Abstract

Using the experimental energy levels of Gd<sup>3+</sup> in six hexagonal crystals as a basis, we discuss modifications to the electrostatic-approximation crystal-field model caused by nonlinear shielding, nephelauxetic, and covalency-induced molecular orbital effects. The crystal-field fit improves when levels belonging to different irreducible representations (crystal quantum numbers) are fitted separately and when levels of different spectroscopic terms are fitted separately. Nephelauxetic and covalency effects are related for the same crystal structure and are strongly structure dependent. Nonlinear shielding and/or term-dependent configuration-interaction effects are shown to be important but not simply related to the host structure.

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  1. G. Racah, Phys. Rev. 63, 367 (1943).
  2. W. A. Runciman, J. Chem. Phys. 36, 1481 (1962).
  3. R. L. Schwiesow and H. M. Crosswhite, J. Opt. Soc. Am. 59, 592 (1969).
  4. R. L. Schwiesow and H. M. Crosswhite, J. Opt. Soc. Am. 59, 602 (1969).
  5. W. H. Zachariasen, Acta Cryst. 1, 265 (1948).
  6. D. H. Templeton and C. H. Dauben, J. Am. Chem. Soc. 76, 5237 (1954).
  7. K. Schubert and A. Seitz, Z. Anorg. Allgem. Chem. 254, 116 (1947); R. Fricke and W. Dürrächter, Z. Anorg. Allgem. Chem. 259, 305 (1949).
  8. R. Fricke and A. Seitz, Z. Anorg. Allgem. Chem. 254, 107 (1947).
  9. R. W. G. Wyckoff, Crystal Structures, Vol. 2, 2nd ed. (Wiley-Interscience, New York, 1964), pp. 60ff and 77ff ; J. D. H. Donnay and G. Donnay, Crystal Data, 2nd ed. (American Crystallographic Association, New York, 1963); I. Oftedal, Z. Physik. Chem. 5B, 272 (1929); K. Schlyter, Arkiv Kemi 5, 73 (1952).
  10. R. P. Bauman and S. P. S. Porto, Phys. Rev. 101, 842 (1967); G. E. Stedman and D. J. Newman, J. Phys. Chem. Solids 32, 109 (1971).
  11. G. Racah, Phys. Rev. 76, 1352 (1949).
  12. K. Rajnak and B. G. Wybourne, Phys. Rev. 132, 280 (1963).
  13. B. R. Judd, H. M. Crosswhite, and H. Crosswhite, Phys. Rev. 169, 130 (1968); H. Crosswhite, H. M. Crosswhite, and B. R. Judd, Phys. Rev. 174, 89 (1968).
  14. H. M. Crosswhite, R. L. Schwiesow, and W. T. Carnall, J. Chem. Phys. 50, 5032 (1969).
  15. G. Racah, Phys. Rev. 62, 438 (1942).
  16. B. R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw-Hill, New York, 1963), pp. 42 and 72.
  17. C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn and fn Configurations (MIT Press, Cambridge, Mass., 1963).
  18. M. Rotenberg, R. Bivins, N. Metropolis, and J. K. Wooten, Jr., The 3-j and 6-j Symbols (MIT Press, Cambridge, Mass., 1959).
  19. A. J. Freeman and R. E. Watson, Phys. Rev. 133, A1571 (1964); 139, A1606 (1965).
  20. B. G. Wybourne, Spectroscopic Properties of Rare Earths (Wiley-Interscience, New York, 1965), p. 215.
  21. M. T. Hutchings and D. E. Ray, Proc. Phys. Soc. (London) 81, 663 (1963).
  22. C. K. Jorgensen, Orbitals in Atoms and Molecules (Academic, New York, 1962).
  23. H. S. Jarrett, J. Chem. Phys. 31, 1579 (1959).
  24. D. J. Newman, Advan. Phys. 20, 197 (1971).
  25. D. A. Wensky and W. G. Moulton, J. Chem. Phys. 53, 3957 (1970).
  26. J. C. Eisenstein, J. Chem. Phys. 39, 2128 (1963).

