Nature of the 5f states in actinide metals

64 Pages·2009·2.91 MB·English

REVIEWSOFMODERNPHYSICS,VOLUME81,JANUARY–MARCH2009
Nature of the 5f states in actinide metals
Kevin T. Moore*
ChemistryandMaterialsScienceDirectorate,LawrenceLivermoreNationalLaboratory,
Livermore,California94550,USA
Gerrit van der Laan†
DiamondLightSource,Chilton,Didcot,OxfordshireOX110DE,UnitedKingdom
andSTFCDaresburyLaboratory,WarringtonWA44AD,UnitedKingdom
(cid:1)Published6February2009(cid:2)
Actinide elements produce a plethora of interesting physical behaviors due to the 5f states. This
reviewcompilesandanalyzesprogressintheunderstandingoftheelectronicandmagneticstructure
ofthe5fstatesinactinidemetals.Particularinterestisgiventoelectronenergy-lossspectroscopyand
many-electron atomic spectral calculations, since there is now an appreciable library of core d
→valenceftransitionsforTh,U,Np,Pu,Am,andCm.Theseresultsareinterwovenanddiscussed
against published experimental data, such as x-ray photoemission and absorption spectroscopy,
transport measurements, and electron, x-ray, and neutron diffraction, as well as theoretical results,
suchasdensity-functionaltheoryanddynamicalmean-fieldtheory.
DOI:10.1103/RevModPhys.81.235 PACSnumber(cid:1)s(cid:2): 71.10.(cid:1)w,71.70.Ej,71.70.Gm,79.20.Uv
CONTENTS 1. Inversephotoemission 266
2. Valence-bandphotoemission 266
3. 4fcorephotoemission 267
I. Introduction 235
D. Photoemissionasaprobefor5flocalizationinPu 268
A. Theactinideproblem:Notenoughdata 235
V. ElectronicStructureofActinideMetals 268
B. Actinideseriesoverview 236
A. Thorium 268
II. ElectronEnergy-LossSpectroscopy 242
B. Protactinium 270
A. TheO (cid:1)5d→5f(cid:2)edge 245
4,5 C. Uranium 270
B. TheN (cid:1)4d→5f(cid:2)edge 246
4,5 1. WhydoesUmetalexhibitLScoupling? 270
III. Many-ElectronAtomicSpectralCalculations 247
2. SuperconductivityinTh,Pa,andU 272
A. Ground-stateHamiltonian 248
3. Charge-densitywavesin(cid:2)-U;in(cid:2)-Npand
1. Spin-orbitinteraction 248 (cid:2)-Pualso? 272
2. Electrostaticinteractions 249
4. Intrinsiclocalizedmodes 273
3. LS-couplingscheme 251
D. Neptunium 273
4. jj-couplingscheme 252
E. Plutonium 276
5. Intermediate-couplingscheme 253
1. Whatweknow 276
B. Spin-orbitsumrule 254
2. Density-functionaltheory 278
1. wtensors 254
3. Dynamicalmean-fieldtheory 279
2. Derivationofthesumrule 255
4. Crystallatticedynamics 281
3. Limitationsofthesumrule 257
5. Effectsofaging 282
4. jjmixing 258
6. Superconductivityat18.5K 282
C. Many-electronspectralcalculations 258
F. Americium 283
1. TheO (cid:1)5d→5f(cid:2)edge 260
4,5 1. Pressure-dependentsuperconductivity 285
2. TheN (cid:1)4d→5f(cid:2)edge 261
4,5 G. Curium 286
IV. PhotoemissionSpectroscopy 263
H. Berkelium 288
A. Basics 263
VI. CommentsandFutureOutlook 288
B. Theoryinanutshell 264
Acknowledgments 291
1. Screeningofthephotoinducedhole 264 References 291
2. Kondoresonance 265
C. Experimentalresults 266
I.INTRODUCTION
A.Theactinideproblem:Notenoughdata
*Authortowhomcorrespondenceshouldbeaddressed.Fax:
The electronic and magnetic structure of most el-
[email protected].
†Also at School of Earth, Atmospheric, and Environmental ementalmetalsinthePeriodicTableiswellunderstood.
Sciences, University of Manchester, Manchester M13 9PL, Some exceptions to this are manganese, which has a
UnitedKingdom. complicated magnetic structure that is still being inves-
0034-6861/2009/81(cid:1)1(cid:2)/235(cid:1)64(cid:2) 235 ©2009TheAmericanPhysicalSociety
236 KevinT.MooreandGerritvanderLaan: Natureofthe5f statesinactinidemetals
tigated (cid:1)Hafner and Hobbs, 2003; Hobbs et al., 2003(cid:2), physics involved and the lack of a healthy body of ex-
cerium, which has an apparent isostructural fcc→fcc perimental data from which to validate the theory.
phase transformation with a volume change of (cid:3)17% In order to counter the lack of experimental data,
that is due to a fundamental change in the behavior we are progressively recording the various core d
of the 4f states (cid:1)Johansson, 1974; Koskenmaki and →valence f transitions of the actinides using electron-
Gschneidner, 1978; Allen and Martin, 1982(cid:2), and pluto- energy-loss spectroscopy (cid:1)EELS(cid:2) in a transmission elec-
nium, which not only exhibits a wide variety of exotic tron microscope (cid:1)TEM(cid:2) (cid:1)Moore et al., 2003; Moore,
behaviorsduetothecomplexnatureofthe5fstates,but Chung, Morton, et al., 2004; Moore, Wall, Schwartz, et
also sits at the nexus of an anomalous (cid:3)40% volume al.,2004;vanderLaanetal.,2004;Moore,vanderLaan,
change that occurs in the actinide series (cid:1)Zachariasen, Haire, et al., 2006; Moore, van der Laan, Tobin, et al.,
1973; Hecker, 2000, 2004; Albers, 2001(cid:2). 2006; Moore and van der Laan, 2007; Moore, van der
Focusing on the actinides, it is apparent that only Laan, Haire, et al., 2007; Moore, van der Laan, Wall, et
modest attention has been given to the light to middle al., 2007; Butterfield et al., 2008(cid:2). Once acquired, the
metals in the series, excluding uranium (cid:1)Lander et al., spectra are analyzed using multielectron atomic spectral
1994(cid:2). There have been experimental investigations on calculations (cid:1)Thole and van der Laan, 1987, 1988a,
the phase transformations (cid:1)Ledbetter and Moment, 1988b; van der Laan and Thole, 1988a, 1996(cid:2) to discern
1976; Zocco et al., 1990; Hecker, 2004; Blobaum et al., fundamentalaspectsoftheelectronicstructureofthe5f
2006(cid:2), electronic structure (cid:1)Baer and Lang, 1980; Nae- statesintheactinidemetals,suchasangularmomentum
geleetal.,1984;Havelaetal.,2002;Gouderetal.,2005(cid:2), coupling mechanisms, electron filling, and limits on the
charge-density waves (cid:1)Smith et al., 1980; Smith and number of valence electrons. We purposefully focus on
Lander, 1984; Marmeggi et al., 1990; Moore et al., 2008(cid:2), the 5f states, since they are the main culprit for most of
phonon-dispersion curves (cid:1)Manley, Lander, Sinn, et al., the odd behaviors observed in actinide metals, alloys,
2003; Wong et al., 2003(cid:2), effects of self-induced irradia- and compounds.
