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

2.04 Thermodynamic and Thermophysical Properties of 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 2.04.1 2.04.1.1 2.04.1.2 2.04.1.2.1 2.04.1.2.2 2.04.1.2.3 2.04.1.2.4 2.04.2 2.04.2.1 2.04.2.2 2.04.2.2.1 2.04.2.2.2 2.04.2.2.3 2.04.2.2.4 2.04.2.2.5 2.04.2.2.6 2.04.3 2.04.3.1 2.04.4 2.04.4.1 2.04.4.2 2.04.4.2.1 2.04.4.2.2 2.04.4.2.3 2.04.4.2.4 2.04.4.2.5 2.04.4.2.6 2.04.5 2.04.5.1 2.04.5.2 2.04.6 2.04.6.1 2.04.6.2 2.04.6.2.1 2.04.6.2.2 2.04.6.2.3 2.04.6.2.4 2.04.6.2.5 2.04.6.2.6 2.04.6.2.7 2.04.6.2.8 2.04.6.2.9 Introduction Carbides General Properties of Actinide Carbides Structure of the matter Phase stability Preparation Applications Thorium Carbides Phase Relationships Physicochemical Properties Crystallography Thermodynamic properties Transport properties Mechanical properties Optical properties Multielement thorium carbides Protactinium Carbides Properties Uranium Carbides Phase Relationships Physicochemical Properties Crystallography Thermodynamic properties Transport properties Mechanical properties Optical properties Multielement uranium carbides Neptunium Carbides Preparation Properties Plutonium Carbides Phase Relationships Physicochemical Properties Triplutonium dicarbide Pu3C2 Plutonium monocarbide PuC Plutonium sesquicarbide Pu2C3 Plutonium dicarbide Vapor pressures Transport properties Mechanical properties Optical properties Plutonium carbide oxides and nitrides 89 89 89 90 93 93 95 96 96 97 97 99 102 103 103 104 104 105 105 105 107 107 109 113 115 117 118 121 121 122 122 122 123 123 124 125 125 126 126 127 127 127 87 88 Thermodynamic and Thermophysical Properties of the Actinide Carbides 2.04.7 2.04.7.1 2.04.7.2 2.04.8 2.04.8.1 2.04.8.2 2.04.9 References Minor Actinide Carbides Americium Carbides Curium Carbides Mixed Carbides Thorium–Uranium Carbides Plutonium–Uranium Carbides Summary Abbreviations 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) EAM Embedded atom method EMF Electromotive force EOS Equation of state (equation relating the parameters of a thermodynamic system to its state functions) fcc Face-centered cubic crystal structure GFR Gas fast reactor HTR High-temperature reactor HV Vickers Hardness LWR Light water 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 TOF Time of Flight Va Vacancy VHTR Very high-temperature reactor XRD X-ray diffraction Symbols a aT aT Lattice parameter Linear thermal expansion coefficient; aT ¼ l0À1(dl/dT) Average linear thermal expansion coefficient 128 128 128 128 129 130 133 133 aY B c c cij Cp Cv d D0 DYx Y Dx E EF G(x) H(x) kB m n n N P P pi q QS QX R S t T Tc Tm TN Vaporization coefficient of species Y Bulk modulus; B ¼ VÀ1(@ 2E/@V2) Lattice parameter (cell height in noncubic lattices) Velocity of light in vacuum Adiabatic elastic constants (ij component of the elastic tensor) Heat capacity at constant pressure Heat capacity at constant volume Crystal grain size Diffusion coefficient Self-diffusion coefficient of species x in the compound Y Chemical diffusion coefficient of species x in the compound Y Young elastic modulus Fermi Energy (Fermi level) Gibbs free energy (of component x) Enthalpy (of component x) Boltzmann’s constant Mass Refractive index (real part) Neutron absorption (in nuclear reactions) Number of electrons in a given state (e.g., N(EF) ¼ number of electrons at the Fermi energy) Porosity fraction Total pressure Partial pressure of the component i Heat flux Activation energy for Soret’s diffusion Activation energy for the diffusion of species X Ideal gas constant Entropy Time Absolute temperature Critical temperature Melting point (melting temperature) Ne´el temperature Thermodynamic and Thermophysical Properties of the Actinide Carbides V VFY VMY x xY y b Df AY Dm AY Dmix A Dsub AY Dvap AY DfG DvapG DfH DmH DvapH « «_ «, «l «t g g g k l l lPH lE n uD uE r r rc s sc Volume Energy of formation of a vacancy for the species Y Energy of migration of a vacancy for the species Y Stoichiometry parameter in carbides Molar fraction of species Y Stoichiometry parameter in carbides Beta decay (in nuclear reactions) Variation of the thermodynamic function A upon formation of compound Y Variation of the thermodynamic function A upon melting of compound Y Variation of the thermodynamic function A upon mixing Variation of the thermodynamic function A upon sublimation of compound Y Variation of the thermodynamic function A upon vaporization of compound Y Gibbs free energy of formation Gibbs free energy of vaporization Enthalpy of formation Enthalpy of melting Enthalpy of vaporization Elastic deformation, elongation Deformation rate (creep) Spectral emissivity Total emissivity Temperature coefficient of the electronic heat capacity Gamma decay (in nuclear reactions) Average volumetric thermal expansion coefficient Optical absorption constant Wavelength of the electromagnetic