Comprehensive nuclear materials 2 02 thermodynamic and thermophysical properties of the actinide oxides

Comprehensive nuclear materials 2 02 thermodynamic and thermophysical properties of the actinide oxides Comprehensive nuclear materials 2 02 thermodynamic and thermophysical properties of the actinide oxides Comprehensive nuclear materials 2 02 thermodynamic and thermophysical properties of the actinide oxides Comprehensive nuclear materials 2 02 thermodynamic and thermophysical properties of the actinide oxides Comprehensive nuclear materials 2 02 thermodynamic and thermophysical properties of the actinide oxides

the Actinide Oxides

C Gue´ neau, A Chartier, and L Van Brutzel

Commissariat a` l’Energie Atomique, Gif-sur-Yvette, France

ß 2012 Elsevier Ltd All rights reserved.

DFT Density functional theory

EMF Electromotive force

EXAFS Extended X-ray absorption fine

OECD The Organisation for Economic

Co-operation and Development

XAS X-ray absorption spectroscopy

XPS X-ray photoelectron spectroscopy

Owing to the wide range of oxidation statesþ2, þ3,

þ4, þ5, and þ6 that can exist for the actinides, the

chemistry of the actinide oxides is complex The

main known solid phases with different

stoichiome-tries are shown inTable 1

Actinide oxides mainly form sesquioxides and

dioxides Theþ3 oxides of actinides have the general

formula M2O3, in which ‘M’ (for metal) is any of the

actinide elements except thorium, protactinium,

ura-nium, and neptunium; they form hexagonal, cubic,

and/or monoclinic crystals

Crystalline compounds with the þ4 oxidation

state exist for thorium, protactinium, uranium,

nep-tunium, plutonium, americium, curium, berkelium,

and californium The dioxides MO2are all

isostruc-tural with the fluorite face-centered cubic (fcc)

structure Most of these actinide compounds can beprepared in a dry state by igniting the metal itself, orone of its other compounds, in an atmosphere ofoxygen The stability of the dioxides decreases withthe atomic number Z All dioxides are hypostoichio-metric (MO2  x) Only uranium dioxide can becomehyperstoichiometric (MO2 þ x) The thermodynamicproperties of the dioxides vary with both temperatureand departure from the stoichiometry O/M¼ 2.Only uranium, neptunium, and protactinium formoxide phases with oxygen/metal ratio>2 An oxida-tion state greater thanþ4 can exist in these phases.The þ6 state exists for uranium and neptunium in

UO3 and NpO3 Intermediate states are found in

U4O9and U3O8arising from a mix of several tion states (þ4, þ5, þ6)

oxida-Detailed information on the preparation of thebinary oxides of the actinide elements can be found

in the review by Haire and Eyring.1The absence of features at the Fermi level in theobserved XPS spectra indicates that all the dioxidesare semiconductors or insulators.2

Systematic investigations of the actinide oxidesusing first-principles calculations were very useful

to explain the existing oxidation states of the differentoxides in relation with their electronic structure.For example, Petit and coworkers3,4clearly showedthat the degree of oxidation of the actinide oxides islinked to the degree of f-electron localization In theseries from U to Cf, the nature of the f-electronschanges from delocalized in the early actinides tolocalized in the later actinides Therefore, in theearly actinides, the f-electrons are less bound tothe actinide ions which can exist with valencies ashigh asþ5 and þ6 for uranium oxides, for example

In the series, the f-electrons become increasinglybound to the actinide ion, and for Cf only the þ3valency occurs With the same method, Andersson

et al.5studied the oxidation thermodynamics of UO2,NpO2, and PuO2 within fluorite structures Theresults show that UO2exhibits strong negative energy

of oxidation, while NpO2 is harder to oxidize andTable 1 Known stable phases of actinide oxides The phases marked with * are considered as metastable phases

U3O8

PuO2 has a positive or slightly negative oxidation

energy As in Petit and coworkers,3,4 the authors

showed that the degree of oxidation is related to the

position of the 5f electrons relative to the 2p band

For PuO2, the overlap of 5f and 2p states suppresses

oxidation The presence of H2O can turn oxidation of

PuO2 into an exothermic process This explains

clearly why hyperstoichiometric PuO2 þ x phase is

observed only in the presence of H2O or hydrolysis

products.6

Solid actinide monoxides ‘MO’ were reported to

exist for Th, Pu, and U According to the

experimen-tal characterization of plutonium oxide phases by

Larson and Haschke,7 these phases are generally

considered as metastable phases or as ternary phases

easily stabilized by carbon or/and nitrogen From

first-principles calculations, Petit et al.3 confirmed

that the divalent configuration M2þis never favored

for the actinides except maybe for EsO On the

contrary, the monoxides of actinide MO(g) are stable

as vapor species that are found together with other

gas species M(g), MO2(g), MO3(g) which fraction

depends on oxygen composition and temperature

when heating actinide oxides

InSections 2.02.2 and 2.02.3, the phase diagrams

of the actinide–oxygen systems, the crystal structure

data, and the thermal expansion of the different oxide

phases will be described The related thermodynamic

data on the compounds and the vaporization behavior

of the actinide oxides will be presented inSections

2.02.4 and 2.02.5 Finally, the transport properties

(diffusion and thermal conductivity) and the thermal

creep of the actinide oxides will be reviewed in

Sections 2.02.6 and 2.02.7

Actinide–Oxygen Systems

There is no available phase diagram for the Ac–O,

Pa–O, Cf–O, and Es–O systems For the other

sys-tems, the phase diagrams remain very uncertain

In most of the cases, only the regions of the diagrams

relevant to the binary oxides have been investigated

because of the great interest in actinide oxides as

nuclear fuels As a consequence, the metal-oxide

part of the actinide–oxygen systems is generally not

well known except for the U–O system, which is

the most extensively investigated system For the

acti-nide–oxygen systems, a miscibility gap in the liquid

state is generally expected at high temperature like

in many metal–oxygen systems; it leads to the

simultaneous formation of a metal-rich liquid in librium with an oxide-rich liquid But the extent of themiscibility gap and the solubility limit of oxygen in theliquid metals are generally not known The existingphase diagram data on the binary U–O, Pu–O, Th–O,Np–O, Am–O, Cm–O, Bk–O, and ternary U–Pu–O,