1971

D. J. Newman, Advan. Phys. 20, 197 (1971).

1970

D. A. Wensky and W. G. Moulton, J. Chem. Phys. 53, 3957 (1970).

1969

H. M. Crosswhite, R. L. Schwiesow, and W. T. Carnall, J. Chem. Phys. 50, 5032 (1969).

R. L. Schwiesow and H. M. Crosswhite, J. Opt. Soc. Am. 59, 592 (1969).

R. L. Schwiesow and H. M. Crosswhite, J. Opt. Soc. Am. 59, 602 (1969).

1968

B. R. Judd, H. M. Crosswhite, and H. Crosswhite, Phys. Rev. 169, 130 (1968); H. Crosswhite, H. M. Crosswhite, and B. R. Judd, Phys. Rev. 174, 89 (1968).

1967

R. P. Bauman and S. P. S. Porto, Phys. Rev. 101, 842 (1967); G. E. Stedman and D. J. Newman, J. Phys. Chem. Solids 32, 109 (1971).

1964

A. J. Freeman and R. E. Watson, Phys. Rev. 133, A1571 (1964); 139, A1606 (1965).

1963

M. T. Hutchings and D. E. Ray, Proc. Phys. Soc. (London) 81, 663 (1963).

J. C. Eisenstein, J. Chem. Phys. 39, 2128 (1963).

K. Rajnak and B. G. Wybourne, Phys. Rev. 132, 280 (1963).

1962

W. A. Runciman, J. Chem. Phys. 36, 1481 (1962).

1959

H. S. Jarrett, J. Chem. Phys. 31, 1579 (1959).

1954

D. H. Templeton and C. H. Dauben, J. Am. Chem. Soc. 76, 5237 (1954).

1949

G. Racah, Phys. Rev. 76, 1352 (1949).

1948

W. H. Zachariasen, Acta Cryst. 1, 265 (1948).

1947

K. Schubert and A. Seitz, Z. Anorg. Allgem. Chem. 254, 116 (1947); R. Fricke and W. Dürrächter, Z. Anorg. Allgem. Chem. 259, 305 (1949).

R. Fricke and A. Seitz, Z. Anorg. Allgem. Chem. 254, 107 (1947).

1943

G. Racah, Phys. Rev. 63, 367 (1943).

1942

G. Racah, Phys. Rev. 62, 438 (1942).

Bauman, R. P.

R. P. Bauman and S. P. S. Porto, Phys. Rev. 101, 842 (1967); G. E. Stedman and D. J. Newman, J. Phys. Chem. Solids 32, 109 (1971).

Bivins, R.

M. Rotenberg, R. Bivins, N. Metropolis, and J. K. Wooten, Jr., The 3-j and 6-j Symbols (MIT Press, Cambridge, Mass., 1959).

Carnall, W. T.

H. M. Crosswhite, R. L. Schwiesow, and W. T. Carnall, J. Chem. Phys. 50, 5032 (1969).

Crosswhite, H.

B. R. Judd, H. M. Crosswhite, and H. Crosswhite, Phys. Rev. 169, 130 (1968); H. Crosswhite, H. M. Crosswhite, and B. R. Judd, Phys. Rev. 174, 89 (1968).

Crosswhite, H. M.

R. L. Schwiesow and H. M. Crosswhite, J. Opt. Soc. Am. 59, 602 (1969).

R. L. Schwiesow and H. M. Crosswhite, J. Opt. Soc. Am. 59, 592 (1969).

H. M. Crosswhite, R. L. Schwiesow, and W. T. Carnall, J. Chem. Phys. 50, 5032 (1969).

B. R. Judd, H. M. Crosswhite, and H. Crosswhite, Phys. Rev. 169, 130 (1968); H. Crosswhite, H. M. Crosswhite, and B. R. Judd, Phys. Rev. 174, 89 (1968).

Dauben, C. H.

D. H. Templeton and C. H. Dauben, J. Am. Chem. Soc. 76, 5237 (1954).

Eisenstein, J. C.

J. C. Eisenstein, J. Chem. Phys. 39, 2128 (1963).

Freeman, A. J.