radiation Thermal conductivity Phonon contribution to the thermal conductivity Electron contribution to the thermal conductivity Poisson’s ratio Debye’s temperature Einstein’s temperature Density Optical reflectivity Critical density Axial stress Compressive rupture axial stress (compressive strength) 89 2.04.1 Introduction Research on actinide carbides as nuclear fuel began in the 1950s Then, uranium dioxide and mixed uranium–plutonium oxides began to be preferred as nuclear fuel in most of the Generation II and III power plants, due to the fact that the option of fast reactors for civil purposes had mostly been abandoned This led to an abrupt interruption in actinide carbide research between the first half of the 1970s and 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 high burnup and high-temperature operation with a reduced ‘margin to melting,’ in the framework of the ‘Generation IV’ nuclear systems development.1 Consequently, actinide carbides are now being studied with more and more advanced methods, both experimental and computational The goal of the present monograph is to summarize the state-of-the-art knowledge of the most relevant physical and chemical properties of actinide carbides This work is largely based on a few earlier reviews on the same subject: Storms,2 Rand,3 Holley et al.,4 Matzke,5 the Gmelin Handbooks,6–9 and the OECD-NEA reviews.10–13 More detailed and/or more recent data are taken from single references 2.04.1.1 Carbides Carbides are chemical compounds in which carbon bonds with less electronegative elements Depending on the difference in electronegativity and the valence state of the constituting elements, they exist as different bonding types Accordingly, they are classified as salt-like compounds (in which carbon is present as a pure anion and the other elements are sufficiently electropositive), covalent compounds (SiC and B4C), interstitial compounds (with transition metals of the groups 4, 5, and except chromium), and ‘intermediate’ transition metal carbides.14 In general, carbides display metallic properties, and they are mostly refractory (high melting) Their more specific properties depend on the constituting elements 2.04.1.2 General Properties of Actinide Carbides Actinides are known to form three main types of stoichiometric carbides (Table 1): monocarbides of the type AnC, sesquicarbides of the type An2C3, 90 Thermodynamic and Thermophysical Properties of the Actinide Carbides 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, americium, and, recently, curium Other types of actinide carbides such as CmC3 and Pu3C2 have 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, ‘C4À’ in the monocarbides; as two atom Table units, ‘C2À ’ in the acetylides; and as three atom units,‘C2À ’ in the sesquicarbides This model, useful for a first visual description of these materials, is physically inconsistent with their essentially metallic properties The An–C bonds are certainly more covalent than ionic, as recently confirmed.16 Actinide compounds are characterized by a peculiar electronic structure, where the extended nature of the 5f electron wave functions yields a unique interplay between localized and band electrons This feature leads, in particular, to properties associated with covalent bonding in these compounds, which show crystal structures normally associated with ionic bonding.5 Monocarbides AnC1ặx (An ẳ Th, Pa, U, Np, Pu, Am) crystallize in the NaCl-type space group Fm 3m – No 225 (Table 1) The elementary cell is Synopsis of the known actinide carbides Compound and lattice parameters Composition and temperature range Space group ThC1Ỉx 508.8 pm (Th) to 534.4 pm (ThC0.98 in equilibrium with ThC2) C/Th ¼ 0À1.96 Eutectic ThC1Ỉx ¼ 1980 K Congruent Tm ¼ 2780 K for C/Th ¼ 0.975 – NaCl-fcc O5h À Fm3mNr:225ị PaC 506.08 pm UC1ặx 4.9605 A (UC1.0) 4.9563 A (UC0.93) NpC1Ỉx 499.1 pm for NpC0.82 to 501.0 pm for NpC1.0 PuC1Àx a ¼ 498.13 À 1.50 (1 À C/Pu)pm AmC1ỵx 502 pm Th2C3 855.13 a 856.09 pm in a narrow homogeneity range U2C3 808.99 pm Np2C3 810.3 pm Pu2C3 812.1 a 813.4 Am2C3 827.57 pm Cm2C3 839.4 pm Structure - Actinide; -C C/U ¼ 0.82–1.86 Tm ¼ 2780 K for C/U ¼ 0.82 C/Np 1.0 C/Pu ¼ 0.74–0.94 Tperitectic ẳ 1910 ặ 20 K AmC1.04, AmC1.25 Th2C3y (0 y Under high p > 2.8 GPa 0.05) bcc – eight molecules per unit cell Td6 À I 43dðNr:220Þ U2C3 ! UC ỵ UC2 (>2093 K) C/Pu ẳ 1.451.5 Stable under 2300 K – – Continued Thermodynamic and Thermophysical Properties of the Actinide Carbides Table 91 Continued Compound and lattice parameters Composition and temperature range Space group a-ThC2 a ẳ 668.4 ặ 0.02 pm; b ẳ 422.0 ặ 0.1 pm; c ẳ 673.5 ặ 0.2 pm; b ẳ 103.91 Ỉ 0.01 ThC1.94 Stable up to 1713 K Monoclinic C2/c (No 15) Structure - Actinide; c c Th c b a-PuC2 a ¼ 363 pm; c ¼ 6.094 A˚ g-ThC2 a ¼ 581.3–584.1 pm b-UC2 a ¼ 548.8 pm b-PuC2 a ¼ 572 pm c c Th Th c c c c c Th