tion (cid:1)Schwartz et al., 2005(cid:2), and pressure-induced phase Inthisreview,wecoverprogressinunderstandingthe
transformations (cid:1)Roof et al., 1980; Haire et al., 2003; electronic structure of the 5f states in the actinide metal
Heathman et al., 2005(cid:2). Yet even with these and other series. First, we cover EELS for the O (cid:1)5d→5f(cid:2) and
4,5
studies, there are still many unanswered questions, and the N (cid:1)4d→5f(cid:2) edges of thorium (cid:1)Th(cid:2), uranium (cid:1)U(cid:2),
4,5
arguments persist on topics such as the number of elec- neptunium (cid:1)Np(cid:2), plutonium (cid:1)Pu(cid:2), americium (cid:1)Am(cid:2), and
trons in valence states, magnetism, angular momentum curium (cid:1)Cm(cid:2) metal.2 Next, we derive and examine the
coupling,andthecharacterofbonding.Theheaviestac- many-electron atomic spectral calculations for the d→f
tinides have almost no experimental investigations, gen- transitions, paying close attention to the LS-, jj-, and
eratingonlyarudimentarylevelofunderstanding.Thus, intermediate-coupling mechanisms. Returning our at-
the actinide series as a whole is modestly understood, tention to experiment, we cover inverse, valence-band,
with the level of comprehension decreasing with atomic and 4f core x-ray photoemission of the actinide metals
number. The lack of experiments is due to the toxic and up to Am. Finally, with all the EELS, many-electron
radioactive nature of the materials, which makes han- atomic calculations, and photoemission (cid:1)PE(cid:2) spectra
dling difficult and expensive. In addition, the cost of the compiled, the electronic structure of each elemental
materials themselves is exceedingly high, meaning ex- metal is discussed in turn. Further experimental results
periments that need a large amount of materials further are considered, such as x-ray absorption spectroscopy,
increase the expense of research. transport measurements, and electron, x-ray, and neu-
Theoreticalworkonactinidemetalsisextensive,since tron diffraction, as well as theoretical models, such as
theory allows one to circumvent the need to physically DFT and DMFT. The combination of experimental and
handle the materials.1 The theoretical studies range theoretical results forms a cogent picture of the physics
from density-functional theory (cid:1)DFT(cid:2) with either the of the 5f states in the elemental actinide metals.
generalizedgradientapproximation(cid:1)GGA(cid:2)orthelocal-
density approximation (cid:1)LDA(cid:2) to multielectron atomic
B.Actinideseriesoverview
spectral calculations to dynamical mean-field theory
(cid:1)DMFT(cid:2). Regardless of this considerable body of work,
In the Hamiltonian used for electronic-structure cal-
progress in understanding from these calculations has
culations, there are two standard ways to couple the an-
been hampered due to the extreme difficulty of the
gular momenta of multielectronic systems: Russell-
Saunders(cid:1)LS(cid:2) andjj coupling.Inatomswherethespin-
1Examples: Gupta and Loucks, 1969; Skriver et al., 1978; orbit coupling is weak compared to the Coulomb and
exchange interactions, the orbital angular momenta(cid:1) of
Skriver, 1985; Solovyev et al., 1991; Söderlind, Johansson, and
individual electrons are coupled to a total orbital angu-
Eriksson,1995;vanderLaanandThole,1996;Penicaud,1997;
Fastetal.,1998;Söderlind,1998;Erikssonetal.,1999;Savrasov lar momentum L, and likewise the spin angular mo-
and Kotliar, 2000; Savrasov et al., 2001; Dai et al., 2003; Kute-
pov and Kutepova, 2003; Söderlind and Sadigh, 2004; Wills et
al., 2004; Pourovskii et al., 2005; Shick et al., 2005; Moore, 2Wediscussprotactinium(cid:1)Pa(cid:2)andberkelium(cid:1)Bk(cid:2)inthelater
Söderlind,Schwartz,etal.,2006;Shicketal.,2006;Shimetal., sectionseventhoughwepresentnoEELS,valence-band,or4f
2007;Svaneetal.,2007;Marianettietal.,2008. photoemissionspectroscopy.
Rev.Mod.Phys.,Vol.81,No.1,January–March2009
KevinT.MooreandGerritvanderLaan: Natureofthe5f statesinactinidemetals 237
menta s are coupled to a total S. Then L and S are
coupled to form the total angular momentum J. This
approach simplifies the calculation of the Coulomb and
exchange interactions, which commutate with L, S, and
J, and hence are diagonal in these quantum numbers.
