Abstract
The concept of crystalline “module,” that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.
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D. J. Wales, M. A. Miller, and T. R. Walsh, Nature, 1998, 394, 758.
J. S. Bradley, in Clusters and Colloids (From Theory to Applications), Ed. G. Schmid, VCH, Weinheim, 1994, 459.
P. H. Gaskell, in Topics in Applied Physics, Glassy Metals II, Eds. H. Beck and H.-J. Guntherodt, Springer-Verlag, Berlin, 1983, 53, 5.
J. Friedel, J. de Phys., Coll. C2, Suppl., 1977, 38, C2-1.
Phan Van An and N. A. Bulienkov, Mat. Sci. Research Int., 2000, 6, 28.
N. Rösch and G. Pacchioni, in Clusters and Colloids (From Theory to Applications), Ed. G. Schmid, VCH, Weinheim, 1994, 5.
N. N. Medvedev, Metod Voronogo--Delone v issledovanii structury nekristallicheskikh sistem [Method of Voronoi--Delone in the Studies of the Structure of Non-Crystalline Systems], Izd. Sib. Otd. RAN, Novosibirsk, 2000, 209 pp. (in Russian).
N. A. Bulienkov, in Vestnik Nizhegorod. Un-ta im. N. I. Lobachevskogo, Ser. Fizika tv. tela [Nizhny Novgorod Univ. Bull., Solid State Physics Ser.], 1998, Iss. 1, 19 (in Russian).
A. L. Makkei, in Strukturnye issledovaniya kristallov [Studies on Crystal Structure], Nauka, Moscow, 1996, 430 (in Russian).
W. A. de Heer, Rev. Modern Phys., 1993, 65, 612.
M. Schmidt, R. Kusche, B. von Issendorf, and H. Haberland, Nature, 1998, 393, 238.
G. Bertsch, Science, 1997, 277, 1619.
J. A. Barker, J. de Phys., Coll. C2, Suppl., 1977, 38, C2-37.
R. V. Galiulin, Kristallograficheskaya geometriya [Crystallographic Geometry], Nauka, Moscow, 1984, 134 pp. (in Russian).
N. V. Belov, Struktura ionnykh kristallov i metallicheskikh faz [Structure of Ionic Crystals and Metal Phases], Izd. AN SSSR, Moscow, 1947, 236 pp. (in Russian).
N. A. Bulienkov, in Quasicrystals and Discrete Geometry. The Fields Inst. Monogr., Ed. J. Patera, Am. Mathem. Soc., Providence (RI), 1998, 10, 67.
E. S. Fedorov, Simmetriya i struktura kristallov [Symmetry and Crystal Structure], Izd. AN SSSR, Moscow-Leningrad, 1949, 630 pp. (in Russian).
D. Zhang and R. G. Cooks, Int. J. of Mass Spectrometry, 2000, 195/196, 667.
N. A. Bulienkov, Dokl. Akad. Nauk SSSR, 1985, 284, 1392 [Dokl. Chem., 1985 (Engl. Transl.)].
J. D. Bernal, Kristallografiya, 1962, 7, 507 [Sov. Phys.-Crystallogr., 1962, 7 (Engl. Transl.)].
J. D. Bernal and S. H. Carlyle, Kristallografiya, 1968, 13, 927 [Sov. Phys.-Crystallogr., 1968, 13 (Engl. Transl.)].
A. L. Mackay, in Symmetry: Unifying Human Understanding, Ed. J. Hargittai, Pergamon Press, New York, 1986, 21.
N. A. Bulienkov, Kristallografiya, 1988, 33, 422 [Sov. Phys.-Crystallogr., 1988, 33 (Engl. Transl.)].
N. A. Bulienkov, Kristallografiya, 1990, 35, 147 [Sov. Phys.-Crystallogr., 1990, 35 (Engl. Transl.)].
N. A. Bulienkov, Tez. dokl. II s'ezda biofizikov Rossii [Abstrs. IInd Russ. Biophys. Meeting] (Moscow, August 23–27, 1999), Moscow, 1999, 3, 761 (in Russian).
N. A. Bulienkov, Biofizika, 1991, 36, 181 [Biophysics, 1991, 36 (Engl. Transl.)].
J.-M. Lehn, Supramolecular Chemistry, Concepts and Perspectives, VCH, Weinheim-New York-Basel-Cambridge-Tokyo, 1995.