c Th c c c c Stable for 1713 K T 1768 K c Th Th b-ThC2 a ¼ 422.1 pm; c ¼ 539.4 pm (in equilibrium with graphite) a-PaC2 a ¼ 361 pm; c ẳ 611 pm a-UC2 a ẳ 352.45 ỵ 0.75 (C/U-1.80) pm; c ¼ 1.702a Stable in range 1790–2050 K Tm ¼ 2720 K -C Th Th Th c Th c c c c Th c c c c c c c Th Th Th Th c c c c CaC2-tetragonal D17 4h À I4=mmm (Nr 139) Observed around 2500 K C/U ẳ 1.751.9 UC2 ! U2C3 ỵ C (2050 K) Stable for 1933 K T 1983 K Stable above 1768 K Tm ffi 2883 K Stable above 2050 K Tm ffi 2750 K Stable above 1983 K Tm ffi 2520 K KCN-fcc O5h À Fm3mðNr:225Þ Other actinide carbides with little information: PaC2, NpC2, probably isostructural to CaC2, Pu3C2, stable between 300 and 800 K, but unknown structure; Cm3C with fcc Fe4N-like lattice with a ẳ 517.2 ặ 0.2 pm represented by four formula units The lattice parameter 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 to form Thus, Th2C3 was observed only under high pressure (2.8–3.5 GPa), and U2C3 is produced by a complex preparation procedure Both decompose into a mixture of mono- and dicarbides at high temperatures The situation is different in the case of Pu2C3, which is the most stable among the Pu carbides and forms easily at temperatures ranging from Thermodynamic and Thermophysical Properties of the Actinide Carbides DOS (states per eV Th atom) photoelectron spectroscopy, XPS) and theoretically (by tight-binding methods and, more recently, by density functional theory techniques) These compounds are, in general, good electronic and thermal conductors, with a nonzero density of electronic states at the Fermi level (Figure 1) However, the actual filling of the levels largely depends on the peculiar behavior of the 5f electrons, ThC EF -13.6 +13.6 Energy (eV) (a) DOS (states per eV U atom) room temperature to the melting point Unlike the fcc modifications of mono- and dicarbides, sesquicarbides can hardly accommodate lattice defects; therefore, they essentially exist as line compounds Actinide dicarbides AnC2Àx have been observed in a larger variety of allotropes (Table 1) At intermediate 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 established 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 (see Table 1) The second are responsible for the existence of hypostoichiometric monocarbides An1Àx, extending to the pure metal for thorium but only to a narrow UC1Àx 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 peculiar 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 carbides has been studied rather extensively, both experimentally (by low-temperature calorimetry and X-ray UC EF -13.6 +13.6 Energy (eV) (b) DOS (states per eV U atom) 92 b-ThC2 g-ThC2 a-ThC2 ThC2 (c) -9 -8 -7 -6 -5 -4 -3 -2 Energy (eV) -1 EF Figure (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 Thermodynamic and Thermophysical Properties of the Actinide Carbides which tend to be more localized or more itinerant according to the actinide and the compound involved Thus, Pu carbides have much higher electrical resistivity than Th and U carbides Similarly, mono- and dicarbides are better electronic conductors than sesquicarbides are Magnetic transitions have been observed at low temperatures in sesquicarbides, 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 ThC1Àx, 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 ThC1Àx: 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 ThC1Àx, 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 Hill19 that imply that U–U distance is 1923 K) – T > 298 K Total T range Cp (298) ẳ 136.88 ặ 2; Cp ẳ 120.72 ỵ 46.88 103T ỵ 19.46 104T2 Cp (298) ẳ 47.070; dCp/dT ¼ 0.0418 J KÀ2 molÀ1; Cp ¼ 57.887 À 1.45 102T ỵ 7.71 106T2 ỵ 8.618 109T3 – 6.556  105TÀ2 Cp (298) ¼ 114; dCp/dT ¼ 0.100 J KÀ2 molÀ1; Cp ¼ 156.075 À 7.991  102T ỵ 7.045 105T2 5.2 105T2 298 K T 848 K 50 K T 1875 K 50 K T 2285 K a Trend estimated on few experimental points Standard enthalpy and entropy of a-PuC2 at 298 K reported in Table are extrapolated.9 DfG for a-PuC2 (Figure 15) is calculated using the data recommended by Fischer and Holley et al No data are available for b-PuC2 2.04.6.2.5 Vapor pressures Vapor pressures of species in the Pu–C system were reviewed by Marcon,207 Holley et al.,4 and Matzke.5 The vapor phase in equilibrium with Pu carbides is always richer in plutonium than the condensed phase is The partial pressure of Pu(g) dominates over other gaseous species, to the point that those are almost negligible in comparison Therefore, any vaporization study on this system should take into account segregation effects in the condensed phase, and it is impossible to treat the different Pu–C compounds separately Marcon’s results,207 summarized in the following equations, were obtained with longer measurement times in order to vent out oxygen impurities, leading to vapor pressures in equilibrium with pure carbides 18 800 ỵ 4:3 ẵ48 log pPu ¼ À T in the Pu–PuC