Forheavierelementswithlargernuclearcharge,relativ-
istic effects give rise to a large spin-orbit interaction,
which is diagonal in j and J, but not in L and S. There-
fore, in the jj-coupling scheme the spin and orbital an-
gular momenta s and (cid:1) of each electron are coupled to
form individual electron angular momenta j and then
the different j are coupled to give the total angular mo-
mentumJ.ItisknownthatLS couplingholdsquitewell
for transition metals (cid:1)in the absence of crystal field(cid:2) and
for rare-earth metals. Their atoms exhibit a Hund’s rule
groundstatewithmaximumS andL,whicharecoupled
by spin-orbit interaction antiparallel (cid:1)parallel(cid:2) to each
other for less (cid:1)more(cid:2) than half-filled shell, resulting in FIG. 1. (cid:1)Color online(cid:2) Wigner-Seitz radius of each metal as a
J=(cid:4)L−S(cid:4) (cid:1)J=L+S(cid:2). However, for the 5f states of the functionofatomicnumberZforthe5d,4f,and5fmetalseries.
actinidesthespin-orbitinteractionismuchstronger,giv- FromBoringandSmith,2000.Theupper-leftinsetsschemati-
ing a significant mixing of the Hund’s rule ground state cally illustrate localized and delocalized 5f states between ad-
byotherLS stateswiththesameJ value.Hence,theLS jacentactinideatoms.FromAlbers,2001.
states are less pure and there is a tendency toward the
jj-coupling limit. The choice of the coupling limit has
both behaviors. First, a parabolic-like decrease in vol-
profound implications for the expectation value of the
spin-orbit interaction, as well as for any other orbital- umeisobservedwithincreasingf-electroncount,similar
related interactions, such as the orbital magnetic mo- to the 5d series. Then, a large jump in volume occurs in
ment. The safest way to address the 5f states is to use the vicinity of Pu, which is followed by little change for
intermediate coupling, where the actual size of the spin- Am and beyond, similar to the rare-earth series.
orbit and electrostatic interaction is accounted for. In In the 5f states, there is a spin-orbit splitting of
thisreview,weshowthatthiscouplingcanleadtoafew 1–2 eV between the j=5/2 and 7/2 levels due to rela-
surprises, such as the magnetism-driven state of a high- tivistic effects. This causes the 5f electrons to tend to-
pressure phase of Cm metal. ward a jj-coupling mechanism where the early actinide
In order to understand the bonding of the 5f metals metals preferentially fill the j=5/2 level (cid:1)Söderlind,
acrosstheactinideseries,itisinstructivetoconsiderthe 1994; Moore, van der Laan, Haire, et al., 2007; Moore,
4f and 5d metal series. Actinide metal bonding can be van der Laan, Wall, et al., 2007(cid:2). Thus, the first part of
separatedintotwodifferentbehaviors,onewherethe5f the actinide series in Fig. 1 shows a parabolic shape due
electrons strongly participate in bonding and one where to the filling of the bonding and then antibonding states
they offer little or no cohesion. This is schematically il- in the j=5/2 level. Here the 5f states are delocalized,
lustratedinFig.1,wheretheWignerSeitzatomicradius forming bands and they are metallic. However, near the
(cid:1)volume(cid:2) is given for each element in the 5d, 4f, and 5f point where the j=5/2 level is filled with the six elec-
metal series. The 5d transition metals show a parabolic- trons, the 5f electrons retract and localize, leaving the
like change in volume due to an increase in the number (cid:1)spd(cid:2)3 electrons to perform the bulk of the bonding in
of d electrons. In traversing the series, the size of the the metal. The loss of 5f bonding causes the large vol-
atomsfirstdecreasesduetothefillingofthe5d bonding ume increase in the actinide series shown in Fig. 1. In-
states, then begins to increase as the antibonding states terestingly, the crystallographic volume change occurs
are filled. This parabolic-like behavior is indicative of a over a span of six solid allotropic phases of Pu
system with itinerant electrons that participate in the (cid:1)(cid:2),(cid:3),(cid:4),(cid:5),(cid:5)(cid:1),(cid:6);seeFig.2(cid:2),where(cid:2)hasthehighestden-
bonding. In the 4f rare-earth series the opposite case is sity and (cid:5)the lowest. After Pu, the actinide series ap-
observed, one in which the volume changes little be- pears similar to the rare-earth series due to the absence
cause the 4f electrons are localized and do not strongly of appreciable f-electron bonding; accordingly, the 5f
participate in bonding. Rather, the (cid:1)spd(cid:2)3 electrons act states behave in a more atomic fashion.
tobindthemetals,andbecausethespdelectronsdonot The changes that occur in the actinide series can be
vary in count from trivalent along the rare-earth series, visualized in a different manner using the “pseudo-
almostnochangeinpackingdensityisobserved.Excep- binary” phase diagram shown in Fig. 3 (cid:1)Smith and
tionsintherare-earthseries,whichareomittedinFig.1, Kmetko, 1983(cid:2). In this diagram, the binary phase dia-
are Eu and Yb. Both these metals are divalent with grams for each neighboring elemental metals are mar-
(cid:1)spd(cid:2)2andthushavealargervolumethantherestofthe ried together. The phase boundaries that are not exact
trivalent rare-earth metals. Finally, the 5f series shows matches between diagrams are extrapolated using logi-
Rev.Mod.Phys.,Vol.81,No.1,January–March2009
238 KevinT.MooreandGerritvanderLaan: Natureofthe5f statesinactinidemetals
FIG.4. (cid:1)Coloronline(cid:2)A“pseudobinary”phasediagramofthe
light to middle 5f actinide metals as a function of pressure
(cid:1)fromLindbaumetal.,2003,withthephaseboundariesforCm
updated using Heathman et al., 2005, and Cm-Bk alloys from
Heathman et al., 2007(cid:2). The pressure behaviors of Np and Pu
are not shown, but the ground-state crystal structure of each
metalisindicated.
cal guesses based on thermodynamic principles. Thus,
whilethepseudobinaryphasediagramisnotstrictlycor-
rect, it does afford great insight into the general behav-
FIG. 2. (cid:1)Color online(cid:2) Atomic volume of Pu as a function of
ior of the actinide metal series. Examining Fig. 3 shows
temperature, including the liquid phase. The crystal structure
that as the early actinide metals are traversed, several
ofallsixsolidallotropiccrystalstructuresofthemetalisgiven
changesoccurnearPu:themeltingtemperaturereaches
in the lower right-hand side. Note the structure changes from
a minimum (cid:1)Matthias et al., 1967; Kmetko and Hill,
low-symmetry monoclinic to high-symmetry fcc, which occurs
1976(cid:2), the number of phases increases to a maximum,
with exceedingly large volume changes over a short tempera-
and the crystal structures become exceedingly complex
turespan.FromHecker,2000.
