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

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

2.02 Thermodynamic and Thermophysical Properties of the Actinide Oxides C Gue´neau, A Chartier, and L Van Brutzel Commissariat a` l’Energie Atomique, Gif-sur-Yvette, France ß 2012 Elsevier Ltd All rights reserved 2.02.1 Introduction 22 2.02.2 2.02.2.1 2.02.2.2 2.02.2.3 2.02.2.4 2.02.2.5 2.02.2.6 2.02.2.7 2.02.2.7.1 2.02.2.7.2 2.02.2.8 2.02.3 2.02.3.1 2.02.3.1.1 2.02.3.1.2 2.02.3.1.3 2.02.3.2 2.02.3.3 2.02.4 2.02.4.1 2.02.4.1.1 2.02.4.1.2 2.02.4.1.3 2.02.4.2 2.02.4.3 2.02.4.3.1 2.02.4.3.2 2.02.5 2.02.5.1 2.02.5.2 2.02.5.3 2.02.6 2.02.6.1 2.02.6.1.1 2.02.6.1.2 2.02.6.2 2.02.6.2.1 2.02.6.2.2 2.02.7 2.02.8 References Phase Diagrams of Actinide–Oxygen Systems U–O System Pu–O System Th–O and Np–O Systems Am–O System Cm–O System Bk–O System U–Pu–O System UO2–PuO2 U3O8–UO2–PuO2–Pu2O3 UO2–ThO2 and PuO2–ThO2 Systems Crystal Structure Data and Thermal Expansion Actinide Dioxides Stoichiometric dioxides Stoichiometric mixed dioxides Nonstoichiometric actinide dioxides Actinide Sesquioxides Other Actinide Oxides Thermodynamic Data Binary Stoichiometric Compounds Actinide dioxides Actinide sesquioxides Other actinide oxides with O/metal >2 Mixed Oxides Nonstoichiometric Dioxides Defects Oxygen potential data Vaporization Pu–O and U–O U–Pu–O U–Pu–Am–O Transport Properties Self-Diffusion Oxygen diffusion Cation diffusion Thermal Conductivity Actinide dioxides Actinide sesquioxides Thermal Creep Conclusion 23 23 23 25 26 26 27 27 27 27 29 30 30 30 31 33 34 35 36 36 36 38 39 39 40 40 42 46 47 48 48 48 48 49 51 51 51 54 54 55 55 21 22 Thermodynamic and Thermophysical Properties of the Actinide Oxides structure Most of these actinide compounds can be prepared in a dry state by igniting the metal itself, or one of its other compounds, in an atmosphere of oxygen The stability of the dioxides decreases with the atomic number Z All dioxides are hypostoichiometric (MO2 À x) Only uranium dioxide can become hyperstoichiometric (MO2 ỵ x) The thermodynamic properties of the dioxides vary with both temperature and departure from the stoichiometry O/M ¼ Only uranium, neptunium, and protactinium form oxide phases with oxygen/metal ratio >2 An oxidation state greater than ỵ4 can exist in these phases The ỵ6 state exists for uranium and neptunium in UO3 and NpO3 Intermediate states are found in U4O9 and U3O8 arising from a mix of several oxidation states (ỵ4, ỵ5, ỵ6) Detailed information on the preparation of the binary oxides of the actinide elements can be found in the review by Haire and Eyring.1 The absence of features at the Fermi level in the observed XPS spectra indicates that all the dioxides are semiconductors or insulators.2 Systematic investigations of the actinide oxides using first-principles calculations were very useful to explain the existing oxidation states of the different oxides in relation with their electronic structure For example, Petit and coworkers3,4 clearly showed that the degree of oxidation of the actinide oxides is linked to the degree of f-electron localization In the series from U to Cf, the nature of the f-electrons changes from delocalized in the early actinides to localized in the later actinides Therefore, in the early actinides, the f-electrons are less bound to the actinide ions which can exist with valencies as high as þ5 and þ6 for uranium oxides, for example In the series, the f-electrons become increasingly bound to the actinide ion, and for Cf only the ỵ3 valency occurs With the same method, Andersson et al.5 studied the oxidation thermodynamics of UO2, NpO2, and PuO2 within fluorite structures The results show that UO2 exhibits strong negative energy of oxidation, while NpO2 is harder to oxidize and Abbreviations CALPHAD Computer coupling of phase diagrams and thermochemistry CODATA The Committee on Data for Science and Technology DFT Density functional theory EMF Electromotive force EXAFS Extended X-ray absorption fine structure fcc Face-centered cubic IAEA International atomic energy agency MD Molecular dynamics MOX Mixed dioxide of uranium and plutonium NEA The Nuclear Energy Agency of the OECD OECD The Organisation for Economic Co-operation and Development XAS X-ray absorption spectroscopy XPS X-ray photoelectron spectroscopy 2.02.1 Introduction Owing to the wide range of oxidation states ỵ2, ỵ3, þ4, þ5, and þ6 that can exist for the actinides, the chemistry of the actinide oxides is complex The main known solid phases with different stoichiometries are shown in Table Actinide oxides mainly form sesquioxides and dioxides The ỵ3 oxides of actinides have the general formula M2O3, in which ‘M’ (for metal) is any of the actinide elements except thorium, protactinium, uranium, and neptunium; they form hexagonal, cubic, and/or monoclinic crystals Crystalline compounds with the ỵ4 oxidation state exist for thorium, protactinium, uranium, neptunium, plutonium, americium, curium, berkelium, and californium The dioxides MO2 are all isostructural with the fluorite face-centered cubic (fcc) Table Known stable phases of actinide oxides The phases marked with * are considered as metastable phases Ac ỵ2 ỵ3 ỵ4 ỵ5 ỵ6 Th Pa ThO* U Np UO* Ac2O3 ThO2 PaO2 Pa2O5 UO2 U4O9 U3O8 UO3 NpO2 Np2O5 NpO3 Pu Am Cm Bk Cf PuO* Pu2O3 PuO2 Am2O3 AmO2 Cm2O3 CmO2 Bk2O3 BkO2 Cf2O3 CfO2 Es EsO Es2O3 Thermodynamic and Thermophysical Properties of the Actinide Oxides PuO2 has a positive or slightly negative oxidation energy As in Petit and coworkers,3,4 the authors showed that the degree of oxidation is related to the position of the 5f electrons relative to the 2p band For PuO2, the overlap of 5f and 2p states suppresses oxidation The presence of H2O can turn oxidation of PuO2 into an exothermic process This explains clearly why hyperstoichiometric PuO2 ỵ x phase is observed only in the presence of H2O or hydrolysis products.6 Solid actinide monoxides ‘MO’ were reported to exist for Th, Pu, and U According to the experimental characterization of plutonium oxide phases by Larson and Haschke,7 these phases are generally considered as metastable phases or as ternary phases easily stabilized by carbon or/and nitrogen From first-principles calculations, Petit et al.3 confirmed that the divalent configuration M2ỵ is never favored for the actinides except maybe for EsO On the contrary, the monoxides of actinide MO(g) are stable as vapor species that are found together with other gas species M(g), MO2(g), MO3(g) which fraction depends on oxygen composition and temperature when heating actinide oxides In Sections 2.02.2 and 2.02.3, the phase diagrams of the actinide–oxygen systems, the crystal structure data, and the thermal expansion of the different oxide phases will be described The related thermodynamic data on the compounds and the vaporization behavior of the actinide oxides will be presented in Sections 2.02.4 and 2.02.5 Finally, the transport properties (diffusion and thermal conductivity) and the thermal creep of the actinide oxides will be reviewed in Sections 2.02.6 and 2.02.7 2.02.2 Phase Diagrams of Actinide–Oxygen Systems There is no available phase diagram for the Ac–O, Pa–O, Cf–O, and Es–O systems For the other systems, the phase diagrams remain very uncertain In most of the cases, only the regions of the diagrams relevant to the binary oxides have been investigated because of the great interest in actinide oxides as nuclear fuels As a consequence, the metal-oxide part of the actinide–oxygen systems is generally not well known except for the U–O system, which is the most extensively investigated system For the actinide–oxygen systems, a miscibility gap in the liquid state is generally expected at high temperature like in many metal–oxygen systems; it leads to the 23 simultaneous formation of a metal-rich liquid in equilibrium with an oxide-rich liquid But the extent of the miscibility gap and the solubility limit of oxygen in the liquid metals are generally not known The existing phase diagram data on the binary U–O, Pu–O, Th–O, Np–O, Am–O, Cm–O, Bk–O, and ternary U–Pu–O, UO2–ThO2, and PuO2–ThO2 are presented 2.02.2.1 U–O System The phase diagram of the uranium–oxygen system, calculated by Gue´neau et al.8 using a CALPHAD thermochemical modeling, is given in Figure 1(a) and 1(b) from 60 to 75 at.