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Frequency distribution and selection of space groups in inorganic crystal chemistry

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Abstract

Statistical analysis of modern structural databases on inorganic crystals and minerals is carried out to elucidate the classification of crystal structure distributions over space groups. The known fact about extremely uneven occupation of space groups is confirmed; the relative abundance of all and, in particular, 24 most frequent groups (>1%) is derived, and the latter are noted to belong to holohedral and centrosymmetric classes. The data on occupation of extremely rare and empty space groups are analyzed and refined separately, which allows the reduction of a number of unreliable structural data. The theoretical analysis of empirical regularities is performed from the standpoint of filling rules for special structural positions (Wyckoff positions) and the symmetry of lattice complexes. It is shown that only combined consideration of different symmetry rules and restrictions provides an explanation for most regularities observed in occupation of symmetry point groups.

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References

  1. Modern Crystallography in four Volumes [in Russian], Vol. 2, B. K. Vainshtein, V. M. Fridkin, and V. L. Indenbom, Nauka, Moscow (1979).

    Google Scholar 

  2. V. Novatskii, Supplement to the Translation of the Book by P. Niggli “Stereochemistry”; [in Russian], IL, Moscow (1949).

    Google Scholar 

  3. A. I. Kitaigorodskii, Organic Crystal Chemistry [in Russian], Akad. Nauk SSSR, Moscow (1955).

    Google Scholar 

  4. A. Mackay, Acta Crystallogr., 22, No. 3, 29 (1967).

    Article  Google Scholar 

  5. V. K. Belsky and P. M. Zorkii, Kristallografiya, 15, No. 4, 704 (1970).

    Google Scholar 

  6. V. K. Belsky and P. M. Zorkii, Acta Crystallogr., A33, No. 6, 1004 (1977).

    Google Scholar 

  7. N. Yu. Chernikova and P. M. Zorkii, J. Struct. Chem.., 20, No. 3, 384–390 (1977).

    Article  Google Scholar 

  8. N. Yu. Chernikova, V. K. Belsky, and P. M. Zorkii, ibid, 31, No. 4, 661–666 (1990).

    Article  Google Scholar 

  9. P. M. Zorkii and N. Yu. Chernikova, Itogi Nauki i Tekhniki, Crystal Chemistry, 19, 237–279, VINITI, Moscow (1985).

    Google Scholar 

  10. W. Y. C. Wilson, Acta Crystallogr., A44, No. 5, 715 (1988).

    CAS  Google Scholar 

  11. W. Y. C. Wilson, ibid., A46, No. 9, 742 (1990).

    CAS  Google Scholar 

  12. N. Padmaja, S. Ramakumar, and M. A. Visvamitra, ibid., 725.

  13. L. N. Kuleshova and M. Yu. Antipin, Usp. Khim., 68, No. 1, 3 (1999).

    Google Scholar 

  14. N. V. Podberezskaya, Chemistry, Symmetry, Geometry of Crystals [in Russian], in: Vestnik Nizhegorodskogo Universiteta, Ser. Fiz. Tverd. Tela, vyp.1(9), 24 (2006).

