Comprehensive nuclear materials 2 04 thermodynamic and thermophysical properties of the actinide carbides

Comprehensive nuclear materials 2 04 thermodynamic and thermophysical properties of the actinide carbides Comprehensive nuclear materials 2 04 thermodynamic and thermophysical properties of the actinide carbides Comprehensive nuclear materials 2 04 thermodynamic and thermophysical properties of the actinide carbides Comprehensive nuclear materials 2 04 thermodynamic and thermophysical properties of the actinide carbides Comprehensive nuclear materials 2 04 thermodynamic and thermophysical properties of the actinide carbides

the Actinide Carbides

D Manara and F De Bruycker

European Commission, Joint Research Centre, Institute for Transuranium Elements, Karlsruhe, Germany

A K Sengupta, R Agarwal, and H S Kamath

Bhabha Atomic Research Centre, Mumbai, India

ß 2012 Elsevier Ltd All rights reserved.

2.04.7 Minor Actinide Carbides 128

ADS Accelerator-driven system

bcc Body-centered cubic crystal structure

CALPHAD CALculation of PHAse Diagrams

(Thermodynamic optimization of

phase diagrams)

CIM Conductivity integral margin to melting

DFT Density functional theory

DOS Density of states (density of quantum

electronic states per energy unit per

atom)

EOS Equation of state (equation relating the

parameters of a thermodynamic

system to its state functions)

fcc Face-centered cubic crystal structure

HTR High-temperature reactor

PCS Principle of the corresponding

states

SEM Scanning electron microscope

SI International System of units (Meter

Kelvin Second Ampe`re)

SIMS Secondary ion mass spectrometry

TB LMTO Tight-binding linear muffin tin orbital

of the elastic tensor)

Cp Heat capacity at constant pressure

Cv Heat capacity at constant volume

d Crystal grain size D0 Diffusion coefficient

DxY Self-diffusion coefficient of species x in the compound Y

DYx Chemical diffusion coefficient of species x

in the compound Y

EF Fermi Energy (Fermi level)

G(x) Gibbs free energy (of component x) H(x) Enthalpy (of component x)

kB Boltzmann’s constant

n Refractive index (real part)

n Neutron absorption (in nuclear reactions)

N Number of electrons in a given state (e.g., N(EF) ¼ number of electrons at the Fermi energy)

x Stoichiometry parameter in carbides

xY Molar fraction of species Y

y Stoichiometry parameter in carbides

b Beta decay (in nuclear reactions)

Df AY Variation of the thermodynamic function A

upon formation of compound Y

Dm AY Variation of the thermodynamic function A

upon melting of compound Y

DmixA Variation of the thermodynamic function A

upon mixing

DsubAY Variation of the thermodynamic function A

upon sublimation of compound Y

Dvap AY Variation of the thermodynamic

function A upon vaporization of

compound Y

DfG Gibbs free energy of formation

DvapG Gibbs free energy of vaporization

DfH Enthalpy of formation

DmH Enthalpy of melting

DvapH Enthalpy of vaporization

« Elastic deformation, elongation

_« Deformation rate (creep)

«, «l Spectral emissivity

«t Total emissivity

g Temperature coefficient of the electronic

heat capacity

g Gamma decay (in nuclear reactions)

g Average volumetric thermal expansion

coefficient

k Optical absorption constant

l Wavelength of the electromagnetic

Research on actinide carbides as nuclear fuel began

in the 1950s Then, uranium dioxide and mixeduranium–plutonium oxides began to be preferred asnuclear fuel in most of the Generation II and IIIpower plants, due to the fact that the option offast reactors for civil purposes had mostly been aban-doned This led to an abrupt interruption in actinidecarbide research between the first half of the 1970sand the second half of the 1990s In the last decade,there has been renewed interest in actinide carbides

in view of a nuclear fuel more suitable for highburnup and high-temperature operation with areduced ‘margin to melting,’ in the framework ofthe ‘Generation IV’ nuclear systems development.1Consequently, actinide carbides are now being stud-ied with more and more advanced methods, bothexperimental and computational

The goal of the present monograph is to rize the state-of-the-art knowledge of the most rele-vant physical and chemical properties of actinidecarbides This work is largely based on a few earlierreviews on the same subject: Storms,2Rand,3Holley

summa-et al.,4 Matzke,5 the Gmelin Handbooks,6–9 and theOECD-NEA reviews.10–13 More detailed and/ormore recent data are taken from single references.2.04.1.1 Carbides

Carbides are chemical compounds in which carbonbonds with less electronegative elements Depending

on the difference in electronegativity and the valencestate of the constituting elements, they exist as differ-ent bonding types Accordingly, they are classified assalt-like compounds (in which carbon is present as apure anion and the other elements are sufficientlyelectropositive), covalent compounds (SiC and B4C),interstitial compounds (with transition metals of thegroups 4, 5, and 6 except chromium), and ‘intermedi-ate’ transition metal carbides.14

In general, carbides display metallic properties,and they are mostly refractory (high melting) Theirmore specific properties depend on the constitutingelements

2.04.1.2 General Properties ofActinide Carbides

Actinides are known to form three main types ofstoichiometric carbides (Table 1): monocarbides

of the type AnC, sesquicarbides of the type AnC,

and dicarbides of the type AnC2 (sometimes called

‘acetylides’) Mono- and dicarbides have been observed

for protactinium, thorium, uranium, neptunium,

and plutonium Sesquicarbides have been identified

for thorium, uranium, neptunium, plutonium,

ameri-cium, and, recently, curium

Other types of actinide carbides such as CmC3

and Pu3C2have been observed

Data for mixed U–Th and U–Pu carbides, briefly

summarized and discussed in the last section of this

chapter, have mostly been indigenously collected

from the few nuclear plants using this kind of fuel.15

2.04.1.2.1 Structure of the matter

In general, actinide carbides are of the ‘salt-like’ type

In these compounds, carbon is present as single

anions, ‘C4’ in the monocarbides; as two atom

units, ‘C2 ’ in the acetylides; and as three atomunits,‘C3 ’ in the sesquicarbides This model, usefulfor a first visual description of these materials, isphysically inconsistent with their essentially metallicproperties The An–C bonds are certainly more cova-lent than ionic, as recently confirmed.16 Actinidecompounds are characterized by a peculiar elec-tronic structure, where the extended nature of the5f electron wave functions yields a unique interplaybetween localized and band electrons This featureleads, in particular, to properties associated withcovalent bonding in these compounds, which showcrystal structures normally associated with ionicbonding.5

Monocarbides AnC1 x(An¼ Th, Pa, U, Np, Pu,Am) crystallize in the NaCl-type space group

Fm 3m – No 225 (Table 1) The elementary cell is

Table 1 Synopsis of the known actinide carbides

Compound and lattice

parameters

Composition and temperature range

O5 Fm3mðNr:225Þ 508.8 pm (Th) to

534.4 pm (ThC 0.98 in

equilibrium with ThC 2 )

Eutectic ThC 1x ¼ 1980 K Congruent

T m ¼ 2780 K for C/Th ¼ 0.975

represented by four formula units The lattice

param-eter is dependent on the C/An ratio, and the oxygen

and nitrogen impurities The lattice parameter of

pure monocarbides increases with the dissolution of

carbon in the ideal face-centered cubic (fcc) lattice in

an essentially linear manner

The sesquicarbides of Th, U, Np, Pu, Am, and Cm

have been identified to be body-centered cubic (bcc)

of the I 43d type, with eight molecules per unit cell

(Table 1) This structure is more complex than that

of the mono- and dicarbides, and is often difficult toform Thus, Th2C3 was observed only under highpressure (2.8–3.5 GPa), and U2C3 is produced by acomplex preparation procedure Both decomposeinto a mixture of mono- and dicarbides at high tem-peratures The situation is different in the case of

Pu2C3, which is the most stable among the Pu bides and forms easily at temperatures ranging from

car-Table 1 Continued

Compound and lattice

parameters

Composition and temperature range

(No 15)