and PuC–Pu2C3 domain, from room temperature to the melting point 20 200 ỵ 4:23 ẵ49 log pPu ẳ T in the Pu2C3C domain, between 1500 and 2000 K; 25 200 ỵ 6:8 ½50Š log pPu ¼ À T in the Pu2C3–PuC2 domain, between 2000 and 2300 K; 18 150 ỵ 3:15 ẵ51 log pPu ¼ À T in the PuC2–C domain, between 2000 and 2500 K Pu(g) partial pressure over Pu–C system is higher than U(g) pressure over U–C system in the same temperature and composition ranges (Figure 16) The partial pressure pC1of C(g) is much higher than the partial pressures of other carbon-bearing species, which can be neglected in comparison to it In Figure 16, the partial pressure values in equilibrium with PuC(liq) were extrapolated from those in equilibrium with PuC(s) including a correction for the enthalpy of melting 2.04.6.2.6 Transport properties Plutonium carbides have peculiar transport properties with respect to uranium and thorium carbides Although the metallic nature of Pu carbides is confirmed by nonzero DOS at the Fermi level,211 the conduction properties are mostly due to 5f electrons in these compounds, resulting in poorer thermal and electrical conductivities The electrical resistivity of PuC0.90 and Pu2C3, for example, was measured to be about two orders of magnitude higher than in U and Th carbides.9 Matzke5 suggested the following equations: rel ẳ 258 0:029T ỵ 3:2 105 T mOcm ẵ52 for single-phased PuC0.85 rel ẳ 278:5 0:017T þ 3:9  10À5 T mOcm ½53Š for single-phased PuC1.0 (PuC1x ỵ Pu2C3) The thermal diffusivity and conductivity of sintered PuC was also assessed by Matzke5 and measured by Sengupta et al by laser flash.223 The earlier results reported by Matzke are probably correct for almost pure PuC1Àx, because Sengupta’s samples contained a 20 wt% of Pu2C3 Matzke recommends the following equation: lPuC ¼ 7:45 À 4:04  10À3 T ỵ 1:20 105 T WK1 m1 ị ½54Š 373 K T 1573 K Thermodynamic and Thermophysical Properties of the Actinide Carbides lPuCỵ20wt%Pu2 C3 ẳ 7:50 101 5:79 103 T ỵ 1:25 105 T À 1:03  10À9 T ðWKÀ1 mÀ1 Þ ½55Š 373 K T 1573 K More details about these last data are reported in Chapter 3.03, Carbide Fuel of this Comprehensive 2.04.6.2.7 Mechanical properties Pu3C2 density was measured to be 15.3 g cmÀ3.208 The density of the other Pu carbides can be calculated knowing the C/Pu ratio, the lattice structure, and the Pu-isotopic composition: r ¼ 13.51 g cmÀ3 for fcc 239PuC0.88 and r ¼ 12.69 g cmÀ3 for bcc 239 Pu2C3 Hardness of Pu carbides was observed to decrease with increasing carbon content, from 0.8 Ỉ 0.1 GPa for Pu3C2 to Ỉ 0.5 GPa for Pu2C3 PuC1Àx compositions take intermediate values between 0.345 and 0.85 GPa at increasing C content.9 Values of the linear thermal expansion coefficients of PuC1Àx are reported9 between 298 and 1000 K The average thermal expansion coefficient between 298 and 873 K is aT ẳ (10.8 ặ 0.2)106 K1 for PuC0.85 The value recommended for Pu2C3 between 298 and 973 K is aT ¼ 14.8  10À6 KÀ1 2.04.6.2.8 Optical properties Pu carbides have a metallic gray shine A recent multiwavelength pyrometry study169 has shown that the spectral optical emissivity of PuC1Àx is similar to that of UC (close to 0.5) in the spectral range 500 nm l 900 nm 2.04.6.2.9 Plutonium carbide oxides and nitrides O and N dissolve in monocarbide by substituting carbon or by occupying vacant C-sites in the lattice For example, in PuC1Àx, the small oxygen atoms can easily fill the vacant carbon sites, leading to a compound close to stoichiometric PuC can accommodate more oxygen (up to 78 mol% PuO) than UC ( 35 mol% UO), probably because of the smaller size of the Pu atoms.9 Solid compact plutonium carbide has been observed to react slowly with air between room temperature and 573 K However, it can burn in pure oxygen at 673 K.9,224 Pu2C3 was observed to be somewhat more stable than the other Pu carbides with respect to oxidation The pseudobinary PuC–PuO system follows a nearly ideal solution behavior Anselin et al.225 measured the evolution of the PuC1Àx lattice parameter (in the presence of metallic Pu) with the addition of oxygen They noticed a first rapid increase (from 496.1 to 497.3 pm) between and 20 mol% PuO This behavior was explained as resulting from a change in the actual C/Pu ratio and from lattice expansion following the occupation of vacant sites Vegard’s law was then followed for composition richer in oxygen The lattice parameter varied from 497.3 pm at 20 mol% PuO to 495.6 pm at 78 mol% PuO, where the solubility limit was reached (Figure 26) Extrapolated values agree with literature data on the pure compounds The same investigation carried out on the pseudobinary PuC–PuO2 showed very limited variation of the lattice parameter upon oxygen addition.225 XRD and chemical analyses of the Pu–C–O system have shown that both monocarbide and sesquicarbide of plutonium are hypostoichiometric at low oxygen content and become stoichiometric