(cid:1)Zachariasen and Ellinger, 1963(cid:2). Whereas most metals
are usually cubic or hexagonal, U, Np, and Pu exhibit
tetragonal, orthorhombic, and even monoclinic crystal
structures, the last being an atomic geometry usually
found in minerals (cid:1)Klein and Hurlbut, 1993(cid:2).
Pressure also causes rapid and numerous changes in
the actinides metals, particularly the elements beyond
Pu. This is illustrated in the phase diagram in Fig. 4
(cid:1)Lindbaum et al., 2003; Heathman et al., 2005, 2007(cid:2),
where the phase fields for Am, Cm, Bk, and Cf are nu-
merousandcomplicatedcomparedtothelightactinides.
This is due to the fact that as pressure is increased in
these metals, the 5f states begin to actively bond, pro-
ducing low-symmetry crystal structures. Thus, high-
pressure research for Am, Cm, Bk, and Cf is of great
interest and is discussed in detail in the later sections.
Atearlystagesofactinideresearch,thelow-symmetry
crystal structures of the light actinide metals were as-
cribed to directional covalent bonds (cid:1)Matthias et al.,
FIG.3. (cid:1)Coloronline(cid:2)A“pseudobinary”phasediagramofthe 1967(cid:2). However, over time it became evident that the 5f
lighttomiddle5factinidemetalsasafunctionoftemperature.
states in Th-Pu are delocalized and, to varying degrees,
Near Pu, the melting temperature reaches a minimum, the
bandlike.Arkoetal.(cid:1)1972(cid:2)andSkriveretal.(cid:1)1978(cid:2)first
number of phases increases to a maximum, and the crystal
showed that the 5f band is exceedingly narrow, on the
structuresbecomeexceedinglycomplexforametal,exhibiting
order of 2 eV. In turn, it was shown that narrow bands
tetragonal, orthorhombic, and even monoclinic geometries.
This is not entirely a thermodynamically valid phase diagram prefer low-symmetry crystal structures as illustrated by
as some phase boundaries are guesses, however, the diagram the density-functional theory results in Fig. 5, where the
doesofferinsightintothebehaviorandelectronicstructureof calculated total energy of different crystal structures is
themetalsacrosstheseries.FromSmithandKmetko,1983. plottedasafunctionofcalculatedbandwidth(cid:1)Söderlind,
Rev.Mod.Phys.,Vol.81,No.1,January–March2009
KevinT.MooreandGerritvanderLaan: Natureofthe5f statesinactinidemetals 239
Eriksson, Johansson, et al., 1995(cid:2). Four separate metals
are shown, each with different electron bonding states:
Al (cid:1)2p bonding(cid:2), Fe (cid:1)3d bonding(cid:2), Nb (cid:1)4d bonding(cid:2), and
U (cid:1)5f bonding(cid:2). For all four metals, low-symmetry crys-
tal structures are observed when the bandwidth is nar-
row, such as found in the 5f states of the actinides at
ambient pressure. On the other hand, high-symmetry
structuresarefoundforwidebands,similarto4dand5d
metals. This is even true for the 4f and 5f metals when
they are pressurized to the point where the f states be-
come broad enough to support high-symmetry cubic or
hexagonal structures. The difference in bandwidth be-
tweenthes,d,andf statesisschematicallyillustratedin
theinsetoftheFepanelofFig.5.Whereasthesbandis
on the order of 10 eV wide and the d band is on the
order of 6 eV wide, the f band is only about 2 eV wide.
Ofcourse,pressurevariesthesebandwidths,whereposi-
tive pressure widens the band while negative pressure
narrows the bands, reducing the crystal structure sym-
metry (cid:1)Söderlind, Eriksson, Johansson, et al., 1995(cid:2).
The symmetry reduction due to narrow bands shown
by Söderlind, Eriksson, Johansson, et al. (cid:1)1995(cid:2) illus-
trates that the crystal structure of a metal distorts
through a Peierls-like mechanism. The original Peierls-
distortion model was formulated in a one-dimensional
lattice, where a row of equidistant atoms can lower its
total energy by forming pairs. The lower periodicity
causes the degenerate energy levels to split into two
bands with lower and higher energies. The electrons oc-
cupythelowerlevels,sothatthedistortionincreasesthe
bonding and reduces the total energy. In one-
dimensionalsystems,thedistortionopensanenergygap
attheFermilevelmakingthesystemaninsulator.How-
ever, in the higher dimensional systems, the material re-
mains a metal after the distortion because other Bloch
states fill the gap. This mechanism is effective if there
aremanydegeneratelevelsneartheFermilevel,thatis,
if the energy bands are narrow with a large density of
states. This, of course, is the case for the light actinide
metals.
At ambient pressure, U, Np, and Pu exhibit a large
numberofcrystalstructuresasthetemperatureisraised
to melting, due to small energy differences between al-
lotropic phases. The small energy differences between
crystals is a result of a narrow 5f band with a high den-
sity of states at the Fermi energy and a slightly broader
d band, each of which are incompletely filled and close
in energy. The effect on the actinides can be seen in the
rearrangedPeriodicTableshowninFig.6(cid:1)a(cid:2),whichcon-
tains the 4f, 5f, 3d, 4d, and 5d metals (cid:1)Smith and
FIG.5. (cid:1)Coloronline(cid:2)Plotofthecalculatedenergiesasafunc- Kmetko, 1983(cid:2). At ground state, the metals in the lower
tion of the calculated bandwidth for Al, Fe, Nb, and U. Note
left exhibit superconductivity and the metals in the up-
that for all metals, regardless of bonding states, the crystal
per right exhibit a magnetic moment. The white band is
structure adopts a low-symmetry geometry when the band-
a transition region where metals are on the borderline
widthbecomesnarrow.Thisshowsthatthesymmetryofacrys-
between localized (cid:1)magnetic(cid:2) to itinerant (cid:1)conductive(cid:2)
tal structure depends on the bandwidth of the bonding elec-
valence electron behavior. The metals at the transition
tron states. Thus, the narrow 5f bands that are actively
bonding in the light actinides are directly responsible for the betweenmagneticandsuperconductingbehaviorexhibit
low-symmetry crystal structures observed. From Söderlind, numerous crystallographic phases with small energy dif-
Eriksson,Johansson,etal.,1995. ference between crystal structures. This increase in the
Rev.Mod.Phys.,Vol.81,No.1,January–March2009
240 KevinT.MooreandGerritvanderLaan: Natureofthe5f statesinactinidemetals
FIG. 7. (cid:1)Color online(cid:2) A “Hill plot” for a large number of U
compounds. The superconducting (cid:1)T (cid:2) or magnetic ordering
S
(cid:1)T orT (cid:2)temperatureforeachcompoundplottedasafunc-
N C
tion of U-U interatomic distance. The transition from super-
conductivity to magnetism occurs around 3.5Å, with only a
fewexceptions.FromHill,1970.