N. A. Bulienkov and Phan Van An, CD-Proc. 12th Int. Conf. on Composite Materials (Paris, July 5–9, 1999), Paris, 1999, 1.
N. A. Bulienkov, Dokl. Akad. Nauk SSSR, 1986, 290, 605 [Dokl. Chem., 1986 (Engl. Transl.)].
Yu. A. Osip'yan, V. D. Negrii, and N. A. Bulienkov, Izv. Akad. Nauk SSSR, Ser. Fiz., 1987, 51, 1458 [Bull. Acad. Sci. USSR, Phys. Ser., 1987, 51 (Engl. Transl.)].
G. Schmid, in Clusters and Colloids (From Theory to Applications), Ed. G. Schmid, VCH, Weinheim, 1994, 1.
N. A. Bulienkov and V. S. Kraposhin, Pis'ma Zh. Teor. Eksp. Fiz., 1993, 19, 1 [JETP Lett., 1993, 19 (Engl. Transl.)].
N. A. Bulienkov, Kristallografiya, 1990, 31, 155 [Sov. Phys.-Crystallogr., 1990, 31 (Engl. Transl.)].
B. K. Teo and N. J. A. Sloane, Inorg. Chem., 1985, 24, 4545.
T. P. Martin, Phys. Rep., 1996, 273, 199.
V. A. Engel'gardt, Poznanie yavlenii zhizni [Cognition of Life Phenomena], Nauka, Moscow, 1985, 303 pp. (in Russian).
L. Pauling, The Nature of the Chemical Bond, Cornell Univ. Press, Ithaca-New York, 1939.
B. K. Teo, H. Dang, C. F. Campana, and H. Zhang, Polyhedron, 1998, 17, 617.
B. K. Teo and H. Zhang, Inorg. Chem., 1991, 30, 3115.
B. K. Teo, X. Shi, and H. Zhang, J. Chem. Soc., Chem. Commun., 1992, 1195.
P. H. Gaskell, Phil. Mag., 1975, 32, 211.
A. L. Mackay, Acta Crystallogr., 1962, 15, 916.
V. L. Indenbom, N. V. Belov, and N. N. Neronova, Kristallografiya, 1960, 5, 496 [Sov. Phys.-Crystallogr., 1960, 5 (Engl. Transl.)].
N. Doraiswammy and L. L. Marks, Phil. Mag., 1995, B71, 291.
B. E. Williams, H. S. Kong, and J. T. Glass, J. Mat. Res., 1990, 5, 801.
R. V. Galiulin, Kristallografiya, 1998, 43, 366 [Crystallogr. Repts., 1998, 43 (Engl. Transl.)].
H. S. Coxeter, Regular Complex Polytopes, Cambridge University Press, London, 1974.
B. K. Vainshtein, V. M. Fridkin, and V. L. Indenbom, Sovremennaya kristallografiya [Modern Crystallography], Nauka, Moscow, 1979, 2, 359 pp. (in Russian).
D. L. D. Caspar and A. Klug, Cold Spring Harbor Symp. Quant. Biol., 1962, 27, 11.
H. S. M. Coxeter, Introduction to Geometry, J. Wiley and Sons, Inc., New York-London, 1961.
N. V. Belov, Kristallografiya, 1954, 4, 268 [Sov. Phys.-Crystallogr., 1954, 4 (Engl. Transl.)].
F. Banhart and P. M. Ajayan, Nature, 1996, 382, 433.
R. Tenne, L. Margulis, M. Genu, and G. Hodes, Nature, 1992, 310, 444.
R. Tenne, Adv. Mater., 1995, 7, 965.
P. A. Parilla, A. C. Dillon, K. M. Jones, and D. L. Schultz, Nature, 1999, 397, 114.
M. V. Klassen-Neklyudova, Mekhanicheskoe dvoinikovanie kristallov [Mechanical Twinning of Crystals], Izd. AN SSSR, Moscow, 1960, 259 pp. (in Russian).
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Bulienkov, N.A., Tytik, D.L. Modular design of icosahedral metal clusters. Russian Chemical Bulletin 50, 1–19 (2001). https://doi.org/10.1023/A:1009524314066
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DOI: https://doi.org/10.1023/A:1009524314066