Skip to main content
SpringerLink
Log in

Statistics of Interatomic Distances

  • Chapter
Crystallographic Statistics in Chemical Physics

Part of the book series: Inorganic Chemistry Concepts ((INORGANIC,volume 12))

  • 72 Accesses

Abstract

An ideal crystal is usually understood to be a regular array of ions or atoms. However, if we speak of positions of these particles with respect to their crystallographic origin, physical reality forces us to make some approximations. An experiment based on the diffraction of X-ray or neutron radiation by crystal makes it possible to obtain information on the positions of atoms or ions in the form of coordinates of local maxima of electron densities.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Schoenflies, A.: Kristallsysteme und Kristallstruktur, Leipzig 1891

    Google Scholar 

  2. Jorgensen, Ch. K.: Int. Rev. Phys. Chem. 1, 225 (1981)

    Article  Google Scholar 

  3. Weissenberg, K.: Z. Kristallogr. 62, 52 (1925)

    Google Scholar 

  4. Valach, F., Kohout, J., Dunaj-Jurco, M., Hvastijovâ, M., Ga2o, J.: J. Chem. Soc. Dalton 1868 (1979)

    Google Scholar 

  5. Tideswell, N. W., Kruse, F. H., Mc Cullough, D. J.: Acta Crystallogr. 10, 99 (1957)

    Article  CAS  Google Scholar 

  6. Furuseth, S., Selte, K., Kjekshus, A.: Acta Chem. Scand. 19, 257 (1965)

    Article  CAS  Google Scholar 

  7. Wickoff, R. W. G.: Crystal Structures, Vol. 1, p. 110, New York—London—Sydney, Interscience Publ. John Wiley and Sons 19632

    Google Scholar 

  8. Pauling, L.: Phys. Rev. 54, 899 (1938)

    Article  CAS  Google Scholar 

  9. Mott, N. F., Jones, N.: The Theory of the Properties of Metals and Alloys, Oxford, Oxford University Press 1936

    Google Scholar 

  10. Pauling, L.: The Nature of the Chemical Bond, Ithaca Cornell University Press 1960

    Google Scholar 

  11. Goldschmidt, V. M.: Geometrische Verteilungsgesetze der Elemente, Oslo 1926

    Google Scholar 

  12. Pauling, L.: Proc. Natl. Acad. Sci. 18, 293 (1932)

    Article  CAS  Google Scholar 

  13. Pauling, L., Brockway, L. O., Beach, J. Y.: J. Am. Chem. Soc. 57, 2705 (1935)

    Article  CAS  Google Scholar 

  14. Pauling, L.: J. Am. Chem. Soc. 69, 542 (1947)

    Article  CAS  Google Scholar 

  15. Shannon, R. D., Prewitt, C. D.: Acta Crystallogr., Sect. B, 25, 925 (1969)

    Article  CAS  Google Scholar 

  16. Peterson, J. R., Cunningham, B. B.: Inorg. Nucl. Chem. Lett. 3, 327 (1967)

    Article  CAS  Google Scholar 

  17. Peterson, J. R., Cunningham, B. B.: J. Inorg. Nucl. Chem. 30, 1775 (1968)

    Article  CAS  Google Scholar 

  18. Kalman, A.: J. Chem. Soc., Chem. Commun. 1857 (1971)

    Google Scholar 

  19. Seitz, F.: The Modern Theory of Solids, New York, Mc Craw-Hill Book Co. 1940

    Google Scholar 

  20. Fukunaga, O., Fujita, T.: J. Solid State Chem. 8, 331 (1973)

    Article  CAS  Google Scholar 

  21. Greis, O., Petzel, T.: Z. Anorg. Allgem. Chem. 403, 1 (1974)

    Article  Google Scholar 

  22. Knop, O., Carlow, J. S.: Can. J. Chem. 52, 2175 (1974)

    Article  CAS  Google Scholar 

  23. Wolfe, R. W., Newnham, R. E.: J. Electrochem. Soc. 116, 832 (1969)

    Article  CAS  Google Scholar 

  24. Mc Carthy, G. J.: Mater. Res. Bull. 6, 31 (1971)

    Article  Google Scholar 

  25. Shannon, R. D.: Acta Crystallogr., Sect. A“, 32, 751 (1976)

    Article  Google Scholar 

  26. Silva, R. J., Mc Dowell, Keller, W. J., Tarrant, J. R.: Inorg. Chem. 13, 2233 (1974)

    Article  CAS  Google Scholar 

  27. Allen, F. H., Bellard, S., Brice, M. D., Cartwright, B. A., Doubleday, A., Higgs, H., Hummelink, T., Hummelink-Peters, B. G., Kennard, O., Motherwell, W. D. S., Rodgers, J. R. and Watson, D. G.: Acta Crystallogr., Sect. B, 35, 2331 (1979)

    Article  Google Scholar 

  28. Kennard, O., Watson, D. G., Town, W. G.: J. Chem. Doc. 13, 14 (1973)

    Google Scholar 

  29. Allen, F. H., Kennard, O., Motherwell, W. D. S., Town, W. G. and Watson, A. D.: J. Chem. Doc. 13, 119 (1973)

    Article  CAS  Google Scholar 

  30. Allen, F. H., Kennard, O., Motherwell, W. D. S., Town, W. G., Watson, D. G., Scott, T. Y. and Larson, A. C.: J. Appl. Crystallogr. 7, 73 (1974)

    Article  CAS  Google Scholar 

  31. Allen, F. H.: Acta Crystallogr., Sect. B, 37, 890 (1981)

    Article  Google Scholar 

  32. Allen, F. H., Isaacs, N. W., Kennard, O., Motherwell, E. D. S., Petersen, R. C., Town, W. G. and Watson, D. G.: J. Chem. Doc. 13, 211 (1973)