% O In the U–UO2 region, a large miscibility gap exists in the liquid state above 2720 K The homogeneity range of uranium dioxide extends to both hypo- and hyperstoichiometric compositions in oxygen The minimum and maximum oxygen contents in the dioxide correspond to the compounds with the formula of respectively UO1.67 at 2720 K and UO2.25 at approximately 2030 K The phase becomes hypostoichiometric above approximately 1200 K while the dioxide incorporates additional oxygen atoms at low temperature, above 600 K The dioxide melts congruently at 3120 Ỉ 20 K The melting temperature decreases with departure from the stoichiometry The experimental data on solidus/liquidus temperature for UO2 ỵ x from Manara et al.,11 reported in Figure 1(b), are significantly lower than those reported in Baichi et al.9 and will have to be taken into account in new thermodynamic assessments In the UO2–UO3 region (Figure 1(b) and 1(c)), the oxides U4O9, U3O8, and UO3 are formed with different crystal forms U4O9 and U3O8 are slightly hypostoichiometric in oxygen as shown in Figure 1(c) The U3O7 compound is often found as an intermediate phase formed during oxidation of UO2 This compound is reported in the phase diagram proposed by Higgs et al.12 and considered as a metastable phase by Gue´neau et al.8 2.02.2.2 Pu–O System A thermodynamic model of the Pu–O system was proposed by Kinoshita et al.27 and Gue´neau et al.28 The calculated phase diagram by Gue´neau et al.28 reproduces the main features of the phase diagram proposed by Wriedt29 in his critical review (Figure 2) In the Pu–Pu2O3 region of the phase diagram, the experimental data are rare The existence of 24 Thermodynamic and Thermophysical Properties of the Actinide Oxides 4500 Liquid Liquid (L) 4000 3000 Gas 3500 T (K) T (K) UO2 ± x 2500 UO2 + x + gas L+ U O2−x 2000 UO2 + x + gas 2000 1500 U3O8 + gas 1500 1000 (g-U) (b-U) (a-U) 1000 500 (a) UO2 ± x 2500 L + L2 3000 500 UO3 + gas 0.2 0.4 0.6 0.8 0.60 1.0 XO U U4O9 O 0.65 0.70 XO (b) U U3O8 0.75 O Mole fraction of oxygen (xo) 0.655 0.661 1600 0.677 0.683 0.692 0.697 0.701 0.706 UO2+x(S) + U3O8 (U–O)L+ UO2–x(S) UO2+x(S) 1132 ЊC(1405 K) 1000 U(S3)+UO2–x(S) 800 776 ЊC(1049 K) U4O9 + U3O7 UO2+x(S)+b-U4O9-y UO2+x(s)+a-U4O9-y 2.00 2.05 2.10 (c) 2.15 1100 900 200 1.95 1300 g-U4O9-y b-U4O9-y U(S1)+UO2–x(S) 1.90 1500 1127 ЊC(1400 K) 2.24 (0.69) UO2+x(S) + g-U4O9-y 669 ЊC(942 K) 600 1700 U4O9 + U3O8 U(S2)+UO2–x(S) 400 0.688 UO2–x(S) 507 ЊC(780 K) U3O7 + U3O8 a-U4O9-y 2.20 2.25 2.30 2.35 Temperature (K) Temperature (ЊC) 1200 0.672 U3O7 1400 0.667 700 500 300 2.40 O/U ratio Bannister and Buykx17 Ishii et al.21 Markin and Bones25 Roberts and Walter14 Saito18 Blackburn22 Gronvold26 Kotlar et al.15 Aronson et al.19 Kovba23 Nakamura and Fujino16 Schaner20 Van lierde et al.24 Anthony et al.13 *The horizontal line constructions (gray) at 80 and 550 ЊC reflect the inability to distinguish the transformation temperatures in the adjacent two-phase fields Figure U–O phase diagram (a) calculated using the model derived by Gue´neau et al.8; (b) calculated from 60 to 75 at.% O8; the green points come from the critical review by Baichi et al.9 and Labroche et al.10 and the blue points show the results of Manara et al.11; (c) calculated from O/U ¼ 1.9 to 2.4 after Higgs et al.12 The references of the experimental data are given in Higgs et al.12 ã Elsevier, reprinted with permission a miscibility gap in the liquid state was shown by Martin and Mrazek.30 The monotectic reaction was measured at 2098 K.30 There are no data on the oxygen solubility limit in liquid plutonium More data are available in the region between Pu2O3 and PuO2 The phase relations are complex below 1400 K PuO2 À x starts to lose oxygen above approximately 900 K A narrow miscibility gap was found to exist in the fluorite phase below approximately 900 K leading to the simultaneous presence of two fcc phases with different stoichiometries in oxygen Two intermediate oxide phases were found to exist with the formula PuO1.61 and PuO1.52 The PuO1.61 phase exhibits a composition range and is Thermodynamic and Thermophysical Properties of the Actinide Oxides 3000 Liquid (L) 2700 2400 L1 + L2 T (K) 2100 PuO2 - x 1800 L + PuO2 - x 1500 1200 900 600 300 (e–Pu) (d–Pu) (g–Pu) (b–Pu) (a–Pu) Pu2O3 0.1 0.2 0.3 Pu (a) 0.4 0.5 0.6 0.7 O xO 2700 Liquid 2400 T (K) 2100 PuO2 − x 1800 1500 1200 PuO1.61 900 600 300 0.58 (b) chemical interaction by using rhenium instead of tungsten for the container Very recently, a reassessment of the melting temperature of PuO2 was performed by De Bruycker et al.33 using a novel experimental approach used in Manara et al.11 for UO2 The new value of 3017 Ỉ 28 K exceeds the measurement by Kato et al by 174 K The noncontact method and the short duration of the experiments undertaken by De Bruycker et al.33 give confidence to their new value which has been very recently taken into account in the thermodynamic modeling of the Pu-O system.42 Both studies agree on the fact that the values measured in the past were underestimated 2.02.2.3 3000 Pu2O3 0.60 PuO1.52 0.62 0.64 0.66 0.68 xO Figure (a) Calculated Pu–O phase diagram after Gue´neau et al.28 on the basis of the critical analysis by Wriedt29; (b) calculated phase diagram with experimental data from 58 to 68 at.% O as reported in Gue´neau et al.28 stable between 600 and 1400 K The PuO1.52 compound only exists at low temperature (T < $700 K) Above $1400 K, the dioxide PuO2 À x exhibits a large homogeneity range with a minimum O/Pu ratio equal to approximately 1.6 and is in equilibrium with the sesquioxide Pu2O3 The liquidus temperatures between Pu2O3 and PuO2 remain uncertain and would need future determinations The melting temperature of PuO2 is still a subject of controversy The recommended value for the melting of PuO2 was for a long time Tm ¼ 2674 Æ 20 K, based on measurements from Riley.31 Recent measurements are available that suggest higher values In 2008, Kato et al.32 measured the melting point of PuO2 at 2843 K that is higher by 200 K than the previous measurements The authors used the same thermal arrest method as in previously published works but paid more attention to the sample/crucible 25 Th–O and Np–O Systems The Th–O and Np–O phase diagrams, according to the experimental studies by Benz34 and Richter and Sari35 are given, respectively, in Figure 3(a) and 3(b) In the Th–O phase diagram (Figure 3(a)), only the dioxide ThO2 exists At low temperature, according to Benz,34 the oxygen solubility limit in solid Th is low (O/Th < 0.003) A eutectic reaction occurs at 2008 Ỉ 20 K with a liquid composition very close to pure thorium The existence of a miscibility gap has been found to occur above 3013 Ỉ 100 K that leads to the formation of two liquid phases with O/Th ratios equal to 0.4 and 1.5 Ỉ 0.2, respectively The phase boundary of ThO2 À x in equilibrium with liquid thorium was measured The lower oxygen composition for ThO2 À x at the monotectic reaction corresponds to O/Th ẳ 1.87 ặ 0.04 The melting point of ThO2 recommended by Konings et al.36 is Tm ¼ 3651 Ỉ 17 K This value corresponds to the measurement by Ronchi and Hiernaut,37 which is in good agreement with the one reported on the phase diagram proposed by Benz34 in Figure 3(a) The Np–O phase diagram looks very similar to the Th–O system but the experimental information is very limited In the Np–NpO2 region, a miscibility gap in the liquid system is expected but no experimental data exist on the oxygen solubility limit in liquid neptunium and on the extent of this miscibility gap The dioxide exhibits a narrow hypostoichiometric homogeneity range (NpO2 À x) for temperatures above 1300 K The phase boundary of NpO2 À x in equilibrium with the liquid metal is not well known The minimum O/Np ratio is estimated to be about 1.9 at approximately 2300 K according to Figure 3(b) The recommended melting point for NpO2 is Tm ẳ 2836 ặ 50 K.36,38 Only the part richer in oxygen differs from Th–O with the presence of the 26 Thermodynamic and Thermophysical Properties of the Actinide Oxides 4273 3000 3663 K L 2500 Th(liquid) 3273 3013 ± 100 K T (K) T (K) 2000 Th(liquid) + ThO2 2273 2027 ± 15 K a 1500 A+a 2008 ± 20 K β - Th + ThO2 1643 ± 30 K 1000 A + CЈ C + CЈ 1.0 (a) 2.0 500 1.50 O/Th ratio L2 ? L1 + L2 ? L1 a1 + a2 CЈ CЈ + a α - Th + ThO2 1273 L+a A+L C C+a 1.60 1.70 1.80 1.90 2.00 O/Am L2+ NpO2 - x NpO2 - x Figure Am2O3–AmO2 phase diagram from Thiriet and Konings.40 ã Elsevier, reprinted with permission ? 