Th Th

Th Th

c

c c c

c c

c c

c c

c c

room temperature to the melting point Unlike the

fcc modifications of mono- and dicarbides,

sesquicar-bides can hardly accommodate lattice defects;

there-fore, they essentially exist as line compounds

Actinide dicarbides AnC2x have been observed

in a larger variety of allotropes (Table 1) At

inter-mediate temperatures, generally between 1700 and

2050 K, Th, U, Pu, and probably, Pa and Np, form

tetragonal dicarbides of the type CaC2 (I4mmm –

Group 139) Th also forms a monoclinic C2/c (No 15)

substoichiometric dicarbide that is stable from room

temperature to 1713 K The high-temperature form

of actinide dicarbides has been observed to be fcc of

the type KCN, which belongs to the same symmetry

group as NaCl, Fm 3m Such structure, clearly

estab-lished for g-ThC2, was observed with more difficulty

by high-temperature X-ray diffraction (XRD) for

b-UC2 and b-PuC2 The lattice transition between

tetragonal and cubic fcc dicarbide (a! b for U and

Pu, b! g for Th) is diffusionless of the martensitic

type It occurs very rapidly despite its important

enthalpy change, mostly due to the lattice strain

contribution For this reason, the high-temperature

cubic modification is impossible to quench to room

temperature, hence the difficulty in investigating its

properties fcc allotropies of mono- and dicarbides

are mostly miscible at high temperature, and for

uranium and thorium, they can be considered as a

single high-temperature cubic phase with a wide

nonstoichiometry range In fact, this solid solution

can easily accommodate interstitial excess carbon

atoms and lattice vacancies The first ensure the

existence of a broad hypostoichiometry range of the

dicarbides, where most of the excess carbons form C2

dumbbells in the (½,0,0), (0,½,0), and (0,0,½) positions

as in the KCN lattice (seeTable 1) The second are

responsible for the existence of hypostoichiometric

monocarbides An1x, extending to the pure metal for

thorium but only to a narrow UC1x domain for

uranium The situation is different for Pu carbides

due to the high stability of Pu2C3 up to its melting

point and to the fact that fcc plutonium monocarbide

exists only in a vacancy-rich hypostoichiometric form,

with 0.74 C/Pu  0.94 This originality, common to

other Pu compounds, is certainly related to the

pecu-liar behavior of the six 5f electrons of plutonium,

which exhibit behavior on the limit between valence

and conduction, and can follow one or the other

(or both) in different compounds

The electronic (band) structure of actinide

car-bides has been studied rather extensively, both

exper-imentally (by low-temperature calorimetry and X-ray

photoelectron spectroscopy, XPS) and theoretically(by tight-binding methods and, more recently, bydensity functional theory techniques) These com-pounds are, in general, good electronic and thermalconductors, with a nonzero density of electronic states

at the Fermi level (Figure 1)

However, the actual filling of the levels largelydepends on the peculiar behavior of the 5f electrons,

(b)

(c)

4 3 2 1 0

4

3 2

1

1 2 3 4 5

6

g-ThC2a-ThC2

2 3 0

Figure 1 (a, b) The theoretical density of electronic states

in thorium and uranium monocarbides Reproduced from Das, T.; Deb, S.; Mookerjee, A Phys B 2005, 367, 6–18 The original calculation was performed using Rydberg energy units The agreement with low-temperature calorimetric measurements is only qualitative (c) The theoretical density of electronic states in thorium dicarbides Reproduced from Shein, I R.; Ivanovskii, A L.

J Nucl Mater 2009, 393, 192–196.

which tend to be more localized or more

itiner-ant according to the actinide and the compound

involved Thus, Pu carbides have much higher

elec-trical resistivity than Th and U carbides Similarly,

mono- and dicarbides are better electronic

conduc-tors than sesquicarbides are Magnetic transitions

have been observed at low temperatures in

sesqui-carbides, and Np and Pu monocarbides

The electronic structure dependence on defect

and impurity concentrations has been studied in a

number of cases For example, in ThC1x, the density

of states (DOS) increases with increasing carbon

vacancy concentration Auskern and Aronson17

showed by thermoelectric power and Hall coefficient

measurements that a two-band conductivity model

can be applied for ThC1 x: the bands overlap more

and the number of carriers increases with decreasing

C/Th ratio The valence bands have mainly a carbon

2p and a thorium 6dg character, while the Th-6de

character dominates the conduction bands Also, the

increase of the DOS at the Fermi level with vacancy

concentration is due to the 6d thorium electronic

states In stoichiometric ThC, the 6d Eg states are

hybridized with the 2p states of carbon and are

split between low-energy bonding and high-energy

antibonding states In hypostoichiometric ThC1x,

the 6d Eg dangling bonds contribute to an increase

of the DOS in the vicinity of the Fermi level.18

For uranium carbides, it was shown that, following

the general rules of Hill19that imply that U–U

dis-tance is<3.54 A˚, these compounds exhibit a metallic

electronic structure due to the overlaps of f-orbitals

This rule applies to uranium monocarbide for which

the U–U distance is 3.50 A˚ , as shown by experimental

measurements as well as by ab initio calculations.20,21

For hyperstoichiometric uranium carbides, the

metal-lic character persists and the C–C bonds are covalent

as in graphite In an X-ray and ultraviolet

photoelec-tron spectroscopy (XPS and UPS) study of sputtered

UCxthin films (0< x < 12), Eckle et al.22

showed thatthe U-4f core levels do not change strongly with

increasing carbon content, and demonstrated the

pre-dominantly itinerant character of U-5f electrons

Similarly, valence region spectra show three types of

carbon species for different UCx films, which are

differentiated by their C-2p signals A strong

hybri-dization between C-2p and U-5f states is detected in

UC, while the C-2p signal in UC2 appears only

weakly hybridized, and for higher carbon contents, a

p-band characteristic of graphite appears

Calculated charge distribution maps for

stoichio-metric fcc ThC and tetragonal b-ThC 23are shown

inFigure 2, giving an idea of the covalent or ionicnature of the different bonds in these structures.The analysis by Shein et al.23 revealed thatbonding in ThC2 polymorphs is of a mixedcovalent–ionic–metallic character That is, the cova-lent bonding is formed due to the hybridizationeffects of C–C states (for C2dumbbells) and C2–Thstates In addition, ionic bonds emerge between thethorium atoms and C2dumbbells owing to the chargetransfer Th! C2, with about 1.95 electrons redistrib-uted between the Th atoms and C2 dumbbells Themetallic Th–Th bonds are formed by near-Fermidelocalized d and f states Similar charge distributionshave been calculated for uranium carbides.24

2.04.1.2.2 Phase stabilityThe composition versus temperature phase diagramconstitutes the most basic information for each car-bide system, fundamental to correlate thermophysi-cal, thermodynamic, and chemical data of compounds

in a consistent way Thus, phase stability data are firstgiven for each actinide carbide system, followed by areview of the available information on physicochemi-cal data

Although the general properties have beenassessed, especially for the most studied systems,Th–C, U–C, and Pu–C, doubts still remain aboutthe effective stability or ‘meta’-stability of certaincrucial phases (e.g., UC2at room temperature) Thecurrent phase diagrams, often completed with newerdata and assessed by more recently developed ther-modynamic optimization methods (CALPHAD),seem to generally, but not always, confirm the dataobtained in the 1950s–1960s with traditional thermalanalysis techniques The discrepancies are sometimeslinked to the deviation of the samples investigatedfrom an ideal behavior, mostly due to oxygen andnitrogen contamination, a well-known and commonissue related to carbides

A short discussion of the most common actinidecarbide oxides and carbide nitrides is, therefore, pre-sented, with the goal of providing a hint of the maineffects of oxygen and nitrogen additions on the phys-icochemical properties of pure carbides

2.04.1.2.3 PreparationActinide mono- and dicarbides for research purposesare preferentially prepared by arc-melting a mixture

of metal and graphite in the right proportions Thisprocess is normally performed under 1 bar ofhelium or argon Special care is needed to avoidoxygen, nitrogen, and water impurities in the furnace

The preparation of oxygen and nitrogen-free

car-bides is hardly possible

Probably the most used method for industrial

applications is the carbothermic reaction of AnO2,

based on a reaction of the type:

normally performed under vacuum (1.25 105bar)

at 1700–1850 K for 4 h

Other possible preparation methods are reaction of

An hydrides with carbon, aluminothermic reaction

of AnF4, pyrolytic reaction of AnCl4 with CH4,

and An–Hg amalgam distillation in a hydrocarbon

atmosphere Single crystals have been obtained

by electron-beam melting, quenching, and

anneal-ing of polycrystalline samples Potter25 showed that

carbothermic reduction of PuO2cannot yield

oxygen-free Pu monocarbide, because the very high Pu

pressures corresponding to the Pu2C3–PuC1xOx

equilibrium would lead to the formation of Pu2O3

or Pu C in equilibrium with PuC1x

The preparation of sesquicarbides is more cated Th2C3 and U2C3 have been obtained withcomplex experimental procedures, whereas the prep-aration of Pu2C3 is rather straightforward, thanks

compli-to the high thermodynamic stability of this phase

Th2C3 was successfully synthesized by Krupka andcoworkers26,27 starting from arc-melted 57–67 at.%

C alloys then sintered in a belt-type high pressuredie under a pressure of 2.8–3.5 GPa between 1323and 1623 K for 1 h

