Foreword Actinides, the chemical elements with atomic numbers ranging from 89 to 103, form the heaviest complete series in the Periodic Table. They are radioelements, either naturally occurring or synthesized by nuclear reac- tions. Their predominant practical application depends on the nuclear prop- erties of their isotopes: decay, spontaneous or induced fission. Their chemi- cal and physical properties reflect a very complex electronic structure, and their study and understanding are a challenge to experimentalists and theoreticians. The research programme of the European Institute for Transuranium Elements was, from its very beginning, devoted to both basic research on advanced plutonium containing fuel and to fundamental research on actinide elements. Non-fuel actinide research in Europe started more than 20 years ago with the reprocessing of irradiated actinide samples. Since the first isolation and purification of transplutonium elements, actinide research developed steadily in close contact and cooperation with specialised laboratories in Western Europe and in the United States. The separation and purification of multigram amounts of mA34Z and mC442 in the late sixties at Karlsruhe allowed studies at a scale interesting solid state physicists. On the basis of the first results obtained, a programme "Actinide Research" at the European Institute for Transuranium Elements was established with the aim of investigating the contribution of 5 f electrons to the chemical bond. This programme comprised the preparation of actinide containing samples (metals, intermetallics, binary compounds), their analysis and characterisation and, finally, the study of bond-related thermodynamical, structural and electronic properties. The experimental effort of the programme was complemented by theory. As the Institute for Transuranium Elements has become a "focal point" of actinide research in Europe, it seemed appropriate to assemble actual experimental and theoretical results to describe the state of the art in form of a monograph on Solid State Properties of Acfinides. W. Mtiller General Introduction The properties of actinide solids have been particularly at the center of scientific attention as soon as their investigation raised the first suggestions that, at least in the first part of the series, the unsatured 5f shell had an important role in establishing the chemical bond of the solid, especially the metallic bond. This book attempts to give an overview of the state of knowledge cur- rently available on the solid state physics of actinides. Emphasis will be placed on the basic concepts underlying the treatment of actinide systems. Therefore, the aim of the book is not to be comprehen- sive in all aspects, but rather to present a coherent picture which may be useful to the beginner in actinides and also to the specialist who might feel that a unified picture can help him in interpreting his results and promote further progress. Appropriate examples are chosen for this purpose. Theoretical concepts and the description of experimental methods utilized in actinide research are usually scattered in many textbooks and in the general literature. A further aim of the book is therefore to assemble them in a well connected way. The book is organized as follows: - Chapter A is intended to be an extended overview, where: (1) the prob- lems of actinide solids are presented (Part I); (2) the conceptual context is indicated in which the problems have been partially solved (Parts II and III); (3) relevant experimental evidence for understanding the solid state behaviour of aetinide materials (Parts IV and V) is reviewed. Since the book consists of separate monographic contributions, the authors of Chapter A have attempted to give it a self-consistent character. Chapter B focuses attention on the preparation and characterization of - samples suitable for actinide solid state research. In this context, it is perhaps worthwhile to remark how actinide solid state physics has been, in these years, a subject in which interdisciplinary cooperation has been strongly needed and achieved, perhaps more than in other fields. Chapters C, D and E, discuss thermodynamic and