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