A. J. Freeman and R. E. Watson, Phys. Rev. 133, A1571 (1964); 139, A1606 (1965).

Fricke, R.

R. Fricke and A. Seitz, Z. Anorg. Allgem. Chem. 254, 107 (1947).

Hutchings, M. T.

M. T. Hutchings and D. E. Ray, Proc. Phys. Soc. (London) 81, 663 (1963).

Jarrett, H. S.

H. S. Jarrett, J. Chem. Phys. 31, 1579 (1959).

Jorgensen, C. K.

C. K. Jorgensen, Orbitals in Atoms and Molecules (Academic, New York, 1962).

Judd, B. R.

B. R. Judd, H. M. Crosswhite, and H. Crosswhite, Phys. Rev. 169, 130 (1968); H. Crosswhite, H. M. Crosswhite, and B. R. Judd, Phys. Rev. 174, 89 (1968).

B. R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw-Hill, New York, 1963), pp. 42 and 72.

Koster, G. F.

C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn and fn Configurations (MIT Press, Cambridge, Mass., 1963).

Metropolis, N.

M. Rotenberg, R. Bivins, N. Metropolis, and J. K. Wooten, Jr., The 3-j and 6-j Symbols (MIT Press, Cambridge, Mass., 1959).

Moulton, W. G.

D. A. Wensky and W. G. Moulton, J. Chem. Phys. 53, 3957 (1970).

Newman, D. J.

D. J. Newman, Advan. Phys. 20, 197 (1971).

Nielson, C. W.

C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn and fn Configurations (MIT Press, Cambridge, Mass., 1963).

Porto, S. P. S.

R. P. Bauman and S. P. S. Porto, Phys. Rev. 101, 842 (1967); G. E. Stedman and D. J. Newman, J. Phys. Chem. Solids 32, 109 (1971).

Racah, G.

G. Racah, Phys. Rev. 76, 1352 (1949).

G. Racah, Phys. Rev. 63, 367 (1943).

G. Racah, Phys. Rev. 62, 438 (1942).

Rajnak, K.

K. Rajnak and B. G. Wybourne, Phys. Rev. 132, 280 (1963).

Ray, D. E.

M. T. Hutchings and D. E. Ray, Proc. Phys. Soc. (London) 81, 663 (1963).

Rotenberg, M.

M. Rotenberg, R. Bivins, N. Metropolis, and J. K. Wooten, Jr., The 3-j and 6-j Symbols (MIT Press, Cambridge, Mass., 1959).

Runciman, W. A.

W. A. Runciman, J. Chem. Phys. 36, 1481 (1962).

Schubert, K.

K. Schubert and A. Seitz, Z. Anorg. Allgem. Chem. 254, 116 (1947); R. Fricke and W. Dürrächter, Z. Anorg. Allgem. Chem. 259, 305 (1949).

Schwiesow, R. L.

R. L. Schwiesow and H. M. Crosswhite, J. Opt. Soc. Am. 59, 592 (1969).

H. M. Crosswhite, R. L. Schwiesow, and W. T. Carnall, J. Chem. Phys. 50, 5032 (1969).

R. L. Schwiesow and H. M. Crosswhite, J. Opt. Soc. Am. 59, 602 (1969).

Seitz, A.

R. Fricke and A. Seitz, Z. Anorg. Allgem. Chem. 254, 107 (1947).

K. Schubert and A. Seitz, Z. Anorg. Allgem. Chem. 254, 116 (1947); R. Fricke and W. Dürrächter, Z. Anorg. Allgem. Chem. 259, 305 (1949).

Templeton, D. H.

D. H. Templeton and C. H. Dauben, J. Am. Chem. Soc. 76, 5237 (1954).

Watson, R. E.

A. J. Freeman and R. E. Watson, Phys. Rev. 133, A1571 (1964); 139, A1606 (1965).

Wensky, D. A.

D. A. Wensky and W. G. Moulton, J. Chem. Phys. 53, 3957 (1970).

Wooten, Jr., J. K.

M. Rotenberg, R. Bivins, N. Metropolis, and J. K. Wooten, Jr., The 3-j and 6-j Symbols (MIT Press, Cambridge, Mass., 1959).

