Several intermetallic compounds (N> 3) appear in the phase diagrams between actinide and Group VIII metals, with the exception of Th-Os, U-Fe, Np-Fe, and Pu-Fe systems, in which N = 2 or 3. This sug­gests that the ordering between actinide and Group VIII metals is preferred to the random configuration, and the Gibbs energy of formation of these com­pounds is expected to be much larger than what appears in the actinide-Group IVa or VIIa metal systems. Table 14 summarizes the various interme­tallic compounds reported for the actinide-Group VIII metal systems as well as the actinide-Mn system. A systematic variation is seen in the table with increasing atomic number of actinide or Group VIII metal. A unique feature is especially observed in the actinide-Fe systems. Five kinds of intermetallic com­pounds exist in the Th-Fe system (Th2Fe7 has two different allotropes)170,171,185 and these compositions are rather similar to those observed in the other Th-Group VIII metal systems. On the other hand, the U-Fe, Np-Fe, and Pu-Fe systems have only two kinds of intermetallic compounds (although PuFe2 has three different allotropes) and are more similar to the Mn-related systems. This variation may corre­spond to the difference in the Gibbs energy of for­mation of these intermetallic compounds. Here, the existence of Np6Fe has not been directly confirmed yet. A compatibility test between the U-Pu-Zr-Np — Am-Ce-Nd alloy and stainless steel was performed,1 0 in which two or three kinds of phases were detected in the interaction layer, such as the MFe2-type, M6Fe — type, and RE-rich type (M: mixture of actinides). The existence of Np in the M6Fe-type phase was detected,

Table 14 Intermetallic compounds between actinide and Mn, Fe, Co, or Ni

Group Vila VIII

Element

Mn Fe Co Ni

aAccording to systematic similarity, other intermetallic compounds are expected in the Np-Co, Np-Ni, Am-Co, and Am-Ni systems. According to the expected similarity of the Am-Mn system against the Ce-Mn system,4 there might be no intermetallic compounds in the Am-Mn system.

NA: there is no available information.

ND: the crystal structure is not determined yet.

and the composition of U and Np in M6Fe was almost the same as that in the original alloy. This suggests that Np6Fe might be formed in the equilibrium Np-Fe phase diagram.

Figures 54 and 55 show the U-Fe phase diagram and the variation in the U activity in the U-Fe system,89 in which the assessment of the U-Fe sys­tem was performed by thermodynamic modeling (CALPHAD approach) based on the available data given in Leibowitz eta/.,85 Gordon and Kaufmann,186 Grogan,187 Michaud,188 Chapman and Holcombe,175 and Gardie et a/.176 The calculated results overlap well with the experimental data points in these dia­grams. The U activity deviates slightly to the negative direction from Raoult’s law, but not too significantly. Figures 56 and 57 show the Np-Fe and Pu-Fe phase diagrams shown also in Kurata,7 in which thermo­dynamic modeling was performed for the Pu-Fe system using the works in Konobeevsky,17 Bochvar
et a/.,116 Mardon et a/.,181 Avivi,182 and Ofte and Wittenberg,189 and then the Np-Fe system was esti­mated using the work of Gibson et a/.190 by assuming initially that the various interaction parameters in the Np-Fe system are almost the same as those in the Pu-Fe system. The calculated result for the Np-Fe system is similar to that for the Pu-Fe system, and the results reasonably overlap with the experi­mental data. Thermodynamic data were partially obtained for the Th-Fe, U-Fe, and U-Ni systems, as summarized in Tables 15 and 16. The partial Gibbs energy for the Pu2Ni17-Ni two-phase region and the Gibbs energy of formation of the Pu2Ni17 were estimated in Chiotti et a/.191 from the EMF measurement192 as follows:

AGpu = — 83.76

+ 12.34 x 10-3T(kJmol-1)(930 — 1113K)

Df G0(Pu2Ni17) = -167.8

+ 24.69 x 10-3T(kJmol-1)(913 — 1125K)

Regarding the Fe-related system, the Gibbs energies were also estimated by Kurata,7 and are given in Table 17. The difference between the values shown in Tables 16 and 17 originates from the difference in the estimation of the Gibbs energy for the solution phases.