at high oxygen content (!6000 ppm oxygen) In the biphasic mixed carbide system, MCO ỵ MC1.5, calculations indicate that carbon activity increases with ‘O’ substitution in the monocarbide This carbon activity increase is, however, less pronounced than it is in U-rich fuel, due to the higher tolerance of ‘O’ substitution in PuC1Àx, which also implies a lower pCO in Pu-rich fuels PuC and PuN form solid solutions As in the case of the Pu–C–O system, the high vacancy concentration of PuC and the preferential formation of Pu2C3 498.0 497.5 Lattice parameter/pm Sengupta’s values are lower, showing that the sesquicarbide has an even lower thermal conductivity than the monocarbide: 127 497.0 Pu C 496.5 Pu xO 1– x 0.2 U 0.8 C xO 1− 496.0 PuCxO1–x+ Pu2O3 + Pu x 495.5 Pu0.2U0.8CxO1–x+Pu0.2U0.8O2–y 495.0 494.5 20 40 60 80 100 O/(C+O)% Figure 26 Lattice parameter of plutonium monocarbide oxides and mixed plutonium–uranium carbide-oxides Reproduced from Holleck, H.; Kleykamp, H In Gmelin Handbook of Inorganic Transurane Teil C: Verbindungen; Springer-Verlag: Berlin, 1972 128 Thermodynamic and Thermophysical Properties of the Actinide Carbides 496.5 496.0 495.5 Lattice parameter (pm) 495.0 494.5 494.0 493.5 493.0 PuCxN1–x+ Pu2C3 492.5 x N 1– Cx 492.0 Pu 491.5 491.0 490.5 490.0 20 40 60 80 100 C (mol%) Figure 27 Lattice parameter of plutonium monocarbide nitride Reproduced from Holleck, H.; Kleykamp, H In Gmelin Handbook of Inorganic Chemistry Transurane Teil C: Verbindungen; Springer-Verlag: Berlin, 1972 lead to important deviations from Vegard’s law in the C-rich part of the PuC–PN pseudobinary system (Figure 27).9 The PuC hypostoichiometry is curtailed at high temperature by the addition of nitrogen, especially near the PuN side N addition increases the carbon activity and reduces the actinide activity in monocarbides Moreover, nitrogen was observed to stabilize PuC2 below its decomposition temperature.9 2.04.7 Minor Actinide Carbides Among the minor actinides, only carbides of americium and curium have been identified and investigated so far 2.04.7.1 Americium Carbides The two most stable isotopes of americium, 241Am (432.2 years) 243Am (7370 years), are formed by b-decay of 241Pu and 243Pu, respectively Therefore, a certain percentage (order of 10À1 at.%) of americium is commonly present in plutonium As a consequence, traces of americium carbides can be formed in plutonium or mixed carbide matrices.226 Although the Am–C phase diagram has not been investigated in any detail, the monocarbide and the sesquicarbide have been identified, prepared by carbothermic reduction and arc-melting.227 Samples of nominal composition Am1.04 and Am1.25 were thus obtained and annealed at 1273 K for 24 h, and then characterized by XRD at room temperature The main phase displayed a fcc NaCl Fm 3m lattice, with lattice parameter a ¼ 502 pm Although the precise composition and the oxygen and nitrogen contents were not determined, this phase corresponded most probably to the monocarbide Traces of a bcc phase (most likely the sesquicarbide) were also detected Mitchell and Lam199 prepared americium sesquicarbide Am2C3 and analyzed it by XRD at room temperature The material was found to be isostructural with Pu2C3, bcc, I 43d, with eight formula units per unit cell After annealing, the lattice parameter was found to be a ¼ 827.57 Ỉ 0.2 pm Holley et al.4 estimated the thermodynamic functions for the formation of americium sesquicarbide: DfH (298) ¼ À75 Ỉ 20 kJ molÀ1, DfS (298) ¼ Æ k J KÀ1 molÀ1, and DfG (298) ¼ À77 Ỉ 20 kJ molÀ1 These values were estimated by assuming that Am2C3 is similar to Pu2C3 and that the trend toward lower values of DfH and DfG with increasing atomic number continues beyond Pu2C3 2.04.7.2 Curium Carbides Curium has a few long-lived isotopes, some of which are strong a-emitters (particularly 242Cm and 244 Cm) Their formation in U–Pu nuclear fuel, therefore, increases the radiotoxicity of the waste However, even after a few years of irradiation at burnups >100 GWd tonÀ1, the total Cm concentration in MOX was observed to be very low, $10À3 at.%.228 In this scenario, the rare literature studies on Cm carbides have an essentially academic profile The substantially covalent (s) Cm–C bonding in gaseous curium–carbon complexes obtained by laser metal–polymer coablation was studied in the late 1990s.229 More recently, Radchenko et al.230 prepared the first samples of curium carbides by high-vacuum high-temperature condensation of metallic 244Cm onto an iridium support coated with amorphous carbon Cm2C3 and Cm3C, isostructural to Am2C3 and Sm3C, respectively, were identified by XRD Cm2C3 has a bcc crystal lattice of the I 43d space group with a ẳ 839.04 ặ 0.05 pm Cm3C has fcc Fe4N-like lattice (already observed for some lanthanides) with a ẳ 517.2 ặ 0.2 pm Since no other carbides were detected at any carbon concentration, these