Cluster Self-Organization of Intermetallic Systems: Precursor Clusters K3, K4, K5, and K6 in the Self-Assembly of Crystalline Structures Sm6Pd10Sn11-mS54 and Sm3Pd5Sn5-mS52

Using computational methods (ToposPro software package), a combinatorial–topological analysis and modeling of cluster self-assembly are carried out. The crystal structures Sm6Pd10Sn11-mS54 (a = 17.386 Å, b = 4.514 Å, c = 16.926 Å, β = 121.38°, V = 1134.46 Å3, C2/m) and Sm3Pd5Sn5-mS52 (a = 17.205 Å, b = 4.520 Å, c = 14.206 Å, β = 99.71°, V = 1088.8 Å3, C2/m) are studied. For Sm6Pd10Sn11-mS54, 48 variants for identifying cluster structures with the number of clusters N = 3 (15 variants), 4 (22 variants), and 5 (11 variants) are established. The self-assembly of a crystal structure involving a cluster is considered. Cluster K6-1 = 0@6(Sm2Sn2Pd2) has the form of a double tetrahedron with the center at C1(4e, –1); cluster K6-2 = 0@6(Sm2Pd2Sn2) is a double tetrahedron with the center at C2(4f, –1); cluster K5 = 1Sn@4(Pd2Sn2) has the form of two linked three-atom PdSn2 rings with a common Sn atom at the 2c position with 2/m symmetry; cluster K4 = 0@4 (Pd2Sn2) is a tetrahedron with the center at the 4g position with symmetry 2; and cluster K3 = 0@3(SmSnPd) is formed by three atomic rings with the center at the 8j position. For Sm3Pd5Sn5-mS52, 41 variants of identifying cluster structures with the number of clusters N = 3 (21 variants) and 4 (20 variants) are established. The self-assembly of the crystal structure involving a cluster is considered. Cluster K6-1 = 0@6(Sm2Pd2Sn2) is a double tetrahedron with the center at C1(4e, –1); cluster K6-2 = 0@6(Sm2Pd2Sn2) is a double tetrahedron with the center at C2(8j, 1); cluster K5 = 1Sn@4(Pd2Sn2) consists of linked PdSn2 rings with a common Sn atom at position 2a with 2/m symmetry; and cluster K3 = 0@3(SnPd2) is formed by three rings with the center at position 4h (1/2, 1/3, 1/2). The symmetry and topological code of the self-assembly processes of 3D structures from precursor clusters was reconstructed in the following form: primary chain → layer → framework.