2000 NpO2+O2 Np2O5 T (K) L1 + NpO2 - x 1000 g-Np + NpO2 NpO2+ Np2O5 b-Np + NpO2 a-Np + NpO2 (b) 1.0 O/Np ratio 2.0 Figure Th–O (a) and Np–O (b) phase diagrams after respectively Benz34 and Richter and Sari.35 ã Elsevier, reproduced with permission Np2O5 oxide which decomposes at 700 K to form NpO2 and gaseous oxygen The thermodynamic properties of the Np–O system were modeled by Kinoshita et al.39 using the CALPHAD method, but the calculated phase diagram does not reproduce correctly the available experimental data for the oxygen solubility limit in NpO2 À x in equilibrium with liquid neptunium 2.02.2.4 Am–O System The tentative Am–O phase diagram between Am2O3 and AmO2 shown in Figure has been proposed by Thiriet and Konings,40 based on an analysis of the experimental data available in the literature No data are available in the Am–Am2O3 region The Am2O3–AmO2 region looks very similar to the Pu2O3–PuO2 phase diagram (Figure 2(b)) The sesquioxide Am2O3 exists with hexagonal (A) and cubic (C) forms The dioxide AmO2 (a) starts to lose oxygen above approximately 1200 K AmO2 À x has a wide composition range at high temperature with a minimum O/Am ratio equal to approximately 1.6 As in the Pu–O system, the existence of a narrow miscibility gap in the fcc phase and an intermediate oxide phase with the formula AmO1.62 (C0 ) were found by Sari and Zamorani.41 A thermodynamic model of the Am-O system has been very recently derived by Gotcu-Freis et al.42 using the CALPHAD method The calculated phase diagram is quite consistent with the proposed one by Thiriet and Konings.40 2.02.2.5 Cm–O System A complete review of the Cm2O3–CmO2 region of the Cm–O phase diagram was performed by Konings43 who proposed the revised tentative Cm2O3–CmO2 phase diagram in Figure 5, on the basis of the suggestion by Smith and Peterson.44 The sesquioxide exists in several forms: cubic (C-type), monoclinic (B-type), and hexagonal (A-type) and X Intermediate phases were observed: a bcc phase s, with a variable composition (O/Cm between 1.52 and 1.64), a rhombohedral phase with the formula CmO1.71 (l), and a fluorite phase CmO1.83 (d) CmO2 (a) is stable up to 653 K at which temperature it Thermodynamic and Thermophysical Properties of the Actinide Oxides phase B-Bk2O3 transforms to the hexagonal form A-Bk2O3 (hexagonal) at approximately 2023 K, which melts at 2193 K 3000 L X + gas 2500 27 B + gas 1500 1000 2.02.2.7 A + gas Cm + B B+s T (K) 2000 L+B L+A H + gas s + gas s d + gas ι+ gas s+ι 500 1.50 ι+d d d+a a 2.00 1.75 O/Cm Figure The tentative Cm2O3–CmO2 phase diagram (pO2 ¼ 0.2 bar) according to the critical review by Konings.43 ã Elsevier, reprinted with permission 1100 1000 T (K) 900 U–Pu–O System It is important to mention that the phase diagram of the U–Pu–O system is still not well known There are no data on the metal-oxide region U–Pu–Pu2O3–UO2 of the U–Pu–O phase diagram The solubility of the oxide phases in the metallic liquid (U,Pu) is not known Only few experimental data exist in the region of stability of the oxide phases delimited by the compounds U3O8–UO2– Pu2O3–PuO2 2.02.2.7.1 UO2–PuO2 UO2 and PuO2 form a continuous solid solution and the solidus and liquidus temperatures show a nearly ideal behavior, as shown in the UO2–PuO2 pseudobinary phase diagram in Figure 7(a) As expected, the melting point of the mixed oxide decreases with the plutonium content in the solid solution The recommended equations for the solidus and liquidus curves from Adamson et al.51 are Tsolidus Kị ẳ 3120 355:3x þ 336:4x À 99:9x ½1Š BkO2 − x (a) 800 Tliquidus Kị ẳ 3120 388:1x 30:4x 708 700 C-Bk2O3 a1 + a2 600 500 59 60 61 62 63 64 at.% O 65 66 67 Figure Partial Bk–O phase diagram according to Okamoto.45 decomposes into gas and intermediate oxides (CmO1.83 and CmO1.71) CmO2 À x exhibits a small range of composition with a minimum O/Cm ratio of 1.97 2.02.2.6 Bk–O System A partial phase diagram of the Bk–O system is shown in Figure as proposed in the review by Okamoto.45 A high-temperature X-ray diffraction study by Turcotte et al.46 showed the existence of C-Bk2O3 (bcc) and a-BkO2 (fcc) oxides A miscibility gap in the a-BkO2 fcc phase was found to exist below 708 K The sesquioxide exists with several forms: C-Bk2O3 (bcc) transforms to B-Bk2O3 (monoclinic) at 1473 Ỉ 50 K according to Baybarz.47 The monoclinic ½2Š It must be mentioned that recent measurements were performed by Kato et al.32 on UO2–PuO2 solid solutions The resulting solidus and liquidus temperatures are higher than those from the previous studies (eqns [1] and [2]) As reported in Section 2.02.2.2, the melting point of pure oxide PuO2 measured by Kato et al and later by De Bruycker et al.33 was higher than the recommended value New determinations are necessary to confirm the validity of these new data Recent measurements on hypostoichiometric solid solutions (U,Pu)O2 À x were also performed by Kato et al.50 The solidus temperatures decrease with increasing Pu content and with decreasing O to metal ratio A congruent melting line was found to exist that connects the hypostoichiometric PuO1.7 to stoichiometric UO2 2.02.2.7.2 U3O8–UO2–PuO2–Pu2O3 Isothermal sections of the U–Pu–O phase diagram in the oxide-rich region are available only at 300, 673, 873, and 1073 K according to the review by Rand and Markin52 which is mainly on the basis of the 28 Thermodynamic and Thermophysical Properties of the Actinide Oxides 3200 Liquid T (K) 3000 2800 2600 2400 (U,Pu)O2 50 PuO2 (mol%) (a) 100 u) M3O8 - z + M4O9 MO2 ± x MO2 – x + Metal 0.1 0.2 (b) 1.8 C-M2O3 M4O9+ MO2 + x 1.6 C-M2O3 + Metal 0.3 0.4 0.5 Pu: (U + Pu) 0.6 0.7 u) 2.0 MO2 - x + C-M2O3 +P O: MO2 - x + MO2 - x1 M4O9 (U (U +P M3O8 - z + MO2 + x O: 2.6 2.4 2.2 2.0 M 3O C-M2O3 0.8 0.9 1.0 A-M2O3 Figure U–Pu–O phase diagram at room temperature (a) UO2–PuO2 region; the circles correspond to the experimental data by Lyon and Bailey,48 the triangles by Aitken and Evans,49 and the squares by Kato et al.50; the solid lines represent the recommended liquidus and solidus by Adamson et al.,51 the broken line represents the ideal liquidus and solidus based on Lyon and Bailey,48 and the dotted line the liquidus and solidus suggested by Kato et al.50 (b) U3O8–UO2–PuO2–Pu2O3 region at room temperature Reproduced from Konings, R J M.; Wiss, T.; Gue´neau, C In The Chemistry of the Actinide and Transactinide Elements 4th ed.; Morss, L R., Fuger, J., Edelstein, N M., Eds.; Nuclear Fuels; Springer: Netherlands, 2010; Vol 6, Chapter 34, pp 3665–3812 ã Springer, reprinted with permission experimental investigation by Markin and Street.53 The isothermal section at room temperature was later slightly modified by Sari et al.54 The fluorite-type structure of the mixed oxide (U,Pu)O2 has the ability to tolerate both addition of oxygen (by oxidation of the uranium) and its removal (by reduction of the plutonium only), leading to the formation of a wide homogeneity range of formula MO2 Ỉ x Thus, at high temperature, the solid solution is a single phase that extends toward hypo- and hyperstoichiometry But the extent of the single-phase domain is not well known at high temperature At low temperature, as shown in Figure 7(b) (redrawn in Konings et al.55 from Rand and Markin,52 Markin and Street,53 and Sari et al.54), the oxide-rich part of the U–Pu–O phase diagram is complex:  Region with O/metal ratio 20 at.% enter a two-phase region that leads to the decomposition into two fcc oxide phases with two different stoichiometries x and x1 in oxygen, MO2 À x and MO2 À x1 This is consistent with the existence of a miscibility gap in the fcc phase in the Pu–O system This phase separation was recently observed in mixed oxides (U,Pu)O2 with small addition of Am and Np by Kato and Konashi.56 For higher Pu contents ( y > 50 at.