Abstract

Theoretical energy-level schemes are derived to first order of perturbation theory and compared with those empirically derived for both a crystal of CaF2:Sm3+ and one of CdF2:Sm3+ in a crystal field of tetragonal symmetry. The resulting deviation of the energies between the theoretical and empirical schemes is within 40 cm−1 for ten of the twelve crystal-field energy levels of the ground 6H multiplet states terminating the observed fluorescence lines. The theoretical schemes are derived for a unique set of values for the five crystal-field parameters of the tetragonal field. This is substantial additional support for an assignment of tetragonal symmetry for both of these crystals. Tables are given of the resulting approximate values of the crystal-field parameters, level energies, and level eigenfunctions.

© 1967 Optical Society of America

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References

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  1. B. G. Wybourne, Spectroscopic Properties of Rare Earths (Interscience Publishers, John Wiley & Sons, New York, 1965).
  2. M. J. Weber and R. W. Bierig, Phys. Rev. 134, A1492 (1964), and the references therein.
    [Crossref]
  3. E.g., Z. Kiss, J. Chem. Phys. 38, 1476 (1956).
    [Crossref]
  4. N. Rabbiner, Phys. Rev. 130, 502 (1963).
    [Crossref]
  5. E.g., N. Rabbiner, Phys. Rev. 132, 224 (1963). Yu. K. Voron’ko, V. V. Osiko, V. T. Udovenchk, and M. M. Fursikov, Soviet Phys.—Solid State 7, 204 (1965).
    [Crossref]
  6. N. Rabbiner, J. Opt. Soc. Am. 57, 217 (1967).
    [Crossref]
  7. K. W. H. Stevens, Proc. Phys. Soc. (London) A65, 209 (1952).
    [Crossref]
  8. For example, see M. T. Hutchings, Solid State Phys. 16, 227 (1964).
  9. J. S. Prener and J. D. Kingsley, J. Chem. Phys. 38, 667 (1963).
    [Crossref]
  10. T. F. Ewanizky, P. J. Caplan, and J. R. Pastore, J. Chem. Phys. 43, 4351 (1965).
    [Crossref]
  11. N. Rabbiner, J. Opt. Soc. Am. 57, 217 (1967); Ph.D. thesis, New York University (1967).
    [Crossref]
  12. B. G. Wybourne, J. Chem. Phys. 36, 2301 (1962).
    [Crossref]

1967 (2)

1965 (1)

T. F. Ewanizky, P. J. Caplan, and J. R. Pastore, J. Chem. Phys. 43, 4351 (1965).
[Crossref]

1964 (2)

For example, see M. T. Hutchings, Solid State Phys. 16, 227 (1964).

M. J. Weber and R. W. Bierig, Phys. Rev. 134, A1492 (1964), and the references therein.
[Crossref]

1963 (3)

N. Rabbiner, Phys. Rev. 130, 502 (1963).
[Crossref]

E.g., N. Rabbiner, Phys. Rev. 132, 224 (1963). Yu. K. Voron’ko, V. V. Osiko, V. T. Udovenchk, and M. M. Fursikov, Soviet Phys.—Solid State 7, 204 (1965).
[Crossref]

J. S. Prener and J. D. Kingsley, J. Chem. Phys. 38, 667 (1963).
[Crossref]

1962 (1)

B. G. Wybourne, J. Chem. Phys. 36, 2301 (1962).
[Crossref]

1956 (1)

E.g., Z. Kiss, J. Chem. Phys. 38, 1476 (1956).
[Crossref]

1952 (1)

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

Bierig, R. W.

M. J. Weber and R. W. Bierig, Phys. Rev. 134, A1492 (1964), and the references therein.
[Crossref]

Caplan, P. J.

T. F. Ewanizky, P. J. Caplan, and J. R. Pastore, J. Chem. Phys. 43, 4351 (1965).
[Crossref]

Ewanizky, T. F.

T. F. Ewanizky, P. J. Caplan, and J. R. Pastore, J. Chem. Phys. 43, 4351 (1965).
[Crossref]

Hutchings, M. T.

For example, see M. T. Hutchings, Solid State Phys. 16, 227 (1964).

Kingsley, J. D.

J. S. Prener and J. D. Kingsley, J. Chem. Phys. 38, 667 (1963).
[Crossref]

Kiss, Z.

E.g., Z. Kiss, J. Chem. Phys. 38, 1476 (1956).
[Crossref]

Pastore, J. R.

T. F. Ewanizky, P. J. Caplan, and J. R. Pastore, J. Chem. Phys. 43, 4351 (1965).
[Crossref]

Prener, J. S.

J. S. Prener and J. D. Kingsley, J. Chem. Phys. 38, 667 (1963).
[Crossref]

Rabbiner, N.

N. Rabbiner, J. Opt. Soc. Am. 57, 217 (1967).
[Crossref]

N. Rabbiner, J. Opt. Soc. Am. 57, 217 (1967); Ph.D. thesis, New York University (1967).
[Crossref]

N. Rabbiner, Phys. Rev. 130, 502 (1963).
[Crossref]

E.g., N. Rabbiner, Phys. Rev. 132, 224 (1963). Yu. K. Voron’ko, V. V. Osiko, V. T. Udovenchk, and M. M. Fursikov, Soviet Phys.—Solid State 7, 204 (1965).
[Crossref]

Stevens, K. W. H.