FIG.6. (cid:1)Coloronline(cid:2)Theground-statebehaviorandnumber
of solid allotropic phases of all the five metal series. (cid:1)a(cid:2) Rear- near, the transition. Examples where pressure is used to
ranged Periodic Table where the five transition-metal series, change the 5f states of actinides from localized to delo-
4f,5f,3d,4d,and5dareshown.Whencooledtogroundstate, calized via a diamond anvil cell are Am (cid:1)Lindbaum et
themetalsinthelowerleftexhibitsuperconductivitywhilethe al., 2001(cid:2), Cm (cid:1)Heathman et al., 2005(cid:2), Bk (cid:1)Haire et al.,
metals in the upper right exhibit a magnetic moment. The 1984(cid:2),Cf(cid:1)Petersonetal.,1983(cid:2),andBk-Cfalloys(cid:1)Itieet
whitebandrunningdiagonallyfromupperlefttolowerrightis al., 1985(cid:2). In each case, as the pressure is increased, the
whereconductionelectronstransitionfromitinerantandpair-
structure changes from a high-symmetry, high-volume
ing to localized and magnetic. Slight changes in temperature,
cubic or hexagonal structures to low-symmetry, low-
pressure, or chemistry will move metals located on the white
volume orthorhombic or monoclinic structures that are
bandtoeithermoreconductiveormoremagneticbehavior.(cid:1)b(cid:2)
Version of (cid:1)a(cid:2) where the number of solid allotropic crystal indicativeofactive5fbonding.ExaminingAm,Cm,and
Bk in Fig. 4 clearly illustrates this loss of symmetry as
structures for each metal is indicated by gray scale. Lighter
pressureisincreased.Inanoppositebutsimilarmanner,
shades indicate more phases. Notice that a band of lighter
shadesmirrorsthewhitebandin(cid:1)a(cid:2),showingthatmetalsonor Pu metal can be transformed from the low-symmetry
nearthetransitionbetweenmagneticandsuperconductivebe- monoclinic(cid:2)phasetothehigh-symmetryface-centered-
havior exhibit numerous crystal phases. From Smith and cubic (cid:5)phase by raising the temperature from ambient
Kmetko,1983andBoringandSmith,2000. conditions to (cid:3)600 K, as shown in Fig. 2. The high-
temperature (cid:5)phase of Pu can also be retained to room
temperature by the addition of a few atomic percent of
number of phases near the transition is clearly shown in Al,Ce,Ga,orAm(cid:1)HansonandAnderko,1988;Hecker,
Fig. 6(cid:1)b(cid:2), where gray scale indicates the number of solid 2000(cid:2). Indeed, the crystal structure of U, Np, Pu, and
allotropic phases observed. The diagonal of lighter Am can all be changed by alloying with small amounts
shades (cid:1)more phases(cid:2) in Fig. 6(cid:1)b(cid:2) matches the white ofdopantsduetothesensitivityofthe5fstates.Thefact
bandinFig.6(cid:1)a(cid:2).Thus,eachofthemetalsthatlieonthe thatthecrystalstructureofmostmiddleactinidescanbe
localized-itinerant band has frustrated valence electrons easily altered by pressure, temperature, and chemistry
andexhibitsnumeroussolidallotropiccrystalstructures. makes for rather interesting and unique physics.
U,Np,Pu,andAmallexhibitnumerousphaseswithPu Given the small energy differences between multiple
showing an unsurpassed six different crystal structures structures in actinide metals near the itinerant-localized
that are almost energetically degenerate. transition in Fig. 6(cid:1)a(cid:2), subtle changes can have dramatic
Returning our attention to Figs. 3 and 4, we now see effectsonthemagneticbehaviorofU,Np,Pu,andAm.
why the crystal structure of the actinide metals near Pu An example of this is shown in Fig. 7, where the super-
are so sensitive to temperature and pressure. The close conducting and magnetic transition temperatures for a
energylevelsofbondingstatesandsubsequentlargede- number of U metals, alloys, and compounds are plotted
gree of hybridization in the actinides near the itinerant- againsttheU-Uinteratomicspacing.Theoriginaltheory
localizedtransitionallowthemetal’sbehaviortobeeas- by Hill (cid:1)1970(cid:2) is that the degree of overlap of the
ily changed or “tuned” via pressure, temperature, and f-electron wave functions between neighboring actinide
chemistry. This again is due to the small energy differ- atoms dictates whether a compound is magnetic or su-
ences between crystal structures of the metals on, or perconducting,independentofcrystalstructureorother
Rev.Mod.Phys.,Vol.81,No.1,January–March2009
KevinT.MooreandGerritvanderLaan: Natureofthe5f statesinactinidemetals 241
clearlyshowthatPuisatorneara5f5configurationwith
at least one hole in the j=5/2 level (cid:1)Moore et al., 2003;
Moore, van der Laan, Haire, et al., 2006, 2007; Moore,
van der Laan, Wall, et al., 2007(cid:2). With the hole in the j
=5/2 level, there should be an incomplete cancellation
ofelectronspinand,accordingly,ameasurablemagnetic
moment. How then is there no magnetic moment in the
metal? Several explanations have been proposed, in-
cluding Kondo shielding (cid:1)Shim et al., 2007(cid:2) and electron
pairing correlations (cid:1)Chapline et al., 2007(cid:2). Kondo
shielding, which is schematically shown in Fig. 8(cid:1)a(cid:2), oc-
curs when s, p, and d conduction electrons cloak the
