Abstract

The scattering tensor for the 7F17F0 and 7F27F0 electronic Raman transitions of the trivalent europium ion has been calculated for cases in which the rare-earth ion experiences a crystal field of cubic, hexagonal, and tetragonal symmetry. It is shown that such crystal fields give rise to Raman spectra of which polarization features are direct indications of the symmetry of the environment. The 7F17F0 transitions are all related to the antisymmetry of a scattering tensor, whereas the 7F27F0 transitions are related to a symmetric tensor. According to theory, the latter transitions should be more intense than the former.

© 1968 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Rasetti, Z. Physik 66, 646 (1930).
    [Crossref]
  2. J. T. Hougen and S. Singh, Phys. Rev. Letters 10, 406 (1963).
    [Crossref]
  3. J. Y. H. Chau, J. Chem. Phys. 44, 1708 (1966).
    [Crossref]
  4. J. A. Koningstein, J. Chem. Phys. 46, 2811 (1967).
    [Crossref]
  5. J. A. Koningstein and O. Sonnich Mortensen, Phys. Rev. Letters 18, 831 (1967).
    [Crossref]
  6. J. A. Koningstein and O. Sonnich Mortensen, Nature 217, 445 (1968).
    [Crossref]
  7. G. B. Wright and A. Mooradian, Phys. Rev. Letters 18, 608 (1967).
    [Crossref]
  8. O. Sonnich Mortensen and J. A. Koningstein, J. Chem. Phys. 48, 3971 (1968).
    [Crossref]
  9. J. A. Koningstein and O. Sonnich Mortensen, Phys. Rev. 169, 75 (1968).
    [Crossref]
  10. G. Placzek, in Handbuch der Radiologie, Bd VI, Teil II, E. Marx, Ed. (Akademische Verlagsgesellshaft, Leipzig, 1934), p. 205.
  11. H. A. Bethe, Ann. Physik 3, 133 (1929).
    [Crossref]
  12. G. H. Dieke and H. M. Crosswhite, Appl. Opt. 2, 675 (1963).
    [Crossref]
  13. See for instance, H. H. Caspers, H. E. Rast, and J. L. Fry, J. Chem. Phys. 47, 4505 (1967).
    [Crossref]
  14. See: C. Gottfried and F. Schossberger, compilers, Strukturbericht Vol. III (Akademische Verlagsgesellschaft, Leipzig, 1937), p. 423.
  15. C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn and fn Configurations (M.I.T. Press, Cambridge, Mass., 1963).
  16. K. W. H. Stevens, Proc. Phys. Soc. (London) A65, 209 (1952).
  17. R. J. Elliott and K. W. H. Stevens, Proc. Roy. Soc. (London) A218, 553 (1953).
  18. B. R. Judd, Proc. Roy. Soc. (London) A227, 552 (1955).
  19. B. R. Judd, Proc. Phys. Soc. (London) 74, 330 (1959).
    [Crossref]
  20. H. Winston and R. S. Halford, J. Chem. Phys. 17, 607 (1949).
    [Crossref]
  21. R. Pappalardo, Nuovo Cimento 26, 4748 (1962).

1968 (3)

J. A. Koningstein and O. Sonnich Mortensen, Nature 217, 445 (1968).
[Crossref]

O. Sonnich Mortensen and J. A. Koningstein, J. Chem. Phys. 48, 3971 (1968).
[Crossref]

J. A. Koningstein and O. Sonnich Mortensen, Phys. Rev. 169, 75 (1968).
[Crossref]

1967 (4)

G. B. Wright and A. Mooradian, Phys. Rev. Letters 18, 608 (1967).
[Crossref]

J. A. Koningstein, J. Chem. Phys. 46, 2811 (1967).
[Crossref]

J. A. Koningstein and O. Sonnich Mortensen, Phys. Rev. Letters 18, 831 (1967).
[Crossref]

See for instance, H. H. Caspers, H. E. Rast, and J. L. Fry, J. Chem. Phys. 47, 4505 (1967).
[Crossref]

1966 (1)

J. Y. H. Chau, J. Chem. Phys. 44, 1708 (1966).
[Crossref]

1963 (2)

J. T. Hougen and S. Singh, Phys. Rev. Letters 10, 406 (1963).
[Crossref]

G. H. Dieke and H. M. Crosswhite, Appl. Opt. 2, 675 (1963).
[Crossref]

1962 (1)

R. Pappalardo, Nuovo Cimento 26, 4748 (1962).

1959 (1)

B. R. Judd, Proc. Phys. Soc. (London) 74, 330 (1959).
[Crossref]

1955 (1)

B. R. Judd, Proc. Roy. Soc. (London) A227, 552 (1955).

1953 (1)

R. J. Elliott and K. W. H. Stevens, Proc. Roy. Soc. (London) A218, 553 (1953).

1952 (1)

K. W. H. Stevens, Proc. Phys. Soc. (London) A65, 209 (1952).

1949 (1)

H. Winston and R. S. Halford, J. Chem. Phys. 17, 607 (1949).
[Crossref]

1930 (1)

F. Rasetti, Z. Physik 66, 646 (1930).
[Crossref]

1929 (1)

H. A. Bethe, Ann. Physik 3, 133 (1929).
[Crossref]

Bethe, H. A.