Wybourne, B. G.

K. Rajnak and B. G. Wybourne, Phys. Rev. 132, 280 (1963).

B. G. Wybourne, Spectroscopic Properties of Rare Earths (Wiley-Interscience, New York, 1965), p. 215.

Wyckoff, R. W. G.

R. W. G. Wyckoff, Crystal Structures, Vol. 2, 2nd ed. (Wiley-Interscience, New York, 1964), pp. 60ff and 77ff ; J. D. H. Donnay and G. Donnay, Crystal Data, 2nd ed. (American Crystallographic Association, New York, 1963); I. Oftedal, Z. Physik. Chem. 5B, 272 (1929); K. Schlyter, Arkiv Kemi 5, 73 (1952).

Zachariasen, W. H.

W. H. Zachariasen, Acta Cryst. 1, 265 (1948).

Other

G. Racah, Phys. Rev. 63, 367 (1943).

W. A. Runciman, J. Chem. Phys. 36, 1481 (1962).

R. L. Schwiesow and H. M. Crosswhite, J. Opt. Soc. Am. 59, 592 (1969).

R. L. Schwiesow and H. M. Crosswhite, J. Opt. Soc. Am. 59, 602 (1969).

W. H. Zachariasen, Acta Cryst. 1, 265 (1948).

D. H. Templeton and C. H. Dauben, J. Am. Chem. Soc. 76, 5237 (1954).

K. Schubert and A. Seitz, Z. Anorg. Allgem. Chem. 254, 116 (1947); R. Fricke and W. Dürrächter, Z. Anorg. Allgem. Chem. 259, 305 (1949).

R. Fricke and A. Seitz, Z. Anorg. Allgem. Chem. 254, 107 (1947).

R. W. G. Wyckoff, Crystal Structures, Vol. 2, 2nd ed. (Wiley-Interscience, New York, 1964), pp. 60ff and 77ff ; J. D. H. Donnay and G. Donnay, Crystal Data, 2nd ed. (American Crystallographic Association, New York, 1963); I. Oftedal, Z. Physik. Chem. 5B, 272 (1929); K. Schlyter, Arkiv Kemi 5, 73 (1952).

R. P. Bauman and S. P. S. Porto, Phys. Rev. 101, 842 (1967); G. E. Stedman and D. J. Newman, J. Phys. Chem. Solids 32, 109 (1971).

G. Racah, Phys. Rev. 76, 1352 (1949).

K. Rajnak and B. G. Wybourne, Phys. Rev. 132, 280 (1963).

B. R. Judd, H. M. Crosswhite, and H. Crosswhite, Phys. Rev. 169, 130 (1968); H. Crosswhite, H. M. Crosswhite, and B. R. Judd, Phys. Rev. 174, 89 (1968).

H. M. Crosswhite, R. L. Schwiesow, and W. T. Carnall, J. Chem. Phys. 50, 5032 (1969).

G. Racah, Phys. Rev. 62, 438 (1942).

B. R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw-Hill, New York, 1963), pp. 42 and 72.

C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn and fn Configurations (MIT Press, Cambridge, Mass., 1963).

M. Rotenberg, R. Bivins, N. Metropolis, and J. K. Wooten, Jr., The 3-j and 6-j Symbols (MIT Press, Cambridge, Mass., 1959).

A. J. Freeman and R. E. Watson, Phys. Rev. 133, A1571 (1964); 139, A1606 (1965).

B. G. Wybourne, Spectroscopic Properties of Rare Earths (Wiley-Interscience, New York, 1965), p. 215.

M. T. Hutchings and D. E. Ray, Proc. Phys. Soc. (London) 81, 663 (1963).

C. K. Jorgensen, Orbitals in Atoms and Molecules (Academic, New York, 1962).

H. S. Jarrett, J. Chem. Phys. 31, 1579 (1959).

D. J. Newman, Advan. Phys. 20, 197 (1971).

D. A. Wensky and W. G. Moulton, J. Chem. Phys. 53, 3957 (1970).

J. C. Eisenstein, J. Chem. Phys. 39, 2128 (1963).

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