localmagneticmomentthatshouldbepresentinPudue
to the 5f5 configuration. Electron pairing correlation is
another theory to explain the absence of magnetism in
Pu,andisshownschematicallyinFig.8(cid:1)b(cid:2).Whenlattice
distortions are present that lead to internal electric
fields, spin-orbit effects can cause the spontaneous ap-
pearance of spin currents and pairing of itinerant f elec-
trons with opposite spin. Simple symmetry consider-
ationsimplythatanelectricfieldcanleadtospinpairing
only if spin-orbit interactions are important, which is in-
deed known to be true for Pu. Recent magnetic suscep-
tibility measurements have in fact shown that magnetic
moments on the order of 0.05(cid:7)/atom form in Pu as
B
damage accumulates due to self-irradiation (cid:1)McCall et
al., 2006(cid:2). This suggests that small perturbations to the
delicate balance of electronic and magnetic structure of
FIG.8. (cid:1)Coloronline(cid:2)Schematicdiagramof(cid:1)a(cid:2)Kondoshield- Pu metal may destroy or degrade whatever mechanism
ingofthe5fmomentbys,p,anddconductionelectrons(cid:1)Mc- is responsible for the lack of magnetism in Pu. Finally,
Calletal.,2007(cid:2)and(cid:1)b(cid:2)electronpairingcorrelations(cid:1)Chapline spin fluctuations have been proposed as the reason for
etal.,2007(cid:2).Eithermechanismmayberesponsibleformasking the anomalous low-temperature resistivity behavior of
themagneticmomentinPuthatshouldbepresentduetothe Pu that shows no magnetism in the metal (cid:1)Nellis et al.,
5f5 configuration (cid:1)Moore et al., 2003; Moore, van der Laan, 1970; Arko et al., 1972; Coqblin et al., 1978(cid:2). Spin fluc-
Haire, et al., 2007; Moore, van der Laan, Wall, et al., 2007; tuations can be thought of as spin alignments that have
Shimetal.,2007(cid:2). lifetimes less than (cid:3)10−14 s and are therefore too short
to see via specific heat, susceptibility, or nuclear mag-
atomic species present in the compound or alloy. Super- netic resonance (cid:1)Brodsky, 1978(cid:2).
conducting compounds tend to have short distances be- The next logical question is what exactly is the under-
tween actinide atoms, while magnetic compounds tend lying physics that causes the large volume change at the
to have large distances between actinide atoms. Most localized-delocalizedtransitionintheactinideseries?To
materials follow this behavior and for U the address this, we first look toward a metal with similar
superconducting-magnetic transition is found to be near issues that also falls on the localized-itinerant transition
3.5 Å. Exceptions to this are U PtC , UGe , UPt , inFig.6,the4fmetalCe.Atambientpressure,Cemetal
2 2 3 3
UB ,andUN.UGe hasaU-Udistanceof0.42 nm,yet exhibits four allotropic crystal structures between abso-
isno13nmagnetic.Follo3wingtheHillcriteria,thefstatesin lutezeroanditsmeltingtemperatureat1071 K:(cid:2),(cid:3),(cid:4),
UGe should be localized with an atomic magnetic mo- and (cid:5). There are large hystereses between the transfor-
3
ment. The lack of magnetism is due the 5f electrons hy- mations of (cid:2), (cid:3), and (cid:4), causing phase boundaries to be
bridizing into bands with the Ge p states, in turn break- kinetic approximations and mixtures of two or even
ingdowntheHillcriteria.Thus,whilethistypeofplotis threephasestometastablypersistinthethermodynami-
useful, being able to successfully predict the transition cally single-phase fields (cid:1)McHargue and Yakel, 1960;
between magnetism and superconductivity in Ce, Np, Rashid and Altstetter, 1966(cid:2). When fcc (cid:4)-Ce transforms
and Pu (cid:1)Smith, 1980(cid:2), it fails for some cases. to fcc (cid:2)-Ce upon cooling, it undergoes an isostructural
While magnetism in actinide compounds is widely volume collapse of 17%. Several interpretations as to
studied and accepted (cid:1)Santini et al., 1999(cid:2), magnetism in why this collapse occurs are available, such as the pro-
pure Pu is often debated, even though there is no con- motion of the single 4f electron from localized and non-
vincingexperimentalevidenceofmomentsinanyofthe bonding to delocalized and bonding (cid:1)Lawson and Tang,
six allotropic phases of the metal (cid:1)Lashley et al., 2005; 1949(cid:2), a metal-to-insulator Mott transition (cid:1)Johansson,
Heffner et al., 2006(cid:2). EELS and x-ray absorption (cid:1)XAS(cid:2) 1974(cid:2), and a Kondo volume collapse (cid:1)Allen and Martin,
Rev.Mod.Phys.,Vol.81,No.1,January–March2009
242 KevinT.MooreandGerritvanderLaan: Natureofthe5f statesinactinidemetals
atomiclike behavior. This frustrated behavior is exactly
what is shown for Ce and Pu in Fig. 6. The DMFT ap-
proach can discern between a metal-to-insulator Mott
transitionandaKondocollapsescenario.MuchlikeCe,
the exact physics driving the volume anomaly near Pu
remains unanswered. Since Pu metal has necessitated
the greatest advances in computational techniques for
the actinide metals due to its difficult and interesting
physics,adetailedandhistoricalperspectiveofDFTand
DMFT will be presented in the Pu section.