authors concluded that Cm2C3 and Cm3C are the only existing Cm carbides 2.04.8 Mixed Carbides Holleck and Kleykamp8 assessed the solubility of actinide mono- and dicarbides (Figure 28) Thermodynamic and Thermophysical Properties of the Actinide Carbides ThC PaC UC NpC PuC (+) + + + (+) (+) (+) (+) + ThC2 ThC ThC2 PaC (+) UC + (+) NpC + (+) (+) PuC + (+) + (+) (+) UC2 + PuC2 + UC2 PuC2 + + 129 + + (b) (a) Figure 28 The solubility of pseudobinary actinide monocarbides (a) and dicarbides(b) ỵ, complete solubility demonstrated and (ỵ), complete solubility supposed Reproduced from Holleck, H.; Kleykamp, H In Gmelin Handbook of Inorganic Chemistry U Supplement Volume C12; Springer-Verlag: Berlin, 1987 Complete solubility is likely to occur in all the actinide binary mono- and dicarbide systems, although probably not at all temperatures Mixed actinide carbides have technological importance in the nuclear industry Among these systems, the ternary U–Pu–C has been broadly investigated in the last five decades in the framework of the U–Pu fuel cycle Similarly, the system Th–U–C has been investigated in the framework of the Th–U fuel cycle, although the latter has been less frequently considered as a fuel option Other mixed actinide carbide systems (Th–Pu–C, Th–U–Pu–C, etc.) have been occasionally studied; however, they are not addressed in this chapter Some details about the physicochemical properties of the ternary Th–U–C and U–Pu–C systems are given in this section More technical information related to the in-pile behavior of U–Pu carbides can be found in Chapter 3.03, Carbide Fuel of this Comprehensive 2.04.8.1 Thorium–Uranium Carbides The monocarbides UC and ThC are completely miscible,8 and the lattice parameter obeys Vegard’s law, probably with a small negative deviation Slightly hypostoichiometric Th-rich mixed (U,Th) carbides are miscible, but it seems that only small amounts of uranium are soluble in ThC1Àx with x > 0.5 Most of the results available in carbon-rich samples were obtained on quenched specimens,231 making them a relevant source of uncertainty, as most high-temperature phase transitions in this system occur with fast kinetics It is therefore impossible to recommend any sound ternary phase diagram For example, the phase boundaries of the monoclinic to tetragonal transformation in (U,Th) C2 is still unclear The monoclinic form is probably stable at T 1500 K and for Th contents >45 at.%, the tetragonal phase more likely below 1500 K both in the U-rich and in the Th-rich domain, but a miscibility gap between (U,Th)C2Àx and (Th,U)C2Àx is believed to exist The high-temperature fcc form of the mixed dicarbide is stable and completely miscible above approximately 2100 K For 1500 K T 2100 K, this homogeneity range shrinks, and around 1500 K and 40 at.% Th, the cubic dicarbide is believed to decompose eutectoidally into the U-rich tetragonal and the Th-rich monoclinic (or tetragonal) forms The solidus temperatures for the (U, Th)C2 system are reported to increase from 2750 Ỉ 25 K for pure UC2 to 2883 Æ 50 K for pure ThC2, but the observed solidus seems to stay almost constant within the experimental uncertainty up to 67 at.% UC2 The heat capacity of (U,Th)C containing up to 15 at.% Th was measured between 1.5 and 4.2 K.56 The resulting temperature coefficient of the electronic heat capacity was observed to decrease from $19.4 to 16.7 mJ KÀ2 molÀ1 with increasing UC content, corresponding to 3.97–3.11 states per eV per molecule at the Fermi level Theoretical values of the magnetic susceptibility determined from these data were lower than the experimental values by a factor 3–4.70 Thermodynamic and Thermophysical Properties of the Actinide Carbides l ẳ 9:8182 ỵ 0:0066T Wm1 K1 ị ẵ57 for U0.1Th0.9C and l ẳ 16:236 ỵ 0:0080T Wm1 K1 ị ẵ58 for U0.1Th0.9C2 Electrical and magnetic properties of the (U,Th)C solid solution up to 0.15 at.% UC were studied elsewhere.233 The electrical resistivity was observed to increase up to 1.81 mO m for 0.05 at.% UC and then decrease for higher uranium contents The hemispherical spectral emissivity of U0.8Th0.2C is reported to be el ¼ 0.6 at 650 nm and 1900 K.8 2.04.8.2 Plutonium–Uranium Carbides Phase relationships in the U–Pu–C system have been studied extensively in Los Alamos Scientific Lab of the University of California and Argonne National Laboratory.234–237 The most recent review of the U–Pu–C system is due to Fischer.238 A few general results are commonly accepted: with increasing ‘Pu’ content, the sesquicarbide becomes more stable segregation occurs, resulting in a sesquicarbide phase richer in plutonium238 the lattice defect concentration typical of Pu–C compounds decreases with the addition of uranium the melting point decreases with increasing Pu content.239,240 50 % C 50 %C Thermal conductivity measurements were performed on arc-melted U0.1Th0.9C and U0.1Th0.9C2 samples between 473 and 1273 K The results are summarized in the following equations8: 60 (U,Pu)C 40 30 ζ + (U,Pu)C η + (U,Pu)C β U + (U,Pu)C )C Pu ẵ56 60 (U, Dmix G ẳ À200xð1 À xÞðkJmolÀ1 Þ Single-phase Two-phase u+ αP Data exist on the linear thermal expansion coefficient a and average linear thermal expansion coefficient aT of mixed (U, Th) dicarbides.8 aT was observed to monotonically increase from 8.7Â10À6 KÀ1 for pure ThC2 to 13.5Â10À6 KÀ1 for pure UC2, but a shows a less regular behavior probably reaching a maximum of around 17Â10À6 KÀ1 at $65 at.