).
Not named in ASE - lower-row ontop1-fold
Above an exposed atom in the next height level.
(u,v) = (0.2979, 0.5959)s = s₁ · support shell: mean Δz = -1.042 Å from L1Projection of the L2 atom at (0.2979, 0.5959).
Not named in ASE - row bridge2-fold
Between nearest periodic atoms in the upper row.
(u,v) = (0.0923, 0.1845)s = (s₁ + s₂) / 2 · support shell: mean Δz = +0.000 Å from L1Periodic midpoint of L1 (-0.4077, -0.8155) and L1 (0.5923, -0.8155).
Not named in ASE - cross-row bridge2-fold
Between atoms on consecutive height levels.
(u,v) = (0.9451, 0.3902)s = (s₁ + s₂) / 2 · support shell: mean Δz = -0.521 Å from L1Periodic midpoint of L1 (0.5923, 0.1845) and L2 (1.2979, 0.5959).
Not named in ASE - mixed-height hollow3-fold
A three-atom pocket supported by several corrugated rows.
(u,v) = (0.2979, 0.9292)s = (Σᵢ sᵢ) / 3 · support shell: mean Δz = -1.042 Å from L1Least-squares centroid of the 3-atom projected shell: L1 (-0.4077, 1.1845), L2 (-0.7021, 0.5959), L3 (-0.9964, 1.0072).
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
Alternating corner and body-centred planes create a dense sequence of height levels. Projected triangular motifs therefore require explicit layer labels.
Cell
Geometry at a glance
The spacing is \(d_{111}^{-2}=2/a^2+1/c^2\); the odd body-centred phase inserts atom-bearing sublayers at half this crystallographic spacing.
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 import Atoms
from ase.build import surface
a, c = 3.25, 4.95
indium = Atoms("In2", scaled_positions=[(0, 0, 0), (.5, .5, .5)],
cell=[(a, 0, 0), (0, a, 0), (0, 0, c)], pbc=True)
slab = surface(indium, (1, 1, 1), 10, vacuum=10)
Things that are easy to misread
- Treating [111] as the Cartesian plane normal when a and c differ.
- Assuming BCT(111) retains the threefold metric symmetry of a cubic (111) face.