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

Weber, M. J.

M. J. Weber and R. W. Bierig, Phys. Rev. 134, A1492 (1964), and the references therein.
[Crossref]

Wybourne, B. G.

B. G. Wybourne, J. Chem. Phys. 36, 2301 (1962).
[Crossref]

B. G. Wybourne, Spectroscopic Properties of Rare Earths (Interscience Publishers, John Wiley & Sons, New York, 1965).

J. Chem. Phys. (4)

E.g., Z. Kiss, J. Chem. Phys. 38, 1476 (1956).
[Crossref]

J. S. Prener and J. D. Kingsley, J. Chem. Phys. 38, 667 (1963).
[Crossref]

T. F. Ewanizky, P. J. Caplan, and J. R. Pastore, J. Chem. Phys. 43, 4351 (1965).
[Crossref]

B. G. Wybourne, J. Chem. Phys. 36, 2301 (1962).
[Crossref]

J. Opt. Soc. Am. (2)

Phys. Rev. (3)

N. Rabbiner, Phys. Rev. 130, 502 (1963).
[Crossref]

E.g., N. Rabbiner, Phys. Rev. 132, 224 (1963). Yu. K. Voron’ko, V. V. Osiko, V. T. Udovenchk, and M. M. Fursikov, Soviet Phys.—Solid State 7, 204 (1965).
[Crossref]

M. J. Weber and R. W. Bierig, Phys. Rev. 134, A1492 (1964), and the references therein.
[Crossref]

Proc. Phys. Soc. (London) (1)

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

Solid State Phys. (1)

For example, see M. T. Hutchings, Solid State Phys. 16, 227 (1964).

Other (1)

B. G. Wybourne, Spectroscopic Properties of Rare Earths (Interscience Publishers, John Wiley & Sons, New York, 1965).

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Figures (2)

Fig. 1
Fig. 1

Revised empirical crystal-field-split energy-level scheme for the fluorescent line spectra of a crystal of CdF2:Sm3+ reported by Prener and Kingsley.9

Fig. 2
Fig. 2

Revised empirical crystal-field-split energy-level scheme for the fluorescent line spectra of a cristal of CaF2:Sm3+ reported by Rabbiner.4

Tables (4)

Tables Icon

Table I Operator-equivalent factors for Sm3+

Tables Icon

Table II Approximate values for parameters of the crystal field, (B’s), for Sm3+ in CaF2 and Sm3+ in CdF2 (cm−1)

Tables Icon

Table III Energy values of crystal-field-split levels of Sm3+ in CaF2 and Sm3+ in CdF2 (cm−1).

Tables Icon

Table IV Approximate eigenfunctions of Sm3+ in a tetragonal crystal field in CaF2 and CdF2.

Equations (10)

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H ( tetragonal ) = B 2 0 O 2 0 + B 4 0 O 4 0 + B 4 4 O 4 4 + B 6 0 O 6 0 + B 6 4 O 6 4 .
B n m = η n A n m r n .
H ( tetragonal ) = C n i X i n
5 2 3 2 1 2 1 2 3 2 5 2 5 2 a b 3 2 d b 1 2 c 1 2 c 3 2 b d 5 2 b a
a = 10 B 2 0 + 60 B 4 0 ; b = 12 ( 5 ) 1 2 B 4 4 ; c = 8 B 2 0 + 120 B 4 0 ; d = 2 B 2 0 180 B 4 0 .
7 2 5 2 3 2 1 2 1 2 3 2 5 2 7 2 7 2 l e 5 2 f g 3 2 h g 1 2 i e 1 2 e i 3 2 g h 5 2 g f 7 2 e l
l = 21 B 2 0 + 420 B 4 0 + 1260 B 6 0 ; e = 180 ( 35 ) 1 2 B 6 4 + 12 ( 35 ) 1 2 B 4 4 ; f = 3 B 2 0 780 B 4 0 6300 B 6 0 ; g = 420 3 B 6 4 + 60 3 B 4 4 ; h = 9 B 2 0 180 B 4 0 + 11 340 B 6 0 ; i = 15 B 2 0 + 540 B 4 0 6300 B 6 0 .
9 2 7 2 5 2 3 2 1 2 1 2 3 2 5 2 7 2 9 2 9 2 j k 7 2 m n 5 2 p q 3 2 r q 1 2 k s n 1 2 n s k 3 2 q r 5 2 q p 7 2 n m 9 2 k j
j = 36 B 2 0 + 1512 B 4 0 + 15 120 B 6 0 ; k = 36 ( 14 ) 1 2 B 4 4 + 1800 ( 14 ) 1 2 B 6 4 ; m = 12 B 2 0 1848 B 4 0 55 440 B 6 0 ; n = 60 ( 14 ) 1 2 B 4 4 + 360 ( 14 ) 1 2 B 6 4 p = 6 B 2 0 1428 B 4 0 + 50 400 B 6 0 ; q = 60 ( 21 ) 1 2 B 4 4 960 ( 21 ) 1 2 B 6 4 ; r = 18 B 2 0 + 252 B 4 0 + 30 240 B 6 0 ; s = 24 B 2 0 + 1512 B 4 0 40 320 B 6 0 .
F . M . = | Dev . | ( col . 3 ) Avg . of | differences | of Exp . ( col . 2 ) from center of gravity .