    Google Scholar 

  15. V. S. Urusov and T. N. Nadezhdina, Vestn. Mosk Gos. Univ., Ser. 4, Geologiya, No. 5, 52 (2006).

    Google Scholar 

  16. A. D. Mighell and J. R. Rodgers, Acta Crystallogr., A36, No. 2, 321 (1980).

    CAS  Google Scholar 

  17. W. H. Baur and D. Kassner, ibid., B48, No. 4, 356 (1992).

    CAS  Google Scholar 

  18. V. A. Blatov, A. P. Shevchenko, and V. N. Serezhkin, Kristallografiya, 38, No. 6, 149 (1993).

    CAS  Google Scholar 

  19. V. A. Blatov, A. P. Shevchenko, and V. N. Serezhkin, ibid., 42, No. 5, 773 (1997).

    CAS  Google Scholar 

  20. R. E. Marsh, Acta Crystallogr., B55, No. 6, 931 (1999).

    CAS  Google Scholar 

  21. R. E. Marsh, ibid., B61, No. 3, 359 (2005).

    CAS  Google Scholar 

  22. A. L. Spek, J. Appl Cryst., 36, No. 1, 7 (2003).

    Article  CAS  Google Scholar 

  23. R. E. Marsh, Acta Crystallogr., B42, No. 2, 193 (1986).

    CAS  Google Scholar 

  24. R. E. Marsh and F. H. Herbstein, ibid., B44, No. 1, 77 (1988).

    CAS  Google Scholar 

  25. R. E. Marsh and I. Bernal, ibid., B51, No. 3, 300 (1995).

    CAS  Google Scholar 

  26. R. E. Marsh, ibid., B53, No. 2, 317 (1997).

    CAS  Google Scholar 

  27. F. H. Herbstein and R. E. Marsh, ibid., B54, No. 5, 677 (1998).

    CAS  Google Scholar 

  28. F. H. Herbstein, ibid., B56, No. 4, 547 (2000).

    CAS  Google Scholar 

  29. R. E. Marsh and A. L. Spek, ibid., B57, No. 6, 800 (2001).

    CAS  Google Scholar 

  30. W. H. Baur and E. Tillmanns, ibid., B46, No. 1, 95 (1986).

    Google Scholar 

  31. D. A. Clemente and A. Marzotto, ibid., B60, No. 3, 287 (2004).

    CAS  Google Scholar 

  32. O. V. Yakubovich, Ya. M. Still, P. G. Gavrilenko, and V. S. Urusov, Kristallografiya, 50, No. 2, 226 (2004).

    Google Scholar 

  33. K. Cenzual, L. M. Celato, M. Penzo, and E. Parthe, Acta Crystallogr., B47, No. 4, 433 (1991).

    CAS  Google Scholar 

  34. J. Donohue, ibid., A41, No. 2, 203 (1985).

    CAS  Google Scholar 

  35. R. Srinivastan, ibid., A48, No. 6, 917 (1992).

    Google Scholar 

  36. P. Brock and J. D. Dunitz, ibid., A47, No. 6, 854 (1991).

    CAS  Google Scholar 

  37. C. Frondel, Silica Minerals, vol. III of Dana’s System of Mineralogy, 7th edn., J. Wiley, New York (1962).

  38. V. S. Urusov, in: Smirnov Collection-2007 [in Russian], VINITI RAN, Moscow (2007), pp. 11–40.

    Google Scholar 

  39. S. F. Mason, Nature, 311, 19 (1984).

    Article  CAS  Google Scholar 

  40. V. S. Urusov, Dokl. Akad Nauk, 386, No. 3, 379 (2002).

    Google Scholar 

  41. V. I. Vernadskii, Crystallography [in Russian], V. S. Urusov (ed.), Nauka, Moscow (1988).

    Google Scholar 

  42. A. V. Shubnikov, Izv. Ross. Akad Nauk, Ser. 6, 16, Nos. 1–18, 515 (1922).

    CAS  Google Scholar 

  43. V. V. Dolivo-Dobrovol’skii, Zapiski VMO, 116, No. 1, 7 (1987).

    Google Scholar 

  44. S. K. Filatov, High Temperature Crystal Chemistry [in Russian], Nauka, Leningrad (1990).

    Google Scholar 

  45. Yu. A. Pyatenko, Zapiski VMO, 94, No. 6, 655 (1965).

    Google Scholar 

  46. V. S. Urusov, Vestn. Mosk Gos. Univ., Ser. 4, Geologiya, No. 5, 3 (1991).

    Google Scholar 

  47. P. Niggli, Von der Symmetrie und den Baugezetzen der Kristalle, Leipzig (1941).

  48. R. V. Galiulin and S. E. Sigalev, Dokl. Akad. Nauk, 293, No. 1, 99 (1987).

    CAS  Google Scholar 

  49. V. N. Serezhkin, D. V. Pushkin, and L. B. Serezhkina, ibid., 413, No. 1, 60 (2007).

    Google Scholar 

  50. E. Heiner and H. Sowa, Physics Data, Nr. 16-3. ISSN 0344-8401, Karlsruhe (1985).

  51. V. V. Dolivo-Dobrovol’skii, Zapiski VMO, 131, No. 1, 3 (2002).

    Google Scholar 

  52. P. M. Zorkii, Symmetry of Molecules and Crystal Structures [in Russian], Mosk. Gos. Univ., Moscow (1986).

    Google Scholar 

  53. G. Filippini and A. Gavezzotti, Acta Crystallogr., B48, No. 2, 230 (1992).

    CAS  Google Scholar 

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    V. S. Urusov & T. N. Nadezhina

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  1. V. S. Urusov
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  2. T. N. Nadezhina
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Correspondence to V. S. Urusov.

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Original Russian Text Copyright © 2009 by V. S. Urusov and T. N. Nadezhina

Translated from Zhurnal Strukturnoi Khimii, Vol. 50, Supplement, pp. S26–S43, 2009.

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Urusov, V.S., Nadezhina, T.N. Frequency distribution and selection of space groups in inorganic crystal chemistry. J Struct Chem 50 (Suppl 1), 22–37 (2009). https://doi.org/10.1007/s10947-009-0186-9

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