Electronic structure of actinide intermetallic compounds

Journal

of the Less-Common

Metals,

ELECTRONIC STRUCTURE COMPOUNDS* BORJE

JOHANSSON

and OLLE

133

(1987)

25

25 - 29

OF ACTINIDE

INTERMETALLIC

ERIKSSON

Condensed Matter Theory Group, Department Box 530, S-751 21 Uppsala (Sweden)

of Physics,

University

of Uppsala,

M. S. S. BROOKS European (F.R.G.) HANS

Institute

for Transuranium

Elements,

Postfach

2340,

D-7500

Karlsruhe

L. SKRIVER

NORDITA,

Blegdamsvej

17, Copenhagen

DK-2100

(Denmark)

Summary The electronic structure of the actinides (An) is briefly reviewed and special emphasis is given to the drastic change in 5f electron behaviour which takes place when one proceeds from the light to the heavy elements. A similar change is found in our calculations for the AnRh, intermetallic systems as a function of the actinide atomic number, although the transition seems more gradual than for the pure elements. A study of the bulk properties of UPt, and related compounds suggests that a 5f2 local configuration should be an appropriate starting point to describe its electronic properties. Here aspects of magnetism are considered together with equilibrium volumes, and in general good agreement with experiment is obtained.

1. Introduction Much attention is at present directed towards the fundamental question about the nature of the 5f electrons in actinide solids, namely whether they have localized or delocalized (itinerant) properties [ 11. This is of basic importance for the understanding of the chemical and physical behaviour of actinide materials. If delocalized, the 5f electrons participate in a significant way in the bonding [Z, 31 and also strongly affect physical properties such as magnetism and electrical conductivity. The relatively recent discovery [4] of *Paper presented at a Symposium on Solid-State held at the 192nd National Meeting of the American September 7 - 12, 1986. 0022-5088/87/$3.50

0 Elsevier

Actinide Chemical

Chemistry and Physics, Society, Anaheim, CA,

Sequoia/Printed

in The Netherlands

26

the heavy fermion superconductors UPt3 and UBe,, has led to a very widespread interest in the electronic properties of 5f systems. When localized, the 5f electrons will normally form a configuration with a magnetic moment. However, it is well known that itinerant electrons may also give rise to magnetism [5]. Therefore, a magnetic moment is not necessarily a sign of a 5f localization, and more detailed investigations are required before the nature of the 5f electrons can be determined. Owing to the difference in bonding characteristics between local and itinerant 5f electrons it appears possible to use the bond length as a tool to monitor localization. The main problem is, however, to know the bond length when the 5f electrons are localized or when they are itinerant. By comparison with corresponding lanthanide and heavy actinide systems it might be possible to estimate relatively accurately the appropriate bonding length for a local 5f state. Unfortunately, experimental deviations from such expected values can also be a sign of an intermediate valence state [6] rather than of 5f itinerancy. In this situation it might be most instructive to use theoretically calculated equilibrium volumes, where the 5f electrons are treated as itinerant, i.e. bonding, and compare with experiments. Large deviations would then be a sign of localized 5f behaviour. This could be a useful method to distinguish between localized and itinerant 5f states provided the calculated equilibrium volumes are accurate. 2. Actinide

Metals

For the pure elements the presently available evidence strongly suggests a sharp distinction between local and itinerant 5f states. The large volume increase between plutonium and americium has been successfully accounted for by electronic structure calculations [7]. In plutonium metal the 5f electrons are itinerant and in americium metal the 5f electrons are localized (with a trivalent 5f6 configuration). Experimentally determined structural changes [8] suggest that high pressure induces a delocalization of the local 5f configurations in transplutonium elements. Also here theoretical calculations support this picture [ 91. Turning to compounds, intermetallic compounds and alloys the situation is as the moment much less definite. For example the existence of the so-called heavy fermion systems [lo] seems to indicate that a clear separation between localized and itinerant behaviour might not be possible or that at least the distinction is more delicate than previously thought. Extensive research will be necessary before a consistent picture can be developed. 3. AuRh, intermetallic

compounds

Among actinide intermetallic compounds the AnRh3 systems form a very interesting class of materials to study since they are all isostructural (AuCu3 structure). Therefore the change in behaviour with a change of the

27

AnRh,

I

IAuCu+tructure) .

2_ .

l

I

I

W 7,,

_ lAuCuTstructure)

_ .

: 3

68-

spin-

_

-------,

,‘F-,’ sptn,I polarized ,’

unpolarized

l =experiment

I

Th

9’

I

I

I

t

I

Pa

U

Np

Pu

Am

I,

Cm

I

I

I

Ru

Rh

I

1

Pd

Fig. 1. Experimental and theoretical lattice constants for the AnRh3 systems. Fig. 2. Experimental and theoretical equilibrium volumes for uM3 systems (M = Ru, Rh and Pd); the calculations were all performed for the AUCUJ structure. Notice that experimentally UPd3 has the hexagonal TiNi structure.

actinide element is not obscured by effects associated with structural differences. In Fig. 1 the lattice constant is plotted for the known AnRhs systems. It should be noticed that the trend is similar to that of the pure elements: for example there is a distinctive jump in the lattice constant between PuRhs and AmRhs. In the same figure the results of linear muffin-tin orbital (LMTO) electronic structure calculations [ll - 131 are shown. For the earlier compounds (ThRh3, PaRh, and URhs) there is good agreement between the calculated paramagnetic equilibrium volumes and experiment. For NpRh3, PuRhs and especially AmRh3 there are very clear discrepancies between the paramagnetic (unpolarized) calculations and experiment. However, allowing for spin-polarization we find a much better agreement. Especially large effects are seen for AmRh3, where an almost fully spin-polarized 5f-state is obtained as the ground-state. Thereby the 5f contribution to the bonding is very much reduced and this is interpreted as a 5f localization in AmRhs. Thus, as for the pure elements, there is also a change from itinerant to localized 5f behaviour for the AnRhs systems. A difference is, however, that this change seems to be more gradual than for the pure elements since NpRh3 and PuRhs exhibit an intermediate behaviour.

