Faceting preferences for Au(N) and Pd(N) nanoclusters with high-symmetry motifs

The structural preferences of nanoparticles are important for understanding their chemical properties and potential applications, and remain widely debated. Based on recent experimental observations, we present calculations on the stability of high-symmetry AuN and PdN clusters of various structural motifs, performing a systematic search of faceting preferences using mathematical constructs, a semi-empirical potential with two different parameter sets, and a quasi-Newtonian minimisation technique. We have studied the preferred ratios of (100) and (111) faces for two experimentally observed nanostructures: (a) FCC crystals, comparing octahedra with 8 (111) faces to cuboctahedra where the vertices have been systematically removed (for N < 1500); and (b) Marks-decahedra, with differing "stellation" depths (for N < 6000). For PdN and AuN we see preference towards minimisation of (100) surfaces using the parameter sets of both Cleri and Rosato [Cleri and Rosato, Phys. Rev. B: Condens. Matter Mater. Phys., 1993, 48, 22] and Baletto et al. [Baletto et al., J. Chem. Phys., 2002, 116, 3856]. Fully stellated Marks-decahedra are found to be unfavourable at large sizes, with truncated facets identified which are similar to recent experimental observations. We find however that these stellations are deeper in PdN particles than AuN. Truncated-octahedra are found to prefer much reduced (100) surfaces and increased (111) surface areas.