FIG.9. (cid:1)Coloronline(cid:2)Schematicdiagramoftheproductionof If the complex physics of the 5f states and the toxic
a U and He atom through a decay of Pu. This self-induced natureofthematerialsarenotenough,addthefactthat
irradiation slowly damages the crystal structure over time, most actinide metals accumulate damage over time due
making understanding the physics of the metal even more toself-inducedradiation.Thiscomesintheformof(cid:2),(cid:3),
challenging. and(cid:4)decaythatoccursindifferentamounts,depending
on element and isotope (cid:1)Poenaru et al., 1996(cid:2). For ex-
ample, (cid:2)decay occurs in Pu, as shown in Fig. 9. In this
1982(cid:2). The promotional model was challenged when
Gustafson et al. (cid:1)1969(cid:2) showed that there was no signifi- process,aHeatomisejectedwithanenergyof(cid:3)5 MeV
and a uranium atom recoils with an energy of (cid:3)86 keV
cantchangeinthenumberoffelectronsbetween(cid:2)-and
(cid:1)Wolfer,2000(cid:2).TheHeatomcreateslittledamagetothe
(cid:4)-Ce via positron lifetime and angular correlation mea-
lattice;however,theUatomdislodgesthousandsofplu-
surements. The promotion model was further ques-
tonium atoms from their normal positions in the crystal
tioned by Compton scattering data (cid:1)Kornstädt et al.,
lattice, producing vacancies and interstitials known as
1980(cid:2)andx-rayabsorptionmeasurementsoftheLedges Frenkelpairs.Within(cid:3)200 ns,mostoftheFrenkelpairs
(cid:1)Lengeler et al., 1983(cid:2) that showed no substantial va-
annihilate, leaving a small amount of damage in the lat-
lence change between (cid:2)- and (cid:4)-Ce. In disagreement
tice. Over time, this damage accumulates in the form of
withametal-to-insulatorMotttransition,photoemission
defects, such as vacancies, interstitials, dislocations, and
experiments (cid:1)Allen et al., 1981(cid:2) showed the f level is He bubbles (cid:1)Hecker, 2004; Schwartz et al., 2005(cid:2). What
located between 2 and 3 eV below the Fermi energy in
this means is that not only are actinide metals intrinsi-
both phases, never crossing the Fermi level. Magnetic
cally complicated, but lattice damage accumulates over
formfactor(cid:1)Muranietal.,2005(cid:2)andphonondensitiesof
time due to self-irradiation, further complicating the
states(cid:1)Manley,McQueeney,Fultz,etal.,2003(cid:2)measure-
physics of the materials.
ments also disagree with a metal-to-insulator Mott tran- The discussion here is meant to serve as a general
sition by showing that the magnetic moments remain overviewoftheactinideseries,wherethephysicsispre-
localized in both phases. To date, the Kondo volume sentedinamannerthatisapproachableformembersof
collapse, where the 4f level is always below the Fermi numerous scientific and engineering communities. More
energy and results in a localized 4f magnetic moment, precise and detailed discussion of the electronic and
seems the most plausible scenario. Indeed, DMFT cal- magnetic structure of each elemental 5f metal, where
culationsoftheopticalpropertiesof(cid:2)-and(cid:4)-Ce(cid:1)Haule various experimental and theoretical data are discussed,
etal.,2005(cid:2)areinagreementwiththeopticaldataofvan will be given later. Before this, we compile all the O
4,5
der Eb et al. (cid:1)2001(cid:2), supporting the Kondo picture. and N EELS edges, derivate and summarize the mul-
4,5
Nonetheless, the Ce issue is still not yet resolved and tielectron atomic spectral calculations used to analyze
there is theoretical evidence supporting a combination the EELS data, and assemble the published inverse,
of all three effects (cid:1)Held et al., 2001(cid:2). valence-band, and 4f photoemission data. While there
Similar arguments are made for Pu, which also sits are several books on actinide physics and chemistry,
directly on the localized-delocalized transition, but has such as Freeman and Darby (cid:1)1974(cid:2), Freeman and
five 5f electrons rather than one 4f electron as in the Lander (cid:1)1985(cid:2), and Morss et al. (cid:1)2006(cid:2), we strive
caseofCe.Themixed-levelmodel(cid:1)Erikssonetal.,1999; throughout to reference the original publications when
Joyceetal.,2003;Willsetal.,2004(cid:2)postulatesthatwhile possible. Lastly, unpublished research that is in progress
allfive5felectronsareactivelybondingin(cid:2)-Pu,thereis is discussed and referenced at points, since presenting
only one actively bonding in (cid:5)-Pu with the other four suchdataandideas,albeitpreliminary,benefitsthecom-
electrons effectively localized. This argument has some munity.
similarity to the promotion model for Ce. DMFT pro-
videsadescriptionoftheelectronicstructureofstrongly
correlatedmaterialsbytreatingboththeHubbardbands II.ELECTRONENERGY-LOSSSPECTROSCOPY
and quasiparticle bands on an equal footing (cid:1)Kotliar et
al., 2006(cid:2). In strongly correlated materials, there is a Before progressing to the EELS spectra, the question
competitionbetweenthetendencytowarddelocalization of why TEM is used for spectral acquisition should be
of the bonding states, which leads to band formation, addressed. This has several answers. First, TEM utilizes
and the tendency toward localization, which leads to small samples, allowing one to avoid handling appre-
Rev.Mod.Phys.,Vol.81,No.1,January–March2009
KevinT.MooreandGerritvanderLaan: Natureofthe5f statesinactinidemetals 243
amination of only the phase(cid:1)s(cid:2) of interest. An example
of this is shown in Fig. 10, where (cid:1)a(cid:2) is a bright-field
TEM image of an fcc CmO particle in a dhcp (cid:2)-Cm
2
metal matrix, (cid:1)b(cid:2) is an (cid:5)0001(cid:6) diffraction pattern of the
metal,and(cid:1)c(cid:2)isan(cid:5)001(cid:6)diffractionpatternofCmO .A
2
field-emission-gun TEM, such as the one used in these
experiments, can produce an electron probe of (cid:3)5 Å,
meaning recording spectra from a single phase when
performing experiments is easily achieved. Quantita-
tively measuring the reflections in the electron diffrac-
tion pattern in Figs. 10(cid:1)b(cid:2) and 10(cid:1)c(cid:2), as well as other
crystallographic orientations, proves that the correct
phaseisexamined(cid:1)ZuoandSpence,1992;Moore,Wall,
and Schwartz, 2002(cid:2).
