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Terms of parity and distortion of coordination polyhedra in inorganic crystal chemistry

  • The Bridging and Bonding Role of Crystallography
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Abstract

The coordination number parity law is formulated: the coordination polyhedra (CP) with the odd number of vertices, except for 3 (CP is a triangle), occur far less often than the polyhedra with the even number of vertices. CP with the odd number of vertices, except for the triangle, cannot be regular and have at least two different types of vertices and two sets of interatomic lengths. The main and first c.n. always keeps parity. A CP distortion due to crystal chemical causes tends to be minimum, obeying the pseudo-symmetry laws. A CP distortion, other things being equal, leads to an increase in the average bond length as compared to the regular polyhedron (distortion theorem). The value of the increase in the average interatomic distance depends on the degree of distortion by the linear or (for a very strong distortion) the square dependence. The histograms of the distribution frequencies of the interatomic lengths have a positive deviation from the Gauss normal distribution law. A free molecule or a complex ion having a distortion due to the directed configuration of chemical bonds or to the electronic effects of the Jahn-Teller type for transition metals, maintain it in the crystal structure as well. During the polymerization of radicals there arise specific distortion effects due to a various coordination environment of the bridging and apical ligands. One of the most general rules of the CP distortion is associated with a less symmetric and less homogenous environment of anions in comparison with that of cations and a higher polarizability of anions. An important exception from this rule is the group of compounds with the so called anion-centered tetrahedra in which more symmetrical positions are occupied, as a rule, by anions in the center of the tetrahedra.

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References

  1. V. S. Urusov and N. N. Eremin, Kristallografiya, No. 4, 634–648 (2004).

    Google Scholar 

  2. V. S. Urusov and N. N. Eremin, Atomistic Computer Simulation of the Structure and Properties of Crystals, their Defects, and Solid Solutions [in Russian], GEOS, Moscow (2012).

    Google Scholar 

  3. S. V. Borisov, J. Struct. Chem. 43, No. 5, 734–742 (2002).

    Article  CAS  Google Scholar 

  4. S. V. Borisov and N. V. Podberezkaya, Stable Cationic Frameworks in the Structures of Fluorides and Oxides [in Russian], Nauka, Novosibirsk (1984).

    Google Scholar 

  5. L. A. Aslanov, Structures of Atoms, Molecules, and Crystals [inRussian], Izd. MGU, Moscow (1985).

    Google Scholar 

  6. Landmark Papers. Structure Topology, No. 2, selected by F. C. Hawthorne, Mineralogical Society of Great Britain and Ireland (2006).

  7. Modern Crystallography. Structure of Crystals [in Russian], Vol. 2, Nauka, Moscow (1979).

  8. W. H. Baur and D. Kassner, Acta Crystallogr., B48, No. 4, 356–369 (1992).

    Article  CAS  Google Scholar 

  9. V. S. Urusov and T. N. Nadezhina, J. Struct. Chem., 50, Suppl., S22–S37 (2009).

    Article  CAS  Google Scholar 

  10. E. S. Fedorov, Zap. AN Fiz.-Mat. Otd., 14, No. 2, 1–148 (1903).

    Google Scholar 

  11. E. V. Chuprunov, Kristallografiya, 52, No. 1, 5–16 (2007).

    Google Scholar 

  12. A. Werner, Neerere Anschaungen auf dem Gebeite der anorganischen Chemie., Braunschweig (1905).

    Google Scholar 

  13. W. Kossel, Ann. Phys., 42, 229 (1916).

    Article  Google Scholar 

  14. A. Kapustinsky, Z. Phys. Chemie B, 8, S. 72–80 (1930).

    Google Scholar 

  15. A. F. Kapustinsky,, Zhurn. Fiz. Khim., 5, 73–76 (1934).

    Google Scholar 

  16. R. C. Menzies, J. Chem. Soc., 1755–1758 (1934).

    Google Scholar 

  17. A. E. Van Arkel and J. H. de Boer, Chemische Binding Als Electrostatische Erscheinung, Leipzig (1931).

    Google Scholar 

  18. Yu. V. Khodakov, Elements of the Electrostatic Chemistry [in Russian], Goskhimtekhizdat, Moscow (1934).

    Google Scholar 

  19. A. E. Fersman, Geochemistry [in Russian], Vol. 3, ONTI-KHIMTEORET, Leningrad (1937).

    Google Scholar 

  20. I. I. Shafranovskii, New Ideas in Genetric Mineralogy [in Russian], Nauka, Leningrad (1983), pp. 113–117.

    Google Scholar 

  21. F. C. Frank and J. C. Kasper, Acta Cryst., 11, 184–190 (1958).

    Article  CAS  Google Scholar 

  22. P. I. Kripyakevich, Structural Types of Intermetallic Compounds [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  23. E. A. Lord, A. L. Mackay, and S. Ranganathan, New Geometry for New Materials, University Press, Cambridge (2006).

