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The prediction and interpretation of bond lengths in crystals

  • M. O'Keeffe
Conference paper
Part of the Structure and Bonding book series (STRUCTURE, volume 71)

Abstract

The concept of bond valence and its correlation with bond length are reviewed. It is shown how to augment bond valence sums at an atom with other constraints so that bond lengths can be predicted for a given topology. These constraints can be read directly from the connectivity matrix for the structure. The physical reasons for the constraints are analysed, and this analysis leads in turn to a reformulation of Pauling's electrostatic valence sum rule. The apparent valences of atoms, calculated as a sum of bond valences derived from bond lengths, are often significantly different from the actual valences. It is demonstrated that such observations are often diagnostic of non-bonded repulsions. Limitations and possible extensions of the method are outlined.

Keywords

Bond Length Bond Valence Connectivity Matrix Inverse Spinel Inverse Spinel Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Brown ID (1978) Chem. Soc. Rev. 7: 359CrossRefGoogle Scholar
  2. 2.
    Brown ID (1981) In: O'Keeffe M, Navrotsky A (eds) Structure and bonding in crystals II. Academic, New YorkGoogle Scholar
  3. 3.
    O'Keeffe M, Hyde BG (1985) Structure and Bonding 61: 79Google Scholar
  4. 4.
    Pauling L (1947) J. Amer. Chem. Soc. 69: 542CrossRefGoogle Scholar
  5. 5.
    Byström A, Wilhelmi K-A (1951) Acta Chem. Scand. 5: 1003CrossRefGoogle Scholar
  6. 6.
    Bragg WL (1920) Phil. Mag. 40: 169Google Scholar
  7. 7.
    Slater JC (1965) Quantum Theory of Molecules and Solids 2, McGraw-Hill, New YorkGoogle Scholar
  8. 8.
    Shannon RD, Prewitt CT (1969) Acta Crystallogr. B25: 925Google Scholar
  9. 9.
    O'Keeffe M (1981) In: O'Keeffe M, Navrotsky A (eds) Structure and bonding in crystals I. Academic, New YorkGoogle Scholar
  10. 10.
    Pauling L (1960) The nature of the chemical bond, Cornell University Press, IthacaGoogle Scholar
  11. 11.
    Adamson A (1979) A textbook of physical chemistry, Academic, New YorkGoogle Scholar
  12. 12.
    Johnston HS (1966) Gas phase reaction theory, Ronald, New YorkGoogle Scholar
  13. 13.
    Zachariasen WH (1963) Acta Crystallogr. 16: 385CrossRefGoogle Scholar
  14. 14.
    Brown ID, Altermatt D (1985) Acta Crystallogr. B41: 244Google Scholar
  15. 15.
    Brown ID (1977) Acta Crystallogr. B33: 1305Google Scholar
  16. 16.
    Mackay AL, Finney JL (1973) J. Appl. Crystallogr. 6: 284CrossRefGoogle Scholar
  17. 17.
    Horiuchi H, Sawamoto H (1981) Amer. Mineral. 66: 568Google Scholar
  18. 18.
    O'Keeffe M, Hyde BG (1978) Acta Crystallogr. B34: 3519Google Scholar
  19. 19.
    Laurent Y, Guyader J, Roult G (1981) Acta Crystallogr. B37: 911Google Scholar
  20. 20.
    Marezio M (1965) Acta Crystallogr. B37: 481CrossRefGoogle Scholar
  21. 21.
    Hesse K-F (1977) Acta Crystallogr. B33: 901Google Scholar
  22. 22.
    Völlenkle H, Wittmann J (1968) Mh. Chem. 99: 244Google Scholar
  23. 23.
    O'Keeffe M, Hansen S (1988) J. Am. Chem. Soc. 110: 1506CrossRefGoogle Scholar
  24. 24.
    Harris LA, Yakel HL (1969) Acta Crystallogr. B25: 1647Google Scholar
  25. 25.
    Geller S (1960) J. Chem. Phys. 33: 676CrossRefGoogle Scholar
