Sibasankar Panigrahy

FacetLab

Build FCC metal nanoparticles atom by atom, see which facets, edges and vertices they expose, and estimate ligand coverage.

What do the site types and GCN mean?

An atom's coordination number CN\mathrm{CN} counts its nearest neighbours: 12 in the bulk, 9 on a {111} terrace, 8 on a {100} terrace, 7 on edges and 6 or fewer on vertices. The generalized coordination number also weights each neighbour by how coordinated it is itself,

CN‾i=∑j∈nn(i)CNjCNmax⁡,CNmax⁡=12,\overline{\mathrm{CN}}_i = \sum_{j \in \mathrm{nn}(i)} \frac{\mathrm{CN}_j}{\mathrm{CN}_{\max}}, \qquad \mathrm{CN}_{\max} = 12,

and tracks adsorption energies on metal surfaces almost linearly, which is why it is used to rank catalytic sites (Calle-Vallejo et al., 2015). Infinite terraces have CN‾=7.5\overline{\mathrm{CN}} = 7.5 on {111} and 6.676.67 on {100}.

About FacetLab

Gold and other FCC nanoparticles are rarely spheres. Their facets, edges and vertices decide where ligands, citrate or reactants bind. FacetLab builds the exact lattice structure for the common shapes, classifies every surface atom, and exports coordinates ready for a simulation.

Python package and command line: pip install git+https://github.com/siba-p/nanomatkit, then nanomatkit np --shape truncated_octahedron -k 2 -o Au201.xyz.

Method

Construction. FCC sites r=a2(i,j,k)\mathbf{r} = \tfrac{a}{2}(i,j,k) with i+j+ki+j+k even, kept if

∣x∣+∣y∣+∣z∣≤S{111},max⁡(∣x∣,∣y∣,∣z∣)≤M{100}.|x|+|y|+|z| \le S \quad \{111\}, \qquad \max(|x|,|y|,|z|) \le M \quad \{100\}.

Wulff shape: plane distances scale with surface energy,

MS/3=γ100γ111.\frac{M}{S/\sqrt{3}} = \frac{\gamma_{100}}{\gamma_{111}}.

Equivalent diameter from the FCC volume per atom a3/4a^3/4:

d=(6π Na34)1/3.d = \left(\frac{6}{\pi}\,\frac{N a^3}{4}\right)^{1/3}.

Ligands: Nlig=σgAN_\mathrm{lig} = \sigma_g A, with AA summed over surface atoms (34a2\tfrac{\sqrt3}{4}a^2 per {111}-like site, a22\tfrac{a^2}{2} per {100} site).

Checks: magic numbers 13, 55, 147, 309 (cuboctahedra) and 38, 201, 586, 1289 (truncated octahedra); Au201\mathrm{Au}_{201} has 122 surface atoms.

  1. F. Calle-Vallejo et al., Science 350, 185 (2015) (generalized coordination numbers).
  2. L. D. Marks & L. Peng, J. Phys.: Condens. Matter 28, 053001 (2016) (nanoparticle shape).