structural properties, - magnetism, and photoelectron spectroscopy of actinide systems in their relation to bonding. - Chapter F presents the most advanced theory of 5 f bonding. An effort was made by the author (as in the rest of the book) to present the essential theoretical formalism in a simplified and hopefully understand- able manner. At least, the reader should be able to find in this chapter a help to introduce himself to the most refined theoretical treatments which are nowadays of great relevance in actinide solid state physics. Table of Contents Chapter A Actinide Solids: 5 f Dependence of Physical Properties J. M. Fournier, L. Manes .................. Chapter B The Preparation of High Purity Actinide Metals and Compounds W. M/iller, J.-C. Spirlet .................. 57 Chapter C Structural and Thermodynamic Properties of Actinide Solids and Their Relation to Bonding L. Manes, U. Benedict ................... 75 Chapter D Magnetic Properties of Actinide Solids J. M. Fournier ....................... 127 Chapter E Localization and Hybridization of 5 f States in the Metallic and Ionic Bond as Investigated by Photoelectron Spectroscopy J. R. Naegele, J. Ghijsen .................. 197 Chapter F The Theory of 5 f Bonding in Actinide Solids M. S. S. Brooks ...................... 263 General Conclusions and Trends in Actinide Research .... 295 Author Index Volumes 1-60 ................. 299 Chapter A Actinide Solids 5 f Dependence of Physical Properties J. M. Fournier I and L. Manes 2 I University of Grenoble and Centre d'Etudes Nucl6aires de Grenoble, Grenoble, France 2 Commission of the European Communities, Joint Research Centre, Karlsruhe Establishment, European Institute of Transuranium Elements, 7500 Karlsruhe, F.R.G. This chapter is an introduction to the main concepts underlying the present unterstanding of the physical properties of actinide solids. In the first half of the actinide series the elements behave as 5 f transition metals; 5 f electrons are then described as itinerant in metallic solids. Between plutonium and americium a cross-over from itineracy to localization, i.e. a true Mott transition is observed. Heavier actinides have a lanthanide-like behaviour, the 5 f states exhibiting similar properties to the 4 f states in lanthanides, The characteristics of 5 f wavefunctions in the actinide atom as well as in actinide solids are reviewed. In the latter, overlapping of 5f wavefunctions between neighbouring atoms as well as their hybridization with other orbitals (actinide 6 d, or orbitals of non-actinide elements in com- pounds) are pointed out as being the two phenomena determining physical properties and bonding characteristics, in particular magnetism. Theories describing them, in particular Stoner's and Mott- Hubbard's models, are discussed in the light of their application to actinide physics. A short summary is presented of the main experimental evidence which justifies the theoretical decription of actinide solids. I. Introduction: Problems of the Actinide Series ..................... 3 .1 Radon Core and Then What? ............................ 3 2. A Short Discussion on the Chemistry of Actinides ................. 3 3. The Metallic Valence: From Chemistry to a Solid State Case ............ 6 a. The Case of Lanthanides ............................ 7 b. The Case of Actinides .............................. 9 4. Conclusions ..................................... 31 II. The Free Actinide Atom ................................ 41 .1 Introduction .................................... 41 2. The Central Field Approximation (Non-Relativistic) ................ 41 a. Electrostatic and Spin-Orbit Interaction .................... 51 b. Models of Couplings (For Two-Electrons Configurations) ........... 61 3. The Relativistic Central Field Approximation ................... 71 4. The Electronic Structure of the Actinide Atoms .................. 71 a. Atomic Wave Functions ............................ 71 b. Atomic Eigenvalues and Electronic Configurations of the Atom ........ 12 Structure and Bonding 06/95 © Springer-Verlag Berlin Heidelberg 5891 2 J.M. Fournier and L. Manes III. General Concepts in Actinide Solid State Physics .................... 