equi-UO2–ThO2, and PuO2–ThO2are presented

2.02.2.1 U–O SystemThe phase diagram of the uranium–oxygen system,calculated by Gue´neau et al.8 using a CALPHADthermochemical modeling, is given in Figure 1(a)and1(b) from 60 to 75 at.% O In the U–UO2region,

a large miscibility gap exists in the liquid state above

2720 K The homogeneity range of uranium dioxideextends to both hypo- and hyperstoichiometriccompositions in oxygen The minimum and maxi-mum oxygen contents in the dioxide correspond

to the compounds with the formula of tively UO1.67at 2720 K and UO2.25at approximately

respec-2030 K The phase becomes hypostoichiometricabove approximately 1200 K while the dioxideincorporates additional oxygen atoms at low tem-perature, above 600 K The dioxide melts con-gruently at 3120 20 K The melting temperaturedecreases with departure from the stoichiometry Theexperimental data on solidus/liquidus temperature for

UO2 þ xfrom Manara et al.,11reported inFigure 1(b),are significantly lower than those reported in Baichi

et al.9 and will have to be taken into account in newthermodynamic assessments

In the UO2–UO3region (Figure 1(b) and 1(c)),the oxides U4O9, U3O8, and UO3 are formed withdifferent crystal forms U4O9 and U3O8 are slightlyhypostoichiometric in oxygen as shown inFigure 1(c).The U3O7 compound is often found as an inter-mediate phase formed during oxidation of UO2 Thiscompound is reported in the phase diagram proposed

by Higgs et al.12and considered as a metastable phase

by Gue´neau et al.82.02.2.2 Pu–O System

A thermodynamic model of the Pu–O system wasproposed by Kinoshita et al.27 and Gue´neau et al.28The calculated phase diagram by Gue´neau

et al.28 reproduces the main features of the phasediagram proposed by Wriedt29 in his critical review(Figure 2)

In the Pu–Pu2O3 region of the phase diagram,the experimental data are rare The existence of

a miscibility gap in the liquid state was shown by

Martin and Mrazek.30 The monotectic reaction was

measured at 2098 K.30There are no data on the

oxy-gen solubility limit in liquid plutonium

More data are available in the region between

Pu2O3 and PuO2 The phase relations are complex

below 1400 K PuO2  x starts to lose oxygen above

approximately 900 K A narrow miscibility gap wasfound to exist in the fluorite phase below approxi-mately 900 K leading to the simultaneous presence

of two fcc phases with different stoichiometries inoxygen Two intermediate oxide phases were found

to exist with the formula PuO1.61and PuO1.52 ThePuO1.61 phase exhibits a composition range and is

2500 2000

1500 1000 500

b-U4O9-y

U4O9+

U3O7

U3O7+

U3O8

U4O9+

U3O8

UO2+x(S)+

Van lierde et al.24

Markin and Bones 25

Nakamura and Fujino 16

Figure 1 U–O phase diagram (a) calculated using the model derived by Gue´neau et al 8 ; (b) calculated from 60 to 75 at.%

O 8 ; the green points come from the critical review by Baichi et al 9 and Labroche et al 10 and the blue points show the results of Manara et al 11 ; (c) calculated from O/U ¼ 1.9 to 2.4 after Higgs et al 12 The references of the experimental data are given in Higgs et al 12 ã Elsevier, reprinted with permission.

stable between 600 and 1400 K The PuO1.52

com-pound only exists at low temperature (T < 700 K)

Above 1400 K, the dioxide PuO2  xexhibits a

large homogeneity range with a minimum O/Pu

ratio equal to approximately 1.6 and is in equilibrium

with the sesquioxide Pu2O3 The liquidus

tempera-tures between Pu2O3and PuO2remain uncertain and

would need future determinations

The melting temperature of PuO2is still a subject

of controversy The recommended value for the

melt-ing of PuO2 was for a long time Tm¼ 2674  20 K,

based on measurements from Riley.31 Recent

mea-surements are available that suggest higher values

In 2008, Kato et al.32 measured the melting point of

PuO2 at 2843 K that is higher by 200 K than the

previous measurements The authors used the same

thermal arrest method as in previously published

works but paid more attention to the sample/crucible

chemical interaction by using rhenium instead of sten for the container Very recently, a reassessment ofthe melting temperature of PuO2 was performed by

tung-De Bruycker et al.33 using a novel experimentalapproach used in Manara et al.11 for UO2 The newvalue of 3017 28 K exceeds the measurement

by Kato et al by 174 K The noncontact method andthe short duration of the experiments undertaken

by De Bruycker et al.33 give confidence to their newvalue which has been very recently taken into account

in the thermodynamic modeling of the Pu-O system.42Both studies agree on the fact that the values measured

in the past were underestimated

2.02.2.3 Th–O and Np–O SystemsThe Th–O and Np–O phase diagrams, according tothe experimental studies by Benz34 and Richter andSari35are given, respectively, inFigure 3(a) and 3(b)

In the Th–O phase diagram (Figure 3(a)), onlythe dioxide ThO2exists At low temperature, accord-ing to Benz,34the oxygen solubility limit in solid Th

is low (O/Th< 0.003) A eutectic reaction occurs at

2008 20 K with a liquid composition very close topure thorium The existence of a miscibility gap hasbeen found to occur above 3013 100 K that leads tothe formation of two liquid phases with O/Th ratiosequal to 0.4 and 1.5 0.2, respectively The phaseboundary of ThO2  xin equilibrium with liquid tho-rium was measured The lower oxygen compositionfor ThO2  xat the monotectic reaction corresponds

to O/Th¼ 1.87  0.04 The melting point of ThO2

recommended by Konings et al.36is Tm¼ 3651  17 K.This value corresponds to the measurement by Ronchiand Hiernaut,37which is in good agreement with theone reported on the phase diagram proposed byBenz34inFigure 3(a)

