Structure of icosahedral nanoobjects

Glass Physics and Chemistry

Volumn 31, Issue 6, 2005, Pages 823-828

  Shevchenko, V Ya ^a   Samoilovich, M I ^b   Talis, A L ^a   Madison, A E ^a  

^a GREBENSHCHIKOV INSTITUTE OF SILICATE CHEMISTRY   (Russian Federation)

^b OAO Central Research Technological Institute tekhnomash   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; CRYSTALLOGRAPHY; SYNTHESIS (CHEMICAL);

ICOSAHEDRAL NANOOBJECTS; NANOSTATES;

NANOSTRUCTURED MATERIALS;

EID: 29344456442     PISSN: 10876596     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10720-005-0132-7     Document Type: Article

References (45)

1. Fedorov, E.S., Symmetry of Regular Systems of Figures, Zap. S.-Peterb. Mineral. O-va, Ser. 2,1891, no. 4, pp. 1-227.
2. Schoenflies, A., Kristallsysteme und Kristallstruktur, Leipzig: Teubner, 1891.
3. Wigner, E.P., The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Commun. Pure Appl. Math., 1960, vol. 13, no. 1, pp. 1-14.
4. Bernal, J.D. and Carlisle, C.H., Fields of Application of Generalized Crystallography, Kristallografiya, 1968, vol. 13, no. 5, pp. 927-951.
5. Mackay, A.L., Generalized Crystallography, J. Mol. Struct. (THEOCHEM), 1995, vol. 336, nos. 2-3, pp. 293-303.
6. Mackay, A.L., Generalized Crystallography, Struct. Chem., 2002, vol. 13, nos. 3-4, pp. 215-220.
7. Manoharan, V.N., Elsesser, M.T., and Pine, D.J., Dense Packing and Symmetry in Small Clusters of Microspheres, Science (Washington, D.C., 1883-), 2003, vol. 301, pp. 483-487.
8. Rossi, G., Rapallo, A., Mottet, C., Fortunelli, A., Baletto, F., and Ferrando, R., Magic Polyicosahedral Core-Shell Clusters, Phys. Rev. Lett., 2004, vol. 93, p. 105503.
9. 13 Icosahedron, J. Chem. Soc., Dalton Trans., 2001, pp. 2731-2748.
10. Kondo, K. and Takayannagi, K., Synthesis and Characterization of Helical Multi-Shell Gold Nanowires, Science (Washington, D.C., 1883-), 2000, vol. 289, pp. 606-608.
11. Gülseren, O., Ercolessi, F., and Tosatti, E., Non-Crystal-line Structures of Ultrathin Unsupported Nanowires, Phys. Rev. Lett., 1998, vol. 80, pp. 3775-3778.
12. Dress, A.W.M. and Brinkmann, G., Phantasmagorical Fulleroids, Match, 1996, vol. 33, pp. 87-100.
13. Delgado Friedrichs, O. and Deza, M., More Icosahedral Fulleroids, in Discrete Mathematical Chemistry, Hausen, P., Fowler, P., and Zheng, M., Eds., DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 2000, vol. 51, pp. 97-115.
14. Hervieu, M., Mellène, B., Retoux, R., Boudin, S., and Raveau, B., The Route to Fullerenoid Oxides, Nature Mater., 2004, vol. 3, pp. 269-273.
15. Ugarte, D., Curling and Closure of Graphitic Networks under Electron-Beam Irradiation, Nature (London), 1992, vol. 359, pp. 707-709.
16. 154 Oxide Clusters into Vesicles, Nature (London), 2003, vol. 426, pp. 59-62.
17. Colomer, J.F., Henrard, L., Van Tendeloo, G., Lucas, A., and Lambin, P., Study of the Packing of Double-Walled Carbon Nanotubes onto Boundless by Transmission Electron Microscopy and Electron Diffraction, J. Mater. Sci., 2004, vol. 14, pp. 603-606.
18. Conway, J.H., Hardin, R.H., and Sloane, N.J.A., Packing Lines, Planes, Etc.: Packings in Grassmannian Spaces, Exp. Math., 1996, vol. 5, pp. 139-159.
19. Shevchenko, V.Ya., Khasanov, O.L., Yur'ev, G.S., and Ivanov, Yu.F., Coexistence of Cubic and Tetragonal Structures in an Yttria-Stabilized Zirconia Nanoparticle, Neorg. Mater., 2001, vol. 37, pp. 950-952.
20. Shevchenko, V.Ya., Khasanov, O.L., Madison, A.E., and Lee, J.Y., Investigation of the Structure of Zirconia Nanoparticles by High-Resolution Transmission Electron Microscopy, Fiz. Khim. Stekla, 2002, vol. 28, no. 5, pp. 459-464
21. [Glass Phys. Chem. (Engl. transl.), 2002, vol. 28, no. 5, pp. 322-325].
