Electronic structure of cubic uranium compounds

(1)

HAL Id: jpa-00218802

https://hal.archives-ouvertes.fr/jpa-00218802

Submitted on 1 Jan 1979

HAL

is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire

HAL, est

destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Electronic structure of cubic uranium compounds

J. Keller, M. Erbudak

To cite this version:

J. Keller, M. Erbudak. Electronic structure of cubic uranium compounds. Journal de Physique

Colloques, 1979, 40 (C4), pp.C4-22-C4-23. �10.1051/jphyscol:1979406�. �jpa-00218802�

(2)

JOURNAL DE PHYSIQUE Colloque C4, supplLment au no 4, Tome 40, avril 1979, page C4-22

Electronic structure of cubic uranium compounds

J. Keller (*) and M. Erbudak (**)

Eidgenossische Technische Hochschule, 8093 Zurich, Switzerland

R6sumC.

-

La mBthode de la diffusion multiple self-consistante est appliquBe B 1'Btude de la densit6 d'6tats Blectroniques de UN et de US. Le rtsultat principal est le melange des Btats s, p, d et f de l'uranium dans la bande de valence et la bande de conduction. Les rBsultats thBoriques sont en accord avec les spectres de photoBmission, pour des Bnergies d'excitation 20 < hu < 80 eV.

Abstract. - Self-consistent cellular multiple scattering techniques are used to study the density of states of UN and US. The main results refer to the mixing of the s, p, d and f-states of uranium into a valence and a conduction band. The theoretical results compare favorably with the photoemission energy distribution curves taken at 20 < hv < 80 eV.

1. Introduction.

-

The cubic salts of uranium present special characteristics associated with the presence of an unfilled Sf-shell near the Fermi level.

Photoelectron spectroscopy from these materials show trends which are difficult to reconcile with a naive rigid band picture. Nevertheless, the energy dependence of the spectra shows that the assumed conduction band of UN and US has a very large energy enhancement which could indicate that f- levels are within the conduction band.

Here we used a self consistent cellular multiple scattering technique for a finite cluster in condensed-matter-like boundary conditions to study the electronic structure of UN and US [I].

2. Methods.

-

The calculation uses multiple scattering techniques, where the local density of states for the atomic species i, at energy E is given by the diagonal elements of the imaginary part of the Green's function

The radial lscal charge density p, ( r ' ; E ) is written in terms of the R1(rf ; E ) , solutions for energy E of the radial Schrodinger equation for scatterer i in the (self-consistent) atomic potential V(rl) with the boundary condition :

R l ( r l ; E ) = jl(Kr') cos 77, - nl(Krl) sin ^{g ,}

.

(*) Institut fur theoretische Physik, on leave from FQ-UNAM Mexico 20, DF.

(**) Laboratorium fiir Festkorperphysik.

p, ( r ; E ) can be used to evaluate the above atomic quantities or other integrals depending on the local charge density. The potentials are computed from p, ( r ; E ) using the local exchange Xa, technique 123.

Details of the analysis is presented elsewhere [3].

The calculation is done in the continuum spectrum and is not a molecular calculation [I].

3. Results. - A self-consistent potential was ob- tained for the salts with lattice constant 10.372 a.u.

for US and 9.230 a.u. for UN using the approxima- tion of different potentials for different spins with a final magnetization of 2.02 p B for UN and 2.06 p, for US per formula unit. In the muff intin approxima- tion, the sphere radii were 2.835 a.u. for U , 2.351 a.u. for S and 1.780 3 a.u. for N. The cluster consisted of 8 atoms (4 U

+

4 non-metal), the inters- titial potential was found to be Vi, = - 0.75 for US and Vi,, = - 0.78 for UN, relative to atomic zero.