The Np–O phase diagram looks very similar tothe Th–O system but the experimental information isvery limited In the Np–NpO2region, a miscibilitygap in the liquid system is expected but no experi-mental data exist on the oxygen solubility limit inliquid neptunium and on the extent of this miscibilitygap The dioxide exhibits a narrow hypostoichio-metric homogeneity range (NpO2  x) for tempera-tures above 1300 K The phase boundary of NpO2  x

in equilibrium with the liquid metal is not wellknown The minimum O/Np ratio is estimated to

be about 1.9 at approximately 2300 K according to

Figure 3(b) The recommended melting point forNpO2is Tm¼ 2836  50 K.36,38

Only the part richer

in oxygen differs from Th–O with the presence of the

Figure 2 (a) Calculated Pu–O phase diagram after

Gue´neau et al.28on the basis of the critical analysis

by Wriedt29; (b) calculated phase diagram with

experimental data from 58 to 68 at.% O as reported in

Gue´neau et al.28

Np2O5 oxide which decomposes at 700 K to form

NpO2 and gaseous oxygen The thermodynamic

properties of the Np–O system were modeled by

Kinoshita et al.39 using the CALPHAD method, but

the calculated phase diagram does not reproduce

correctly the available experimental data for the

oxy-gen solubility limit in NpO2  xin equilibrium with

liquid neptunium

2.02.2.4 Am–O System

The tentative Am–O phase diagram between Am2O3

and AmO2shown inFigure 4has been proposed by

Thiriet and Konings,40 based on an analysis of the

experimental data available in the literature

No data are available in the Am–Am2O3 region.The Am2O3–AmO2 region looks very similar

to the Pu2O3–PuO2 phase diagram (Figure 2(b)).The sesquioxide Am2O3 exists with hexagonal (A)and cubic (C) forms The dioxide AmO2(a) starts tolose oxygen above approximately 1200 K AmO2  x

has a wide composition range at high temperaturewith a minimum O/Am ratio equal to approximately1.6 As in the Pu–O system, the existence of a narrowmiscibility gap in the fcc phase and an intermediateoxide phase with the formula AmO1.62(C0) were found

by Sari and Zamorani.41A thermodynamic model ofthe Am-O system has been very recently derived byGotcu-Freis et al.42using the CALPHAD method Thecalculated phase diagram is quite consistent with theproposed one by Thiriet and Konings.40

2.02.2.5 Cm–O System

A complete review of the Cm2O3–CmO2region of theCm–O phase diagram was performed by Konings43who proposed the revised tentative Cm2O3–CmO2

phase diagram inFigure 5, on the basis of the tion by Smith and Peterson.44

sugges-The sesquioxide exists in several forms: cubic(C-type), monoclinic (B-type), and hexagonal (A-type)and X Intermediate phases were observed: a bccphase s, with a variable composition (O/Cm between1.52 and 1.64), a rhombohedral phase with the formulaCmO1.71(l), and a fluorite phase CmO1.83(d) CmO2(a)

is stable up to 653 K at which temperature it

1.50 500 1000 1500 2000 2500

Figure 3 Th–O (a) and Np–O (b) phase diagrams after

respectively Benz34and Richter and Sari.35ã Elsevier,

reproduced with permission.

decomposes into gas and intermediate oxides (CmO1.83

and CmO1.71) CmO2  xexhibits a small range of

com-position with a minimum O/Cm ratio of 1.97

2.02.2.6 Bk–O System

A partial phase diagram of the Bk–O system is shown

inFigure 6as proposed in the review by Okamoto.45

A high-temperature X-ray diffraction study by

Turcotte et al.46 showed the existence of C-Bk2O3

(bcc) and a-BkO2 (fcc) oxides A miscibility gap in

the a-BkO2fcc phase was found to exist below 708 K

The sesquioxide exists with several forms: C-Bk2O3

2.02.2.7 U–Pu–O System

It is important to mention that the phase diagram

of the U–Pu–O system is still not well known.There are no data on the metal-oxide regionU–Pu–Pu2O3–UO2 of the U–Pu–O phase diagram.The solubility of the oxide phases in the metallicliquid (U,Pu) is not known Only few experimentaldata exist in the region of stability of the oxidephases delimited by the compounds U3O8–UO2–

Pu2O3–PuO2.2.02.2.7.1 UO2–PuO2

UO2and PuO2form a continuous solid solution andthe solidus and liquidus temperatures show a nearlyideal behavior, as shown in the UO2–PuO2pseudo-binary phase diagram in Figure 7(a) As expected,the melting point of the mixed oxide decreases withthe plutonium content in the solid solution Therecommended equations for the solidus and liquiduscurves from Adamson et al.51are

TsolidusðKÞ ¼ 3120  355:3x þ 336:4x2 99:9x3 ½1

TliquidusðKÞ ¼ 3120  388:1x  30:4x2 ½2

It must be mentioned that recent measurements wereperformed by Kato et al.32on UO2–PuO2solid solu-tions The resulting solidus and liquidus tempera-tures are higher than those from the previous studies(eqns [1] and [2]) As reported in Section 2.02.2.2,the melting point of pure oxide PuO2 measured

by Kato et al and later by De Bruycker et al.33 washigher than the recommended value New determina-tions are necessary to confirm the validity of thesenew data

Recent measurements on hypostoichiometricsolid solutions (U,Pu)O2  xwere also performed byKato et al.50The solidus temperatures decrease withincreasing Pu content and with decreasing O to metalratio A congruent melting line was found to exist thatconnects the hypostoichiometric PuO1.7 to stoichio-metric UO2

2.02.2.7.2 U3O8–UO2–PuO2–Pu2O3Isothermal sections of the U–Pu–O phase diagram

in the oxide-rich region are available only at 300,

673, 873, and 1073 K according to the review by Randand Markin52 which is mainly on the basis of the

Figure 5 The tentative Cm2O3–CmO2 phase diagram

(pO2 ¼ 0.2 bar) according to the critical review by Konings 43

ã Elsevier, reprinted with permission.

