Geometrical optimization of Cu-Au-Pd clusters based on the construction of inner cores

Abstract

The trimetallic cluster has become a hot topic in the field of basic scientific research due to its special catalytic, magnetic and chemical activities. It is very important to determine the stable structures of clusters. In order to optimize the stable structure of large size Cu-Au-Pd cluster, a modification algorithm of adaptive immune optimization algorithm based on the construction of inner cores, called AIOA-IC algorithm, is proposed. The only difference between AIOA and AIOA-IC lies in their starting structures. Instead of generating the starting structure randomly in AIOA, an inner core in the AIOA-IC method is used for generating the starting structure. Several motifs, such as decahedron, icosahedron, face centered cubic, six-fold pancake structure, and Leary tetrahedron, are randomly selected as the inner cores. The size of the inner core is determined according to the cluster size. The Gupta potential based on the second moment approximation of tight binding potential is used to describe the interatomic interaction between Cu-Au-Pd clusters, and the corresponding potential parameters, such as the cohesive energy, lattice constants, and elastic constants are obtained by fitting the experimental values. To test the efficiency of the proposed algorithm, the stable structure of Ag-Pd-Pt cluster with 60 atoms is optimized. The results show that the new structure has lower energy than the cluster reported in the literature. It can be seen that the AIOA-IC algorithm has a stronger ability to search for the potential energy surface of the Gupta potential. Furthermore, the proposed algorithm is used to optimize the stable structures of 38-atom and 55-atom Cu-Au-Pd clusters. The structures of the investigated Cu6AunPd32-n, CunAu6Pd32-n and CunAu32-nPd6 (n=1-31) clusters can be categorized into three types:five-fold, six-fold, and truncated octahedron. Moreover, it is found that the compositions of Cu, Au and Pd atoms in the trimetallic clusters affect the structural type of the cluster. However, the Cu13AunPd42-n, CunAu13Pd42-n, and CunAu42-nPd13 (n=1-41) clusters each have a structure of complete Mackay icosahedron. Furthermore, the order parameter results show that Cu, Au and Pd atoms each have a significant segregation phenomenon. For the 147-atom Cu12Au93Pd42 cluster, the structure is also of an icosahedron. The central atom is Au, and the inner shell and sub-outer shell are occupied by 12 Cu and 42 Pd atoms, respectively. The outer shell is filled with 92 Au atoms. The results show that the Cu, Pd and Au atoms tend to be distributed in the inner shell, sub-outer shell, and outer shell, respectively. This can be further explained by the results of the atomic radius and the surface energy.