H. A. Bethe, Ann. Physik 3, 133 (1929).
[Crossref]

Caspers, H. H.

See for instance, H. H. Caspers, H. E. Rast, and J. L. Fry, J. Chem. Phys. 47, 4505 (1967).
[Crossref]

Chau, J. Y. H.

J. Y. H. Chau, J. Chem. Phys. 44, 1708 (1966).
[Crossref]

Crosswhite, H. M.

Dieke, G. H.

Elliott, R. J.

R. J. Elliott and K. W. H. Stevens, Proc. Roy. Soc. (London) A218, 553 (1953).

Fry, J. L.

See for instance, H. H. Caspers, H. E. Rast, and J. L. Fry, J. Chem. Phys. 47, 4505 (1967).
[Crossref]

Halford, R. S.

H. Winston and R. S. Halford, J. Chem. Phys. 17, 607 (1949).
[Crossref]

Hougen, J. T.

J. T. Hougen and S. Singh, Phys. Rev. Letters 10, 406 (1963).
[Crossref]

Judd, B. R.

B. R. Judd, Proc. Phys. Soc. (London) 74, 330 (1959).
[Crossref]

B. R. Judd, Proc. Roy. Soc. (London) A227, 552 (1955).

Koningstein, J. A.

J. A. Koningstein and O. Sonnich Mortensen, Nature 217, 445 (1968).
[Crossref]

O. Sonnich Mortensen and J. A. Koningstein, J. Chem. Phys. 48, 3971 (1968).
[Crossref]

J. A. Koningstein and O. Sonnich Mortensen, Phys. Rev. 169, 75 (1968).
[Crossref]

J. A. Koningstein, J. Chem. Phys. 46, 2811 (1967).
[Crossref]

J. A. Koningstein and O. Sonnich Mortensen, Phys. Rev. Letters 18, 831 (1967).
[Crossref]

Koster, G. F.

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

Mooradian, A.

G. B. Wright and A. Mooradian, Phys. Rev. Letters 18, 608 (1967).
[Crossref]

Nielson, C. W.

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

Pappalardo, R.

R. Pappalardo, Nuovo Cimento 26, 4748 (1962).

Placzek, G.

G. Placzek, in Handbuch der Radiologie, Bd VI, Teil II, E. Marx, Ed. (Akademische Verlagsgesellshaft, Leipzig, 1934), p. 205.

Rasetti, F.

F. Rasetti, Z. Physik 66, 646 (1930).
[Crossref]

Rast, H. E.

See for instance, H. H. Caspers, H. E. Rast, and J. L. Fry, J. Chem. Phys. 47, 4505 (1967).
[Crossref]

Singh, S.

J. T. Hougen and S. Singh, Phys. Rev. Letters 10, 406 (1963).
[Crossref]

Sonnich Mortensen, O.

J. A. Koningstein and O. Sonnich Mortensen, Nature 217, 445 (1968).
[Crossref]

O. Sonnich Mortensen and J. A. Koningstein, J. Chem. Phys. 48, 3971 (1968).
[Crossref]

J. A. Koningstein and O. Sonnich Mortensen, Phys. Rev. 169, 75 (1968).
[Crossref]

J. A. Koningstein and O. Sonnich Mortensen, Phys. Rev. Letters 18, 831 (1967).
[Crossref]

Stevens, K. W. H.

R. J. Elliott and K. W. H. Stevens, Proc. Roy. Soc. (London) A218, 553 (1953).

K. W. H. Stevens, Proc. Phys. Soc. (London) A65, 209 (1952).

Winston, H.

H. Winston and R. S. Halford, J. Chem. Phys. 17, 607 (1949).
[Crossref]

Wright, G. B.