% UC2 Data on the relative partial molar Gibbs energy of UC, ThC, and Th, plus the free energy of mixing of the (U,Th)C solid solution as a function of the UC mole fraction at 1173 K were measured.232 The free energy of mixing for UxTh1ÀxC follows approximately the equation: αU + (U ,Pu )C 130 40 30 Figure 29 Phases present in the ternary U–Pu–C phase diagram around the MC composition at 843 K according to Rosen et al.234 Many properties of (U,Pu) mixed carbides can be deduced from these points Uranium monocarbide forms a complete solid solution with plutonium monocarbide An isothermal section at 843 K of the ternary U–Pu–C diagram is shown in Figure 29 The (U,Pu)C phase is stoichiometric in regard to its carbon content in a composition range from to 35 at.% Pu With a further increase in Pu content, it tends to become hypostoichiometric The biphasic field, MCỵMC1.5, exists between 50 and 60 at.% C, depending upon the Pu/U ratio Mardon and Potter241 calculated segregation in the MCỵM2C3 region at 1200 and 1800 K Holleck242 reports segregation at 1773 K at two defined M2C3 ¼ 0.172] and [xMC conodes: [xMC Pu ¼ 0.095, xPu Pu ¼ 0.17, M2C3 xPu ¼ 0.264], indicating that the higher the plutonium content, the more pronounced is the plutonium segregation into two phases This effect is reduced at higher temperature Accordingly, the lattice parameter trend in the pseudobinary UC–PuC1Àx and U2C3–Pu2C3 systems often deviates from Vegard’s law (Figure 30) This behavior has been explained as due to the abundant lattice vacancies and the phase segregation toward the formation of the sesquicarbide in the Pu-rich composition range (!65 at.% PuC1Àx) Interestingly, a clear negative deviation from Vegard’s law and from the ideal solution behavior was observed in the U-rich carbides too.235 A slightly negative deviation from Vegard’s law was also reported for the solid solution U2C3–Pu2C3.9 Ohse and Capone240 studied (U0.8Pu0.2)–C in the temperature range 1773–2731 K, and the composition range, C/M ¼ 0.95–1.4, and reported (i) MC/(MCỵM2C3) phase boundaries: 2000 K for xc ẳ 0.517, 2100 K for xc ¼ 0.524 and 2200 K for xc ẳ 0.532; (ii) MC/(MCỵM2C3ỵMC2) phase boundary: 2300 K, xc ẳ 0.539; and (iii) MC/(MCỵMC2) Thermodynamic and Thermophysical Properties of the Actinide Carbides 131 499.5 499.0 Extrapolated stoichiometric PuC 498.0 High-C boundary 497.5 497.0 law inar Cb 496.5 rd’s a Veg Pu- 496.0 y Lattice parameter (pm) 498.5 Low-C boundary 495.5 495.0 Defective Structure Stoichiometric Monocarbide 494.5 UC 10 20 30 40 50 PuC1–x 60 PuC 70 Atomic % Pu in UPuC1-x Figure 30 Lattice parameter as a function of plutonium content in (U, Pu)C1Àx Reproduced from Rosen, S.; Nevitt, M V.; Barker, J J J Nucl Mater 1963, 9, 128–136 phase boundaries: 2400 K for xc ¼ 0.547 and 2500 K for xc ¼ 0.551 The (U,Pu)C1.0 solidus–liquidus curves are plotted together with experimental data in Figure 31 The higher solidus line was calculated by assuming an ideal solution behavior of both solid and liquid (U, Pu)C However, solidus data reported by Dalton by high-temperature XRD243 are lower, and in better agreement with the phase boundary calculated by Fischer238 using a substitutional solution model This confirms the nonideal behavior of the (U,Pu)C solution The formation of a M2C3 phase in the Pu-rich part of the UC–PuC diagram explains the partial disagreement between the observed melting temperature of high-Pu mixed carbides and the peritectic of pure PuC1Àx131,238 (cf Figure 32(b) below) Complete solubility of plutonium sesquicarbide in uranium sesquicarbide has been observed below 2033 K The equilibrium temperature of the transformation MC1.5 ! MCỵMC2 increases with increasing plutonium content from 2106 K for UC1.5 to 2273 K for (U0.9Pu0.1)0.45C0.55 and 2445 K for (U0.9Pu0.2)C1.5 However, this decomposition reaction is not observed for (U0.9Pu0.1)0.48C239 0.52 as uraniumrich monocarbide can accommodate extra carbon at high temperatures By mass spectrometry and electron microprobe analyses, Browning et al.244 established the reaction MC2!M2C3ỵC for Pu/(UỵPu) ẳ 0.575 at 2128 ặ 10 K, 100 K higher than Dalton243 and Reavis et al.132 At high temperatures, U-rich MC2Àx forms a continuous solid solution with MC, as observed for the binary U–C system However, small amounts of plutonium get segregated