Classical Point-Charge Model

  • C. A. Morrison
Part of the Lecture Notes in Chemistry book series (LNC, volume 47)

Abstract

In the simplest model of the crystal field, the point-charge model introduced by Bethe (1929), the lattice is replaced by an array of point charges placed at the nuclei of the constituent ions. A multipole expansion is made of the point-charge potential energy at the rare-earth site.

Keywords

Monoclinic Space Group International Table Crystal Field Effect Angular Relationship Calcium Tungstate 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography and References

  1. Bethe, H. A. (1929), Termaufspaltung in Kristallen (translation: Splitting of Terms in Crystals, by Consultants Bureau, Inc., New York, NY), Ann. Physik (Leipzig) 3, 133.CrossRefGoogle Scholar
  2. Bethe, H. (1930), Zur Theorie des Zeemaneffektes an den Salzen der seltenen Erden, Z. Physik 60, 218.CrossRefGoogle Scholar
  3. Carlson, B. C, and G. S. Rushbrooke (1950), On the Expansion of a Coulomb Potential in Spherical Harmonics, Proc. Camb. Phil. Soc. 46, 626.CrossRefGoogle Scholar
  4. Faucher, M., and P. Caro (1977), A Quickly Converging Method for Computing Electrostatic Crystal Field Parameters, J. Chem. Phys. 66, 1273.CrossRefGoogle Scholar
  5. Faucher, M., and D. Garcia (1983a), Crystal Field Effects in Rare-Earth-Doped Oxyhalides: Ab-Initio Calculations Including Effects of Dipolar and Quadrupolar Moments, Solid State Chemistry, Proceedings of the Second European Conference (7–9 June 1982, Veldhoven, Netherlands), Elsevier, Amsterdam, Netherlands, p 547.Google Scholar
  6. Faucher, M., and D. Garcia (1983b), Crystal Field Effects on 4f Electrons: Theories and Reality, J. Less-Common Metals 93, 31.CrossRefGoogle Scholar
  7. Faucher, M., and D. Garcia (1982), Electrostatic Crystal-Field Contributions in Rare-Earth Compounds with Consistent Multipolar Effects: I—Contribution to K-Even Parameters, Phys. Rev. B 26, 5451.CrossRefGoogle Scholar
  8. Garcia, D. (1983), Simulation ab-initio des parametres du champ des ligandes, thesis, L’Ecole Centrale des Arts et Manufactures.Google Scholar
  9. Garcia, D., and M. Faucher (1984), Crystal-Field Parameters in Rare-Earth Compounds: Extended Charge Contributions, Phys. Rev. A 30, 1703.Google Scholar
  10. Garcia, D., M. Faucher, and O. L. Malta (1983), Electrostatic Crystal-Field Contributions in Rare-Earth Compounds with Consistent Multipolar Effects: II.—Contribution to K-Odd Parameters (Transition Probabilities), Phys. Rev. B 27, 7386.CrossRefGoogle Scholar
  11. Hutchings, M. T., and D. K. Ray (1963), Investigations into the origin of Crystalline Electronic Field Effects on Rare-Earth Ions: I—Contributions from Neighbouring Induced Moments, Proc. Phys. Soc. 81, 663.CrossRefGoogle Scholar
  12. International Tables for X-Ray Crystallography (1952), Vol. I.Google Scholar
  13. Karayianis, N., and C. A. Morrison (1973), Rare-Earth Ion-Host Lattice Interactions: 1.—Point Charge Lattice Sum in Scheelites, Harry Diamond Laboratories, HDL-TR-1648.Google Scholar
  14. Kittel, C. (1956), Introduction to Solid State Physics (2nd ed.), Wiley, New York, NY.Google Scholar
  15. Leavitt, R. P., and C. A. Morrison (1980, 15 July), Crystal Field Analysis of Triply Ionized Rare Earth Ions in Lanthanum Trifluoride: II—Intensity Calculations, J. Chem. Phys. 73 749.CrossRefGoogle Scholar
  16. Morrison, C. A. (1976), Dipolar Contributions to the Crystal Fields in Ionic Solids, Solid State Commun. 18, 153.CrossRefGoogle Scholar
  17. Morrison, C. A., and R. P. Leavitt (1982), Spectroscopic Properties of Triply Ionized Lanthanides in Transparent Host Materials, in Volume 5, Handbook of the Physics and Chemistry of Rare Earths, ed. by K. A. Gschneidner, Jr., and L. Eyring, North-Holland Publishers, New York, NY.Google Scholar
  18. Morrison, C. A., and R. P. Leavitt (1979, 15 September), Crystal Field Analysis of Triply Ionized Rare Earth Ions in Lanthanum Trifluoride, J. Chem. Phys. 71, 2366.CrossRefGoogle Scholar
  19. Morrison, C. A., G. F. de Sa, and R. P. Leavitt (1982), Self-Induced Multipole Contribution to the Single-Electron Crystal Field, J. Chem. Phys. 76, 3899.CrossRefGoogle Scholar
  20. Rose, M. E. (1957), Elementary Theory of Angular Momentum, Wiley, New York, NY.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • C. A. Morrison
    • 1
  1. 1.Harry Diamond LaboratoriesAdelphiUSA

Personalised recommendations