The bands are of very special character near the Fermi level but otherwise typical of transition metal cubic salts [4]. In the case of US the s-band of S begins at - 1.36 Ry and extends up to above the Fermi level. The p-band of S begins at some higher energy ( - 1.08 Ry) and extends also beyond the Fermi level for both spins. The amount of f and d character on the S side is very small. On the U side, on the contrary, the amount of s and p character is small. A U d-band begins at - 0.98 Ry for both spins. The f-band has a resonance at - 0.41 Ry for minority spin and at - 0.47 Ry for majority spin which almost coincides with the Fermi level of the salt, E , ⁼^-0.51 Ry. For UN, the situation is not very different. The f-resonances are lower in energy but almost in the same position relative t o the Fermi level.

Single crystals of UN and US were cleaved in a vacuum of lo-'' torr range and irradiated by mono-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979406

(3)

ELECTRONIC S T R U W R E OF CUBIC URANIUM COMPOUNDS C4-23 chromatized synchrotron radiation. Photoelectrons

are energy-analysed with a resolution of typically 0.20 eV. Experimental details are described elsewhere [5].

The EDC's (energy distribution curves) taken at hv = 20,30 and 40 eV for US and at hv = 30,40 and 79 eV for UN are displayed in figure 1, after sub- tracting the secondary electrons. In US, we observe an f-d conduction band right below E,, with high density of states at E,. The behaviour of this band with increasing photon energy indicates the high 1-character of electrons emitted. This band is almost 2 eV wide at half maximum. A valence band starts at about 2.5 eV below E , and extends to about 12 eV.

In UN, the relative emission intensity of the valence band is higher. This band is located at lower binding energies compared to the valence band of US. The f-d conduction band is even narrower than for US, again with very high density of states at the Fermi level.

URANIUM SULFIDE U R A N I U M NITRIDE

I N I T I A L ENERGY (eV)

Fig. 1.

-

Energy distribution curves obtaikd from US and U N at different photon energies. Electron energies in eV prior to excitation are plotted with respect to the Fermi level.

4. Discussion.

-

The density of states for both spins, shown in figure 2, has two well defined re- gions. The one at lower energies is of almost exclu- sive anion s-p character. The second, an upper band of U d-f character starts almost at the value of the interstitial potential and can then be considered a conduction band. Near the Fermi level the density of states for minority spin is predominantly U d character and for majority spin U f character. The self- consistent calculation indicates that the U f-band is localized enough to resist a change in its occupation between the nitride and the sulphide, but hybridized emough to have its position at the Fermi level. This behaviour is strikingly different from that of the rare earths where the f-band one electron eigenvalues can be below the Fermi level and nevertheless only partially filled.

I = rnlnor~ty

~. .

:::URANIUM d-ELECTRONS

EF 1111 URANIUM 1- ELECTRONS

ELECTRON ENERGY I Ry

Fig. 2.

-

Local density of states for both spins per formula unit and By are plotted for US and UN. For bulk properties of U N only the sum is relevant. The hatched and dotted areas indicate the f and d contributions, respectively.

Acknowledgments.

-

^{We thank}D. E. Eastman and J. L. Freeouf for their contribution in collecting the photoemission data and M. Castro for his help in the Computer Centre.

[I] KELLER, J., R o c . I11 Int. c o d . Computers in Ch- [3] KELLER, J. and ERBUDAK, M., to be published in 2. Phys. B.

Research, Education and Technology, 4 s . Ludeik, [4] WEINBERGER, P., Berichte der Bunsen -Gesellschaft 81 (1977) E. V., Sabelli, N . and Wahl, A. C. (New York) 1977, W.

p. 225, also KELLER, J . , J. Physique CoNoq. 33 (1972) 153 EASTMAN, D. E., FREEOUF, J. and ERBUDAK, M., J. Phys. C 6 C3-241 and KELLER, J., FRITZ, J. and GARRITZ, A., J. (1973) 37.

Physique Colloq. 35 (1974) (24-379.

[2] HERMAN, F . , VAN DYKE, J. P., ORTENBURGER, I. B., Phys.

Rev. Lett. 22 (1%9) 807.