Zeitschrift für Physik B Condensed Matter

, Volume 96, Issue 3, pp 325–332 | Cite as

Crystal-field induced dipoles in heteropolar crystals I: Concept

  • Mario Birkholz


The electrostatic part of the internal energy of heteropolar crystals is largely assumed to be purely of the Coulomb or monopole type. Here, it is argued, ions in a crystal lattice may not only bear a net charge, but also higher electrostatic moments. This applies explicitly for dipole moments. Dipoles are assumed to occur only for ions on lattice sites where the point symmetry allows a non-vanishing crystal electric field to cause a polarization. Infinite lattice sums that account for the electrostatic interaction between point charges and dipoles are given, with the Madelung constant being the first of them in a more general Taylor expansion. An expression for the binding energy of heteropolar solids is hereby presented. The share due to induced dipoles is always negative if dipole-dipole interactions are neglected, i.e. it increases the strength of crystal binding. The concept, which is developed for crystals of arbitrary symmetry is explained on the basis of the examples (i) sphalerite (ZnS), (ii) pyrite (FeS2), (iii) rutile (TiO2), and (iv) orthorhombic La2CuO4.


05.50.+q 61.50.Lt 


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  1. 1.
    Madelung, E.: Phys. ZS.XIX, 524 (1918)Google Scholar
  2. 2.
    Born, M.: Problems of atomic dynamics, p. 168–170. Cambridge: MIT Press 1926Google Scholar
  3. 3.
    Khan, M.A.: J. Phys. C9, 81 (1976)Google Scholar
  4. 4.
    Ashcroft, N.W., Mermin, N.D.: Solid State Physics, p. 407, 555. Tokyo: CBS Publishing Japan 1981Google Scholar
  5. 5.
    Kröger, F.A.: The chemistry of imperfect crystals, p. 249. Amsterdam: North-Holland 1974Google Scholar
  6. 6.
    O'Regan, B., Grätzel, M.: Nature353, 737 (1991)Google Scholar
  7. 7.
    Ennaoui, A., Fiechter, S., Pettenkofer, Ch., Alonso-Vante, N., Büker, K., Bronold, M., Höpfner, Ch., Tributsch, H.: Sol. Energy Mater. Sol. Cells29, 289 (1993)Google Scholar
  8. 8.
    Baur, W.H.: Acta Crystallogr.14, 209 (1961)Google Scholar
  9. 9.
    Birkholz, M.: J. Phys.: Condens. Matter4, 6227 (1992)Google Scholar
  10. 10.
    Kanamori, J., Moriya, T., Motizuki, K., Nagamiya, T.: J. Phys. Soc. Jap.10, 93 (1955)Google Scholar
  11. 11.
    Nijboer, B.R.A., de Wette, F.W.: Physica23, 309 (1957)Google Scholar
  12. 12.
    de Wette, F.W., Nijboer, B.R.A.: Physica24, 1105 (1958)Google Scholar
  13. 13.
    de Wette, F.W.: Physica25, 1225 (1959)Google Scholar
  14. 14.
    Bertaut, E.F.: J. Phys. (Paris)39, 1331 (1978)Google Scholar
  15. 15.
    de Wette, F.W.: Phys. Rev.123, 103 (1961)Google Scholar
  16. 16.
    Taylor, T.T.: Phys. Rev.127, 120 (1962)Google Scholar
  17. 17.
    Hewitt, R.R., Taylor, T.T.: Phys. Rev.125, 524 (1962)Google Scholar
  18. 18.
    Taylor, T.T., Das, T.P.: Phys. Rev.133, A1327 (1964)Google Scholar
  19. 19.
    Sharma, R.R., Das, T.P.: J. Chem. Phys.41, 3581 (1964)Google Scholar
  20. 20.
    Artmann, J.O.: Phys. Rev.143, 541 (1966)Google Scholar
  21. 21.
    Artmann, J.O.: Phys. Rev.173, 337 (1968)Google Scholar
  22. 22.
    Buckingham, A.D.: In: Intermolecular Forces, p. 107. Hirschfelder, J.O. (ed.). New York: Interscience 1967Google Scholar
  23. 23.
    Stone, A.J., Price, S.L.: J. Phys. Chem.92, 3325 (1988)Google Scholar
  24. 24.
    Kitaigorodski, A.I.: Molekülkristalle. Berlin: Akademie-Verlag 1979Google Scholar
  25. 25.
    Metzger, R.M. (ed.): Crystal cohesion and conformational energies. Berlin: Springer 1981Google Scholar
  26. 26.
    Rozenbaum, V.M.: JETP Lett.59, 173 (1994)Google Scholar
  27. 27.
    Birkholz, M.: Z. Phys. B96, 333 (1995)Google Scholar
  28. 28.
    Jenkins, H.D.B.: In: CRC Handbook of chemistry and physics, p. D100. Weast, R.C. (ed.). Boca Raton: CRC Press 1986Google Scholar
  29. 29.
    Jackson, J.D.: Classical electrodynamics, Chap. 4. New York: Wiley 1975Google Scholar
  30. 30.
    Bhagavantam, S., Suryanarayana, D.: Acta Crystallogr.2, 21 (1949)Google Scholar
  31. 31.
    Rudert, R.: (Personal communication 1992)Google Scholar
  32. 32.
    Radzig, A.A., Smirnov, B.M.: Reference data on atoms, molecules and ions. Berlin: Springer 1985Google Scholar
  33. 33.
    Cotton, F.A., Wilkinson, G.: Advanced inorganic chemistry, p. 58. New York: Wiley 1972Google Scholar
  34. 34.
    Birkholz, M., Fiechter, S., Hartmann, A., Tributsch, H.: Phys. Rev. B43, 11926 (1991)Google Scholar
  35. 35.
    Parker, R.A.: Phys. Rev.124 1713 (1961)Google Scholar
  36. 36.
    Kingsbury, P.L.: Acta Crystallogr. A24, 578 (1968)Google Scholar
  37. 37.
    Jorgensen, J.D., Dabrowski, B., Shiyou, Pei, Hinks, D.G., Soderholm, L., Morosin, B., Schirber, J.E., Venturini, E.L., Ginley, D.S.: Phys. Rev. B38, 11337 (1988)Google Scholar
  38. 38.
    Birkholz, M., Rudert, R.: Z. Phys. B (in preparation)Google Scholar
  39. 39.
    Bednorz, J.G., Müller, K.A.: Z. Phys. B64, 189 (1986)Google Scholar
  40. 40.
    Cava, R.J., Hewat, A.W., Hewat, E.A., Batlogg, B., Marezic, M., Rabe, K.M., Krajewski, J.J., Peck, W.F., Rupp, L.W.: Phys. C165, 419 (1990)Google Scholar
  41. 41.
    Rudert, R., Birkholz, M.: ELC—A Computer Program for the Calculation of Electrostatic Lattice Coefficients 1994Google Scholar
  42. 42.
    Mahan, G.D., Subbaswamy, K.R.: Local Density Theory of Polarizability. New York: Plenum Press 1990Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Mario Birkholz
    • 1
  1. 1.Ingenieurbüro für SolartechnikBerlinGermany

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