The preparation of U2C3is extremely difficult and

it commonly requires a long (1 day) annealing of atwo-phase UCþ UC2metastable starting material in

a narrow temperature range, between approximately

1720 and 1900 K The annealing time can be reduced

to a few minutes under particular conditions, forexample, under high pressure or in a suitable atmo-sphere Several ways of preparing U2C3 have beensuccessfully explored They can be regrouped intwo main categories: those employing the ‘syntheticreaction’

0 0.5

1 0 C

Th–C Th–Th

UCþ UC2! 2U2C3 ½II

and those based on the ‘decomposition reaction’

Several methods based on the synthetic reaction

are available in the literature For example, Matzke

and Politis5 obtained U2C3 by annealing cast UC1.5

two-phase samples at 1720 K for 20 h under high

vacuum U2C3 was also obtained by Krupka28 at

1220 K under a pressure of 15 kbar for 2.75 min In

the light of this latter work, it seems difficult to believe

that the application of mechanical strain has no

influ-ence on the synthesis of U2C3, as proposed by a few

researchers.29,30The work of Henney et al.31showed

that even a high content of oxygen impurities can have

an important influence on the U2C3 synthesis rate

Starting from a UC1.58sample with 2900 ppm of

oxy-gen, these authors obtained almost pure U2C3 after

annealing for 74 h at 1773 K under vacuum The extra

carbon reacted with oxygen to form CO and CO2,

fostering the formation of the sesquicarbide

Producing or quenching cubic fcc-KCN-like

acti-nide dicarbides to room temperature is virtually

impossible due to the martensitic nature of the

cubic!tetragonal transformation and its extremely

fast kinetics Tetragonal dicarbides, on the other

hand, are easily quenched even when they are not

in a thermodynamically stable phase at room

tem-perature (as in the case of a-UC2)

The rate of oxidation of PuC and ThC in air ismuch higher than that of UC and (Th,U)C and(U,Pu)C solid solutions, whereas it is much lower insesquicarbides

The oxidation of actinide carbides occurs times with the formation of flames (pyrophoricity),especially in samples with large specific surface (finepowders)

some-Actinide carbides tend to hydrolyze in water andeven on exposure to laboratory air, where they exfo-liate, increase in weight, and produce final hydrolysisproducts

2.04.1.2.4 Applications

If uncertainties regarding the behavior of An bides, mostly linked to metastability and uncontrol-lable oxygen and nitrogen impurities, still represent

car-an obstacle to the fabrication car-and employment ofthese materials as an alternative nuclear fuel to oxi-des, their higher fissile density constitutes a bigadvantage Moreover, the metallic thermal conduc-tivity (Figure 3) and high melting temperature of Ancarbides ensure a higher conductivity integral margin

to melting (CIM), defined byeqn [1], for these rials with respect to the traditional UO2, UO2–PuO2,and ThO2fuels:

(U 0.3

Pu0.7)C

Here, Top is the reactor operational temperature at

the fuel–cladding interface (around 500 K for light

water reactor (LWR), and up to 1500 K for the

Generation IV very high-temperature reactors,

VHTRs) and Tm is the fuel melting temperature

The better compatibility of carbides with liquid

metal coolants compared to oxides is a further

rea-son for making them good alternative candidates for

high burnup and/or high temperature nuclear fuel

Uranium carbide was traditionally used as fuel

kernel for the US version of pebble bed reactors as

opposed to the German version based on uranium

dioxide.8Among the Generation IV nuclear systems,

mixed uranium–plutonium carbides (U, Pu)C

consti-tute the primary option for the gas fast reactors (GFRs)

and UCO is the first candidate for the VHTR.1In the

former case, the fuel high actinide density and thermal

conductivity are exploited in view of high burnup

performance In the latter, UCO is a good

compro-mise between oxides and carbides both in terms of

thermal conductivity and fissile density However,

in the American VHTR design, the fuel is a 3:1 ratio

of UO2:UC2 for one essential reason, explained by

Olander.32 During burnup, pure UO2 fuel tends to

oxidize to UO2þx UO2þxreacts with the pyrocarbon

coating layer according to the equilibrium:

The production of CO constitutes an issue in the

VHTR because the carbon monoxide accumulates

in the porosity of the buffer layer The CO pressure

in this volume can attain large values and, along

with the released fission gas pressure, it can

compro-mise the integrity of the coating layers and contribute

to the kernel migration in the fuel particle (‘amoeba

effect’) In the presence of UC2, the following reaction

occurs rather thanreaction [IV]in the

hyperstoichio-metric oxide fuel:

UO2 þxþ xUC2! ð1 þ xÞUO2þ 2xC ½V

Because no CO is produced inreaction [V], the latter

is more desirable than [IV] in view of the fuel

integrity

Thanks to its fast neutron spectrum, the GFR can

suit a232Th–233U fuel concept, in the chemical form

of (Th,U)C2 mixed carbides.33,34 However, the

tho-rium cycle is at the moment not envisaged in

Gener-ation IV systems

The use of Pu-rich mixed carbide fuel has recently

been proposed for the Indian Fast Breeder Test

Reactor.35However, pure plutonium carbides present

a low solidus temperature and low thermal tivity, which are important drawbacks, with respect topure U- or mixed carbides, for a nuclear fuel.More details about the use and behavior ofuranium carbides as nuclear fuel can be found inChapter3.03, Carbide Fuel

conduc-2.04.2 Thorium Carbides232

Th, the only natural Th isotope, can absorb mal neutrons to produce fissile233U and is thereforeused as fertile material in breeder reactors Nowa-days, the thorium fuel cycle is mostly envisaged inIndia, which has about one-fourth of the total worldthorium resources, but this option is kept open

ther-in other countries such as Norway and Australia,which also have abundant Th ores.33Thorium dicar-bide is a candidate fertile material for the Generation

IV high-temperature reactor (HTR) and VHTRsystems, and it is also exploitable for accelerator-driven system (ADS) burners Solid solutions of

UC2–ThC2 were candidate fuels for the DragonHigh Temperature Reactor-coated particle fuels.36However, thorium-based fuel is difficult to recyclebecause of the radioprotection issues generated bythe hard g-emission of208Tl (2.6 MeV), formed in the

232

Th–233U spent fuel

2.04.2.1 Phase RelationshipsAtmospheric pressure phase equilibria in the Th–Csystem are reported inFigure 4

Thorium metal has an fcc (a) structure below

1633 K and a bcc structure (b) at higher temperatures.The first can accommodate carbon atoms as intersti-tials, resulting in the formation of thorium monocar-bide without any lattice change.5 The ThC1x fccsolid solution range, extending from pure Th toThC1.96 at high temperatures, is stable betweenThC0.67and ThC0.97below1300 K The exact highcarbon limit is still under debate.37A miscibility gapseems to exist in the ThC1 xphase field, betweenThC0.06around 1000 K,38ThC0.30at 1413 (40) K,39and ThC0.67at 1150 K,2probably extending to roomtemperature with approximately the same composi-tion boundaries At higher temperatures, single car-bon interstitials can be replaced by C2 groups up

to ThC1.96 Thus, only two compounds have beenobserved in the Th–C system at atmospheric pres-sure: the fcc monocarbide with its broad nonstoichio-metry range and the dicarbide, more often observed

as hypostoichiometric (ThC2x) Thorium

sesqui-carbide Th2C3 has been observed only at pressures

above 30 kbar.27At low temperatures (below 1500 K),

ThC2 x is a monoclinic line compound (a) with

composition ThC1.94,40observed in equilibrium with

ThC0.98at 1528 (40) K in the presence of oxygen.41

Around 1528 (40) K, ThC2 xconverts eutectoidally

to a tetragonal phase (b) with a homogeneity range

between C/Th¼ 1.66 at 1528 K and 1.96 at 1713 K,

the temperature at which the a! b ThC2 phase

transition occurs at its C-rich phase boundary.40

Pialoux and Zaug42 reported a different phase

diagram, with higher C/Th ratios for the Th-rich

b-ThC2 phase boundary, extending from 1.96 at

1570 K to 1.85 at 1743 K This phase diagram does

not include the eutectoid decomposition of b-ThC2,

but rather a a! b-phase transition in the line

com-pound at 1570 K All authors agree on the formation

of a cubic fcc ThC2 x modification (g) as the

tem-perature is raised above 1763 (45) A solid

miscibil-ity gap has been observed by Bowman et al.40 in the

ThC–ThC2 x domain, with a maximum at 2123

(40) K and C/Th ¼ 1.22 The same maximum was

observed by Pialoux and Zaug42at 2173 (40) K and

C/Th¼ 1.95 There exists a ThC2–C eutectic of

proba-ble composition ThC2.38and temperature 2718 K

Obvi-ously, some questions on the ThC2xphase boundaries

are still open, often in relation to the large

uncertain-ties in the reported transition temperatures

The commonly accepted melting point of pure Th

is 2020 10 K.6

In the low-carbon domain, a eutectic

(or peritectic) isotherm around 1980 K in the sition range of 0.06< C/Th < 0.13 has been observed.Two congruent melting points were observed in thesolid solution region with 0.13 C/Th  1.96, the first

compo-at T ¼ 2773  35 K and C/Th ¼ 0.97  0.05, thesecond at T ¼ 2883  35 K and C/Th ¼ 1.90  0.06.The boiling point of ThC2was extrapolated to be