%), the mixed oxide can enter other two-phase regions [MO2 À x þ M2O3 (C)] and [MO2 À x þ PuO1.62] The existence of these two-phase regions comes from the complex phase relations encountered in the Pu2O3–PuO2 phase diagram at T < 1400 K (Figure 2(b)) The isothermal sections at 673, 873, and 1073 K in Rand and Markin52 show that the extent of the two-phase regions decreases with temperature The existence Thermodynamic and Thermophysical Properties of the Actinide Oxides In conclusion, no satisfactory description of the U–Pu–O system exists Both new developments of models and experimental data are required of a single phase region M2O3 (C) was reported along the Pu2O3–UO2 composition line  Region with O/metal ratio > At room temperature, the oxidation of mixed oxides with a Pu content lower than 50% results in either a single fcc phase, MO2 ỵ x with a maximum O/M ratio of 2.27, or in two-phase regions [MO2 ỵ x ỵ M4O9], [M4O9 ỵ M3O8] and [MO2 ỵ x ỵ M3O8] The M4O9 and M3O8 phases are reported to incorporate a significant amount of plutonium However, the exact amount is not known 2.02.2.8 UO2–ThO2 and PuO2–ThO2 Systems Bakker et al.59 performed a critical review of the phase diagram and of the thermodynamic properties of the UO2–ThO2 system Solid UO2 and ThO2 form an ideal continuous solid solution The phase diagram proposed by Bakker et al.59 on the basis of the available experimental data is presented in Figure 9(a) The authors report the large uncertainties on the phase diagram because of the experimental difficulties The thermodynamic properties of (Th1 À yUy)O2 solid solutions have been recently investigated by Dash et al.60 using a differential scanning calorimeter and a high-temperature drop calorimeter The ternary compound ThUO5 was synthesized and characterized by X-ray diffraction The thermodynamic data on this compound were estimated Like UO2, PuO2 forms a continuous solid solution with ThO2 in the whole composition range Limited melting point data were measured by Freshley and Mattys.61 The results indicate a nearly constant melting point up to 25 wt.% ThO2 In view of the Yamanaka et al.57 developed a CALPHAD model on the U–Pu–O system that reproduces some oxygen potential data in the mixed oxide (U,Pu)O2 Ỉ x and allows calculating the phase diagram This model predicts the two-phase region [MO2 x ỵ PuO1.62] but does not reproduce the existence of the miscibility gap in the fcc phase This region was recently reinvestigated by Agarwal et al.58 using a thermochemical model The resulting UO2–PuO2–Pu2O3 phase diagram is presented in Figure The extent of the miscibility gap in the fcc phase is described as a function of temperature, Pu content, and O/metal ratio This description of the phase diagram is not complete as it does not take into account the existence of the PuO1.52 and PuO1.61 phases that may lead to the formation of other two-phase regions involving the fcc phase PuO2 0.0 0.9 0.2 xU O 900 K 0.7 900 K 0.6 0.7 700 K 0.4 600 K 500 K 400 K O2 800 K x Pu 850 K 0.6 0.3 0.2 750 K 0.9 Present calculations Tie lines Besmann and Lindemer Isopleths for Figure 800 K 0.5 0.5 1.0 UO2 0.0 ) ) ) ) 0.8 0.3 0.8 ( ( ( ( 1.0 0.1 0.4 0.1 700 K 0.1 0.2 0.3 0.4 29 0.5 0.6 xPuO1.5 0.7 0.8 0.9 0.0 1.0 PuO1.5 Figure Miscibility gap in the fcc phase of the UO2–PuO2–Pu2O3 region according to Agarwal et al.58 ã Elsevier, reprinted with permission 30 Thermodynamic and Thermophysical Properties of the Actinide Oxides instability of PuO2 at high temperature (high pO2 over PuO2), this behavior could be due to a change of the stoichiometry of the samples The available liquidus temperature measurements not reproduce the recommended value for the melting point of PuO2 The full lines in Figure give the solidus and liquidus curves considering an ideal behavior of the PuO2–ThO2 system 2.02.3 Crystal Structure Data and Thermal Expansion The lattice parameters of actinide oxides are usually measured in glove boxes because of radioactivity and chemical hazards In fact, the radioactive decay may drastically modify the cell parameters with 3800 T (K) 3600 3400 3200 3000 (a) 50 ThO2 (mol%) 100 2.02.3.1 Actinide Dioxides 2.02.3.1.1 Stoichiometric dioxides The actinide dioxides exhibit a fluorite or CaF2 structure (Figure 10) Each metal atom is surrounded by eight nearest neighbor O atoms Each O atom is surrounded by a tetrahedron of four equivalent M atoms The cell parameters are reported in Table They are 3800 3400 T (K) characteristic time of months (see measurements on (Pu,Am)O2 by Jankowiak et al.,62 on CmO2 in the review by Konings,43 and on sesquioxides by Baybarz et al.63) Indeed, point defects (caused by irradiation or simply because of off-stoichiometry) may also induce expansion or contraction of the lattices The thermal expansion of the cell usually occurs when increasing the temperature, and it is usually measured starting at room temperature Because of experimental difficulties – already mentioned – for measuring properties (and thus thermal expansion coefficients) in actinides, some ab initio and/or molecular dynamics (MD) calculations are nowadays done In the framework of MD calculations, the evolution of the cell parameter can easily be followed as a function of temperature (see the calculations by Arima et al.64 on UO2 and PuO2, and by Uchida et al.65 on AmO2) The method is slightly different when ab initio calculations are performed (see, e.g., the work of Minamoto et al.66 on PuO2) One currently calculates the phonon spectra, estimates the free energy as a function of temperature by means of quasiharmonic approximation, and then extracts the linear thermal expansion Such procedure may also be based on experimental data assuming some hypothesis and simplifications on the phonon spectra (see, e.g., Sobolev and coworkers67–69) 3000 2600 2200 (b) 50 ThO2 (mol%) 100 Figure Pseudobinary (a) UO2–ThO2 and (b) PuO2–ThO2 phase diagrams The solid lines represent the liquidus and solidus assuming an ideal solid solution Details on the experimental data are given in Bakker et al.59 Reprinted with permission from Konings, R J M.; Wiss, T.; Gue´neau, C Chemistry of the Actinide and Transactinide Elements, 4th edn.; Springer, 2010; Vol 6, Chapter 24 (in press) ã Springer Uranium fcc sublattice Oxygen cubic sublattice Figure 10 UO2 fluorite (CaF2) structure; the actinide (left) sublattice is fcc while the oxygen (right) sublattice is primitive cubic Thermodynamic and Thermophysical Properties of the Actinide Oxides data on the pure oxides, the oxygen potential of (U,Pu)O2 Ỉ x increases with the plutonium content and temperature In the hypostoichiometric region, the oxygen potentials were analyzed considering the change of the oxidation state of Pu from 4ỵ to 3ỵ by Rand and Markin.52 T=1473 K – Woodley189 T=1273 K – Woodley189 T=1073 K – Markin and Mclver190 -100 m(O2) (kJ mol–1) -200 -300 -400 -500 -600 -700 1.95 2.05 2.00 (a) 2.10 O/(U+Pu) T = 1815 K – Chilton and Edwards191 T = 1810 K – Chilton and Edwards191 -100 T = 1713 K – Chilton and Edwards191 T = 1623 K – Kato et al.170 m(O2) (kJ mol–1) -200 T = 1473 K – Vasudeva et al.172 T = 1423 K – Kato et al.170 T = 1273 K – Vasudeva et al.172 -300 T = 1273 K – Kato et al.170 T = 1223 K – Markin and Mclver190 T = 1073 K – Vasudeva et al.172 -400 T = 1073 K – Markin and Mclver190 -500 -600 -700 1.90 (b) 1.95 2.00 O/(U+Pu) 2.05 2.10 Figure 23 The oxygen potential of (a) (U0.9Pu0.1)O2 Ỉ x at 1073, 1273, and 1473 K and (b) (U0.7Pu0.3)O2 Ỉ x at 1073, 1273, 1473, 1673, and 1873 K as derived from the model proposed by Besmann and Lindemer.173,175 Table 15 45 2.02.4.3.2.2.2 UO2 Ỉ x, PuO2 À x, and (U,Pu)O2 Ỉ x containing minor actinides The effect of the minor actinides Am, Np, and Cm on the oxygen potential of uranium and plutonium oxides and mixed oxides was investigated for different compositions as presented in Table 15 As expected from the data for the binary oxides UO2 À x, PuO2 À x, and AmO2 À x (see Figure 22), the presence of americium leads to an increase of the oxygen potential in the ternary oxides (U,Am)O2 À x and (Pu,Am)O2 À x (Figure 24) According to the comparison performed by Osaka et al.,196 for a O/metal ratio above 1.96, the oxygen potential is the highest for AmO2 À x, then (Pu0.91Am0.09)O2 À x followed by (U0.5Am0.5)O2 À x, (U0.685Pu0.270Am0.045)O2 À x, PuO2 À x, and finally (U0.6Pu0.4)O2 À x The experimental data are analyzed by considering the change of the oxidation states of the actinides Am and Pu When the O/metal ratio decreases with stoichiometry, Am is first reduced from Am4ỵ to Am3ỵ, then after all Am is reduced, Pu is similarly reduced The recent Calphad model on the Am-Pu-O system derived by Gotcu-Freis et al.42 allows the description of the oxygen potential in the whole