Abstract
The geometric and topological analyses of the K44In80-hR366 (space group R\(\bar {3},\) a = b = 17.214 Å, c = 44.612 Å) and K34In82-cF464 (space group Fd\(\bar {3}\)m, a = 24.241 Å, V= 14244.64 Å3) crystal structures are implemented by computer-based methods (ToposPro program). The framework-forming 142-atom icosahedral nanocluster K142 is determined by the method of the complete decomposition of the 3D atomic network of the K44In80 intermetallide into cluster structures. The K142 nanoclusters with the symmetry \(\bar {3}\) are three-layer with the shell composition of 0@12In@32(K26In6)@98(K26In72). The first two shells form the Bergman cluster. The third shell of 98 atoms is formed by 5-, 6-, and 7-atom rings (554.638.76) and contained 98 apexes, 270 edges, and 174 faces. The K142 nanoclusters form closely packed two-dimensional layers 36 located with a shift along [001]. The distance between the K142 cluster centers determines the translation vector value ahex = 17.214 Å. Voids in the 3D framework are occupied by 0@K6In2 spacers. Suprapolyhedral clusters K141 with the symmetry –43m comprising four Bergman clusters 0@12In@32 (K20In12), each of which have the symmetry \(\bar {3}\)m, are formed in the K34In82 intermetallide. Voids in the 3D framework are occupied by In(In4) spacers in the form of tetrahedra with the central atom In, which have the symmetry of –43m. For the K44In80 and K34In82 intermetallides, the symmetric and topological code for the self-assembly processes of the 3D structure from nanocluster precursors K142 and K141 is determined in the following form: primary chain → layer → framework.
Similar content being viewed by others
REFERENCES
Villars, P. and Cenzual, K., Pearson’s Crystal Data-Crystal Structure Database for Inorganic Compounds (PCDIC), Materials Park, OH: ASM Int., 2007.
Inorganic Crystal Structure Database (ICSD), Germany: Fachinformationszentrum Karlsruhe, USA: Natl. Inst. Standard Technol.
Brussone, G., The D13 structure type in intermetallic compounds, Acta Crystallogr., B, 1969, vol. 25, pp. 1206–1207.
Blase, W. and Cordier, G., Crystal structure of potassium indium (8/11), K8In11, Z. Kristallogr., 1991, vol. 194, pp. 150–151.
Lin, B. and Corbett, J.D., Synthesis and characterization of the new cluster phase K39In80. Three K-In compounds with remarkably specific and transferable cation dispositions, Inorg. Chem., 2003, vol. 42, pp. 8768–8772.
Cordier, G. and Mueller, V., Crystal structure of potassium indium (22-x/39+x) (x = 0.67), K21.33In39.67, Z. Kristallogr., 1992, vol. 198, pp. 302–303.
Cordier, G. and Mueller, V., Crystal structure of potassium indium (17/41), K17In41, Z. Kristallogr., 1993, vol. 205, pp. 353–354.
Shevchenko, V.Ya., Blatov, V.A., and Ilyushin, G.D., Cluster self-organization of intermetallic systems: K66 and K130 clusters for the self-assembly of the K78In160-hP238 crystal structure and K17 clusters for the self-assembly of the K8In11-hR114 crystal structure, Glass Phys. Chem., 2020, in press.
Blatov, V.A., Shevchenko, A.P., and Proserpio, D.M., Applied topological analysis of crystal structures with the program package ToposPro, Cryst. Growth Des., 2014, vol. 14, pp. 3576–3585.
Ilyushin, G.D., Theory of cluster self-organization of crystal-forming systems. Geometrical-topological modeling of nanocluster precursors with a hierarchical structure, Struct. Chem., 2012, vol. 20, no. 6, pp. 975–1043.
Ilyushin, G.D., Modeling of the self-organization processes in crystal-forming systems. Tetrahedral metal clusters and the self-assembly of crystal structures of intermetallic compounds, Crystallogr. Rep., 2017, vol. 62, pp. 670–683.
Blatov, V.A., Ilyushin, G.D., and Proserpio, D.M., New types of multishell nanoclusters with a Frank-Kasper polyhedral core in intermetallics, Inorg. Chem., 2011, vol. 50, pp. 5714–5724.
Ilyushin, G.D., Symmetry and topology code of the cluster self-assembly of intermetallic compounds \({\text{A}}_{{\text{2}}}^{{[{\text{16}}]}}{\text{B}}_{{\text{4}}}^{{[{\text{12}}]}}\) of the Friauf families Mg2Cu4 and Mg2Zn4, Crystallogr. Rep., 2018, vol. 63, pp. 543–552.
Ilyushin, G.D., Modeling of self-organization processes in crystal-forming systems: symmetry and topology code for the cluster self-assembly of crystal structures of intermetallic compounds, Russ. J. Inorg. Chem., 2017, vol. 62, pp. 1730–1769.
Shevchenko, V.Ya., Blatov, V.A., and Ilyushin, G.D., Modeling the processes of self-organization in crystal-forming systems: New two-layer clusters–precursors 0@(Na2Cd6)@(Na12Cd26) and 0@(Na3Cd6)@(Na6Cd35) for the self-assembly of the Na26Cd141–hP168 crystal structure, Glass Phys. Chem., 2019, vol. 45, no. 5, pp. 311–316.
Shevchenko, V.Ya., Medrish, I.V., Ilyushin, G.D., and Blatov, V.A., From clusters to crystals: scale chemistry of intermetallics, Struct. Chem., 2019, vol. 30, no. 6, pp. 2015–2027.
Funding
This study was supported by the Ministry of Science and Higher Education as part of a state order of the Federal Research Center “Crystallography and Photonics” of the Russian Academy of Sciences and the Russian Science Foundation (RSF no. 20-13-00054).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by D. Marinin
Rights and permissions
About this article
Cite this article
Shevchenko, V.Y., Blatov, V.A. & Ilyushin, G.D. Cluster Self-Organization of Intermetallic Systems: New Three-Layer Cluster K142 for the Self-Assembly of the K44In80-hR366 Crystal Structure and the Bergman Tetracluster K141 for the Self-Assembly of the K34In82-cF464 Crystal Structure. Glass Phys Chem 46, 370–377 (2020). https://doi.org/10.1134/S1087659620050107
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1087659620050107