experimental investigation by Markin and Street.53

The isothermal section at room temperature was later

slightly modified by Sari et al.54 The fluorite-type

structure of the mixed oxide (U,Pu)O2has the ability

to tolerate both addition of oxygen (by oxidation of the

uranium) and its removal (by reduction of the

pluto-nium only), leading to the formation of a wide

homo-geneity range of formula MO2  x Thus, at high

temperature, the solid solution is a single phase that

extends toward hypo- and hyperstoichiometry But

the extent of the single-phase domain is not well

known at high temperature

At low temperature, as shown in Figure 7(b)

(redrawn in Konings et al.55from Rand and Markin,52

Markin and Street,53and Sari et al.54), the oxide-rich

part of the U–Pu–O phase diagram is complex:

 Region with O/metal ratio <2

The mixed oxide (U100  yPuy)O2  xwith y  20 at

% of Pu is a single phase The hypostoichiometric

oxide is in equilibrium with (U,Pu) alloy

At T < 900 K, the mixed oxides (U100  yPuy)O2  x

with a plutonium content y > 20 at.% enter atwo-phase region that leads to the decompositioninto two fcc oxide phases with two differentstoichiometries x and x1 in oxygen, MO2  x and

MO2  x1 This is consistent with the existence

of a miscibility gap in the fcc phase in the Pu–Osystem This phase separation was recentlyobserved in mixed oxides (U,Pu)O2with small addi-tion of Am and Np by Kato and Konashi.56For higher Pu contents ( y > 50 at.%), the mixedoxide can enter other two-phase regions [MO2  xþ

M2O3(C)] and [MO2  xþ PuO1.62] The existence

of these two-phase regions comes from the complexphase relations encountered in the Pu2O3–PuO2

phase diagram at T < 1400 K (Figure 2(b)) Theisothermal sections at 673, 873, and 1073 K in Randand Markin52show that the extent of the two-phaseregions decreases with temperature The existence

(a)

0 2400 2600

2.0 2.2 2.4 2.6

O: (U

+ Pu)

Pu: (U + Pu)

1.6 1.8 2.0

MO2± x

C-M2O3C-M2O3+ Metal

M3O8

M4O9

Figure 7 U–Pu–O phase diagram at room temperature (a) UO2–PuO2 region; the circles correspond to the

experimental data by Lyon and Bailey, 48 the triangles by Aitken and Evans, 49 and the squares by Kato et al 50 ; the solid lines represent the recommended liquidus and solidus by Adamson et al., 51 the broken line represents the ideal

liquidus and solidus based on Lyon and Bailey, 48 and the dotted line the liquidus and solidus suggested by Kato et al 50

(b) U3O8–UO2–PuO2–Pu2O3 region at room temperature Reproduced from Konings, R J M.; Wiss, T.; Gue´neau, C.

In The Chemistry of the Actinide and Transactinide Elements 4th ed.; Morss, L R., Fuger, J., Edelstein, N M., Eds.; Nuclear Fuels; Springer: Netherlands, 2010; Vol 6, Chapter 34, pp 3665–3812 ã Springer, reprinted with permission.

of a single phase region M2O3 (C) was reported

along the Pu2O3–UO2composition line

 Region with O/metal ratio > 2

At room temperature, the oxidation of mixed

oxides with a Pu content lower than 50%

results in either a single fcc phase, MO2 þ xwith a

maximum O/M ratio of 2.27, or in two-phase

regions [MO2 þ xþ M4O9], [M4O9þ M3O8] and

[MO2 þ xþ M3O8] The M4O9 and M3O8 phases

are reported to incorporate a significant amount of

plutonium However, the exact amount is not known

Yamanaka et al.57developed a CALPHAD model on

the U–Pu–O system that reproduces some oxygen

potential data in the mixed oxide (U,Pu)O2  x and

allows calculating the phase diagram This model

pre-dicts the two-phase region [MO2  xþ PuO1.62] but

does not reproduce the existence of the miscibility

gap in the fcc phase This region was recently

reinves-tigated by Agarwal et al.58 using a thermochemical

model The resulting UO2–PuO2–Pu2O3 phase

dia-gram is presented inFigure 8 The extent of the

mis-cibility gap in the fcc phase is described as a function of

temperature, Pu content, and O/metal ratio This

description of the phase diagram is not complete as it

does not take into account the existence of the PuO1.52

and PuO1.61phases that may lead to the formation of

other two-phase regions involving the fcc phase

In conclusion, no satisfactory description of theU–Pu–O system exists Both new developments ofmodels and experimental data are required

2.02.2.8 UO2–ThO2and PuO2–ThO2

SystemsBakker et al.59 performed a critical review of thephase diagram and of the thermodynamic proper-ties of the UO2–ThO2 system Solid UO2 andThO2form an ideal continuous solid solution Thephase diagram proposed by Bakker et al.59 on thebasis of the available experimental data is presented

inFigure 9(a) The authors report the large tainties on the phase diagram because of the experi-mental difficulties The thermodynamic properties

uncer-of (Th1  yUy)O2 solid solutions have been recentlyinvestigated by Dash et al.60 using a differentialscanning calorimeter and a high-temperature dropcalorimeter The ternary compound ThUO5 wassynthesized and characterized by X-ray diffraction.The thermodynamic data on this compound wereestimated

Like UO2, PuO2forms a continuous solid solutionwith ThO2in the whole composition range Limitedmelting point data were measured by Freshley andMattys.61The results indicate a nearly constant melt-ing point up to 25 wt.% ThO2 In view of the

Present calculations Tie lines

Besmann and Lindemer Isopleths for Figure 3

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0

) ) )

( ( (

Figure 8 Miscibility gap in the fcc phase of the UO2–PuO2–Pu2O3 region according to Agarwal et al.58ã Elsevier, reprinted with permission.