composition range of the (Am,Pu)O2ỵ/x solid solution Hirota et al.201 derived a thermochemical model for the (U,Pu,Np)O2 Ỉ x oxide using the CALPHAD method According to these calculations and to the experimental data of Morimoto et al.199 on (U0.58Pu0.3Np0.12)O2, it was found that Np has a small influence on the oxygen chemical potential of (U,Pu)O2 À x Oxygen potential measurements in mixed oxides with minor actinides Oxide Method References (U0.5Am0.5)O2Àx (Pu0.91Am0.09)O2Àx (Am0.5Pu0.5)O2Àx (Am0.5Np0.5)O2Àx (U0.65Pu0.3Np0.05)O2 (U0.58Pu0.3Np0.12)O2 (U0.685Pu0.270Am0.045)O2Àx (U0.66Pu0.30Am0.02Np0.02)O2Àx Gas equilibration Thermogravimetry Electromotive force method Electromotive force method Bartscher and Sari195 Osaka et al.196 Otobe et al.197 Otobe et al.198 Morimoto et al.199 Osaka et al.200 Kato et al.189 Thermogravimetry Gas equilibration method 46 Thermodynamic and Thermophysical Properties of the Actinide Oxides -100 Osaka et al.175 – (Pu0.91 Am0.09)O2 – T = 1123 K -50 -100 175 Osaka et al – (Pu0.91 Am0.09)O2 – T = 1273 K Osaka et al.175 – (Pu0.91 Am0.09)O2 – T = 1423 K Otobe et al.164 – (Pu0.5 Am0.5)O2 – T = 1333 K -150 -200 m(O2) (kJ mol–1) m(O2) (kJ mol–1) -150 -250 -300 -350 -200 -250 (Th0.95U0.05)O2 + x -300 (Th0.90U0.10)O2 + x -400 -450 -500 1.75 1.80 (a) 1.85 1.90 1.95 2.00 O/Am m(O2) (kJ mol–1) -100 T = 1577 K Bartscher and San174 T = 1373 K Bartscher and San174 T = 1273 K Bartscher and San174 T = 1123 K Bartscher and San174 T = 973 K Bartscher and San174 T = 873 K Bartscher and San174 -200 -300 -500 1.85 1.90 1.95 2.00 -400 4.00 UO2 + x 4.05 4.10 4.15 Uranium valence 4.20 4.25 Figure 25 Oxygen potential data of (Th1yUy)O2 ỵ x solid solutions at 1473 K for various values of y after Ugajin.206 -400 (b) (Th0.80U0.20)O2 + x -350 2.05 2.10 O/Am Figure 24 Oxygen potential data (a) in (Am0.5Pu0.5)O2Àx at 1333 K according to Otobe et al.197 and in (Am0.09Pu0.91)O2Àx at 1273 and 1423 K by Osaka et al.196; (b) in (Am0.5U0.5)O2 at 873–1577 K by Bartscher and Sari.195 The oxygen potentials were measured for (U0.66Pu0.30Am0.02Np0.02)O2 À x at 1473–1623 K by a gas equilibration method using (Ar, H2, H2O) mixture by Kato et al.189 The values were compared to the oxygen potential data in (U0.7Pu0.3)O2 À x188 without minor actinides The m(O2) data are 10 kJ molÀ1 higher in the mixed oxide containing Am and Np The increase might be due to Am content 0.244, by Roberts et al.203 using pressure measurements for y ¼ 0.05–0.06, by Aronson and Clayton204 using electromotive force method for y ¼ 0.3–0.9, by Tanaka et al.205 using electromotive force method for y ¼ 0.05–0.3, by Ugajin206 using thermogravimetry for y ¼ 0.05–0.2, by Matsui et al.207 using thermogravimetry for y ¼ 0.2–0.4, and by Anthonysamy et al.208 for y ¼ 0.54–0.9 using a gas equilibration method The analysis by Ugajin206 suggests that the oxygen potential is controlled by the change of uranium oxidation state as shown in Figure 25 The results show that there is a systematic increase of the oxygen potential values with increasing thorium content The oxygen potential data were retrieved and analyzed by Schram209 using the thermochemical model of Lindemer and Besmann with a mixture of the species ThO2, UO2, and UaOb for UO2 ỵ x Recent experimental data on enthalpy increments and heat capacities of (U0.1Th0.9)O2, (U0.5Th0.5)O2, and (U0.9Th0.1)O2 solid solutions were measured by Kandan et al.210 using, respectively, drop calorimetry at 479–1805 K and differential scanning calorimetry at 298–800 K The results show that the solid solutions obey the Neumann–Kopp’s rule 2.02.5 Vaporization 2.02.4.3.2.2.3 (U,Th)O2 and (Th,Pu)O2 solid solutions Oxygen potential of (UyTh1 y)O2 ỵ x solid solutions was measured by Anderson et al.202 using thermogravimetry for y ¼ 0.03, 0.063, and The known gaseous actinide oxide molecules are listed in Table 15 Experimental data exist only from Th to Cm oxides The thermochemical properties of these Thermodynamic and Thermophysical Properties of the Actinide Oxides Th Pa U Np Pu Am Cm ThO ThO2 PaO PaO2 UO UO2 UO3 NpO NpO2 NpO3 PuO PuO2 PuO3 AmO AmO2 CmO CmO2 Table 17 Thermodynamic data on gaseous actinide oxides molecules according to Konings et al.38 DfH (298.15 K) (kJ molÀ1) S (298.15 K) (J KÀ1 molÀ1) À21.5 Ỉ 10.0 À435.6 Ỉ 12.6 Ỉ 30 À514 Ỉ 30 21.4 Ỉ 10.0 À462.1 Ỉ 12 À795.0 Ỉ 10.0 À16.6 Æ 10 À444 Æ 20 À51.7 Æ 15 À411.9 Æ 15 À567.6 Ỉ 15 À15 Ỉ 50 À75.4 Ỉ 20 240.1 Ỉ 2.0 285.2 Ỉ 2.0 250.8 Ỉ 276.7 Æ 252.14 Æ 277.0 Æ 2.5 310.6 Æ 3.0 253.0 Ỉ 277.2 Ỉ 6.0 252.2 Ỉ 3.0 278.7 Ỉ 319.4 Ỉ 259.1 Ỉ 10 259.1 Æ 10.0 ThO ThO2 PaO PaO2 UO UO2 UO3 NpO NpO2 PuO PuO2 PuO3 AmO CmO gaseous species reviewed and compiled by Konings et al.38 are listed in Tables 16 and 17 The recommended vapor pressures over solid UO2, ThO2, PuO2, and liquid UO2 are given in the review by IAEA.212 The equation of state of uranium dioxide was investigated by Ronchi et al.211 2.02.5.1 PuO2 - x -6 P(tot) -8 -10 Pu(g) O(g) -12 -14 Pu2O3 +PuO2 - x p(tot.) Ackermann Pu(g) Ackermann Pu(g) Battles PuO2(g) Ackermann PuO2(g) Battles PuO(g) Ackermann PuO(g) Battles O2(g) -16 1.5 1.6 (a) UO 1.7 1.8 O/Pu ratio 1.9 2.0 S pi -5 UO2 -6 U -7 -8 -9 UO3 -10 O Pu–O and U–O In the system Pu–O, the partial pressures of the gaseous species Pu(g), PuO(g), and PuO2(g) vary with the O/Pu ratio and temperature as a large composition range exists for PuO2 À x The variation of the gaseous species calculated at 1970 K is shown in Figure 26(a) as a function of the O/Pu ratio using the CALPHAD model developed by Gue´neau et al.28 In the two-phase region [Pu2O3 ỵ PuO2 x], the major species are PuO(g), Pu(g), and PuO2(g) With increasing O/Pu ratio in PuO2 À x phase, the partial pressures of PuO(g) and Pu(g) decrease whereas PuO2(g) partial pressure slightly increases Close to the stoichiometry, O(g) and O2(g) become the major gaseous species The curve giving the total pressure of the gas as a function of the O/Pu ratio shows a minimum that corresponds to the congruent vaporization of plutonia occurring for a slightly hypostoichiometric oxygen composition PuO(g) PuO2(g) log(p) in bar ỵ2 ỵ4 ỵ6 Known gaseous actinide oxides log10(p) in bar Table 16 47 L+UO2 - x 1.85 (b) UO2 - x 1.90 1.95 O/U ratio UO2 + x 2.00 Figure 26 Calculated partial pressures of (a) Pu(g), PuO(g), PuO2(g), O(g), and O2(g) in the Pu–O system at 1970 K as a function of the O/Pu ratio derived from the thermochemical model developed by Gue´neau et al.28; see Gue´neau et al.28 for information on experimental data; (b) of UO(g), UO2(g), U(g), UO3(g), and O(g) at 2250 K in the U–O system according to the measurements using mass spectrometry by Pattoret.213 In the U–O system, the vaporization is more complex due to the existence of both the hypo- and hyperstoichiometric composition ranges of uranium dioxide According to the measurements by Pattoret213 using mass spectrometry, reported in Figure 26(b), a sample with a composition UO2 À x heated at 2250 K will tend to lose preferentially U via UO(g) to reach the 48 Thermodynamic and Thermophysical Properties of the Actinide Oxides congruent composition UO2 À x with a O/U ratio equal to 1.987 Ỉ 0.01 corresponding to the minimum in total pressure, that is, the congruency A sample with a composition UO2 or UO2 ỵ x will lose oxygen via UO3(g) to reach the same congruent composition Above solid UO2, the largest contribution is from UO2(g) above MOX with up to 40% mol PuO2 The different studies show that a quasi-congruent vaporization is reached where (O/Metal)vapor¼(O/Metal)solid which corresponds to a slightly hypostoichiometric mixed oxide in oxygen like in the binary oxides UO2 and PuO2 2.02.5.2 2.02.5.3 U–Pu–O The partial pressures of the different gaseous actinide oxide molecules were calculated by Rand and Markin52 over U0.85Pu0.15O2 Ỉ x at 2000 K using the thermodynamic data on the solid and gas phases (Figure 27) UO3(g) is the predominant gas species in the hyperstoichiometric region This is due to the fact that in the MOX, the oxygen potentials are higher than in UO2 (see Section 2.02.4.2.2) The composition of the vapor is enriched in uranium and oxygen in comparison to the solid It means that the solid will lose uranium and oxygen In the hypostoichiometric region, the uranium species are less in the vapor than in the solid for O/metal ratio below 1.96 It means that the solid