G. D. Ilyushin

Structures of the ZrZn22 family: suprapolyhedral nanoclusters, methods of self-assembly and superstructural ordering

A combinatorial topological analysis is carried out by means of the program package TOPOS4.0 [Blatov (2006), IUCr Comput. Commun. Newsl. 7, 4-38] and the matrix self-assembly is modeled for crystal structures of the ZrZn22 family (space group Fd3m, Pearson code cF184), including the compounds with superstructural ordering. A number of strict rules are proposed to model the crystal structures of intermetallics as a network of cluster precursors. According to these rules the self-assembly of the ZrZn22-like structures was considered within the hierarchical scheme: primary polyhedral cluster --> zero-dimensional nanocluster precursor --> one-dimensional primary chain --> two-dimensional microlayer --> three-dimensional microframework (three-dimensional supraprecursor). The suprapolyhedral cluster precursor AB2X37 of diameter approximately 12 A and volume approximately 350 A3 consists of three polyhedra (one AX16 of the 43m point symmetry and two regular icosahedra BX12 of the 3m point symmetry); the packing of the clusters determines the translations in the resulting crystal structure. A novel topological type of the two-dimensional crystal-forming 4,4-coordinated binodal net AB2, with the Schläfli symbols 3636 and 3366 for nodes A and B, is discovered. It is shown that the ZrZn22 superstructures are formed by substituting some atoms in the cluster precursors. Computer analysis of the CRYSTMET and ICSD databases shows that the cluster AB2X37 occurs in 111 intermetallics belonging to 28 structure types.

New types of multishell nanoclusters with a Frank-Kasper polyhedral core in intermetallics.

A comprehensive study of the occurrence of two-shell clusters with the first shell as a Frank-Kasper polyhedron Z12, Z14, Z15, or Z16 (Frank-Kasper nanoclusters) is performed for 22,951 crystal structures of intermetallics containing only metal atoms. It is shown that besides the familiar Bergman and Mackay clusters, two more types of high-symmetrical icosahedron-based nanoclusters are rather frequent; they both have a 50-atom second shell. Moreover, two types of high-symmetrical Frank-Kasper nanoclusters with a Friauf-polyhedron (Z16) core are revealed; these nanoclusters have 44 and 58 atoms in the second shell. On the contrary, Z14 and Z15 Frank-Kasper polyhedra have been found to be rare and improper to form distinct nanoclusters in crystals. The second shells of Frank-Kasper nanoclusters have been revealed possessing their own stability: they can be realized in nanoclusters with different internal polyhedra and can shift around the core shell. The role of Frank-Kasper nanoclusters in assembling intermetallic crystal structures is illustrated by several examples.

γ‑Brass Polyhedral Core in Intermetallics: The Nanocluster Model

Using the TOPOS program package, 26-atom nanoclusters of the γ-brass (Cu5Zn8) type (0@4@22 or 0@8@18) were found in 5918 crystal structures of cubic intermetallics. The nanocluster models were built for all the intermetallics using a recently developed algorithm implemented into TOPOS. The relations of the structures based on the 0@4@22 core are explored as a result of migration of atoms between different shells of the nanoclusters. It is shown that the 0@4@22 nanoclusters frequently occur as building units of intermetallics of different composition and structure type. Regularities in chemical composition of 702 γ-brass-type nanoclusters were found within both the nanoclusters approach (multishell structure) and the nested-polyhedra model. A database containing all topological types of γ-brass nanoclusters is created with which one can search for the corresponding atomic configuration in any intermetallics.

Orthotetrahedral crystal structures My(TO4)z (T = Si, Ge, P, As, S, Se, Cl, Br, I): geometrical-topological analysis, quasi-binary representation, and comparison with the AyXz compounds by the method of coordination sequences

Abstract Topological analysis of atomic nets in the crystal structures of 284 anhydrous inorganic salts My(TO4)z (T = Si, Ge, P, As, S, Se, Cl, Br, I) containing isolated orthogroups TO4 was performed by means of the program package TOPOS 3.2. The topological relations were found among the My(TO4)z salts and 1164 topological types of the binary compounds AyXz at the two levels: grey isomorphism and partial isotypism. Using the method of coordination sequences nearly a half (47.5%) of the ortho structures in the quasi-binary representation My[T]z were found to match 27 frequent topological types of the binary compounds (NaCl, NiAs, FeB, α-Al2O3, etc.). The model of cation arrays was shown to sometimes disagree with the model of atomic nets while comparing; the reasons of such disagreements were discussed.

Computer simulation of the self-assembly of paulingite crystal structure from suprapolyhedral nanocluster precursors K6, K16, and K20

AbstractA combinatorial and topological analysis of the paulingite crystal structure (a = 35.093 Å, V = 43 217 Å3; sp. gr. Im

New method for computer analysis of complex intermetallic compounds and nanocluster model of the samson phase Cd3Cu4

\bar 3

Cluster self-organization theory for crystal-forming systems: The geometrical and topological model of formation, selection, and evolution of precursor nanoclusters of molecular and framework compounds

m) has been performed by computational methods using the TOPOS program package. The application of the complete expansion of the 3D factor graph into nonintersecting substructures of a cluster type has revealed three types of nanocluster precursors in the tetrahedral T framework: K6, K16, and K20; they consist of 6T, 16T, and 20T tetrahedra, which are involved in the matrix self-assembly of the crystal structure. The translated cell contains 44 clusters (8 K6+ 24 K16 + 12 K20). None of the clusters have shared T tetrahedra. Three cluster precursors form a crystallochemically complex structure with extraframework Na+/Ca2+ and K+/Ba2+ cations which carry out two structural functions as templates (stabilizing nanocluster precursors) and as spacers (filling the voids between precursors). The self-assembly code of the 3D structure from complementary bound nanocluster precursors is completely reconstructed in the form primary chain → microlayer → microframework → … framework.

Cluster self-organization of inorganic crystal-forming systems: Templated nanocluster precursors and self-assembly of framework MT structures of A/B,Zr silicates (A = Na, K; B = Ca, Sr)

New types of 63-atom two-layer nanoclusters based on the icosahedral core and having the maximum symmetry D3d or Th in crystal have been found using the method of the nanocluster analysis (the TOPOS program package) in the database that was created of crystal structures of intermetallides containing 20319 compounds. It has been shown that these nanoclusters may participate in assembling the crystal and/or be present there as stable fundamental configurations of atoms. The possibilities of the method of the nanocluster analysis have been demonstrated by the example of calculating the chemical composition of the crystal presented as an ensemble of nanoclusters.