Enumeration of surface site nuclearity and shape in a database of intermetallic low-index surface facets
Unnatti Sharma, Angela Nguyen, John R. Kitchin, Zachary W. Ulissi and Michael J. Janik, “Enumeration of surface site nuclearity and shape in a database of intermetallic low-index surface facets”, Journal of Catalysis 440, 115795 (2024). https://doi.org/10.1016/j.jcat.2024.115795
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Question
Ordered intermetallics made of a minority late transition metal (the “active” metal) in a majority post-transition metal host can expose surfaces where the active atoms form isolated clusters of a well-defined size and arrangement, which is attractive for controlling selectivity (for example, Pd1 and Pd3 sites in Pd-Zn intermetallics for acetylene semi-hydrogenation). The paper asks how to systematically find which intermetallic compositions and surface terminations expose active-metal clusters of a given nuclearity (number of active atoms in an isolated surface cluster) and shape, and whether these site geometries correlate with bulk properties in a way that narrows the search (Sharma et al. 2024).
Approach
The authors chose five post-transition metal hosts (Zn, Al, Ga, In, Cd) and six late transition metals treated as active (Pd, Pt, Rh, Ru, Ir, Ag). The active/inactive labels rest broadly on hydrocarbon and hydrogen binding and are noted not to apply to oxygen binding or oxidizing conditions. Structures were taken from the AFLOW library: of 88,672 binaries with formation energies below -0.1 eV, 3,477 belonged to the chosen host/active pairs, and 1,323 lay within 0.05 eV of their convex hull. Pymatgen enumerated all unique slabs with Miller indices below three and varied terminations, giving 29,002 surfaces.
Each slab went through a new Surface Nuclearity Calculator. A Voronoi-based neighbor analysis (with ASE covalent-radius cutoffs and periodic images) builds an adjacency matrix; surface atoms are identified by reduced coordination, so low-index stepped surfaces are handled like flat ones. Restricting the matrix to surface active atoms gives a graph whose connected components are the active ensembles; component size is the nuclearity, and shapes are classed by graph isomorphism with a shape-ID per isomorphism class. To detect clusters that do not terminate, the nuclearity of a single cell is compared with that of a 2 x 2 supercell: equal values mean finite nuclearity, a factor of 2 means “semi-finite” (1D-infinite stripes), and a factor of 4 means 2D-infinite (a connected mesh). The cutoff radius affects which atoms count as surface atoms and neighbors, so it influences the result. Computations were parallelized with Dask, and the results are released as an interactive catalog and code (github.com/ulissigroup/NuclearityCalculation).
Key findings
About 80% of the 29,002 surfaces had finite nuclearities, ranging from 0 to 16, and monomeric (nuclearity 1) sites made up 60% of the finite cases; about 14,000 surfaces were identified as stable “single atom” intermetallic surfaces. The most stable bulk structures (by formation enthalpy) frequently exposed surfaces with nuclearity below 4. Bravais lattice was informative: simple cubic, face-centered orthorhombic, triclinic, BCC, monoclinic and FCC lattices showed narrow ranges concentrated at low nuclearity, while rhombohedral structures had the highest average nuclearity but a narrow range (0 to 6), with about 40% of their surfaces showing dimers (versus 4% for hexagonal and cubic and 10% for FCC). Hexagonal, cubic and FCC lattices were where monomers were most likely.
Trends versus composition were consistent across host/active pairs: the range of nuclearities grew with the active mole fraction, with a broad spike near 0.33 and a narrow constriction between 0.4 and 0.5, the latter attributed to stable alternating A-B structures that expose monomers. The highest active fraction showing any finite nuclearity was 0.89. Shape analysis up to nuclearity 5 found 21 distinct shapes, with the number of shapes rising rapidly with nuclearity; some shapes occur only in narrow composition windows. Because shapes are defined by connectivity, visually different sites can share a shape-ID. The authors suggest, for example, that a search for triangular sites can skip structures with active fraction below 0.67 except at 0.5 and 0.33.
Significance
The tool turns site geometry, often discussed qualitatively as ensemble effects, into a searchable descriptor for screening intermetallic catalysts, and shows that bulk lattice type and composition can prune the search. The authors list caveats: the analysis is limited to AFLOW structures, ignores surface segregation and reconstruction, and does not tell which facet a particle will expose; one facet can expose several nuclearities, and step versus terrace sites of the same nuclearity may behave differently. They propose extending the method to ternary and higher intermetallics and testing nuclearity as a selectivity descriptor (for example, small ensembles that allow C-H bond formation while avoiding C-C coupling and coking). Although “machine-learned potential” appears among the keywords, the text reports no machine-learned potential calculations.