5400 K at 1 atm.432.04.2.2 Physicochemical Properties2.04.2.2.1 Crystallography

2.04.2.2.1.1 Thorium monocarbide ThC

The lattice parameter of fcc ThC1xis dependent onthe C/Th ratio and the oxygen and nitrogen impu-rities It increases linearly for pure a-Th with thedissolution of carbon in the fcc lattice, as shown inFigure 5.6,44

It was observed to decrease by0.2 pm per 0.1 wt%

N at low nitrogen content High-temperature latticeparameter measurements have been performed byXRD on single-phase and two-phase Th–C com-pounds The lattice parameter of ThC varies from534.4 pm at room temperature to 545 pm at 2273 K.45The linear thermal expansion (lT l0)/l0and thelinear thermal expansion coefficient aT¼ l0 1

(dl/dT)(where l0 is the sample length at 293 K) were deter-mined either by dilatometry or by XRD at differenttemperatures (Figure 6) and carbon contents.46

In the solid solution between ThC0.67and ThC0.98,

the value of a , lower than the thermal expansion

1000

1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200

ThC1−x+α-ThC2−xLiquid + ThC1−x

fcc ThC1+x

Xc

ThC 1−x +

γ -ThC2−xThC1−x+

β -ThC2−x

Figure 4 The Th–C phase diagram.

coefficient of pure Th (aThffi 11.6 106K1 at

room temperature47), increases slightly with carbon

content and seems to have little dependence on

oxy-gen and nitrooxy-gen impurities

2.04.2.2.1.2 Thorium sesquicarbide Th2C3

The lattice parameter of Th2C3varies between 855.13

and 856.09 pm in a narrow homogeneity range Th2C3y

(0 y  0.05) The compound synthesized and

ana-lyzed by Krupka27 had a composition of Th2C2.96

with a lattice parameter of 855.13 pm, corresponding

to a theoretical density r¼ 10.609 g cm3

2.04.2.2.1.3 Thorium dicarbide ThC2

Gantzel and Baldwin48published an XRD pattern for

monoclinic ThC2 x, completed by Jones et al.49 by

neutron diffraction analysis The assessed values

for the room-temperature lattice parameters arereported in Table 1 Shein and Ivanovskii50 per-formed ab initio density functional theory (DFT)calculations on a-, b-, and g-ThC2, obtaining goodagreement with the experimental results, and alsosuggesting a C–C distance of 132.8 pm Pialoux andZaug42measured the lattice parameters a, b, c, and b

of a-ThC2by XRD as a function of temperature up

to 1673 K The results are plotted inFigure 7.Bowman et al.40provided the most recent experi-mental data for the lattice parameters of b-ThC2 inequilibrium with graphite and 550 ppm O2at 1723 K:

a ¼ 422.1  0.3 pm and c ¼ 539.4  0.3 pm Pialouxand Zaug42studied the dependence of a and c on thetemperature, composition, and purity of b-ThC2.While the parameter a of b-ThC2in equilibrium with

C at 1740 K seems in good agreement with the values

of Bowman et al.,40the lattice parameter a for phase b-ThC2was observed to increase from around

single-420 pm at 1640 K to 422 pm at 1740 K b-ThC2 inequilibrium with ThC shows a lattice parameter a ofthe order of 417 pm at 1640 K, decreasing to about414.5 pm at 1768 K The parameter c was observed toincrease with temperature for b-ThC2in equilibriumwith ThC, varying from 540 pm at 1613 K to 545 pm at

1768 K, while the value c ¼ 541  1 pm is acceptable

at all temperatures at which b-ThC2is the equilibrium

as a pure phase or with graphite 0 K DFT calculations

of structural parameters by Shein and Ivanovskii50arenot in agreement with the experimental results forb-ThC2 Obviously, ideal ordering of C2 dumbbellsalong the c axis and exact 2.00 stoichiometry, bothpostulated in Shein and Ivanovskii’s model, constitutetoo rough hypotheses for this phase This complex part

of the phase diagram needs further assessment

500 550 600 650 700

103.8 103.9 104.0 104.1 104.2 104.3 104.4 104.5

T (K)

β°

β a

b c

Figure 7 The temperature dependence of the lattice parameters in monoclinic a-ThC 2 Reproduced from Pialoux, A.; Zaug, J J Nucl Mater 1976, 61, 131–148.

The high-temperature g-modification of ThC2

has an fcc KCN-like structure The C2 dumbbells,

centered in the (1/2, 1/2, 1/2) position, rotate

freely.6,40 The lattice parameter of g-ThC2 was

measured by Pialoux and Zaug42 between 1858 and

2283 K, and observed to vary between 581.3 and

584.1 pm, respectively The same authors observed

that the lattice parameter of g-ThC2 in equilibrium

with ThO2 depends on the CO partial pressure Its

value is constant and close to 570 pm between 2173

and 2228 K for pCO< 103bar, but increases to

584 pm for higher pCO The nearest C–C distance

was estimated by Bowman et al.40 to be 124 4 pm

The b! g-ThC2 transformation is diffusionless,51

which explains why all attempts to quench g-ThC2

to room temperature failed.52

The linear thermal expansion (lT l0)/l0 and

the linear thermal expansion coefficient aT were

measured by dilatometry up to 1323 K53 and by

XRD54 up to 1608 K for a-ThC2x, and up to

2028 K for g-ThC2x Values are reported inFigure 6

for samples with510 ppm O2

Ganzel et al.54 reported aT¼ 8.7 106K1 for

g-ThC2xbetween 1813 and 2028 K

The average volumetric thermal expansion

coeffi-cient g was estimated to be 78 106K1 between

298 and 2883 K.6

Ganzel et al.54estimated that the volume increase

on the a! b-ThC2 xtransformation was 0.8% and

0.7% for the b! g-ThC2 xtransformation Dalton

et al.55 estimated the overall volume expansion for

both transformations to be 1.3%

2.04.2.2.2 Thermodynamic properties

Heat capacity and Gibbs energy of formation data for

thorium carbides are summarized inTables 2 and 3

andFigures 8 and 9

Formation enthalpies, corrected for impurities,were measured by Huber et al.59and Lorenzelli et al.60The Gibbs energy of formation of ThC0.97at itshomogeneity range upper boundary was reviewed byHolley et al.4according to the reported heat capacity

as inTable 3andFigure 8.Vaporization studies performed on ThC0.891,ThC0.975, ThC1.007, and ThC1.074 between 2060 and

2330 K by Knudsen effusion and mass spectrometry61yielded DfG(ThC,s) values in fair agreement withthe earlier ones According to this study, atomic Th isthe predominant species in the gaseous phase, andpartial molar sublimation enthalpies are 522 kJ mol1for ThC0.891, 553 kJ mol1for ThC0.975, 660 kJ mol1for ThC1.007, and 578 kJ mol1for ThC1.074

The equation of state (EOS) of solid ThC wasstudied by Das et al by density functional and

Table 2 The heat capacity C p of thorium carbides at atmospheric pressure (in J K1mol1)

ThC 2.12 10 3 T

þ 108 10 6 T 3

5 þ 6R467T 2

exp 467T

exp 467T

tight-binding linear muffin tin orbital method (TB

LMTO) calculations,16 obtaining a bulk modulus

B ¼ V1(@2

E/@V2)¼ 43 GPa This differs by almost

exactly a factor 3 from the value, 125 MPa,

recom-mended by Gomozov et al.62In this case, the

discrep-ancy might be attributed to some factor (probably

dimensional) missing in the calculations A reasonable

value for B is actually around 120 MPa, also directly

deduced from the elastic constants reported in

Section 2.04.2.2.4

The EOS of liquid ThC was studied starting from

the significant structure theory, which takes into

account the complex vaporization behavior of

ThCx.63The resulting enthalpy of melting is 35.2 kJ

mol1 This value is considerably lower than that

estimated by applying Richard’s law to the accepted

melting temperature.64,65 A direct measurement of

DmH (ThC) is still required to solve this discrepancy

Gigli et al.63 obtained the following values from

their EOS for liquid ThC: S¼ 207.6 J K1mol1;