  26. 26.
    Marezio M, Remeika JP (1967) J. Chem. Phys. 46: 1862CrossRefGoogle Scholar
  27. 27.
    Daniel F, Moret J, Phillippot E, Maurin M (1977) J. Solid State Chem. 22: 113CrossRefGoogle Scholar
  28. 28.
    Wagner TR, O'Keeffe M (1988) J. Solid State Chem. 73: 211CrossRefGoogle Scholar
  29. 29.
    Baur W (1981) In: O'Keeffe M, Navrotsky A (eds) Structure and bonding in crystals II. Academic, New YorkGoogle Scholar
  30. 30.
    Donnay G, Allmann R (1970) Amer. Mineral. 55: 1003Google Scholar
  31. 31.
    Ribbe PH, Gibbs GV (1971) Amer. Mineral. 56: 24Google Scholar
  32. 32.
    Pauling L (1928) Proc. Nat. Acad. Sci. U.S.A. 14: 603CrossRefGoogle Scholar
  33. 33.
    Bart JCJ, Ragaini V (1979) Inorg. Chim. Acta 36: 261CrossRefGoogle Scholar
  34. 34.
    Le Page Y, Strobel P (1982) J. Solid State Chem. 47: 6CrossRefGoogle Scholar
  35. 35.
    Trömel M (1983) Acta Crystallogr. B39: 664Google Scholar
  36. 36.
    Domengés B, McGuire NK, O'Keeffe M (1985) J. Solid State Chem. 56: 94CrossRefGoogle Scholar
  37. 37.
    Robin MB, Day P (1967) Adv. Inorg. Chem. Radiochem. 10: 247CrossRefGoogle Scholar
  38. 38.
    Hámos LV, Stscherbina W (1931) Nacr. Ges. Wiss. Gotting. Math. Phys. Kl. Fachgruppen 232Google Scholar
  39. 39.
    Ruby SL, Shirane G (1961) Phys. Rev. 123: 1239CrossRefGoogle Scholar
  40. 40.
    Morosin B, Baughman RJ, Ginley DS, Butler MA (1978) J. Appl. Cryst. 11: 121CrossRefGoogle Scholar
  41. 41.
    Bartell LS (1962) Tetrahedron 17: 177CrossRefGoogle Scholar
  42. 42.
    McGuire NK, O'Keeffe M (1984) J. Solid State Chem. 54: 49CrossRefGoogle Scholar
  43. 43.
    O'Keeffe M, Hyde BG (1984) Nature 309: 411CrossRefGoogle Scholar
  44. 44.
    O'Keeffe M, Stuart JA (1983) Inorg. Chem. 22: 177CrossRefGoogle Scholar
  45. 45.
    Zachariasen WH (1978) J. Less-Common Mets. 62: 1CrossRefGoogle Scholar
  46. 46.
    Adelbert P, Traverse JP (1979) Mat. Res. Bull. 14: 303CrossRefGoogle Scholar
  47. 47.
    Bämighausen H, Schulter G (1985) aJ. Less-Common Mets. 110: 385CrossRefGoogle Scholar
  48. 48.
    Beall GW, Milligan WO, Wolcott HA (1977) J. Inorg. Nucl. Chem. 39: 65CrossRefGoogle Scholar
  49. 49.
    Caro P (1972) In: Roth RS, Schneider SJ (eds) Solid state chemistry, N.B.S. Spec. Publ. 364, Washington, p. 367Google Scholar
  50. 50.
    Barbier J, Hyde BG (1985) Acta Crystallogr. B41: 383Google Scholar
  51. 51.
    Burdett JK (1980) Molecular shapes, Wiley, New YorkGoogle Scholar
  52. 52.
    O'Keeffe M (1979) Acta Crystallogr. A35: 776Google Scholar
  53. 53.
    Halot D, Flahaut J (1971) C. R. Acad. Sci. Paris C272: 465Google Scholar
  54. 54.
    Imanov IM, Ragimli NA, Semiletov SA (1975) Soviet Phys. Crystallogr. 19: 466 [trans. of Krystallografiya 19: 751 (1974)]Google Scholar
  55. 55.
    Page L, Adams NI (1931) Principles of electricity, Van Nostrand, New YorkGoogle Scholar
  56. 56.
    Gibbs GV, Boisen MB (1987) Mat. Res. Soc. Symp. Proc. 73: 515Google Scholar
  57. 57.
    Burdett JK (1988) Chem. Revs. 88: 3CrossRefGoogle Scholar
  58. 58.
    Brown ID, Wu KK (1976) Acta Crystallogr. B32: 1957Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • M. O'Keeffe
    • 1
  1. 1.Department of ChemistryArizona State UniversityTempeUSA

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