will preferentially lose plutonium A review of the previous experimental studies on vaporization of (U,Pu)O2 oxides was reported by Viswanathan and Krishnnaiah.214 The authors derived a thermochemical model to calculate the partial and total pressures –3 UO3 –4 –5 –6 Total UO2 log p (atm) –7 PuO2 –8 –9 –10 Pu PuO –11 –12 –13 1.95 UO U 2.00 2.05 O/M ratio 2.10 Figure 27 Calculated partial pressures over U0.85Pu0.15O2 Ỉ x at 2000 K according to Rand and Markin.52 U–Pu–Am–O Calculations of the same type were recently performed by Maeda et al.215 above a mixed oxide with the composition (U0.69Pu0.29Am0.02)O2 Æ x at 2073 and 2273 K (see Figure 28) The results show that in the hyperstoichiometric region, UO3(g) remains the predominant gas species But for O/metal ratio below 1.96 corresponding to the congruent composition, the AmO(g) species becomes the major molecule in the vapor Very recently, an experimental study on vaporization of AmO2 and (Pu,Am)O2 oxides was performed by Gotcu-Freis et al.216,42 using mass spectrometry 2.02.6 Transport Properties 2.02.6.1 Self-Diffusion The diffusion of oxygen or cations has been mainly investigated in the actinide dioxides MO2 with the fluorite structure Usually, the diffusion coefficient D is expressed using an Arrhenius lawtype equation   Emig: ẵ13 D ẳ D0 exp À kBT where D0 is the prefactor, Emig is an effective migration energy, kB is the Boltzmann constant, and T is the temperature While very commonly used, the details of the diffusion are unfortunately hidden behind this equation The prefactor depends upon hopping frequency and geometrical factors while the effective migration energy should be expressed as a free energy (see, e.g., Ando and Oishi217 or Howard and Lidiard218) and should include the formation energy of the migrating defect In pure dioxides, for example, the oxygen diffusion occurs via vacancy/interstitial migration, depending on the stoichiometry – that is, on the oxygen partial pressure (see Section 2.02.4.3.1 on defects) In general, the diffusion depends strongly on any type of defects present in the crystal lattice Also the grain boundaries play a major role, as they act as shortcuts for the diffusion (see Vincent-Aublant et al.219 and Sabioni et al.220) Thus, the reliability of the diffusion measurements is related to the control/measurement of the stoichiometry and microstructure Thermodynamic and Thermophysical Properties of the Actinide Oxides AmO Those experimental issues lead to a very large scatter of data (see, e.g., Sabioni et al.,220 Belle and Berman,221 Sabioni et al.222), and hence complementary ab initio and MD calculations by Terentyev,80 Stan and Cristea,150 Stan,154 Andersson et al.,168 Vincent-Aublant et al.,219 and Kupryazhkin et al.223 are performed to bring microscopic insights to the experiments, but with various degrees of success The proposed models cannot generally overcome the identification of the defects responsible for the diffusion This is because the types of the stable defects themselves (vacancies, interstitials, and also complex defects such as clusters; see Section 2.02.4.3.1) are far from being resolved Hence, the diffusion coefficients as a function of stoichiometry are fitted on semiempirical equations Another way to circumvent this issue is to follow Siethoff.224 He has recently reexhibited a relation between the effective migration energies and the elastic properties in many crystallographic families, including the fluorite structures As many reviews have been written on the selfdiffusion in actinide dioxides in the past, and as the data collected are so inconsistent to each other, we refer the reader to the review done by Belle and Berman221 for UO2, PuO2, and ThO2 for the studies done before 1984 to get the experimental data Recently, new data have been reported, and we refer the reader to the studies by Sabioni et al.,220,222 Mendez et al.,225 Korte et al.,226 Sali et al.,227 Arima et al.,228 Ruello et al.,229 Kato et al.,230 and Garcia et al.231 and references therein In the following, we will limit ourselves to report some semiempirical equations in known cases PuO 2.02.6.1.1 Oxygen diffusion -2 -3 -4 Total -5 UO3 log p (atm) -6 UO2 -7 PuO2 -8 AmO2 UO -9 AmO -10 -11 Pu -12 1.80 1.85 (a) PuO 1.90 1.95 2.00 O/M ratio (-) 2.05 -2 -3 Total -4 UO3 log p (atm) -5 UO2 -6 PuO2 -7 AmO2 Pu -8 -9 U -10 -11 UO -12 1.80 (b) 1.85 1.90 1.95 2.00 2.05 O/M ratio (-) Figure 28 Calculated partial pressures of the actinide oxide gaseous species over (U0.69Pu0.29Am0.02)O2 Ỉ x at 2073 K (a) and 2273 K (b) according to Maeda et al.215 ã Elsevier, reprinted with permission Table 18 Mechanism Vacancy Interstitial 49 As mentioned above, the microscopic mechanisms of oxygen diffusion vary as a function of stoichiometry in the actinide dioxides A schematic view of the (simplified) possible mechanisms has been reported in Table 18 Dorado et al.232 combining both experimental and theoretical approaches identified the oxygen migration as an interstitialcy mechanism For x < in MO2 À x (hypostoichiometric dioxides), the dominant defects in urania and plutonia are the oxygen vacancies Hence, the migration energy could Simplified view of the migration energies of oxygen as a function of stoichiometry in MO2 Ỉ x x0 Ef OFP ị=2 ỵ Eact: VO Ef OFP ị=2 ỵ Eact: I00O Ef OFP ịỵ Eact: VO Eact: I00O Eact and Ef set for activation and formation energies, respectively FP, V, and I set for Frenkel pair, vacancy, and interstitial, respectively 50 Thermodynamic and Thermophysical Properties of the Actinide Oxides -6 -5 1350 K T = 1643 K 1173 K -6 log10 [Ds ] (cm2 s-1) Oxygen self-diffusivity (cm2 s–1) 1773 K -7 T = 1513 K -7 Blocking model This work -8 T = 1073 K -9 Monte Carlo -8 0.00 0.02 0.04 0.06 x in PuO2 - x 0.08 0.10 Figure 29 Oxygen self-diffusion coefficient in PuO2Àx as a function of stoichiometry from Stan et al.153 Symbols are experimental data ã Elsevier, reprinted with permission -10 0.000 0.025 0.050 x in UO2 + x 0.075 0.100 Figure 31 Self-diffusion coefficient of oxygen in hyperstoichiometric UO2 ỵ x Symbols are experimental data From Stan, M Nucl Eng Tech 2009, 41, 39–52, reprinted with permission 2.5 D (108 cm2 s-1) 2.0 1.5 1.0 Experiments Theory 0.5 0.0 0.00 0.05 0.10 0.15 x in UO2 + x 0.20 0.25 Figure 30 Comparison between the experimental self-diffusion coefficients of oxygen in hyperstoichiometric UO2 ỵ x and the calculated ones at 1073 K From Andersson, D A.; Watanabe, T.; Deo, C.; Uberuaga, B P Phys Rev 2009, 80B, 060101 be reduced to the energy for oxygen vacancy À activation Á migration Eact: VO as reported in the Table 18 In fact, Stan et al.150,152 have shown that the point defects in hypostoichiometric plutonia PuO2 À x not reduce to oxygen vacancy They determined (from a point defect model) that five different defects are at work in PuO2 À x and hence contribute to the formation of oxygen vacancies According to them, the prefactor D0 (eqn [13]) can then be written as a function of (i) a stoichiometry-dependent correlation factor from Tahir-Kheli233 and (ii) the formation energy of oxygen vacancy (determined using the point defect model) The results of such a model are reported in Figure 29 Recently Kato et al.230 have studied the oxygen diffusion in hypostoichiometric MOX, and they concluded that the diffusion coefficient of oxygen linearly depends upon the concentration of Pu in MOX For x > in MO2 ỵ x (hyperstoichiometric dioxides), two recent studies evidenced that the oxygen interstitials are not the only contribution to oxygen diffusion Experimental data obtained by Ruello et al.229 in UO2 ỵ x show the important role of the Willis clusters Theoretical calculations based on coupled ab initio/kinetic Monte Carlo done by Andersson et al.168 have shown also that the diinterstitial cluster of oxygen may contribute to the oxygen diffusion for highly hyperstoichiometric UO2 þ x In fact, the diffusion of oxygen in hyperstoichiometric dioxides is due to the diffusion of interstitial oxygen and to the (counteracting) contribution of more complex oxygen clusters Hence, the diffusion coefficient increases with stoichiometry, reaches a maximum, and decreases as may be seen in Figure 30 Recently, Stan et al.153 proposed a semiempirical relation between the diffusion coefficient D and the stoichiometry for UO2 ỵ x that includes a maximum:   E0 expyxị ẵ14 DT ; xị ¼ xD0 exp À kBT In this expression, D0 ¼ 1.3  10–2 cm2 sÀ1, E0 ¼ 1.039 eV, and y ¼ 6.1 The last term of the product corresponds to the blocking effect of the complex oxygen clusters Such a semiempirical model reproduces the experimental data fairly well (see Figure 31), up to x < 0.1 For higher values of x (0.0 < x < 0.2 from 300 up to 1800 K), Ramirez et al.151 established a somewhat different semiempirical relation Thermodynamic and Thermophysical Properties of the Actinide Oxides 2.02.6.1.2 Cation diffusion The cation diffusion occurs in actinide dioxides via cation vacancies in the vicinity of oxygen vacancy according to Jackson et al.234 As a consequence, cation diffusion may occur in hyperstoichiometric dioxides MO2 ỵ x (with x > 0) The diffusion coefficient increases drastically with departure from stoichiometry as x2 in MO2 ỵ x as follows:   E0 ẵ15 Dx; T ị ẳ D0 x exp À kBT Recently, Gao et al.235 obtained the prefactor D0 ¼ 2.341  10–2 m2 sÀ1 and migration energy E0 ẳ 2.5 eV for UO2 ỵ x Knorr et al.236 mentioned that the effect of the intergranular grain boundary is to change the prefactor to a linear dependence upon stoichiometry The diffusion coefficient is expressed as follows:   E0 ẵ16 D ẳ D0 x exp kBT They found for UO2 ỵ x, D0 ẳ 7.5 104 m2 sÀ1 and E0 ¼ 2.47 eV.236 This apparent activation energy is very close to the one obtained by Gao et al.235 A systematic study of the difference between monocrystals and polycrystals done by Sabioni et al.220 led the authors to the conclusion that most of the activation energies reported by previous authors probably refer to polycrystals 2.02.6.2 Thermal Conductivity The thermal conductivity of the actinide dioxides is known to be mainly described by phonon mechanism, and more specifically by longitudinal acoustic modes (Yin and Savrasov237) Other terms (e.g., electronic conductivity) remain at few percent of the total conductivity, except for UO2 (see, e.g., Carbajo et al.84 and Inoue238) where the electronic conductivity increases at high temperatures Any defect (point defect, grain boundary, void, porosity, impurity, etc.; see, e.g., Buyx239), as referred to the ideal perfect lattice, may contribute to decrease the thermal conductivity by phonon scattering (see, e.g., Millet et al.240) The thermal conductivity l may consequently be expressed as   C D ỵ exp ẵ17 lẳ AỵBT T T The last term, that is dependent upon C and D parameters, is related to the electronic conductivity 51 (see Buyx238) A is related to the phonon defect scattering and B to the phonon–phonon scattering The value of A is affected by the concentration of defects (interstitials, vacancies, grain boundaries, dislocations, etc.), and thus does change with stoichiometry (see, e.g., Buyx238) The value of B is less affected by defects, as long as the symmetry of the crystal is preserved Hence, the evolution of the thermal conductivity as a function of composition relies on the variation of the parameter A This parameter has been shown to change linearly with composition according to Murti and Matthews241 and Morimoto et al.242 Indeed, as irradiations produce significant amounts of defects and impurities, they will contribute to the modification of A (see, Ronchi et al.,243 for example) The characterization of the microstructure, the stoichiometry, the purity, etc., of each sample is also of utmost importance for the quality of the experimental data collected From this characterization, ad hoc equations are used in order to infer the thermal conductivity Among the above-mentioned parameters, porosity is one of the most important Usually, the analytical equation of Schulz244 is used to infer the thermal conductivity lTD of the fully dense material: l ¼ lTD Pịx ẵ18 P is the porosity and x is related to the shape of the closed pores; in the spherical case, x ¼ 1.5 Bakker et al.245 proposed a value around 1.7 for nuclear fuel with complex pore shapes and distributions As already mentioned, chemical and radioactive hazards have limited the number of experimental data MD and ab initio calculations are nowadays used to investigate the thermal conductivities of actinides The thermal conductivity is calculated either by a direct method (using the Fick’s law) or equivalently by the Green–Kubo relationship (Schelling et al.246) at different temperatures in the MD framework 2.02.6.2.1 Actinide dioxides 2.02.6.2.1.1 Stoichiometric dioxides The parameters (of eqn [17]) of the thermal conductivities of actinide dioxides have been reported in Table 19 Among the dioxides, UO2 has indeed been subject to many experiments It is the only one to exhibit a nonnegligible electronic conductivity contribution Complementary theoretical calculations (see MD calculations by Arima et al.,64 Uchida et al.,65 Kurosaki et al.,247 or models based on approximated phonon spectra by Sobolev67–69 and Lemehov 52 Thermodynamic and Thermophysical Properties of the Actinide Oxides et al.248) have been performed recently to extend (in temperature and composition) the available experimental data The results obtained recently by Sobolev67–69 reproduce quite well the experimental data available Lemehov et al.248 have shown that such a model works for irradiated dioxides too 2.02.6.2.1.2 Stoichiometric mixed dioxides The thermal conductivity of few mixed dioxides has been investigated experimentally Among the most well known are indeed the uranium–plutonium and the uranium–thorium mixed dioxides Some data are available for (Np,U)O2 (see Lemehov et al.248) and for the rest of mixed dioxides, one can refer to MD calculations (see Arima et al.,64 Terentyev,80 Arima et al.,81 and Kurosaki et al.82) We have gathered the most recently obtained parameters (eqn [17]) of the thermal conductivity (see Yang et al.,78 Duriez et al.,143 Vasudeva Rao et al.,190 Kutty Table 19 ThO2 UO2 NpO2 PuO2 AmO2 et al.,249 and Pillai and Raj252) in Tables 20 and 21, respectively, for U1 À xPuxO2 and for UxTh1 À xO2 Some attempts have been made with various degrees of success to relate the solid solution ratio (x in U1 À xPuxO2 (see Duriez et al.143) or y in Th1-yUyO2 (see Bakker et al.59)) and the parameters A and B (eqn [17]) of the thermal conductivity For example, for Th1 À yUyO2 with y < 0.1, in the temperature range 300–1173 K and a density of 95%, both A and B parameters are related to the stoichiometry by a quadratic dependence by Bakker et al.59: A ẳ 4:195 104 ỵ 1:112y 4:499y and B ¼ 2:248  10À4 À 9:170  10À4 y ỵ 4:164 103 y The thermal conductivity of the more complex americium and neptunium containing MOX dioxides has been recently investigated by Morimoto et al.242,253 In this case, the parameter A of eqn [17] Parameters (of eqn [17]) of the thermal conductivities in stoichiometric dioxides A  102 (mK WÀ1) B  104 (m WÀ1) C  10–11 D  10–4 (K) T (K) References 0.042 6.548 9.447 1.22 0.46 2.1 2.25 2.3533 1.797 2.75 1.282 3.19 – 2.024 – – – – – 1.635 – – – – 300–1800 298–3120 573À1473 Bakker et al.59 IAEA212 Nishi et al.137 Bielenberg et al.250 Gibby251 Bakker et al.59 373À1474 298À1573 Table 20 Parameters (of eqn [17]) of the thermal conductivity of U1ÀxPuxO2 fitted from the data of Vasudeva Rao et al.190 and Duriez et al.143 U1ÀxPuxO2 A  102 (mK WÀ1) B  104 (m WÀ1) T (K) %TD References 0.03 0.06 0.10 0.15 0.21 0.28 0.40 3.96 3.27 3.96 2.17 5.74 17.08 15.81 2.875 2.96 2.894 3.039 1.734 1.157 2.301 300À1300 300À1300 300À1300 300À1300 700À1500 700À1500 700À1500 95 95 95 95 96 96 96 Duriez et al.143 Duriez et al.143 Duriez et al.143 Duriez et al.143 Vasudeva Rao et al.190 Vasudeva Rao et al.190 Vasudeva Rao et al.190 Table 21 Parameters (of eqn [17]) of the thermal conductivity in UxTh1ÀxO2 solid solution, obtained by Kutty et al.,249 252 Pillai and Raj, and Yang et al.78 UxTh1ÀxO2 A  102 (mK WÀ1) B  104 (m WÀ1) T (K) %TD References 0.00 0.00 0.02 0.04 0.20 0.355 0.655 3.34 2.16 4.694 4.97 25.16 14.7 13.3 1.374 2.12 2.13 1.475 2.359 2.13 2.11 400À1800 300À1250 300À1250 400À1800 400À1800 300À1500 300À1500 92 94 94 94 90 96–98 96–98 Kutty et al.249 Pillai and Raj252 Pillai and Raj252 Kutty et al.249 Kutty et al.249 Yang et al.78 Yang et al.78 1.85 0.30 1.80 0.25 1.75 0.20 1.70 0.15 1.65 0.10 1.60 0.05 1.55 0.00 0.00 0.02 0.06 0.04 x in UO2 + x 0.08 53 4.5 O/M = 2.00 O/M = 1.984 O/M = 1.974 O/M = 1.948 4.0 1.50 0.10 3.5 l(W