Cp¼ 89 J K1mol1; Cv¼50 J K1mol1; cubic thermal

expansion coefficient a ¼ 1.4 104K1; isothermal

compressibility k ¼ V1(@V/@P) ¼ 3.7 1011m2N1,

plus the critical constants reported in Table 3

Liquid ThC total pressure was calculated up the

The reported values are consistent with theinequality

DfGðTh2C3;sÞ > DfGðThC;sÞ þ DfGðThC2;sÞ2

which justifies the thermodynamic instability of

Th2C3at atmospheric pressure and all temperatures.The volume change for the reaction ThCþ ThC2¼

Th2C3is DV ¼ 2.32 106m3mol1 Krupka27ing estimated that DfGp¼ (DfG 2.32p) J mol1and

hav-DfG term DfGexffi 7 kJ mol1, the room-temperaturestandard Gibbs energy of formation for Th2C3can beextrapolated as

Table 3 Thermodynamic functions of thorium carbides (in SI units)

Compound D f H

(kJ mol1)

D f G(J mol1)

S(298) (J K1mol1)

Transition DH(J mol1)

Bulk modulus

B ¼ V1( @ 2 E/@V 2 ) (GPa)

(T > 1700 K)

b-ThC2x: 149.2 dB/

dT ffi 4.13

–

D m H¼ 72 000 (R)

g-ThC2x: 0.6 dB/dT ffi

¼3.71

For D H f data, see Holley et al 4

(R) ¼ Richard’s rule and est ¼ estimated.

aTh

2 C 3 is only stable at high pressure D f G p (Th 2 C 3 ) ¼ (D f G   2.32 p kbar 1).

DfG298 ðTh2C3;sÞ ¼ 226  21kJ mol1

Giorgi et al.67–69studied the electronic and magnetic

properties of thorium sesquicarbide The valence

electron concentration of Th2C3is exactly 4.0

Mag-netic susceptibility measurements show a

supercon-ductive transition in ThC1.45 treated under high

pressure The transition temperature is 4.10.2 K,

with a pressure dependence dTc/dp ¼ 0.040 K

kbar1between 0 and 10 kbar

2.04.2.2.2.3 Thorium dicarbide ThC2

Bates and Unstead70suggested the value 3.13 mJ K2

mol1 for the temperature coefficient g of the

electronic heat capacity The heat capacity Cp of

a-ThC2 xwas measured by low-temperature

adia-batic calorimetry between 5 and 350 K, for ThC1.93

by Westrum et al.71 and for nominal ThC by

Takahashi et al.72(Table 2andFigure 8) The valuesmeasured in the two cases were consistent The result-ing standard entropy was S(298) S(0)¼ 68.49 0.07 J K1mol1, which would give S(298) ¼ 70.37 J

K1mol1 if one assumes a randomization entropyS(0) ¼ 1.88 J K1mol1, corresponding to a randommixing of C and C2groups The other recommendedvalues at 298 K are Cp(298)¼ 56.69  0.06 J K1mol1,

H(298) H(0)¼ 10 238  10 J mol1

, and (G(298)

H(0))/298¼ 34.175  0.034 J K1mol1.Holley et al.4estimated the thermodynamic func-tions of a-ThC2at high temperature by extrapolatingthe data of Westrum up to 1400 K The expressionrecommended by these authors up to 1700 K exhibits

a positive curvature of Cp in the high-temperatureregion (298–1700 K), similar to the behavior of UC1.9

(Table 2 and Figure 8).The heat capacities of and g-ThC2between 1700 and 2500 K were estimated

b-by the same authors to be around 84 J K1mol1.Holley et al.4 also estimated the enthalpiesfor a!b- and b!g-ThC2 transformations Thea!b transformation implies minor crystallo-graphic changes and is thus associated with a small

DH, 2.1 kJ mol1

DH for the b!g ThC2formation was estimated to be 10.5 kJ mol1from thesimilar transition occurring in UC2x

trans-The g-ThC2melting enthalpy is estimated to be

DmH ¼ 72 kJ mol1, from Richard’s law The law enthalpy of sublimation of a-ThC2 at 298 K is

third-of the order third-of DsbH 800 kJ mol1.73Many authors have studied the enthalpy andGibbs free energy of formation of ThC2.4 Huber

et al.59 measured the enthalpy of formation ofa-ThC1.91at 298 K by oxygen combustion calorime-try in the presence of 410 ppm O2, obtaining DfH298

(ThC1.91,s)¼ 125  5 kJ mol1 This value is ommended as the most reliable

rec-The Gibbs free energy of formation for ThC2xisrecommended to be 125  6.7 kJ mol1 at roomtemperature,4being the entropy contribution compa-rable to the uncertainty EMF and combustion haveprobably yielded the most reliable DfG data Thegraph of Figure 9 is essentially based on thesedata However, this trend, recommended between

298 and 2718 K, is subject to a large unquantifiableuncertainty due to the unknown oxygen content

in the investigated samples and to the fact thathigh-temperature Cpand entropy values are mostlyestimated

ThC2xin equilibrium with carbon preferentiallyloses gaseous carbon,4 causing the congruentlyvaporizing composition in the Th–C system at

2000–2800 K to lie well within the ThC1 þxdomain.

Gaseous species over the ThC2–ThC system were

generated by thermal ion emission (Langmuir

vapor-ization) and Knudsen effusion, and analyzed by

mass spectrometry.74–76 These studies revealed the

presence of ThCn species up to n ¼ 4 Gupta and

Gingerich77 also detected ThC5 and ThC6 in the

vapor Sasaki et al.75 determined the vaporization

coefficient ratio aThC2/aThto be close to one within

the experimental error The partial pressures of the

species in the vapor differ strongly and only the

ThC2 and ThC4 species seem to have significant

contributions to the total vapor pressure

All these data have been obtained by assuming, in

the entropy calculations, that ThC2and ThC4

mole-cules have linear structure This point has been more

recently discussed by Kova´cs and Konings78who

sug-gest, based on quantum chemical calculations, that

the ThC2 and ThC4 molecules are more likely to

have cyclic structures This result leads to new

entropy values of the gas molecules, higher than the

(deduced) previous ones by5% on average

2.04.2.2.3 Transport properties

2.04.2.2.3.1 Thorium monocarbide

ThC room-temperature thermal conductivity (see

Figure 1) was estimated in an arc-melted specimen

(100% theoretical density assumed) from electrical

resistivity measurements and the Wiedemann–Franz

relationship: l¼ 29 W K1m1at 298 K.41However,

a more recent estimate based on an extrapolation

from the thermal conductivity of (Th,U)C gave

l ¼ 12 W K1m1 at 298 K.6 A more systematic

study of ThCx as a function of both temperature

and composition is needed

The self-diffusion of carbon in fcc a-Th(C) was

measured by Peterson79in a ThC-coated Th cylinder

between 1273 and 1473 K for C concentrations up to

1.1 wt% The best fit over three experimental data

points obtained at 1273, 1373, and 1473 K leads to the

values D0¼ 2.7 106m2s1 and Q ¼ 159 kJ mol1,

to be substituted in

At higher temperatures, between 1713 and 1988 K,

and up to 0.4 wt% of C, Peterson et al.80 found

D0¼ 2.2 106m2s1 and Q ¼ 113 kJ mol1 In the

same work, the electro transport of carbon in b-Th(C)

was measured between 1713 and 1948 K Carbon

migrated in the same direction as the electron flow,

with carbon mobility mC between 1.2 108 and

of ThC1x electrical resistivity (Figure 10) Theresistivity of Th monocarbide appears to be higherthan that of the dicarbides at all temperatures.Further results on Th carbide samples betweenThC0.25 and ThC2 (þC) were obtained up to

2673 K.82 r was observed to reach its highest value(ffi3 mO m) for compositions near ThC and tempera-ture around 2000 K

2.04.2.2.3.2 Thorium dicarbide

The thermal conductivity l of a-ThC2 wasestimated41 from electrical resistivity measure-ments and the Wiedemann–Frantz relationship,giving l¼ 24 W K1m1 at 298 K, for a samplewith assumed 100% th.d Marchal and Trouve´83mea-sured l by a comparative flux method obtaining,for a-ThC2 with 72% th.d., 24.1 W K1m1 at

443 K and 20.5 W K1m1 at 627 K Grossman84obtained l¼ 13 W K1m1 by a radial heat flowmethod for b- and g-ThC2and 1713 K< T < 2333 K.All the ThC2modifications have metallic electri-cal conductivity, as confirmed both experimentally

0.0

0.5 1.0 1.5 2.0

2.5

ThC0.8100% th.d.