    Article  CAS  Google Scholar 

  33. Eisen, M.: Introduction to Mathematical Probability Theory, New Jersey, Prentice-Hall 1969

    Google Scholar 

  34. Feller, W.: An Introduction to Probability Theory and its Applications, Vol. 1, New York, Wiley 1950, Vol. 2, New York, Wiley 1966

    Google Scholar 

  35. Hennequin, P., Tortrat, A.: Théorie des probeblités et quel ques applications, Paris, Mason 1965

    Google Scholar 

  36. Cramér, H.: Mathematical Methods of Statistics, Princeton 1946

    Google Scholar 

  37. Rao, R. C.: Linear Statistical Inference and its Applications, New York, Wiley 1973

    Book  Google Scholar 

  38. Wilks, S.: Mathematical Statistics, New York, Wiley 1962

    Google Scholar 

  39. Guenther, W. C.: Concepts of Statistical Inference, Tokyo, Düsseldorf, Johannesburg, London, Mexico, New Delhi, Panama, Rio de Janeiro, Singapore, Sydney, International Student Edition, Mc Graw-Hill, Kogakusha, Ltd. 19732

    Google Scholar 

  40. Kendall, M. G.: The Advenced Theory of Statistics, Vol. 1, London, Charles Griffin and Co!Ltd. 1951

    Google Scholar 

  41. Richter, H.: Wahrscheinlichkeitstheorie, Berlin, Göttingen, Heidelberg 1956

    Google Scholar 

  42. Warden, B. L.: Mathematische Statistik, Berlin, Göttingen, Heidelberg 1957

    Google Scholar 

  43. Lehman, E. L.: Testing Statistical Hypothesis, New York, Wiley 1959

    Google Scholar 

  44. Hald, A.: Statistical Tables and Formulas, New York, John Wiley and Sons, Inc. 1952

    Google Scholar 

  45. Murray-Rust, P., Raftery, J.: J. Mol. Graphics 3, 50 (1985)

    Article  CAS  Google Scholar 

  46. Doms, L., Van Hemelrijk, D., Van de Mieroop, W., Lenstra, A. T. H. and Geise, H. J.: Acta Crystallogr., Sect. B, 41, 270 (1985)

    Article  Google Scholar 

  47. International Tables for Crystallography, Vol. A, Space-Group Symmetry, Dordrecht, Boston, D. Reidel Publishing Comp. 1983

    Google Scholar 

  48. Delaunay, B. N., Galinlin, R. V., Dolbin, R. V., Zalgaller, V. A. and Stogrin, M. I.: Dokl. Akad. Nauk SSSR 209, 309 (1973)

    Google Scholar 

  49. Delaunay, B. N.: Z. Kristallogr. 84, 109 (1933)

    Google Scholar 

  50. Nowacki, W.: Z. Kristallogr. 85, 331 (1933)

    Google Scholar 

  51. Delone, B.: Acta Crystallogr., Sect. A, 21, 28 (1966)

    Google Scholar 

  52. Minkowski, H.: Algemeine Lehrsätze über die konvexen Polyeder. In Gesammelte Abhandlungen, Leipzig 1911 Chelsea Reprint 1967

    Google Scholar 

  53. Grünbaum, B.: Convex Polytopes, New York, Interscience 1967

    Google Scholar 

  54. Grünbaum, B., Shephard, G. C.: Bull. London Math. Soc. 1, 257 (1969)

    Article  Google Scholar 

  55. Jucovié, E.: Konvexné mnohosteny, Bratislava, Veda 1981

    Google Scholar 

  56. Delone, B. N., Dolbilin, N. P., Stogrin, M. J., Galjulin, M. J.: Dokl. Akad. Nauk SSSR 227, 19 (1976)

    Google Scholar 

  57. Loeb, A. L.: J. Solid State Chem. 1, 237 (1970)

    Article  CAS  Google Scholar 

  58. Statistics of Interatomic Distances

    Google Scholar 

  59. Laves, F.: Crystal structure and atomic size, in: Theory of Alloys, Cleveland, Ohio, Amer. Soc. Met. 1956

    Google Scholar 

  60. Pearson, W. B.: A Handbook of Lattice Spacings and Structures of Metals and Alloys 2, p. 1, Oxford, Pergamon Press 1967

    Google Scholar 

  61. Valach, F., Koren, B., Sivÿ, P. and Melnik, M.: Structure and Bonding 55, 103 (1983)

    Google Scholar 

  62. Cambridge Crystallographic Data Centre (1984), University Chemical Laboratory, Cambridge, England

    Google Scholar 

  63. SIEMENS PBS 4004, MEB METHODENBANK 1973

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Physics and Nuclear Technique, Slovak Technical University, 81237, Bratislava, ČSSR

    Dr. Fedor Valach

  2. Institute of Chemical Technology, Computing Centre, 16628, Prague-6, ČSSR

    Dr. Jan Ondráček

  3. Department of Inorganic Chemistry, Slovak Technical University, 81237, Bratislava, ČSSR

    Dr. Milan Melník

Authors
  1. Dr. Fedor Valach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dr. Jan Ondráček
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dr. Milan Melník
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Valach, F., Ondráček, J., Melník, M. (1988). Statistics of Interatomic Distances. In: Crystallographic Statistics in Chemical Physics. Inorganic Chemistry Concepts, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-01599-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-01599-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-01601-5

  • Online ISBN: 978-3-662-01599-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation