Crystal field effects and shielding of uranium ions

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Crystal field effects and shielding of uranium ions

P. Erdös, H. Razafimandimby

To cite this version:

P. Erdös, H. Razafimandimby. Crystal field effects and shielding of uranium ions. Journal de Physique

Colloques, 1979, 40 (C4), pp.C4-171-C4-172. �10.1051/jphyscol:1979453�. �jpa-00218849�

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JOURNAL DE PHYSIQUE Colloque C4, supplément au n° 4, Tome 40, avril 1979, page C4-171

Crystal field effects and shielding of uranium ions (*)

P. Erdos and H. A. Razafimandimby

Institut de Physique Theorique, Universite de Lausanne, CH-1015 Switzerland

Résumé. — La séparation du niveau fondamental de l'ion libre U4+ a été calculée dans un environnement octahédral et cubique en tenant compte du mélange des différents termes spectroscopiques. Les facteurs d'écrantage de Sternheimer ont été calculés pour les ions U4+ et U'+.

Abstract. — The splitting of the lowest level of the free ion U4+ has been calculated in an octahedral and cubic environment taking into account the mixture of different spectroscopic terms. The Sternheimer shielding factors have been calculated for the ions U and U .

1. Introduction. — The uranium ions have an unfilled 5f shell. The behaviour of these ions in solution or in crystals is determined by the large contribution of the spin-orbit interaction and crystal field potential to the total energy of the 5f electrons.

This is due to the large electric charge of the nucleus, which gives rise to a considerable spin-orbit coupling for the outer electrons, and the large radius of the 5f orbits, which subjects these electrons to strong electric fields by neighbouring ions.

One consequence of this is that the final states will be mixtures of states with different total angular momenta, and the energy level diagrams derived by Lea, Leask and Wolf [1] for f" configurations in crystal field with cubic symmetry become inapplicable.

This has been taken into account by Chan and Lam [2]. These authors have calculated the splitting of the ground state

3

H

4

of U

4+

in an octahedral crystal field. Here, the calculation is performed for a cubic and octahedral fields, using the Coulomb and spin-orbit integral values given by Hecht and Gruber [3], since these values are more accurate than those used by Chan and Lam because they are in agreement with the experimental magnetic sus- ceptibility data on UC1

⁴

[4].

The crystal field parameters are, in general, quan- tities which cannot be successfully calculated, but have to be considered as empirical quantities. This is due partially to the Sternheimer shielding [5].

The crystal field shielding is an effect to which a general meaning can be assigned independent of the composition and structure of the host. This shielding is due to the distortion of the closed shell orbitals of the uranium ion induced by the Coulomb forces created by the surrounding ions. The distorted shells produce an additional potential at the 5f electron site, which is superimposed on the bare crystal field.

(*) With a partial support of the Swiss National Science Foundation Grant n° 2.748-0.77.

The Sternheimer shielding factors have been cal- culated for U

4+

and U

3+

applying the first-order perturbation theory and using the unperturbed wave functions of Lenander [6].

2. Results and comments. — The figure 1 shows the splitting of the

³

H

⁴

level of U

⁴⁺

by a cubic crystal

1 1 1 1

2000 - ^ ^ ^

-2000 - \ ^ \ ^ ^ ^ \ ^ ^ l "

-4000 - V4 \ \ V4 ^ \ "

1 1 1 1 n

T -2000 - \ . ^ O * ; \ NX \ -a -^-=-0 2 \ >N —=-03 \ \ \ \ r

V4 \ ^ 3 V4 \ \ \ \

UJ \ . \ W f i 5 -4000 - \ V X \ -

u 1 1 1 1 X _

-2000 - ^ : ^ \ \ ^ ^ \ \

-4000 - ^§-=-04 K ^ \ -¥§--05 \ \ \

V4 U^ NO\ V« \ V \

-6000 - r' \ v \ r i \ v <r !

0 1000 ioOO ^ 0 -1000 -2000 V4 (cm-i) • -

Fig. 1. — The splitting of the lowest level of U4+ by a cubic crystal field.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979453

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C4-172 P. ERDoS AND H. A. RAZAFIMANDIMBY

field[7] as a function of the crystal field parameters [2]

V,=

A : ( r 4 )

and

V,= A z ( r 6 ) .

We note a difference between our results and those in [I]. In [I] the levels are linear. In our figure they are curve. This is due to the admixture of other

3H

and 'l7 states.

The table

I

shows the Sternheimer shielding factors for

U4'

and

U3'.

We note that only the shielding factor corresponding to the second rank term of the crystal field is large enough. Thus the shielding play

Table

I. - The Stemheimer shielding factors

a,

for U3' and U4'. The factors

a,

are defined by the formulaAT

= ( I - u , ) D T

whereATandDTarethe crystal field parameters with and without shielding respectively.

practically no role for the cubically symmetric crystal field.

References

[I] LEA, K . R., LEASK, M. J. and WOLF, W. P., Phys. Chem. Sol. [4] GRUBER, B. and HECHT, G., J. Chem. Phys. 60 (1974) 1352.

23 (1962) 1381. [S] STERNHEIMER, R. M., Phys. Rev. 146 (1966) 140.

[21 CHAN, S. K. and LAM, D. J., in The Actinides : Electronic [6] LENANDER, C. J., Phys. Rev. 130 (1963) 1033, and a private Structure and Related Properties, edited by A. J. Free- communication.

man and B. J. Darby Jr (Academic Press, New York) [7] The figure corresponding to the octahedral crystal field may

1974. be obtained from the authors.

[31 HECHT, G. and GRUBER, B., J. Chem. Phys. 60 (1974) 4872.