22 1. What is Learnt From the Atomic Wave Functions ................. 22 a. The Actinide Metals .............................. 22 b. The Actinide Compounds ............................ 23 2. Localization vs. Itineracy for 5 f Electrons ..................... 24 a. Physical Properties in the Atomic or in the Band Limit ............. 24 b. The Band Description of Electrons in Narrow Bands .............. 24 c. Effective Potential V~ff for an Electron in an Atom and in a Lattice. Localization vs. Itineracy ............................ 27 d. Localized and Itinerant States in the Fermi-Dirac Statistics ........... 28 e. Physical Properties of Conduction Electrons Dependent on N(~F) ....... 29 3. The One-Electron Hamiltonian and the Local Density of States Approximation . . 30 a. Introduction .................................. 30 b. From the Hamiltonian (17) to the Hamiltonian (11) in the Hartree-Fock Limit . 31 c. The Local Density Approximation (LDA) in the Band Formalism ....... 32 d. LDA Approximation for Actinide Solids .................... 33 4. Narrow Band Magnetism and Spin-Polarization .................. 34 a. The Stoner Model for Band Magnetism ..................... 35 b. The Stoner Parameter I and Spin-Polarization ................. 36 5. The Mott-Hubbard Metal-Insulator Transition ................... 37 6. Conclusions ..................................... 40 IV. The Actinide Metals .................................. 41 1. Experimental Evidence of 5 f-Band Behaviour in Lighter Actinides ........ 41 2. The Mott-Like Transition Between Plutonium and Americium ........... 42 3. The Polymorphism of Plutonium Metal ....................... 44 4. Physical Properties of Actinide Metals up to Pu ................... 45 5. Physical Properties of Actinide Metals From Am on ................ 46 6. Superconductivity and Magnetism in Actinide Metals ............... 47 V. The Actinide Compounds ............................... 47 1. The Hill Plots: Usefulness and Weaknesses ..................... 47 2. Band Formation in Actinide Compounds ...................... 51 VI. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 VII. References ....................................... 54 Actinide Solids I. Introduction: Problems of the Actinide Series 1. Radon Core and Then What? Actinide atoms, in their ground configuration, comprise the closed shell electronic struc- ture of the noble gas radon lS 2 2S 2 2p 6 3S 2 3p 6 3d °1 4s 2 4p 6 4d °1 5S 2 5p 6 4f 41 5d °1 6s 2 6p 6 and from three (Ac) to seventeen (Lr) external electrons. As known from the quantum treatment of the hydrogenoid atom (see, e.g))), these outer electrons may be accommodated in the 5 f, 6 d and 7 s shells. In the forties Np (atomic number Z = 93) and Pu (Z = 94) were added )2 to the already known Ac (Z = 89), Th (Z = 90), Pa (Z = 91) and U (Z = 92). The central question, for the chemistry of these elements, was: i. Which shells are filled by these external electrons, and in which order? ii. Is the actinide series a 6 d transition or a 5 f lanthanide series? The answer was by no means straightforward since the first elements (Th, Pa, U) to be studied displayed properties reminiscent of both a transition series and a lanthanide series. The tendency was to expect that the electrons would follow the same order of filling as for the elements from La to Lu, in which the 4 f shell is filled, giving rise to the lanthanide series, before the filling of the 5 d shell. Consequently, Seaborg )2 proposed the name "actinides" for this 5 f series, Ac being the homologous of Ln. In fact, as early as 1941, Mayer )~ showed by means of a Thomas-Fermi type calcula- tion that the atomic wave functions of the 5 f electrons drop suddenly in energy and spatial extension in the vicinity of Z = 92 (i.e. Uranium). This is consistent with the existence of a second lanthanide series, following Ac (Atomic number Z = 89), and going from Th (Z = 90) to Lr (Z = 103). It is customary to place actinides in Periodic Charts of Elements as a homologous series of the lanthanides, meaning that progressive filling of the 5 f shell occurs throughout the series. The results of atomic spectroscopy as well as atomic