ThC 0.7

and theoretically A review of available electrical

resistivity (r) data for high-density ThC1.93between

298 and 2673 K is provided inFigure 10.82

2.04.2.2.4 Mechanical properties

2.04.2.2.4.1 Thorium monocarbide

The theoretical density of a given crystal structure

can be obtained from the lattice parameters if also the

molecular weight is known Using a ¼ 534.60 pm for

ThC0.98at room temperature yields r¼ 10.60 g cm3

Considering the thermal expansion, the th.d of solid

ThC at the melting point is r¼ 10.2 g cm3

The adiabatic elastic constants cijwere measured

only on a ThC0.063sample by the pulse echo overlap

method between 4.2 and 300 K along the [110]

crys-tallographic directions.85The resulting adiabatic bulk

modulus B ¼ 1/2(c11þ2c12)¼ 60.49 GPa at 300 K

The adiabatic shear modulus was obtained in the

Voigt approximation to be G ¼ 31.87 GPa Geward

et al.86,87 evaluated the isothermal bulk modulus of

ThC0.8 from high-pressure XRD measurements up

to 50 GPa, yielding BThC0.8¼ 109  4 GPa at 300 K,

with dB/dT ffi þ3 As the direct Th–C bonding

for-mation leads to a pronounced increase of structural

rigidity from metal to carbide, the Th carbide bulk

modulus increases with C content starting from

metallic a-Th, and a value of around 120 GPa for B

seems reasonable for stoichiometric ThC

ThC1 xVickers hardness increases from 50 HV

for 0.02 wt% C to 850HV (with a load of 2 N) for

ThC0.98(with 1 at.% of oxygen).6

According to these results, the addition of carbon

to thorium drastically reduces its cold workability

Untempered samples with C contents >6 at.% are

stiff and brittle with room elongations at fracture

eF¼ 0 Thus, tensile properties could be studied for

low C content only The 0.2% offset yield stress s0.2

varies from 165 MPa for 0.10 wt% C to 250 MPa

for 0.20 wt% C The yield stress, sy, varies from

166 MPa for 0.04 wt% C to370 MPa for 0.22 wt%

C (ThC0.05 in equilibrium with ThC0.67 at room

temperature) The elongation at fracture eF goes

from 35% for 0.04 wt% C to 11% in ThC0.05 in

equilibrium with ThC0.67, to nearly zero for higher

C contents In the same composition range, the

ulti-mate tensile strength sU ranges between 250 and

400 MPa at room temperature and rapidly decreases

with temperature (around 50 MPa at 1000 K).6

The creep and flow stress behavior in ThC

alloys up to 2.83 wt% C (ThC0.54) between 4.2 and

573 K was reviewed by Kleykamp et al.6It was found

to be composed of a thermally activated and an

athermal component The first increases with carboncontent and the strain rate The 2% offset yield stress

at a strain rate de/dt ¼ 3.3 105s1was obtained as

a function of temperature At room temperature,

it ranges from 50 MPa for 0.077 wt% C to 250 MPafor 2.83 wt% C This value increases considerably

at 4.2 K, where it is measured around 1.3 GPa

2.04.2.2.4.2 Thorium dicarbide

The theoretical XRD density of monoclinic a-ThC2

is 9.14 g cm3and 8.80 g cm3for tetragonal b-ThC2

with C/Th¼ 1.94 at 1768 K Fink et al.43

estimatedthe density of g-ThC2to be around 9.0 g cm3at themelting point

Oikawa and Hanaoka88 give a value of Young’smodulus E ¼ 1–2 GPa and a compressive strength

suc¼ 20 MPa for low-density ThC2 xin equilibriumwith C at room temperature Room temperatureVickers hardness of arc-melted, two-phase a-ThC2

in equilibrium with C under a load of 2 N is 600 HV.This value is increased up to 650 HV after heattreatment to 1873 K, and it obviously depends onthe oxygen-impurity content, which can make itincrease up to 970 HV.6,89

Values of the bulk modulus B ¼ V1(@2

E/@V2)¼

V1(@P/@V) and its pressure derivative B0¼ @B/@Preported in Table 3 were calculated at 0 K for thethree ThC2 xallotropies by Shein and Ivanonvskii.502.04.2.2.5 Optical properties

2.04.2.2.5.1 Thorium monocarbide

Freshly broken surfaces of ThC have a shiny metallicgray color which darkens in the presence of oxygen.Optical constants of nearly stoichiometric ThC havebeen measured in liquid samples by Bober et al.90by

a laser integrating sphere reflectometer between

2900 and 3900 K and l¼ 458, 514, 647, and 752 nm.For unpolarized light, r at the melting point (2773 K)was measured to be close to 0.45 at l¼ 647 nm and

y ¼ 45, this value not being very much dependent onthe angle Optical constants are deduced from theseresults: the real refractive index n (between 1.6 and2.0) and the absorption constant k (between 1.7and 2.5) Both n and k slightly increase with wave-length and decrease with temperature

2.04.2.2.5.2 Thorium dicarbide

a-ThC2 xcrystals are transparent and look yellowishunder the optical microscope Freshly broken sur-faces of ThC2xcrystals display a very pale metallicyellowish appearance which darkens with time in thepresence of oxygen.6

Grossman84 reported measurements of spectral

normal emissivity elof ThC2 x(9.24 wt% C,<0.5%

O2) for 1500 K< T < 2100 K, yielding an average

value el¼ 0.58  0.03 The same author also reported

an average value of the total spherical emissivity

between 1800 and 2150 K, et¼ 0.475  0.025

2.04.2.2.6 Multielement thorium carbides

A number of multielement thorium carbides have

been studied They occur as mixed phases of binary

thorium carbides with other elements by the

forma-tion of either continuous solid soluforma-tions, like ternary

carbides, or immiscible compounds The most

inter-esting are certainly the carbide-oxides and-nitrides

They form relatively easily during the ThCx

prepa-ration and on exposure to air It is therefore useful

to explore some of their properties, at least for the

Th-rich compositions

2.04.2.2.6.1 Thorium carbide oxides

The Th–C–O ternary system6 was extensively

studied by Potter.66It is characterized by a

hypostoi-chiometric Th monocarbide oxide fcc solid solution

Th(C,O)1xwith x > 0, stable around 1800 K It was

experimentally observed that the maximum

solubil-ity of oxygen in ThC in equilibrium with ThC2and

ThO2 corresponds to the composition ThC0.8O0.2

(1.3 wt% oxygen) Heiss and Djemal91observed that

the maximum solubility of oxygen in ThC1.94

corre-sponds to the composition ThC1.94O0.04 (0.25 wt%

oxygen), at 2273 K The room-temperature lattice

parameter of oxygen-saturated ThC0.8O0.2 is

esti-mated to be between 532.6 and 532.9 pm

2.04.2.2.6.2 Thorium carbide nitrides

The Th–C–N system has been investigated more

than the Th–C–O system, thanks in particular to

Benz et al.,92Pialoux,93and Benz and Troxel.94

For low nitrogen contents, the addition of nitrogen

has been observed to raise the a!b transition

tempera-ture of Th-rich ThC2x The effect on the same

transi-tion in C-saturated ThC2 xand on the b!g transition

temperature seems negligible, indicating that N is

prob-ably more soluble in a-ThC2 xthan it is in g-ThC2 x

Similar to oxygen, the addition of nitrogen to the fcc

ThC1 xphase reduces its lattice parameter

For N contents >0.05 at.%, literature data are

few and scattered The Th–Th(C,N) region is

char-acterized by a continuous fcc NaCl-type solid

solu-tion between ThN, stoichiometric ThC, and slightly

hypostoichiometric ThC1x Hyperstoichiometric

Th(C,N)1 þx exists as a solid solution on the ThCside above 2073 K ThN and very hypostoichiometricThC1 x are separated by a two-phase field Noeutectic has been observed in the Th–ThC–ThNregion, but a peritectic four-phase equilibriumbetween a-Th, b-Th, Th(C,N), and liquid is postu-lated at 1993  30 K Alloys with C/Th 1 wereobserved to melt at 2473 K under 2 bar of N2, and aternary eutectic exists just below 2500 K with compo-sition Th0.38C0.35N0.27 The lattice parameter of theTh(C,N) solid solution between ThC and ThN fol-lows Vegard’s law almost exactly, from approximately

534 pm for ThC to 516 pm for ThN The latticeparameter of Th(C,N) in equilibrium with Th3N4

and ThCN, a ¼ 522.4  0.6 pm, corresponds to thecomposition ThC0.35N0.65and is almost independent

of temperature ThC0.35N0.65is also the congruentlymelting composition of the Th(C,N) solid solution,with Tm¼ 3183  35 K The solidus temperature wasobserved to increase with nitrogen pressure

The lattice parameter of Th(C,N) in librium with ThC2 and ThCN, a ¼ 519.7  0.5 pm,corresponds to the composition ThC0.20N0.80 TheTh(C,N)–C region is characterized by the ternarycompound ThCN, which exists in two modifications.a-ThCN crystallizes in the prototype C-centeredmonoclinic structure, with space group C2/m(No 12) and lattice parameters a ¼ 702.5  0.5 pm,

and C at sufficiently high nitrogen pressure

The metallic electrical resistivity of the Th(C,N)solid solution decreases from 1.8 to<0.05 mO m withincreasing nitrogen content and decreasing tempera-ture The electrical properties of this phase dependprimarily on the conduction electrons and the vacancyconcentration in the fcc lattice.95Th(C,N) becomessuperconducting at low temperature, with a maximumtransition temperature of 5.8 K for the compositionThC0.78N0.22, sharply decreasing with increasing car-bon content The decrease is more gradual at highernitrogen content, up to 3.2 K for pure ThN