instability of PuO2 at high temperature (high pO2

over PuO2), this behavior could be due to a change

of the stoichiometry of the samples The available

liquidus temperature measurements do not

repro-duce the recommended value for the melting point

of PuO2 The full lines in Figure 9give the solidus

and liquidus curves considering an ideal behavior of

the PuO2–ThO2system

Thermal Expansion

The lattice parameters of actinide oxides are usually

measured in glove boxes because of radioactivity

and chemical hazards In fact, the radioactive decay

may drastically modify the cell parameters with

characteristic time of months (see measurements on(Pu,Am)O2 by Jankowiak et al.,62 on CmO2 in thereview by Konings,43and on sesquioxides by Baybarz

et al.63) Indeed, point defects (caused by irradiation

or simply because of off-stoichiometry) may alsoinduce expansion or contraction of the lattices.The thermal expansion of the cell usually occurswhen increasing the temperature, and it is usuallymeasured starting at room temperature Because ofexperimental difficulties – already mentioned – formeasuring properties (and thus thermal expansioncoefficients) in actinides, some ab initio and/or molec-ular dynamics (MD) calculations are nowadays done

In the framework of MD calculations, the evolution

of the cell parameter can easily be followed as afunction of temperature (see the calculations byArima et al.64 on UO2 and PuO2, and by Uchida

et al.65 on AmO2) The method is slightly differentwhen ab initio calculations are performed (see, e.g.,the work of Minamoto et al.66 on PuO2) One cur-rently calculates the phonon spectra, estimates thefree energy as a function of temperature by means ofquasiharmonic approximation, and then extracts thelinear thermal expansion Such procedure may also

be based on experimental data assuming somehypothesis and simplifications on the phonon spectra(see, e.g., Sobolev and coworkers67–69)

2.02.3.1 Actinide Dioxides2.02.3.1.1 Stoichiometric dioxidesThe actinide dioxides exhibit a fluorite or CaF2struc-ture (Figure 10) Each metal atom is surrounded byeight nearest neighbor O atoms Each O atom is sur-rounded by a tetrahedron of four equivalent M atoms.The cell parameters are reported inTable 2 They are

Figure 9 Pseudobinary (a) UO2–ThO2 and (b) PuO2–ThO2

phase diagrams The solid lines represent the liquidus and

solidus assuming an ideal solid solution Details on the

experimental data are given in Bakker et al 59 Reprinted with

permission from Konings, R J M.; Wiss, T.; Gue´neau, C.

Chemistry of the Actinide and Transactinide Elements,

4th edn.; Springer, 2010; Vol 6, Chapter 24 (in press).

ã Springer.

Uranium fcc sublattice Oxygen cubic sublattice Figure 10 UO2 fluorite (CaF2) structure; the actinide (left) sublattice is fcc while the oxygen (right) sublattice

is primitive cubic.

indeed (almost) linearly dependent upon the ionic

radius of the actinide cations (see Figure 11) It is

noteworthy that the cell parameters reported may be

significantly affected by self-irradiation, as

men-tioned, for example, in CmO2 by Konings43based

on measurements by Mosley.70

A first review of the linear thermal expansion of

stoichiometric actinide dioxides has been done by

Fahey et al.75 in the 1970s This has been updated

by Taylor76 in the 1980s and later by Yamashita

et al.71and Konings43in the 1990s In the simple case

of cubic crystals (such as actinide dioxides; see below),

the evolution of the cell parameter as a function of

temperature is fitted using a polynomial expression

up to the third (sometimes fourth) degree as follows:

aðT Þ ¼ b0þ b1T þ b2T2þ b3T3 ½3

Selected values of the parameters obtained are shown

in Table 2 Overall, the values reported for the b1

parameters are of the same order of magnitude

In fact, the recommended values77for UO2are asfollows:

For 273K< T < 923K: aðTÞ ¼ a273ð9:973  101

þ 9:082  106T  2:705  1010T2

þ 4:391  1013T3Þ ½4For 923K< T < 3120K: aðTÞ

¼ a273ð9:9672  101þ 1:179  105T

 2:429  109T2þ 1:219  1012T3Þ ½5Sobolev and coworkers67–69recently proposed analternative approach for determining the thermalexpansion of actinide dioxides from experimentaldata It is based on the evaluation (from experiments)

of the specific heat CVfrom the phonon spectra at theexpense of some approximations The thermal expan-sion aPis then deduced using the following relation:

apðV ; TÞ ¼gGCVðV ; TÞ

BTðV ; TÞV ½6The thermal expansion coefficient aPdepends uponthe bulk modulus BT, the heat capacity CV, and theGru¨neisen parameter gG The results obtained bySobolev (see figures in Sobolev and coworkers67–69)reproduce quite well the available experimental dataand allow the extrapolation to temperatures higherthan the measurements

2.02.3.1.2 Stoichiometric mixed dioxidesFew binary, ternary, and quaternary mixed acti-nide dioxides have been investigated experimentally.The cell parameters at room temperature along themixed oxides solid solutions usually follow theVegard’s law quite well – that is, a linear evolutionbetween the end members of the solid solution

Table 2 Cell parameters and thermal expansion coefficients ( eqn [3] ) of actinides dioxides

b0 (pm) b1  10 3 (pm K1) b2  10 7 (pm K2) b3  10 10 (pm K3) a298 (pm) References

No thermal expansion data are available for PaO2and CfO2.

ThO2

BkO2

CmO2 PuO2

Figure 11 Evolution of the lattice parameters at room

temperature as a function of the ionic radii 73 plotted using

the data from Table 2

This has been evidenced for Th1  xUxO2 by

Bakker et al.59 on the basis of collected

experi-mental data (see Figure 12) and observed later by

Yang et al.78

According to experimental work by Tsuji et al.,79

Lyon and Bailey,48and Markin and Street,53Vegard’s

law applies for U1  xPuxO2too (seeFigure 12), and

this trend is nicely reproduced by MD calculations

by Terentyev80 and Arima et al.81 (see Figure 13)

MD calculations are consequently currently used

for more complex mixed dioxides, for example, by

Kurosaki et al.82 on the ternary mixed dioxides

U0.7  xPu0.3AmxO2

Recently, experimental measurements done

by Kato et al.56 showed that the Vegard’s law is

valid for ternary and quaternary mixed dioxides

The evolution of the lattice parameter a in

U1  z  y 0  y 00PuzAmy0Npy00O2.00 for low contents of

Am, Pu, and Np obeys quite well the following

linear relation with the ionic radii rU, rPu, rAm,

rNp, and rOand the composition:

Kato et al.56tried to extract the valence of americium

in U1  z  yPuzAmyO2.00, from the evolution of the

cell parameter as a function of the americium

content They deduced that americium isþ4 ratherthanþ3 for the U1  z  y 0  y 00PuzAmy0Npy00O2.00solidsolution, owing to the fact that the ionicradii depend on both the nature and the valence ofthe element

The thermal expansion of mixed actinide dioxides

NpxPu1xO2has been measured by Yamashita et al.71The thermal expansion coefficients are so similar

to each other along the mixed oxide solid solution(see Table 3) that Carbajo et al.84 recommended in

5.600

5.575 5.550 5.525 5.500 5.475 5.450 5.425 5.400

by Tsuji et al 79 (triangles), Lyon and Bailey 48 (open circles), and Markin and Street 53 (squares) The lines represent the Vegard’s law.

U 0.7 Pu 0.3 O 2

U0.8Pu0.2O2

U 0.9 Pu 0.1 O 2

Figure 13 Evolution of the lattice parameter as a function

of temperature of ternary mixed (U,Pu)O2 obtained by molecular dynamics calculations From Arima, T.;

Yamasaki, S.; Inagaki, Y.; Idemitsu, K J Alloys Comp.

2006, 415, 43–50.

their review a single equation for the whole solid

solution The thermal expansion coefficients as a

function of neptunium and thorium composition in

UO2 have been measured by Yamashita et al.,83and

by Anthonysamy et al.85 The data are reported in

Tables 4 and 5 In the UxTh1  xO2 solid solution,

the evolution of those coefficients bi (0 i  3,

eqn [3]) follows a quadratic relation with the

compo-sition, as shown by Anthonysamy et al.85 or Bakker

et al.59But in many cases, the simple Vegard’s law is

applied to the evolution of lattice parameters as a

function of composition and temperature Results

obtained by MD calculations show that such a

simpli-fication works well in the MOX (see Arima et al.81

inFigure 13 or Kurosaki et al.82 for ternary mixed

(U,Pu,Am)O2)

2.02.3.1.3 Nonstoichiometric actinide

dioxides

Interestingly, the lattice parameters also depend

linearly on the stoichiometry in hypo- and

hyper-stoichiometric actinide (mixed or not) dioxides

The variation of the volume DO/O induced by single

isolated defects may be related to the variation ofthe macroscopic volume DV/V, as follows:

DV

Depending on the sign of DO, there will be a swelling

or a contraction of the volume The evolution of thecell parameter is linear as function of stoichiometry

x in UO2 þ xand (U,Pu)O2  x(see Figure 14), withdifferent slopes for hypo- and hyperstoichiometricdioxides from Javed,86 Grønvold26 in UO2 þ x, andMarkin et al.53 in (U,Pu)O2  x This is because theformation volumes DO of oxygen defects are different.Concerning the thermal expansion, the coefficients areroughly similar to each other, whatever be the stoichi-ometry considered, as can be seen inFigure 15 Such

a behavior is well reproduced by MD calculations(see Watanabe et al.87and Yamasaki et al.88)

The evolution of the lattice parameters as a tion of stoichiometry has been summarized byKato et al.56in minor actinides containing MOX (see

func-Figure 16(b)) The hypostoichiometry induces aswelling of the lattice as in UO2 þ x Such behaviorhas been seen in americium containing PuO by

Table 3 Thermal expansion coefficients of the NpxPu1x O2 obtained by Yamashita et al.71

Miwa et al.90and in pure MOX (see Arima et al.,81and

references therein), and this is qualitatively

repro-duced by MD calculations (see Figure 16(a)) The

thermal expansion coefficients of hypostoichiometric

dioxides (not reproduced here) simply follow the

Vegard’s law (see Arima et al.81), as evidenced in

urania in the previous section

2.02.3.2 Actinide Sesquioxides

The actinide sesquioxides can crystallize with three

different forms: a hexagonal close-packed (a), a

mono-clinic (b), or a cubic (c) structure The hexagonal form

is in most of the cases the stable phase at room

temperature The cubic phase may be considered as afluorite structure from which 1/4 of the oxygen ionshave been removed The crystal data on the actinidesesquioxides are listed inTable 6

Few experimental data are available concerningthe thermal expansion coefficients of actinide sesqui-oxides The thermal expansion can be fitted with thefollowing equation (in percentage):

DL

L0 ¼ a0þ a1 T þ a2 T2 ½9Konings43has extracted from experiments the ther-mal expansion of monoclinic B-Cm2O3 We havedone the same for Pu2O3 (from Taylor76) In thecase of Am2O3, we have used the data obtained byUchida et al.65 by MD calculations A summary isavailable inTable 7

Figure 15 Thermal expansion of UO2þ x as a function of

stoichiometry x The data are extracted from Grønvold 26

The lines are linear fits.

Figure 14 Evolution of the lattice parameters of UO2þ x

and (U,Pu)O2 x as a function of stoichiometry Circles are

extracted from Javed 86 and squares are extracted from

Grønvold 26 The filled symbols are reported from Markin and

Street 53 The lines are linear fits.