quantum calculations have made it possible to determine the ground state of the free actinide atoms. These results (see Table )41 ) (that will be reviewed in the next section of this Chapter) confirm the pro- gressive filling of the 5 f shell. From the point of view of the electronic structure of the free atom, therefore, question ii. is solved in the sense of actinides being a series in which the unsaturated 5 f shell is progressively filled (only one or two electrons being accomo- dated in the 6 d shell). Only for element 104 could the 6 d shell start to be filled. Chemistry is known for this element (Rutherfordium or Kurchatovium), although only few atoms have been syn- thesized. 2. A Short Discussion on the Chemistry of Actinides The lanthanides have, as known, very similar chemical properties across the series. Writing them in a single separate line in the periodic chart intends to convey this informa- tion to the reader. 4 J.M. Fournier and L. Manes Table .1 Ground state and first excited state configurations, and their energy difference, for lan- thanides and actinides Ground First Distance Ground First Distance state excited (ev) state excited (ev) state state La d s 2 d2s 33.0 Ac d s 2 s2d 41.1 Ce f d s 2 fd2s 0.30 Th s2d 2 s3d 86.0 Pr 2saf 2sd2f 0.50 Pa 2sd2f s2df 2 52.0 Nd 2s4f 2sd3f 0.83 U 2sd3f s2daf 0.77 Pm 2sSf f4ds 2 0.99 Np 2sdaf 2S5f 0,12 Sm 2s6f frds 43.1 Pu 2s6f 2sdSf 0.78 Eu 2s7f sdTf 06.1 Am 2s7f sdTf 08.1 Gd fTds2 s2dTf 0.79 Cm f7ds2 2sSf 51.0 Zb 2s9f sdSf 2 0.04 Bk 2sgf sdSf 2 0.92 Dy fl°s2 fgds2 0.94 Cf 2s0lf fgds 2 11.2 Ho 2sllf 2sd°lf 0.95 Es flls2 2sd°lf 2.36 Er 2s2If fllds2 0.89 Fm 2s21f ps2lf 2.42 Tm 2s31f sd2lf 2 26.1 Md 2salf ps31f 2.48 Yb 2s4mf ps3~f 2.15 No 2s41f ps41f 2.60 Lu flads2 p2s4lf 15.0 Lr p2s41f 2sd41f 0.99 Is the same true for the actinide elements? In Fig. 1, we have plotted the oxidation numbers of the actinides and of the lan- thanides. We see that for the lanthanides the valence 3 is the most stable valence throughout the series. There are exceptions: Ce displays for instance tetravalency in many compounds; Eu and Yb display divalency. These exceptions are understood: e.g., Eu and Yb are at the half-filling and at the filling of the 4f shell, which are stable electronic configurations. There is a tendency for both to share just the two outer 5 s electrons in bonding, displaying therefore, divalency, and preserve these stable configu- rations. On the contrary, there is a spread of oxidation numbers for the light actinides (at least up to Cm), which, for Pu and Np, range from 3 to 7! After Cm, however, the trivalent oxidation state is always met, and this second half of the actinide series approaches more the behaviour of the lanthanides. Thus, the implications about the chemical behaviour derived from a Periodic Chart in which the actinides are all placed in one line may be somewhat misleading. Rather, it appears that we should distinguish two parts in the series: one up to Cm ("light actinides"), another one from Cm on ("heavy actinides"). In Fig. 1, the valences of the transition 3 d-, 4d-, 5 d-series are also plotted. As for what regards the spread of valences, an interesting observation is that, at least for the light actinides (if not for the whole series), there is more similarity between the actinides and the d-transition elements than the actinides and lanthanides. The oxidation number of an element is used by chemists as a formal quantity, and is a count of bonding electrons. It is so useful that it has generated, as we shall see later, the concept of "metallic valence" when dealing with elemental metals and the metallic bond. In this simple context, the comparisons established in Fig. 1 are particularly signifi- cant. Let us take, e.g., the comparison between Sm (4 6f 5 d o 6 s )2 and Pu (5 f6 6 d o 7 s/). Actinide Solids 5 I d- transition series v 3d 6 - • • 4 - • • • • • • • • • • 2 • • • • • • • • d oC e 5 r nM eF oC iN uC Zn elements ' g ' . . . . . . 20 12 22 23 2/. 25 26 27 28 29 30 Z (d°s )2 (d's 12 (d2s 12 (das 12 (dSs 11 (dSs 12 {d6s )2 (dTs 12 (das 12 {d10s 1 (dt°s 11 outer electrons w d4 6 - • • • • 4 - • • • • • • • • • 20 • • Sr ' Zr ' b oM ' cT ' uR ' R' h P'd Ag ' C elements 38 39 40 1./ 42 43 4/. 