2.04.3 Protactinium Carbides

Protactinium (91Pa) is one of the rarest of the naturalelements Its most important isotope is 231Pa (half-life¼ 3.276 104

years), but the most interesting

from an industrial viewpoint is the artificial isotope

233

Pa (half-life¼ 27.0 days) This is an intermediate

isotope in the production of fissile 233U in thorium

breeder reactors

Some studies on PaC and PaC2can be found in the

literature.96–99 Lonsdale and Graves98 prepared a

dilute solution of Pa in ThC2by neutron irradiation

of ThO2, followed by carbothermic reduction The

monocarbide was prepared by carbothermic

reduc-tion of Pa2O5by Lorentz et al.99Products of reaction

at 2473 K contained a second phase, possibly PaC2

Pa metal has been prepared from PaC in the

presence of iodine using the Van Arkel method.100

2.04.3.1 Properties

Lorentz et al.99 found by room- and

high-temperature XRD that PaC is isostructural with

other actinide monocarbides, displaying fcc

sym-metry with a ¼ 506.08  0.02 pm, corresponding to a

theoretical density of 12.95 g cm3 At the highest

temperatures (2500 K), extra lines were observed,

corresponding to a tetragonal body-centered structure

(CaC2type) with a ¼ 361  1 pm and c ¼ 611  1 pm,

attributed to PaC2

Lonsdale and Graves studied, by Knudsen effusion,

the vapor pressure of Pa from a dilute solution of Pa in

ThC2, showing that PaC2has stability similar to ThC2

The formation of Gibbs energy for PaC was

esti-mated to be

DfGðPaCÞ ffi 182:5  0:0841T ðkJmol1Þ ½5

Enthalpy, entropy, and Gibbs energy of formation of

PaC and PaC2are reported inTable 4as estimated

by assuming that the thermodynamic functions for Pa

carbides lie between those of Th and U carbides.4

The considerable uncertainties stem from the large

lack of data

The main application of uranium carbides is as a fuel

for nuclear reactors, usually in the form of pellets or

tablets, but also in nuclear thermal rockets, wheretheir high thermal conductivity and fissile atom den-sity could be entirely exploited

2.04.4.1 Phase RelationshipsThe most recent thermodynamic optimization of theU–C phase diagram is due to Chevalier andFischer.101 An assessment of the uranium–carbonphase diagram is reported inFigure 11

Blumenthal102 studied the constitution of carbon alloys in the uranium–carbon system andproposed three different structures for the puremetal The observed transition temperatures are

low-940 1.3, 1047.8  1.6, and 1405.3  0.8 K for thea–b, b–g transitions and melting point, respectively.The low-temperature solubility of carbon in uranium

is low: <3 ppm in a-uranium, <10 ppm in the b-U,and between 0.07 and 0.09 at.% in g-U In the pres-ence of carbon, the system has a eutectic point

at 1390 K and two eutectoid reactions at peratures slightly lower than the pure crystal struc-ture transition The solubility of carbon in uraniumincreases with temperature A few studies on thesolubility of carbon in liquid uranium between 1500and 2800 K have been assessed in the followingequation103:

tem-ln CU

At a higher carbon content, two more compoundsare known to exist in the U–C system: U2C3 and

UC2 x

If U2C3 is the thermodynamically stable phaseuntil its peritectoid decomposition temperature(2106 K), it is normally not found in samplesquenched from above this temperature, where UCand UC2 are identified instead On the other hand,

as explained in Section 2.04.1.2.3, U2C3, onceproduced, can be easily quenched to room tempera-ture However, its thermodynamic stability below

1250 K is still controversial as some authors reported

Table 4 Thermodynamic functions of protactinium

the decomposition of UC þ C at lower

tempera-ture.105 This sesquicarbide has a body-centered

(bcc) cubic structure of the Pu2C3 type (Table 1)

The study of U2C3presents important experimental

issues, and results are often controversial and affected

by low accuracy Above the peritectoid temperature,

U2C3 decomposes into UC1 þx and b-UC2 y

A miscibility gap between these two phases has

been determined by Sears106by microstructure

anal-ysis on quenched samples Its low-temperature

boundary corresponds to the peritectoid (2106 K)

delimited by UC1.1and UC1.7and its maximum

tem-perature is 2323 K at a composition close to UC1.3

The complex mechanisms of these transformations

were described by Ashbee et al.107At higher

temper-ature, UC1þxand b-UC2yare fully miscible, so that

some authors108identify them rather as UC1þx0and

UC1þx00 Uranium dicarbide exists in two different

structures, a a tetragonal form between 1753 and

2050 K, and a b cubic form at higher temperatures

UC2 decomposes so slowly upon cooling that it is

normally observed as the stable phase in equilibrium

with pure carbon at room temperature It was

therefore decided to establish a ‘metastable’ nium–carbon phase diagram, where U2C3is left outand a-UC2 is the stable phase in equilibrium with

ura-UC and C at room temperature108(Figure 12)

UC2is hypostoichiometric Its phase boundary inequilibrium with C varies from UC1.89at the lowesttemperatures to UC1.92 at the highest.8 Laugier108based on some high-temperature XRD studies, pro-posed the decomposition of tetragonal UC2 into

U2C3 below 1753 K and redefined the transitiondomain between UC2and U2C3 The hypostoichio-metry domain of a-UC2 extends from the carbon-rich boundary to a phase limit in equilibrium with

U2C3, which reaches UC1.77at its maximum ature (2057 K – Figure 11) At higher temperature,

temper-U2C3is in equilibrium with b-UC2x The tic transformation from a- to b-UC2 occurs at

martensi-2050 20 K Bowman et al.109

investigated the bide behavior by high-temperature neutron diffrac-tion They showed that b-UC2is of the type B1 KCN.This result rules out the CaF2 structure previouslyproposed by Wilson (based on high-temperatureXRD analysis)110 and agree with the complete

dicar-1700

1800 1900 2000 2100 2200 2300 2400

UC1+x+ β-UC 2−x (or UC1+x

miscibility of UC and UC2 at high temperature,

already proven by many authors.4,111,112

The liquidus line presents two maxima between

UC and UC2 at 2780 20 K and 2730  20 K

cor-responding to the melting point of UC and UC1.9,

respectively A minimum temperature around 2675 K

is observed between UC1.5 and UC1.6 Although the

literature melting temperature data show some

disper-sion, probably due to the sample impurities and

alter-ation during the heat treatment, the points assessed

by Chevalier and Fischer101and confirmed by Utton

et al.113seem reliable within the reported uncertainties

The liquidus and solidus lines are very close together

at all compositions and can hardly be distinguished

experimentally

2.04.4.2 Physicochemical Properties

2.04.4.2.1 Crystallography

2.04.4.2.1.1 Uranium monocarbide UC

The UC lattice parameter was studied by manyauthors8

as a function of the C/U ratio, temperature, and O and

N impurity level (Figure 13 and Table 1).114The

recommended value is a ¼ 496.05  0.02 pm for pure

UC in equilibrium with higher carbides, and can be

retained as a room-temperature reference The lattice

parameter is slightly smaller for UC in equilibrium with

uranium, strongly dependent on the sample thermal

history For hyperstoichiometric UC1þx, the excess

car-bon is stabilized by substituting a single carcar-bon with

two carbons, leading to a homogeneous transformation

from the NaCl structure of stoichiometric UC to

the isomorphous KCN high-temperature structure ofb-UC2.115For this reason, many of the uranium mono-carbide high-temperature properties, including the lat-tice parameter, extend homogeneously up to the b-UC2

composition

N and O impurities have opposite effects on the

UC lattice parameter The substitution of carbon bynitrogen results in an approximately linear decrease

of a-UC in equilibrium with higher carbides Thesubstitution of carbon by oxygen, instead, gives alattice dilatation with a maximum between 1000and 2000 ppm of oxygen

The electronic structure of uranium carbides

is rather complex The density of state at theFermi level N(EF) can be calculated from the tem-perature coefficient g of the electronic heatcapacity, and an average value can be estimated

to be 18.9 1 mJ K2mol1, to yield N(EF)¼3g/2p2kB2 4.0 eV1atom1 This value, whichexplains the metallic electrical conductivity of UC,agrees only qualitatively with the tight-binding cal-culations by Adachi and Imoto116 and Das et al.16(Figure 1), but the agreement with the self-consistentlinearized ‘muffin tin orbital’ band structure calcula-tions (LMTO) by Brooks is good.117 According tothese calculations, a strong f–p bond exists Wedg-wood118 studied the phonon spectra of UC0.95 bytime-of-flight (TOF) neutron scattering, obtainingrather flat optical branches, resulting from the largemass difference and the weak interaction between