12% Pu–MOX 20% Pu–MOX-1 20% Pu–MOX-2

40% Pu–MOX

30% Pu–MOX Reference

6% Np–MOX

2% Np/Am–MOX

12% Np–MOX MOX-1 1.8% Np/Am–MOX

Reduction limit

1.8 5.44 5.46 5.48 5.5

5.52 5.54

1.85 (a)

2.02.3.3 Other Actinide Oxides

As mentioned inSection 2.02.3.1, the fluorite

struc-ture of UO2has empty octahedral sites that can be

occupied by O2 ions to form UO2 þ x The phase

diagram data show that the maximum oxygen content

corresponds to x ¼ 0.25 (or U4O9) (Figure 1) From

his interpretation of neutron diffraction data on

UO , Willis100 found that the interstitials tend to

aggregate to form clusters made of oxygen tials interacting with normal oxygen anions.101,102The so-called cluster 2:2:2 is composed of two oxygenvacancies and four interstitials Below 1400 K, theseclustered excess oxygens tend to form an orderedphase with the composition U2O9  y

intersti-U4O9 is a narrowly hypostoichiometric phase(U4O9  y) and exists with three different forms:

Table 6 Crystalline structure data of the actinide sesquioxides

c ¼ 0.630(2)

c ¼ 0.5918(1)

c ¼ 0.5971

c ¼ 0.5985(12)

b ¼ 0.364(1) b ¼ 100.5(1)

c ¼ 0.884(3)

c ¼ 0.5958(2)

b ¼ 0.3606(3) b ¼ 100.23(9)

c ¼ 0.8846(5)

c ¼ 0.596(1)

b ¼ 0.3592(4) b¼ 100.34(8)

c ¼ 0.8809(7)

c ¼ 0.60

c ¼ 0.880

Table 7 Thermal expansion of some actinide sesquioxides

a0 a1  10 4 (K1) a2  10 7 (K2) References Data

a-U4O9  y (at T < 353 K), b-U4O9  y (at 353 K<

T < 823 K), and g-U4O9  y(at 823 K< T < 1400 K)

The structure of the b-U4O9 phase was studied

by Bevan et al.103 who showed that this phase is a

superlattice structure based on the fluorite structure

of UO2with a unit cell 64 times the volume of the

UO2 cell The additional O atoms are arranged in

cuboctahedral clusters According to the later

analy-sis by Cooper and Willis,104the centers of the clusters

are unoccupied, whereas they are occupied by single

O-ions according to Bevan et al.103U4O9decomposes

at 1400 K into UO2 þ x (disordered with x  0.25)

and U3O8(seeFigure 1)

U3O8 is a mixed valence compound with U(V)

and U(VI) cations U3O8 exists in several forms as

a function of temperature At room temperature,

a-U3O8is orthorhombic and transforms to a

pseudo-hexagonal structure b-U3O8at 483 K Heat capacity

measurements by Inaba et al.105showed other phase

transitions at 568 and 850 K

UO3can crystallize in six forms The stable form

at room temperature a-UO3is orthorhombic

Partial information on crystal data of plutonium

and curium intermediate oxides with O/metal ratio

below 2 is given inTable 8

2.02.4.1 Binary Stoichiometric Compounds

The thermodynamic data on the actinide oxides are

based on the critical reviews by Konings et al.36,38and

are generally in good agreement with the CODATA

Key values121 and with the NEA reviews.122 The

thermodynamic properties of the binary thorium,

uranium, neptunium, and plutonium oxides are well

established from experimental data For the other

actinide oxides, some experimental data are missing,

and some values were estimated using the analogy

with the lanthanide oxides by Konings et al.36,38

2.02.4.1.1 Actinide dioxides

2.02.4.1.1.1 Standard enthalpy of formation and

entropy

For the actinide dioxides, the enthalpy data inTable 9

are well established for ThO2, UO2, NpO2, PuO2,

AmO2, and CmO2from measurements On the

con-trary, the enthalpy of formation of PaO2, BkO2, and

CfO2 was never measured For these compounds,

the values were estimated from the reaction enthalpy

of the idealized dissolution reaction [AnO2(c)þ

4Hþ(aq)! An4þ

(aq)þ 2HO(l)] that is assumed to

vary regularly in the actinide series as the enthalpy ofdissolution of the dioxides [DfH(AnO2) DfH(An4þ)] is

a function of ionic size

The standard entropies inTable 9were deducedfrom heat capacity measurements for the solid diox-ides from ThO2to PuO2 For the other oxides, thedata were estimated by Konings.43,123 For AmO2

and CmO2, the entropy was modeled as the sum of

a lattice term due to the lattice vibrations and anexcess component arising from f-electron excitation:

S ¼ Slatþ Sexc Slatterm was assumed to be the valuefor ThO2, and Sexcwas calculated from the crystalfield energies of the compounds by Krupa and cow-orkers.124,125 A similar method was applied to esti-mate the entropies of PaO2, BkO2, CfO2, and EsO2

In absence of crystal field data, the excess term wascalculated from the degeneracy of the unsplit groundstate, which probably overestimates the entropy

As shown inTable 9, the stability of the dioxidesdecreases with the atomic number Z This is consis-tent with the fact that the melting points of thedioxides decrease from ThO2 to CmO2 This canexplain that the heavier tetravalent dioxides are dif-ficult to prepare Another difficulty comes from theproduction of daughter products leading to anincreasing contamination of the oxides with time.Finally, the dioxides lose oxygen leading to thedecrease of their oxygen stoichiometry with temper-ature The least stable dioxides CmO2and CfO2canevolve to form Cm2O3and Cf2O3

2.02.4.1.1.2 Heat capacityFor UO2and PuO2, high-temperature measurements

of both heat capacity and enthalpy increment areavailable For ThO2, NpO2, and AmO2, the high-temperature heat capacities were deduced from mea-surements of high-temperature enthalpy increment.The recommended equations for UO2, PuO2,ThO2, AmO2, and NpO2from Konings et al.36,38aregiven inTable 10and inFigure 11

For ThO2, UO2, and PuO2, the data are close

to the Dulong–Petit value between 500 and 1500 K.The lattice contribution is the major one with a smallcontribution of 5f electron excitations, which can becalculated from electronic energy levels

For UO2, above 1500 K, a rapid increase of theheat capacity was observed with a peak measured at

2670 K by Hiernaut et al.133 This unusual behaviorhas been subject of numerous studies that are reported

by Ruello et al.126Several contributions can be takeninto account: the harmonic phonons, the thermalexpansion, the U4þ crystal field, the electronic