45 46 48 Z 47 (d°s )1 (d 1 s )2 {dZs 12 (dZ's 11 (dSs 11 (d6s )1 (dTs )1 (das 11 (d10s °) (dlas 11 (dins )2 outer electrons w d5 6 • - 4 • • • • • - • • • 2o • • , • • ¶ • Yb u'l f~H g'T V~ e~F ds rI iP ~u Hg elements 70 71 72 73 74 75 76 77 78 79 80 Z sOd( 12 (d 1 s )z (d252} (d3s 2 (d4s )2 (dSs z) (dSs )2 (dgs°) (d9s )1 (dl° sl} (d10s z) outer eledrons I f- transition series 6- 4f 4 - • (o} (o) )oC (o) • • • • • • • • • • • • • • • 2 - ~O( • (O) • (O) Lo ' eC ' Pr ' NI d mP ' mS ' UE G d # b Dy . . . aH. Er mT ~b u"L elements 57 58 59 60 16 62 63 64 65 66 67 68 69 70 17 Z (f°dls2) d~f( °21 s°dPt( 12 }Zs°d4f( )Zs°dSf{ )Zs°d6f( }2s°dTf( (f7dls2)(fgd°sZ} (f 1002 d s )(f 11 d 02 s )(f 1202 i:l s ){f 1302 d s )(f ,/1 sOd 2 ) outer electr, 5 f 6 - • • • • • Jo~• ~)oO~C • • • • • tol 4 - • • • • • • • • (01 AOI • • • • • • • • • • • • 2 - )O~ )O( JOI • • • Xc fh Po n ~t p'N Pu I Am I Cm I k31 fC Es I Fm I Md No ~) rL elements 89 90 19 92 93 94 95 96 97 98 99 001 101 201 301 Z (f°dls2l(f°d2s2)(fdsl(fds)(fds)fds)(fdsl(fds)(fdsl(f 212 312 412 602 702 712 912 1002 ds)(f 1102 ds)fi:lsl(f 1202 1302 ds)(f 1402 ds) outer electr. Fig. .1 Oxidation numbers for: - d-transition series', - f-transition series' (lanthanides and actinides); (non-common or uncertain oxidation numbers have been put between )stekcarb We start by considering that the trivalency of La (4 f°6 71d s )2 in its chemistry can be understood with the bonding being performed by the one d and two s outer electrons. In Sm, the trivalency may be understood in the same way with the help of a subsidiary step: the promotion of one f electron to the d shell (from 4f65 d°6 s 2 to 4 f55 dl6 s )2 a process requiring little energy, and which produces the same 5 d16 s 2 outer configurations as La. In fact, for all lanthanides the trivalency may have the same explanation. But com- plementary to this explanation, another statement can be made: for Sm (and for all other 6 J.M. Fournier and L. Manes lanthanides as well) there is a 4f core which is essentially non-bonding: these (five) electrons "cling to the atom". One says that, in lanthanides, the 4f electrons retain atomic properties (a conclusion largely supported by physical properties, e.g. magne- tism). If we turn now to Pu, and seek to explain the large spread of valency by the same naive picture, we are forced to accept one or both of two hypotheses: i. that very little energy may be required to form, from the ground state, a large number of possible configurations by moving 5 f electrons to the d shell; in other words many configurations (5 fx6 d y 7 s )2 (x + y = 6) have similar energies (bonds being formed from 6 d and 7 s electrons only); ii. the 5 f electrons have themselves a tendency to establish bonds. Of course, the two hypotheses are not really independent and only the simplicity of the language employed allows us to state them in such a clear-cut form. Nevertheless, they embody a problem for chemists which is analogous to the one encountered in the chemistry of d-transition series, and which has kept researchers busy for a very long time. 3. The Metallic Valence: From Chemistry to a Solid State Case The concept of valence developed in the preceding section is the basis of the first correla- tions aiming at a global theory of the actinide metallic bond. These correlations were established between the atomic volumes of actinide elemental metals, and the electronic configuration of the actinide atoms 4-s/. Their aim was to provide a general theory of actinides (i.e. to give an answer to the questions i. and ii. of Sect. A.I.1.) within the framework of a simple model of the metallic bond. It is known that the cohesion of a metal is ensured by the electrons partially filling a conduction (or valence) band. The wave functions of these "conduction electrons" are Bloch functions, i.e. amplitude modulated plane waves. Even though these wave func- tions are linear combinations of the electronic wave functions in the isolated atoms, reminiscence of the atomic orbitals is lost (or is eventually contained in the amplitude factor). The conduction electrons are, of course, originally, the outer or valence elec- trons