U and C atoms, with a frequency maximum of11.7 THz at q ¼ 0 The U–C bond force constant

400

600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200

940 K α-U + UC

Liquid + UC1−x

Xc

UC1+x+ β - UC2−x(or UC1+x⬘ + UC1+x⬘⬘)

Metastable domain

Figure 12 The metastable U–C phase diagram.

was calculated to be 4.55 08N m1 According to

these data, it seems reasonable to hypothesize a UC

bulk modulus higher than that calculated by Das et al

(65 GPa) By comparison with the values recently

calculated by Shi et al.,119a value close to BUC¼ 180

GPa seems realistic

Point defect behavior in UC was extensively

studied in the 1970s, and Matzke has highlighted

the complexity of the microscopic mechanisms

in his review.5 The energies of formation (VF) and

migration (VM) of uranium and carbon vacancies

were determined from electrical resistivity

measure-ments of quenched samples Matsui and Matzke120

recommended the following values: VFU¼ 1.55 eV,

VFC¼ 0.8 eV, VMU¼ 2.4 eV, and VMC¼ 0.9 eV For

VMC, the value 1.0 eV should probably be retained,

as it is in better agreement with the sharp rise in

the heat capacity of UC above 1500 K,8 and with

earlier measurements by Schu¨le and Spindler.121

In stoichiometric UC, the carbon octahedral sites

are partly doubly occupied, the resulting carbon

excess being balanced by vacancies At the melting

point (2780 K), the vacancy concentration wasestimated to amount to about 8% for both C and

U sublattices.8The formation of dislocations in radiated and irradiated UC is discussed by Matzke.5Dislocations with a Burgers vector b ¼ a [100] exist

unir-in the (100) plane of a UC–UC2 phase boundary (inthe Widmansta¨tten structure).122 Dislocation loopsformed by precipitation of fission-induced pointdefects and stringers of loops were found adjacent

to UC2platelets

2.04.4.2.1.2 Uranium sesquicarbide U2C3

The lattice parameter of cubic U2C3was studied up

to 2073 K by XRD, and no anomalies were detectedeither at low or high temperature Its values varyfrom 807.3 pm at 10 K123to 825.6 pm at 2073 K.114Oetting et al.124determined the energy of forma-tion for vacancies in the U2C3lattice to be0.8 eV,from the heat capacity increase above 1000 K.The temperature coefficient of the electronic heatcapacity was estimated to be g 84 mJ K2mol1from low T heat capacity measurements, in agree-ment with the metallic character of uranium sesqui-carbide U2C3 is antiferromagnetic below the Ne´eltemperature TN 55  4 K.8

c ¼ 598.9  0.1 pm No phase transitions were tected between 5 and 300 K The c/a ratio decreaseswith increasing temperature above 1473 K Whereas aincreases from 353.6 pm at 1073 K to 362.5 pm at

de-1973 K, there is no complete agreement about thebehavior of c Laugier and Blum108suggested that cdecreases from 605.6 pm at 1073 K to 594.9 pm at

1700 K on the U-rich side of the tetragonal UO2 x

phase field, whereas it varies from 605.6 to 603.9 pm

on the C-rich side

The transformation a!b is diffusionless of themartensitic type It occurs without movement of

Figure 13 (a) The uranium carbide lattice parameter as a

function of the C/U ratio and (b) the uranium carbide

lattice parameter as a function of temperature.

the U atoms, and with a slight deformation of the

C sublattice The transformation shear angle is

between 4 and 6 b-UC2 x crystallizes in a fcc

structure of the KCN-type with a0¼ 548.8 pm.109

UC2xis a metal The UC2electronic state

den-sity at the Fermi level was recently calculated by Shi

et al.,119in reasonable agreement with the

tempera-ture coefficient g of the electronic heat capacity This

was estimated to be 16.3 mJ K2mol1, to yield N

(EF) 3.45 eV1atom1for UC1.90and 16.7 mJ K2

mol1, to yield N(EF) 3.53 eV1atom1for UC1.94

Atoji127 showed that a-UC2x is paramagnetic

down to 5 K, without superconductivity

2.04.4.2.2 Thermodynamic properties

2.04.4.2.2.1 Uranium monocarbide UC

Thermodynamic functions of uranium carbides have

been extensively reviewed by Holley et al.4and, more

recently, by Chevalier and Fisher.101 Numerical

data are reported inTables 5 and 6 and plotted in

Figures 14 and 15

A few authors measured the heat capacity of UC

from low to high temperature Holley et al.4assessed

the temperature coefficient g of the electronic heatcapacity (18.9 1 mJ K2mol1), the Debye temper-ature yD¼ 328 K, and the high-temperature behaviorfor 298 K T  2780 K

Most of the U and Pu carbides show steep increase

in heat capacities at temperatures above 0.6Tm,attributed to the formation of defects.4

The 0 K randomization entropy is zero for chiometric UC, but an additional term S(0) ¼ Rx ln xshould be added for nonstoichiometric UC1þxcompositions The formation enthalpy of stoichio-metric UC was also assessed by Holley et al.4 Itsvalue is composition-dependent and slightly decreas-ing in the hypostoichiometric carbide, as suggested

stoi-by the uranium vaporization study stoi-by Storms128andthe carbon activity measurements of Tetenbaumand Hunt.129The UC room-temperature Gibbs energy

of formation was calculated from the enthalpy and thestandard entropy, and the value DfG (UC, s, 298) ¼

98.89 kJ mol1

was proposed by Holley et al forthe reaction Uþ C ¼ UC The error affecting thisvalue was estimated to be around 2.1 kJ mol1fromthe uncertainty in the U and C activities, strongly

Table 5 The heat capacity C p of uranium carbides at atmospheric pressure (in J K1mol1)

(T > 2070 K)

aNo satisfactory fit for these points, probably due to marked change in slope around 10 K.

Table 6 Thermodynamic functions of uranium carbides (in SI units).

Bulk modulus

B ¼ V1( @ 2

E/@V 2

) (GPa)

Critical parameters

31465.6  499.228T + 64.7501T ln(T) 7984166/T  0.0144T 2

dependent on composition and oxygen impurities.

Sheth et al.130 proposed DmH¼ 48.9 kJ mol1 for

the enthalpy of fusion and the following data for

50 75 100 125 150 175 200 225 250 275 300 325 350

Ideal ‘defect-free’ PuC (Kruger)

U–C and Pu–C systems can be calculated using Gibbs

energy functions given by Chevalier and Fischer101

and Fischer,131respectively To recalculate the Gibbs

energy of formation of the compounds here, the free

energy of the pure elements, in their stable reference

state at a given temperature, is subtracted from that of

the compounds The following expression can be

retained for UC from 298.15 K to the melting point:

DfGðUCÞð Jmol1Þ ¼ 31465:6  499:228T

þ 64:7501T lnðTÞ 7984166=T  0:0144T2 ½10

This temperature dependence of DfG (UC) is shown in

Figure 15and compared with the ones of other

ura-nium and plutoura-nium binary carbides

The partial pressures of the actinide species play

an important role in the redistribution of actinides

and the restructuring of fuel elements during burnup

(Figure 16)

In the case of U–C system, gaseous UCnmolecules

with n ¼ 1–6 have been detected by mass

spectrome-try.8The partial pressure equations of UC2(g), C1(g),

C2(g), and C3(g) are derived from the Gibbs energies

of formation and the activities of uranium and bon.4,132–134In the composition range, C/U¼ 0.92–1.10, the partial pressure of U(g) is almost equal tothe total pressure, the next predominant species being

car-C1(g) The following equations4can be used to late the U sublimation enthalpy in single-phaseregions on the complete U–C system at 2100 K:

calcu-log pð2100 KÞðbarÞ ¼ 2:56

expð29xÞ þ 1

2:34expð10ðx  1ÞÞ þ 1

in the UC1 þ x phase field Correspondingly, the

U enthalpy of vaporization increases with C/U up to711.62 kJ mol1at C/U1.08 The congruent vaporiz-ing composition was recommended as UC1.11 at

2300 K and UC1.84at 2100 K.101At the melting point,

-17

-16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4

C

1 (g),PuC 1.5 C

1 (g),PuC(liq)

C

1 (g),UC

U(g),UC 1.0

Pu(g),PuC

0.88 Pu(g),PuC

1.5

Pu(g),PuC(liq)

Pu(g),(U 0.3 Pu 0.7 )C 1.075