m–1 K–1) 0.35 A(x) B(x) Thermodynamic and Thermophysical Properties of the Actinide Oxides 3.0 2.5 Figure 32 Evolution of A(x) and B(x) as a function of stoichiometry x in UO2 ỵ x from Lucata et al.255 2.0 Thermal conductivity (W m–1 K–1) 10 1.5 600 O/U = 2.00 2.02 2.05 2.15 0 1200 1500 T (K) 1800 2100 Figure 34 Thermal conductivity of 15% plutonium containing UO2 as a function of temperature and stoichiometry from Duriez et al.143 ã Elsevier, reprinted with permission 900 2.11 2.20 500 1000 1500 Temperature (K) 2000 Figure 33 Thermal conductivity of in UO2 ỵ x as a function of stoichiometry x from Amaya et al.256 ã Reprinted with permission (B being fixed) is linearly related to the stoichiometry of Amz1Npz2Pu0.3U0.7 À z1 À z2O2 as follows: A ¼ 0:3583z1 ỵ 0:06317z2 ỵ 0:01595 (mK W1) with B ẳ 2:493  10À4 (m WÀ1) 2.02.6.2.1.3 Nonstoichiometric dioxides In general, the thermal conductivity decreases with departure from stoichiometry This has been seen in AmO2 À x by Nishi et al.254 and in UO2 Ỉ x by Watanabe et al.87 and also by Yamashita et al.88 Lucuta et al.255 found a linear relation between the thermal conductivity and the stoichiometry x in UO2 ỵ x for < x < 0.10 (see Figure 32): Axị ẳ 0:0257 ỵ 3:34x and Bxị ¼ ð2:206 À 6:86xÞ Amaya et al.256 proposed a somewhat different and more complicated expression, but valid for 0.0 < x < 0.20: l ẳ l0 farctanyị=yg ỵ CT ẵ19 p where l0 ẳ 1=A ỵ BT ị; y ¼ D 2xl0 , and D ¼ D0 expðDT Þ The fit performed by Amaya et al.256 leads to A ¼ 3.24  10–2 K m WÀ1, B ¼ 2.51  10–4 m WÀ1, C ¼ 5.95  10–11 W mÀ1 KÀ4, D0 ¼ 3.67 m1/2 K1/2 WÀ1/2, and D1 ¼ À4.73  10–4 KÀ1 It allows a good description of hyperstoichiometric urania (see Figure 33) For even higher-order oxides, in the case of U3O8, the thermal conductivity coefficients are from Pillai et al.257: A ¼ 29.3  10–2 mK WÀ1 and B ¼ 5.39  10–4 m WÀ1 For U1 À yPuyO2 À x with a low amount of Pu, Duriez et al.143 obtained almost no dependence on the plutonium content in the range of 0.03 < y < 0.15 (see Table 19) The extrapolation to pure UO2 indicates that a small amount of Pu is sufficient for altering the thermal conductivity of UO2 Because of the proximity to the pure UO2 end member, Duriez et al.143 found an electronic contribution to the thermal conductivity at high temperature The parameters (of eqn [17]) are Axị ẳ 2:85x ỵ 3:5 102 K m W1, Bxị ẳ 7:15x ỵ 2:86ị104 m WÀ1, C ¼ 1:689  109 W KÀ1 m, and D ¼ 1:3520  104 K As an example for the evolution of the thermal conductivity as a function of temperature and stoichiometry, we show the figure from Duriez et al.143 for a sample containing 15% urania (Figure 34) 54 Thermodynamic and Thermophysical Properties of the Actinide Oxides For higher amount of plutonium (0.15 < y < 0.30), Inoue238 obtained a somewhat different dependence (qualitatively reproduced by MD calculations by p Arima et al.81): Axị ẳ 0:06059 ỵ 0:2754 x K m WÀ1, B ¼ 2:011  10À4 m WÀ1, C ¼ 4:715  109 W KÀ1m, and D ¼ 1:6361  104 K Finally, the thermal conductivity continues to decrease as a function of plutonium content, as shown by Sengupta et al.259 in Pu0.44U0.66O2 Morimoto et al.258 have investigated the effect of hypostoichiometry on the thermal conductivity of U0.68Pu0.30Am0.02O2.00 À x (0.00 < x < 0.08) Both parameters A(x) and B(x) (of eqn [17], C ¼ D ¼ 0) depend on the stoichiometry x as follows: AðxÞ ẳ 3:31x ỵ 9:92 103 K m W1 and Bxị ẳ 6:68x ỵ 2:46ị104 m W1 Lemehov et al.248 brought a physical model for the thermal conductivity of actinide dioxides They were able to fit the few experimental data available and to analyze the effect of hypostoichiometry (and irradiation) in (Am,U)O2 À x and (Am,Np,U)O2 À x solid solutions 2.02.6.2.2 Actinide sesquioxides The parameters of the thermal conductivity as a function of temperature are available only for curium sesquioxide Cm2O3 The values recommended by Konings et al.43 are A ¼ 36.29  10–2 mK WÀ1 and B ¼ 1.78  10–4 m WÀ1 Lemehov248 and Uchida65 have investigated the behavior of Am2O3 But their theoretical results are not consistent to each other and hardly consistent with the few experimental data available 2.02.7 Thermal Creep Creep relates to the slow plastic deformation of the material under the influence of stress and temperature It is a long-term process with different mechanisms Actinide oxides mainly have a brittle behavior Therefore, plastic deformation due to dislocation motion requires high energy to form and move Hence, at low temperature, plasticity occurs at very high stress or operates at very low rates, which are not measurable before the point of catastrophic failure.260 The only measurable plasticity is then because of thermal creep Classically, thermal creep rate is modeled in actinide oxides by the sum of two mechanisms if the fission process is not taken into account The first mechanism is the viscous creep with some grain boundary sliding occurring at low stresses The second mechanism is the dislocation-climb process, which operates at stresses greater than a transition stress that is governed by the grain size.261,262 Over the past few years, several more or less successful models have been proposed to express these two mechanisms Recently, Malygin et al.264 have proposed a model that seems to best fit the experimental data.263–267 This model is described by a sum of two terms, related to the two mechanisms reported above: de aOsDV bs4:5 DV p ỵ ẳ kB TG dt kB T bN m3:5 ½20Š where a and b are constants that depend on the degree of relaxation of the tangential stresses at the boundary of a grain, O is the atomic volume, s is the stress, DV is the volume diffusion coefficient, k is Boltzmann’s constant, T is the absolute temperature, G is the grain size, b is the Burgers vector, N is the density of mobile dislocations, and m is the shear modulus For low stress (s 30–40 MPa), the experimental data show that the thermal creep of UO2 under compression is a linear function of the stress and is inversely proportional to the squared grain size Malygin et al.268 report that at low stress, the creep is controlled by uranium diffusion by a vacancy mechanism At higher stress (s > 40 MPa), a power law dependence with an exponent of 4.5 is observed that is controlled by a dislocation climbing process To model the dependence of the creep rate for a nonstoichiometric UO2, Malygin et al.268 developed a point defect model and a relation giving the diffusion coefficient of uranium vacancies as a function of temperature and composition A final relation is given in Malygin et al.268 to calculate the dependence of the creep rate as a function of temperature, stress, density, grain size, and oxygen stoichiometry The results show that the creep rate increases with the departure from the oxygen stoichiometry (see Figure 35) The same authors have recently performed the same analysis in Malygin et al.269 using the experimental data published in Routbort,270–272 Javed,266 Perrin,273 Caillot274 for mixed uranium–plutonium oxides As shown in eqn [21], the mixed oxides have the same behavior as UO2: de AsDV ẳ ỵ Bs4:5 DV G2 dt ½21Š A and B are coefficients that depend on the oxide density and on the plutonium content Thermodynamic and Thermophysical Properties of the Actinide Oxides 10-2 1673 K 10-3 de/dt (h-1) 1623 K 10-4 1523 K 10-5 1473 K 10-6 10-7 10-5 10-4 10-3 x 10-2 0.1 Figure 35 Comparison between the calculated (lines) and experimental data (symbols) on creep rate of uranium dioxide with grain size of mm on departure from stoichiometry with s ¼ 20 MPa according to Malygin et al.274 2.02.8 Conclusion The most relevant physicochemical properties of actinide oxides were reviewed Numerous studies were done in the past on these materials that are crucial for nuclear applications The current increased interest in oxide fuels for Generation IV systems, and particularly the 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150 130 110 AmO2 NpO2... reported, and we refer the reader to the studies by Sabioni et al. ,22 0 ,22 2 Mendez et al. ,22 5 Korte et al. ,22 6 Sali et al. ,22 7 Arima et al. ,22 8 Ruello et al. ,22 9 Kato et al. ,23 0 and Garcia et al .23 1 and. .. phases Ac 2 ỵ3 ỵ4 ỵ5 ỵ6 Th Pa ThO* U Np UO* Ac2O3 ThO2 PaO2 Pa2O5 UO2 U4O9 U3O8 UO3 NpO2 Np2O5 NpO3 Pu Am Cm Bk Cf PuO* Pu2O3 PuO2 Am2O3 AmO2 Cm2O3 CmO2 Bk2O3 BkO2 Cf2O3 CfO2 Es EsO Es2O3 Thermodynamic