4. Localization

in UPd3

A 5f localization might also take place as a function of the alloying partner. Experimentally, URh3 is classified as an itinerant 5f system while for UPda there are data suggesting a localized 5f2 configuration [ 14, 151. In Fig. 2 we have plotted the experimental equilibrium volumes for URu3, URhs and UPds and compared them with theoretical results. (Unfortunately,

28

UPd3 has the hexagonal TiNis structure, while URus and URhs have the AuCu3 structure. In Fig. 2 the calculations were all performed for the AuCus structure.) Very good agreement is found for URus and URhs, while the paramagnetic solution for UPds gives a volume which clearly deviates from experiments. The ferromagnetic solution gives an improved value, but is still not quite in agreement with the experimental data. It seems significant, however, that the calculated ferromagnetic state gives a 5f configuration which is fully spin-polarized. This suggests that an improved treatment would give a localized 5f state. By artificially removing the 5f bonding contribution from the calculations good agreement with the experimental equilibrium volume is obtained. From the present theoretical results the fundamental electronic structure difference between URhs and UPd, is found to be the position of the 5f state relative to the 4d states. For URhs the 5f states and the Rh4d states overlap in energy and therefore hybridize quite strongly, while in UPds the 5f states are situated energetically above the palladium 4d states thereby drastically reducing the 4d-5f hybridization. Consequently, this gives a much narrower 5f band for UPds than for URhs, which facilitates a 5f localization. We now demonstrate that the 5f localization in UPd, is also associated with a volume jump. To do this we consider the formula unit volume change, AV, upon formation of the compound; AV = V(UM,) - V(U-metal)

- 3V(M-metal)

(1)

In Fig. 3 this quantity has been plotted as a function of the 4d element. As can be noticed immediately there is a drastic difference between on one hand URus and URhs and on the other UPds. For comparison we have included in Fig. 3 the corresponding volume change for thorium and some other tetravalent elements, which all show a very different behaviour than U. This clearly demonstrates that there is a significant change of the electronic structure as one proceeds from URus and URhs to UPds. In Fig. 3, the

5

Ru Rh

Pd

Fig. 3. Formula unit volume change, AV (defined systems (A = U, Th, Hf and Zr; B z Ru, Rh and Pd.)

in eqn. (l)),

for various ABa

29

similarity between thorium and zirconium (or hafnium) shows that in this respect thorium behaves as a normal tetravalent metal. It is also interesting to notice that for URu3 and URhs the compounds have somewhat larger volumes than the sum of the individual metallic volumes. The reason for this can be traced back to the 5f electrons, since in the compounds the 5f band contribution to the bonding is less than in the pure metal. In UPds, because of the 5f localization, this bonding contribution is totally withdrawn, hence AV(UPds) becomes anomalously large (Fig. 3). If in eqn. (1) the volume of the uranium metal is substituted by the hypothetical volume for tetravalent (5f localized, 5f2 configuration) uranium metal, which is about 28 A3 atom-‘, then the corresponding AV value for UPd3 becomes comparable with the AV values for the tetravalent metals thorium, zirconium and hafnium. This is in fact the same 5f configuration as derived from the neutron scattering data for UPd3 [ 141.

Acknowledgment This work was partly supported by the Swedish Natural Science Research Council. The authors wish to acknowledge the Donors of The Petroleum Research Fund, administered by the American Chemical Society, for travel support.

References on the 1 See, for example, articles in A. J. Freeman and G. H. Lander (eds.), Handbook Physics and Chemistry of the Actinides, Vol. 1, North-Holland, Amsterdam, 1984. B. Johansson, Phys. Rev. B, 11 (1975) 2740. B. Johansson, J. Phys. Chem. Solids, 39 (1978) 467. Z. Fisk, H. R. Ott, T. M. Rice and J. L. Smith, Nature, 320 (1986) 124. C. Herring, in G. T. Rado and H. Suhl (eds.), Magnetism, Vol. IV. Academic Press, New York, 1966. North-Holland, Amsterdam, 6 P. Wachter and H. Boppart (eds.), Valence Instabilities, 1982. 7 H. L. Skriver, 0. K. Andersen and B. Johansson, Phys. Rev. Lett., 41 (1978) 42. 8 U. Benedict, J. P. Itie, R. G. Haire and J. R. Peterson, J. Phys. F, 14 (1984) L43. 9 H. L. Skriver, 0. K. Andersen and B. Johansson, Phys. Rev. Lett., 44 (1980) 1230. 10 P. A. Lee, T. M. Rice, J. W. Serene, L. J. Sham and J. W. Wilkins, Comments Condensed Matter Phys., XII (1986) 99. 11 0. K. Andersen, Phys. Rev. B, 12 (1975) 3060. 12 H. L. Skriver, The LMTO Method, Springer-Verlag, Berlin, 1984. 13 B. Johansson, 0. Eriksson, M. S. S. Brooks and H. L. Skriver, Phys. Ser., 13 (1986) 65.

14 N. Shamir, M. Melamud, H. Shaked and M. Wegner, Physica B, 94 (1978) 15 Y. Baer, H. R. Ott and K. Andres, Solid State Commun., 36 (1980) 387.

225.