22. Alok Singh and Tsai, A.P., On the Cubic W Phase and Its Relationship to the Icosahedral Phase in Mg-Zn-Y Alloys, Scr. Mater., 2003, vol. 49, no. 2, pp. 143-148.
23. Sun, W. and Hiraga, K., Al-Ni-Ru Icosahedral Quasicrystal and Coexisting Decagonal Quasicrystals with 0.4 nm Periodicity, Studied by Atomic-Resolution Electron Microscopy Observations, J. Non-Cryst. Solids, 2004, vols. 334-335, pp. 194-197.
24. O'Keeffe, M., Eddaoudi, M., Li, H., Reineke, T., and Yaghi, O.M., Frameworks for Extended Solids: Geometrical Design Principles, J. Solid State Chem., 2000, vol. 152, pp. 3-20.
25. Yaghi, O.M., O'Keeffe, M., Ockwig, N.W., Chae, H.K., Eddaoudi, M., and Kim, J., Reticular Synthesis and the Design of New Materials, Nature (London), 2003, vol. 423, pp. 705-714.
26. Férey, G., Mellot-Draznieks, C., and Loiseau, T., Real, Virtual, and Not Yet Discovered Porous Structures Using Scale Chemistry and/or Simulation: A Tribute to Sten Andersson, Solid State Sci., 2003, vol. 5, no. 1, pp. 79-94.
27. Dubrovin, B.A., Fomenko, A.T., and Novikov, S.P., Modern Geometry: Methods and Applications, Part 2: The Geometry and Topology of Manifolds, Graduate Texts in Mathematics, New York: Springer-Verlag, 1985, vol. 104.
28. Shevchenko, V.Ya., Samoilovich, M.I., Talis, A.L., and Madison, A.E., Nanostructures with Coherent Boundaries and the Local Approach, Fiz. Khim. Stekla, 2004, vol. 30, no. 6, pp. 732-749
29. [Glass Phys. Chem. (Engl. transi.), 2004, vol. 30, no. 6, pp. 537-550].
30. Shevchenko, V.Ya., Samoilovich, M.I., Talis, A.L., Madison, A.E., and Shudegov, V.E., Geometrical Structural Complexes of Zr02 Nanoparticles, Fiz. Khim. Stekla, 2005, vol. 31, no. 2, pp. 252-269
31. [Glass Phys. Chem. (Engl. transl.), 2005, vol. 31, no. 2, pp. 187-200].
32. Volkov, V.V., Van Tendeloo, G., Tsirkov, G.A., Cherkashina, N.V., Vargaftik, M.N., Moiseev, I.I., Novotortsev, V.M., Kvit, A.V., and Chuvilin, A.L., Long- and Short-Distance Ordering of the Metal Cores of Giant Pd Clusters, J. Cryst. Growth, 1996, vol. 163, pp. 377-387.
33. Mackay, A.L., A Dense Non-Crystallographic Packing of Equal Spheres, Acta Crystallogr., 1962, vol. 15, pp. 916-918.
34. Coxeter, H.S.M., Regular Polytopes, New York: Dower, 1973.
35. Pearson, W.B., The Crystal Chemistry and Physics of Metals and Alloys, New York: Wiley, 1972.
36. Puyraimond, F., Quiquandon, M., Gratias, D., Tillard, M., Belin, C., Quivy, A., and Calvayrac, Y., Atomic Structure of the (Al,Si)CuFe Cubic Approximant Phase, Acta Crystallogr., Sect. A: Found. Crystallogr., 2002, vol. 58, pp. 391-403.
37. Abe, E., Yan, Y., and Pennycook, S.J., Quasicrystals as Cluster Aggregates, Nature Mater., 2004, vol. 3, pp. 759-767.
38. Fuller, R.B., Synergetics: Explorations in the Geometry of Thinking, New York: Macmillan, 1975.
39. Fuller, R.B., Synergetics 2: Further Explorations in the Geometry of Thinking, New York: Macmillan, 1979.
40. Sadoc, J.F. and Rivier, N., Hierarchy and Disorder in Non-Crystalline Structures, Philos. Mag. B., 1987, vol. 55, pp. 537-573.
41. Sadoc, J.F. and Mosseri, R., Icosahedral Order, Space, and Quasicrystals, in Aperiodicity and Order, Jaric, M.V. and Gratias, D., Eds., Boston: Academic, 1989, vol. 3, pp. 163-189.
42. Sadoc, J.F. and Rivier, N., Boerdijk-Coxeter Helix and Biological Helices, Eur. Phys. J. B, 1999, vol. 12, pp. 309-318.
43. Sadoc, J.F., Helices and Helix Packings Derived from the {3, 3, 5} Polytope, Eur. Phys. J. E, 2001, vol. 5, pp. 575-582.
44. Lord, E.A. and Ranganathan, S., Sphere Packing, Helices and the Polytope {3, 3, 5}, Eur. Phys. J. D, 2001, vol. 15, pp. 335-343.
45. Conway, J.H. and Sloane, N.J.A., Sphere Packings, Lattices and Groups, Comprehensive Studies in Mathematics, vol. 290, New York: Springer-Verlag 1999, 3rd ed.