G. B. Wright and A. Mooradian, Phys. Rev. Letters 18, 608 (1967).
[Crossref]

Ann. Physik (1)

H. A. Bethe, Ann. Physik 3, 133 (1929).
[Crossref]

Appl. Opt. (1)

J. Chem. Phys. (5)

See for instance, H. H. Caspers, H. E. Rast, and J. L. Fry, J. Chem. Phys. 47, 4505 (1967).
[Crossref]

H. Winston and R. S. Halford, J. Chem. Phys. 17, 607 (1949).
[Crossref]

J. Y. H. Chau, J. Chem. Phys. 44, 1708 (1966).
[Crossref]

J. A. Koningstein, J. Chem. Phys. 46, 2811 (1967).
[Crossref]

O. Sonnich Mortensen and J. A. Koningstein, J. Chem. Phys. 48, 3971 (1968).
[Crossref]

Nature (1)

J. A. Koningstein and O. Sonnich Mortensen, Nature 217, 445 (1968).
[Crossref]

Nuovo Cimento (1)

R. Pappalardo, Nuovo Cimento 26, 4748 (1962).

Phys. Rev. (1)

J. A. Koningstein and O. Sonnich Mortensen, Phys. Rev. 169, 75 (1968).
[Crossref]

Phys. Rev. Letters (3)

G. B. Wright and A. Mooradian, Phys. Rev. Letters 18, 608 (1967).
[Crossref]

J. A. Koningstein and O. Sonnich Mortensen, Phys. Rev. Letters 18, 831 (1967).
[Crossref]

J. T. Hougen and S. Singh, Phys. Rev. Letters 10, 406 (1963).
[Crossref]

Proc. Phys. Soc. (London) (2)

K. W. H. Stevens, Proc. Phys. Soc. (London) A65, 209 (1952).

B. R. Judd, Proc. Phys. Soc. (London) 74, 330 (1959).
[Crossref]

Proc. Roy. Soc. (London) (2)

R. J. Elliott and K. W. H. Stevens, Proc. Roy. Soc. (London) A218, 553 (1953).

B. R. Judd, Proc. Roy. Soc. (London) A227, 552 (1955).

Z. Physik (1)

F. Rasetti, Z. Physik 66, 646 (1930).
[Crossref]

Other (3)

G. Placzek, in Handbuch der Radiologie, Bd VI, Teil II, E. Marx, Ed. (Akademische Verlagsgesellshaft, Leipzig, 1934), p. 205.

See: C. Gottfried and F. Schossberger, compilers, Strukturbericht Vol. III (Akademische Verlagsgesellschaft, Leipzig, 1937), p. 423.

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

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

The polarization spectra of electronic transitions of the Eu3+ ion in a crystal field of cubic symmetry. All intensities with frequencies >600 cm−1 have to be multiplied by a factor [F(2,ν)/F(1,ν)]2. If the first excited-state configuration is at 110 000 cm−1, this factor is 30 when the spectra are excited with the 6328-Å radiation of He–Ne laser. Values of the crystal-field parameters are A40=−250 cm−1 and A44=−1250 cm−1.

Fig. 2
Fig. 2

The polarized Raman spectra of Eu3+ ion in a field of hexagonal symmetry. Values of the crystal-field parameters are A20=250 cm−1 and A40=−250 cm−1.

Fig. 3
Fig. 3

The polarized Raman spectra of Eu3+ ion in a field of tetragonal symmetry. Values of the crystal-field parameters are A20=250 cm−1, A40=−250 cm−1 and A44=−1000 cm−1.

Fig. 4
Fig. 4

The intensity for an antisymmetric scattering (I) tensor ( 0 a 0 - a 0 0 0 0 0 ) and symmetric scattering (II) tensor ( 0 a 0 a 0 0 0 0 0 ) as function of a rotation of ψ0 around the Z axis.

Tables (1)

Tables Icon

Table I Eigenvalues, eigenvectors, and scattering tensors for Eu3+ ion in a tetragonal crystal field.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

( α Q κ ) k n = F ( κ , ν ) γ S L J J z , γ S L J J z a * ( n ; γ S L J J z ) × a ( k ; γ S L J J z ) γ S L J J z u Q κ γ S L J J z ,
F ( κ , ν ) = χ ( ν ˜ χ k ν ˜ χ k - ν + ( - 1 ) κ ν ˜ χ k ν χ h + ν ) × ( n l r n l ) 2 ( 2 κ + 1 ) 1 2 { 1 κ 1 l l l } ( - 1 ) κ .
γ S L J J z u Q κ γ S L J J z = ( - 1 ) J - J z ( J κ J - J z Q J z ) × γ S L J u κ γ S L J ,
γ S L J u κ γ S L J = ( - 1 ) S + L + J + κ [ ( 2 J + 1 ) ( 2 J + 1 ) ] 1 2 × { L J S J L κ } γ S L u κ γ S L .
H C F = - e j V ( r j , θ j , φ j ) .
H C F = h m = n - h k B n m r k m Y h m ( θ κ , φ κ ) .
H C F = α [ A 2 0 O 2 0 + A 2 2 ( O 2 2 + O 2 - 2 ) ] + β [ A 4 0 O 4 0 + A 4 0 ( O 4 2 + O 4 - 2 ) + A 4 4 ( O 4 4 + O 4 - 4 ) ] + terms of higher order .
α ρ σ 2 = κ Q W ρ σ κ Q α Q κ 2 .