EELS spectra collected in the TEM can be compared
to XAS spectra and many-electron atomic spectral cal-
culationswithcompleteconfidence.Atfirstthismaynot
seem a reasonable comparison, since transitions in XAS
are purely electric dipole whereas in EELS there is also
an electric-quadrupole transition due to momentum
transfer (cid:1)Reimer, 1995; Egerton, 1996(cid:2). However, Moser
and Wendin (cid:1)1988, 1991(cid:2) showed on the O (cid:1)5d→5f(cid:2)
4,5
and N (cid:1)4d→5f(cid:2) edge of Th that as the energy of the
4,5
incident electron is increased, the EELS spectral shape
FIG.10. Anillustrationoftheabilityoftransmissionelectron
becamemoresimilartoXAS,andataround2 keVthey
microscopy to image and identify materials at the nanometer
scale. (cid:1)a(cid:2) Bright-field TEM image of a CmO particle con- are close to identical. The incident energy of the TEM
2
tained in a dhcp (cid:2)-Cm metal matrix. (cid:1)b(cid:2) An (cid:5)0001(cid:6) electron- electron source used in these studies is 297 keV, ensur-
diffraction pattern of (cid:2)-Cm metal and (cid:1)c(cid:2) an (cid:5)001(cid:6) pattern of ing the electron transitions are close to the electric-
CmO . Examining the scale bar in (cid:1)a(cid:2) attests to the fact that dipole limit. The use of apertures that remove high-
2
recordingEELSspectraanddiffractionpatternsfromasingle angle Bragg and plural scattering (cid:1)Moore, Howe, and
phase is straightforward given the ability to form an (cid:3)5Å Elbert, 1999; Moore, Howe, Veblen, et al., 1999; Moore,
electron probe in the TEM. Thus, spectral investigations can Stach, Howe, et al., 2002(cid:2) further refines the quality of
beperformedonhighlysite-specificregions,suchasinterfaces, EELS, providing spectra that are practically identical to
dislocations,andgrainboundaries. XAS for transition metals (cid:1)Blanche et al., 1993(cid:2), rare
earths (cid:1)Moore, Chung, Morton, et al., 2004(cid:2), and ac-
tinides(cid:1)Moore,vanderLaan,Tobin,etal.,2006(cid:2).Look-
ciable amounts of toxic and radioactive materials. The
ingspecificallyatactinides,directcomparisonofThand
alternativeisXASperformedatamultiusersynchrotron
U O edge can be made between EELS (cid:1)Moore et al.,
radiation facility, which is less well adapted for the deli- 4,5
2003; Moore, Wall, Schwartz, et al., 2004(cid:2) and XAS (cid:1)for
cate and secure handling of radioactive materials. Sec-
Th:Cukieretal.,1978;Aonoetal.,1981;forU:Cukieret
ond, the technique is bulk sensitive due to the fact that
297-keV electrons traverse (cid:3)40 nm of metal, this being al., 1978; Iwan et al., 1981(cid:2). Similar comparisons can be
made for the N edge of U for EELS (cid:1)van der Laan et
the appropriate thickness for quality EELS spectra of 4,5
al., 2004(cid:2) and XAS (cid:1)Kalkowski et al., 1987(cid:2). In all cases,
actinide materials. A few nanometers of oxide do form
the EELS and XAS spectra are identical within error.
onthesurfacesoftheTEMsamples,butthisisinsignifi-
This equivalence between EELS and XAS is becom-
cant in comparison to the amount of metal sampled
ing stronger now that monochromated TEMs are avail-
through transmission of the electron beam. Third, met-
able that have an energy resolution comparable to
als at or near the localized-itinerant transition in Fig.
6(cid:1)a(cid:2) exhibit numerous crystal structures that can coexist monochromatized synchrotron radiation (cid:1)Lazar et al.,
in metastable equilibrium due to close energy level be- 2006;WaltherandStegmann,2006(cid:2).Infact,someTEMs
tweenphases.Therefore,acquiringsingle-phasesamples can even resolve better than 50 meV (cid:1)Bink et al., 2003(cid:2),
of metals at or near this transition, such as Mn (cid:1)four which is close to the energy of phonon excitations. An
phases(cid:2), Ce (cid:1)four phases(cid:2), and Pu (cid:1)six phases(cid:2), is uncer- example of monochromated EELS with 100 meV en-
tain, making spectroscopic techniques with low spatial ergy resolution as compared to synchrotron XAS is
resolution questionable. Finally, actinide metals readily shown in Fig. 11. The N (cid:1)4d→4f(cid:2) and M (cid:1)3d→4f(cid:2)
4,5 4,5
react with hydrogen and oxygen, producing many un- transitionsof(cid:4)-CeareshownforEELSspectraacquired
wanted phases in the material during storage or prepa- in a monochromated TEM, XAS from the Advanced
ration for experiments. TEM has the spatial resolution Light Source at the Lawrence Berkeley National Labo-
to image and identify secondary phases (cid:1)Hirsch et al., ratory, and many-electron atomic spectral calculations
1977;Reimer,1997;FultzandHowe,2001(cid:2),ensuringex- (cid:1)Moore,Chung,Morton,etal.,2004(cid:2).Notethesimilarity
Rev.Mod.Phys.,Vol.81,No.1,January–March2009
244 KevinT.MooreandGerritvanderLaan: Natureofthe5f statesinactinidemetals
FIG. 11. The N (cid:1)4d→4f(cid:2) and M (cid:1)3d→4f(cid:2) transitions for
4,5 4,5
(cid:4)-Ce metal as acquired by EELS, XAS, and many-electron
atomic spectral calculations. Of particular importance is the
factthattheXASandEELSfromamonochromatedTEMare
essentiallyidenticalinbothresolutionandspectralshape.This
means that comparison between the techniques, as well as to
multielectronicatomiccalculations,isentirelyjustified.
betweenspectra,particularlythetwoexperimentalspec- FIG.12. TheexperimentalO (cid:1)5d→5f(cid:2) EELSedgesforTh,
4,5
tra, which illustrates that EELS in a TEM is practically U,Np,Pu,Am,andCmmetal.Ineachcase,theground-state
identical to synchrotron-radiation-based XAS. Ironi- (cid:2)phasewasexamined.Electrondiffractionandimagingofthe
cally, a monochromated source is not needed for EELS Am sample in the TEM showed that it contained heavy
amounts of stacking faults, which can be argued produces a
measurements on actinides, since the intrinsic core-hole
combination of (cid:2)and (cid:3)phases as it is simply a change in the
lifetime broadening for the actinide d→f transitions is
111 plane stacking. However, spectra taken from areas with
(cid:3)2 eV (cid:1)Kalkowski et al., 1987(cid:2). Nonetheless, the com-
varying amounts of stacking faults showed no detectable dif-
parison of EELS in a monochromated TEM and ference in branching ratio. Thus, (cid:2)- and (cid:3)-Am should have
synchrotron-radiation-based XAS in Fig. 11 firmly dem- verysimilarN spectraand,inturn,branchingratios.
4,5
Rev.Mod.Phys.,Vol.81,No.1,January–March2009