of the atoms; but in a metal, to describe them as s, p, d or f, i.e. with the quantum number proper to the atomic case, has little meaning. They may be considered to many purposes to be "free electrons". The simplest model of a metal is therefore the one in which the metal is depicted as an array of ions "glued together" by conduction (quasi-free) electrons. If this is the case, one may define a "metallic valence" as being, essentially, the charge left in the ion cores when outer electrons have been stripped off. Conversely, the "metallic valence" can be defined as the contribution of outer electrons each atom gives to the "sea" of bonding conduction electrons. The loss of outer electrons from the atoms to a conduction band, in such a simple picture, bears a similarity to the redox process which is supposed to occur in molecular bonds, and which is at the basis of the "oxidation state" or "formal valence" concept. If this is the case, the metallic valence should coincide with one of the valences that one encounters in compounds, possibly with the most stable one. In this model, the binding electrons are often assimilated to a negatively charged, isotropic continuum ("jellium ''5)) surrounding the positively charged ions (the ionic Actinide Solids 7 charge being the metallic valence v). Due to the isotropy of the bonding, one expects "compact" crystal structures to exist in elemental metals (which is the case for most metals, crystallizing in the twelve-coordinated f.c.c, and h.c.p., or in the eight-coordi- nated b.c.c, structure - see Chap. C). The shape of the Wigner-Seitz cell )1 may be safely assimilated to a sphere. The atomic volume Vat, coincides with that of the Wigner-Seitz 3 ~R3s). sphere Vws (Vat = VWS = ~- In this "jellium" model, the equation 9 ~k~v (1) sv~R = 7 can be obtained ,)5 where z,~ is the so-called Fermi-length of a free electron, i.e. the wavelength of a free electron wave, and v is the metallic valence. The quantity kv depends on the detailed description of the total (kinetic and potential) energy of the free- electron. Important contributions are the Coulomb and exchange interactions with the outer electrons of the cores and with other conduction electrons, which add to the electrostatic attraction to the nuclei. However, from (1), one notices that equivalent metals, having approximately the same kr, should have the same Rws. If the radii across a transition series are inspected vs Z, information may be gathered on v. a. The Case of Lanthanides For lanthanides, the metal radii decrease monotonically with increasing atomic number (Fig. 2), with the three anomalies of Ce, Eu and Yb. Let us assume that the metallic valence is three for most lanthanides, and two for Eu and Yb. This is consistent with the chemistry of these elements, since (Fig. 1) three is their most common oxidation number. Trivalency has been explained in the preceeding chapter, by assuming the easy promotion of one 4 f electron to a 5 d level. The conduction quasi-free electrons are therefore of 5 d and 6 s origin. We may say that the conduction band has a prevalent (s, d) character. Two other facts comfort the theory. Firstly, most lanthanide elemental metals crys- tallize in a close-packed structure as expected for the simple model of the metal employed. Secondly, the metals are paramagnetic, and order magnetically (in rather complicated structures). The paramagnetism can be explained by taking into account the magnetic moment of the 4f n configuration which is retained by the ion cores: in fact, paramagnetic moments experimentally determined for metals are almost equal to those of the trivalent, 4 fn, free ions (in compounds, or solutions). One says, therefore, that the 4f n is strongly localized in the lanthanides, meaning that the 4f shell wave functions retain their atomic character. The trend of radii vs. Z shown in Fig. 2 finds then an explanation consistent with the picture of ion cores, each containing a 4 fn non-binding shell. In fact, the 4 fn shells screen only imperfectly the outer electrons. Adding one nuclear charge when going from Z to Z + 1, means increasing the central field of the nucleus, without increasing as efficiently