    Google Scholar 

  24. V. A. Blatov and V. V. Serezhkin, Acta Cryst., A53, 144–160 (1997).

    Article  CAS  Google Scholar 

  25. P. Niggli, Z. Kristallogr., 56, No. 12, 167 (1921).

    Google Scholar 

  26. P. Niggli, Von der Symmetry und von den Baugezetzen der Kristalle, Leipzig (1941).

    Google Scholar 

  27. P. Niggli, Grundlagen der Stereochemie, Verlag E. Birkhäuser, Basel (1945).

    Book  Google Scholar 

  28. V. M. Gol’dshmidt, Crystal Chemistry [in Russian], ONTI-KHIMTEORET, Leningrad (1937).

    Google Scholar 

  29. V. S. Urusov, Theoretical Crystal Chemistry [in Russian], Izd. MGU, Moscow (1987).

    Google Scholar 

  30. P. A. Sandomirskii and N. V. Belov, Crystal Chemistry of Mixed Anion Radicals [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  31. F. Liebau, Structural Chemistry of Silicates: Structure, Bonding, and Classification, Springer-Verlag (1985).

    Book  Google Scholar 

  32. V. S. Urusov, Vest. MGU. Ser. Geol., No. 4, pp. 3–19.

  33. A. V. Shubnikov, Izv. Ros. AN, Ser. 6, 16, No. 1–18, 515–524 (1991).

    Google Scholar 

  34. A. V. Shubnikov, Law of Symmetry and Crystal Chemistry, in: O. Gassel, Crystal Chemistry [in Russian], ONTI, Leningrad (1922), pp. 190–197.

    Google Scholar 

  35. A. V. Shubnikov and V. A. Koptsik, Symmetry in Science and Art [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  36. V. S. Urusov and N. L. Smirnova, Comput. Math. Applicat., Nos. 5–8, 563–567 (1988).

    Google Scholar 

  37. D. I. Brown, Chem. Soc. Rev., No. 7, 359–376 (1978).

    Google Scholar 

  38. R. Allmann, Monatsh.Chem., 106, 779–793 (1975).

    Article  CAS  Google Scholar 

  39. V. S. Urusov, Z. Krystallogr., 218, 709–719 (2003).

    Article  CAS  Google Scholar 

  40. V. S. Urusov, Dokl. AN, 419, No. 3, 358–362 (2008).

    Google Scholar 

  41. V. S. Urusov and V. N. Serezhkin, Kristallografiya, 54, No. 2, 218–222 (2009).

    Google Scholar 

  42. V. N. Serezhkin and V. S. Urusov, J. Struct. Chem., 50, No. 5, 861–866 (2009).

    Article  CAS  Google Scholar 

  43. W. Baur, Acta Cryst., B34, 1751–1756 (1978).

    Article  CAS  Google Scholar 

  44. V. N. Serezhkin, D. V. Pushkin, and L. B. Serezhkina, Dokl. AN, 413, No. 1, 60–65 (2007).

    Google Scholar 

  45. S. V. Krivovichev and S. K. Filatov, Crystal Chemistry of Minerals and Inorganic Compounds with Complexes of Anion-Centered Metal Octahedral, Univ. Press, St. Petersburg (2001).

    Google Scholar 

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  1. Lomonosov Moscow State University, Moscow, Russia

    V. S. Urusov

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Original Russian Text © 2014 V.S. Urusov.

__________

Translated from Zhurnal Strukturnoi Khimii, Vol. 55, Supplement 1, pp. S94–S110, 2014.

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Urusov, V.S. Terms of parity and distortion of coordination polyhedra in inorganic crystal chemistry. J Struct Chem 55, 1277–1292 (2014). https://doi.org/10.1134/S0022476614070117

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