as sesquicarbides phase because PuC1.5 is more stable than PuC2 The compositions U0.5Pu0.5C2 and U0.5Pu0.5C1.5 undergo peritectoid decomposition and melting transitions at 2018 and 2598 K, and 2018 and 2613 K, respectively Data are not always consistent due to inaccurate determination of the C content and the presence of N and O impurities Udovskii and Alekseeva245 used the experimental data from the literature to construct the phase diagram of the U–Pu–C system They also presented a schematic projection of the liquidus surface Similarly, Mardon and Potter241 calculated phase equilibria for isothermal sections at 2573, 2473, 2373, and 2273 K No ternary compounds have been observed in the U–Pu–C system.242 The pseudobinary UC2–PuC2 system is little known and still controversial.9 The solidus–liquidus lines appear rather close to each other and regular between the melting points of the two end members The cubic dicarbide phase appears to be more stable in the mixed dicarbide than it is in the pure Pu dicarbide, and the tetragonal dicarbide seems to exist for U-rich compositions only (PuC2 < 20 at.%) As a summary of the discussed results, Figure 32 (a)–32(d) show the xc ¼ 0.60 isopleth section of the U–Pu–C ternary phase diagram proposed by 132 Thermodynamic and Thermophysical Properties of the Actinide Carbides Liquidus (ideal solution) Solidus (ideal solution) 2800 Liquid MC 2600 T (K) MC + M2C3 2400 So lid us 2000 (lin ea Solid MC 2200 rf it) , L/S238 , L/S240 , Peritectic/solidus4,131 ; , L/S244 ; 1800 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Pu/(Pu + U) Figure 31 Solidus–liquidus temperature of uraniumplutonium mixed carbide fuels as a function of Pu/U ỵ Pu ratio 2673 2900 2573 MC2ss + liquid MC2ss 2473 Temperature (K) Liquidus, solidus Experimental data 2700 MC ss +M C MC + MC (cubic) MC ss 2173 L + MC T (K) 2273 2500 M C +liquid 2373 L 2300 M2C3 MC + MC (cubic) L + M2C3+MC MC 2100 L+ M2C3 MC + MC2(cubic) M2C3 MC + MC (cubic) MC (tet) MC+MC (tet) 2 2073 1900 M2C3 + MC MC + MC (tet) + M C 1973 10 20 30 40 50 60 70 80 90 Pu2C3 (mol%) in M2C3 compositions (a) 1700 100 0.2 (b) 0.4 0.6 2700 2573 2500 Liquidus, solidus Experimental data MC + L T (K) T (K) 2373 MC + MC 2300 2100 M2C3 Liquidus, solidus Experimental data 2173 0.8 L+C MC MC + MC + L L L MC + L 0.8 Mole CPu/(CU + CPu) L + MC2 + C MC2 bct + MC2 + C 1900 bct + M2C3 + C 1973 (c) M2C3 + C 1700 0.2 0.4 0.6 Mole C3Pu2/(C3U2 + C3Pu2) 0.8 (d) 0.2 0.4 0.6 Mole C2Pu/(C2U + C2Pu) Figure 32 (a) Isopleth section of the U–Pu–C phase diagram at constant Xc ¼ 0.6, as proposed by Dalton243 (reproduced from Fischer, E Calphad 2009, 33, 487–494) (b) MC isoplethal section of the U–Pu–C phase diagram optimized by Fischer.238 (c) The M2C3 isoplethal section of the U–Pu–C phase diagram optimized by Fischer.238 (d) The MC2 isoplethal section of the U–Pu–C phase diagram optimized by Fischer.238 Courtesy of Dr E Fischer Thermodynamic and Thermophysical Properties of the Actinide Carbides Dalton243 and the MC, M2C3, and MC2 isoplethal sections optimized by Fischer,238 respectively The thermal conductivity of (U,Pu)C decreases with increasing Pu content (up to 1273 K), as reported in Figure The electrical resistivity increases with increasing Pu content by a factor between 10 at.% PuC and pure PuC Sengupta et al.246,247 observed that the thermal expansion coefficient of (U,Pu) carbides increases with Pu content Although no creep data are available for pure plutonium carbides, Sengupta et al observed that Pu-rich carbide fuel is harder than U-rich fuel up to 1553 K (average volumetric temperature of the fuel pin).248 2.04.9 Summary Research on actinide carbides is seeing a renaissance after the ‘Generation IV’ International Forum relaunched the design of nuclear plants with fast neutron spectra.1 In the last decade, early experimental results have been assessed and reinterpreted in the light of recent theoretical calculations In parallel, a few new experimental results are being produced with novel techniques More complex geometries and interactions are also being studied, as for example, the behavior of coated carbides in fuel particles It appears that the properties of actinide carbides are strongly dependent on the experimentally unavoidable oxygen and nitrogen impurities For this reason, a deeper understanding of the behavior of these materials as a function of oxygen and nitrogen contents will be of fundamental importance This is true for both fundamental physicochemical properties and technologically important ones, such as the mechanical parameters and the behavior under irradiation References US DOE Nuclear Energy Research Advisory Committee and the Generation IV International Forum, A Technology Roadmap for Generation IV Nuclear Energy Systems, Dec 2002 Storms, E K The Refractory Carbides; 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