Table 8 Crystalline data of other actinide oxides

Table 9 Thermodynamic data on the actinide dioxides after Konings et al.36,38

Melting T (K) DfH 0 (298.15 K) (kJ mol1) S 0 (298.15 K) (J K1mol1) DfG 0 (298.15 K) (kJ mol1)

disorder, and the oxygen anti-Frenkel disorder

Accord-ing to the analysis by Ronchi and Hyland,132 the

lambda transition observed at T0.8 Tm is governed

by the formation of anion Frenkel defects From X-ray

and neutron diffraction experiments, Ruello et al.126

measured thermal expansion data that give evidence

of an anomaly near 1300 K, suggesting a new model for

the heat capacity in which an electronic disorder

con-tribution is considered Yakub et al investigated this

premelting l-transition in UO2using a thermodynamic

model127 and MD.128 The authors interpreted this

transition by the increasing instability in the oxygen

sublattice with temperature According to Ruello

et al.,126a coupling of the lattice and electrical defects

is possible Further investigations are still required to

clarify the interpretation of the heat capacity of UO2

For ThO2, an excess enthalpy was measured above

T ¼ 2500 K Ronchi and Hiernaut37 using a thermal

arrest technique concluded that a l-type premelting

transition occurs at 3090 K, which was attributed to

order–disorder anion displacements in the oxygen

sublattice (Frenkel oxygen defects) The

recom-mended equation inTable 10comes from the fit of

the enthalpy measurements by Southard,129 Hoch

and Johnson,130and Fischer et al.131

The same type of effect was observed for the Cpof

PuO2from the enthalpy measurements by Ogard134

for PuO2, with a rapid increase of the heat capacity

above 2370 K This effect was later attributed to an

interaction between the sample and the W crucible

by Fink135and Oetting and Bixby.136New

measure-ments will be helpful

The thermophysical properties of NpO2, AmO2,

and CmO were recently calculated by Sobolev.69

The heat capacity of NpO2 calculated bySobolev69(seeSection 2.02.3) is in good agreementwith the recently measured data from 334 to 1071 K

by Nishi et al.137using a drop calorimetry method andwith the estimated data by Serizawa,138 recom-mended by Konings et al.38Very recent measurements

of enthalpy increments of NpO2 were undertaken

by Benes et al.139 using drop calorimetry from 376

to 1770 K The heat capacity of NpO2 derived fromthese enthalpy measurements is in very good agree-ment with the data of Nishi et al.137 A new heatcapacity function was proposed by Benes et al.139that take into account a value of 66.2 J K1mol1

at 298.15 K

No measurement exists on AmO2 and CmO2.The heat capacity for AmO2calculated by Sobolev69

is in very good agreement with the data estimated

by Thiriet and Konings40 from the heat capacity ofThO2and the crystal field energies for the groundstate and the excited states For CmO2, the heatcapacity data calculated by Sobolev69are lower thanthe data of Konings43estimated by the same methodapplied for AmO2(Figure 17)

2.02.4.1.2 Actinide sesquioxides2.02.4.1.2.1 Standard enthalpy of formationand entropy

The recommended data for the standard enthalpy offormation and entropy are listed inTable 11.The enthalpies of formation of Am2O3, Cm2O3,and Cf2O3 are well established from experimentaldata measured using solution calorimetry The samesystematic approach as the one used for the dioxidesusing the reaction enthalpy of the idealized dissolu-tion reaction [An2O3(cr)þ 6Hþ

(aq)! 2An3þ

(aq)þ3H2O(l)] was applied by Konings et al.38 to estimatethe enthalpy of formation for Ac2O3, Bk2O3, and

Es2O3 taking into account their different crystallinestructures

No low-temperature heat capacity measurementsexist except for Pu2O3, the only phase for which theentropy was derived For the other sesquioxides,the entropy values were estimated by Konings43from the entropy of Pu2O3by calculating the excessentropy term from the crystal field energies Thelattice term was obtained by scaling the values fromthe lanthanide series

As shown in Table 11, the evolution of thestability of the actinide sesquioxides with the atomicnumber Z is less pronounced than for the diox-ides The measured melting points of actinide

Table 10 Heat capacity functions for the actinide

dioxides according to Konings et al.36,38

Oxide Heat capacity equation for the solid oxides

sesquioxides slightly increase from Ac2O3to Cm2O3

for which a maximum is observed and then decrease

from Cm2O3to Cf2O3

2.02.4.1.2.2 Heat capacity

There are no measurements of the heat capacity or

enthalpy at high temperature for Pu2O3, Am2O3, and

Cm2O3 The equations given inTable 12are based

on comparison between actinide and lanthanide

oxi-des by Konings et al.36

2.02.4.1.3 Other actinide oxides with O/

metal >2

The thermodynamic data for uranium and

neptu-nium oxides with oxygen/metal ratios >2 are

reported inTables 13 and14 based on the review

by Konings et al.38

For UO3, the recommended heat capacity

func-tion is based on the fit of the experimental heat

capacity data from Popov et al.140and enthalpy ment by Moore and Kelley.141 For U3O8 and U4O9,the equation for the heat capacity is taken fromCordfunke and Konings.142

incre-2.02.4.2 Mixed OxidesCarbajo et al.84 did a review of the thermophysicalproperties of MOX and UO fuels All the available

230 210 190 170 150

Figure 17 The high-temperature heat capacity of ThO2, UO2, PuO2, NpO2, and AmO2 recommended by Konings

et al.38– the dashed lines correspond to the recent recommendation by Konings et al.36for UO2 and are from the recent enthalpy measurement by Benes et al 139 for NpO2.

Table 11 Thermodynamic data on the actinide sesquioxides after Konings et al 2

Melting T (K) D fH0(298.15 K) (kJ mol1) S0(298.15 K) (J K1mol1) D fG0(298.15 K) (kJ mol1)

Estimated values are in italics.

Table 12 Heat capacity function for actinide ides according to Konings et al.36

sesquiox-Oxide Heat capacity equation for solid oxides (J K1mol1)

Pu2O3 Cp¼ 130:6670 þ 18:4357  10 3 T  1705300T 2

Am2O3 Cp¼ 115:580 þ 22:976  10 3 T  1087100T 2

Cm2O3 Cp¼ 123:532 þ 14:550  10 3 T  1348900T 2