Table Of ContentForeword
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