The ternary phase relation among actinide, Fe, and Zr is particularly important when considering the fuel-cladding chemical interaction (FCCI) between the metallic nuclear fuel and the stainless steel cladding (the details are discussed in another chapter). Regarding the U-Fe-Zr system, the phase relations were studied in the temperature region between 853 and 1073 K.194 Three kinds of ternary intermetallic compounds, e, l, and w, were found in the system. Theses compositions are U-(33-50) at.% Zr-33 at.% Fe; U-(21-25) at.% Zr-6at.% Fe;

Table 16 Thermodynamic functions for U-Fe systems taken from Okamoto19

GO(Fe, liq) = 0 GO(U, liq) = 0

GO(Fe, bcc) = -13800 + 7.169T GO(Fe, fcc) = -14640 + 8.123T GO(U, bcc) = -9142 + 6.492T GO(Fe2U) = -25 314 + 6.202T GO(FeU6) = -26 438 + 17.360T Gex(U-Fe, liq) = xu(1 — Xu) (-38746 — 7 736хи)

region the two-phase region of UFe2 and ZrFe2 appear instead of UFe2 and U6Fe. The phase rela­tion for the U-Pu-Fe system was also evaluated by experiments198 and by thermodynamic modeling.[9] Figure 60 summarizes the results. The phase relation between the M6Fe and liquid phases is of particular importance for evaluating the FCCI to avoid lique­faction during the normal operation (details are dis­cussed in another chapter). Thus, the interaction between U-Pu alloy and Fe was investigated by Nakamura eta/.199 The detected phases agree reason­ably well with the above assessment. Figure 61 shows the calculated phase relation for the U-Np-Fe sys- tem.7 A similar feature as that of the U-Pu-Fe system is speculated. The phase relations in the quaternary U-Pu-Zr-Fe system were evaluated by experi- ments200 and by thermodynamic modeling.89 The mutual diffusion was studied using the diffusion cou­ple of the U-Pu-Zr alloy and Fe.2 1 The partial phase relation in the U-Pu-Fe-Zr quaternary system was constructed from these results, as shown in Figure 62. The observed diffusion path coincides well with the equilibrium phase relations even in the quaternary system.

In the actinide-Co or Ni system, the features of the phase diagrams vary from Th toward Pu due to the difference in the melting point of actinides. Figures 63 and 64 compare the Th-Ni and Pu-Ni systems as an example. The Th-Ni phase diagram was assessed in Cirafici and Palenzona202 based on the observations of Horn and Basserman173 and Thomson,174 in which seven kinds of the interme­tallic compounds appear. The Pu-Ni phase diagram was assessed by Peterson69 based on the observa­tions of Konobeevsky17 and Wensch and Whyte,183

in which six kinds of intermetallic compounds appear. The liquid phase exists in a rather low — temperature region in the Pu-Ni system and there are no Pu-rich intermetallic compounds, as com­pared to the Th-Ni system. This suggests an

asymmetric interaction for the Pu-Ni system. Pos­sibly, far negative deviation from Raoult’s law is speculated only for the Ni-rich region.

As for the actinide-Ru, Rh, or Pd phase rela­tions, a systematic variation such as that seen in the actinide-Ni system is observed, with some excep­tions. Table 18 summarizes the intermetallic com­pounds in the actinide-Ru, Rh, or Pd systems as well as that in the actinide-Tc system. In case of Th, there are many similarities between the Th-Ru and Th-Rh systems. Relatively low eutectic points com­pared to the high melting points of Th (2028 K), Ru (2607 K), and Rh (2239 K) appear near the Th termi­nal, such as at 84 at.% Th (1535 K) and at 80 at.% Th (1510 K) for the Th-Ru and Th-Rh systems. Some intermetallic compounds have the same crystal struc­ture, such as the Th7Fe3-type and the CrB-type. There is a stable Laves phase, such as the ThRu2 and ThRh2, and these melt congruently although the crystal structures ofthe Laves phase are different. These features are generally similar to those appear­ing in the Th-Ni system. The phase relations in the Pd-rich region of the Th-Pd system are, however, different from those in the Th-Ru and Th-Rh systems, although the Th-rich region shows some

similarities. There is no Laves phase and significant solid solubility (14at.%Th at the maximum) in the Pd-rich region of the Th-Pd system. In the case of U, some general similarities are still observed among the U-Ru, U-Rh, and U-Ni systems. There are several intermetallic compounds and relatively low eutectic points near the U terminal, such as 81.5 at.% U (1159 K), 75.5at.%U (1128 K), and 67at.%U (1013 K). There appears to be several percent of solid solubility of Ru or Rh in the g-U (bcc structure). The phase relations in the U-Pd

system are rather different from those in the U-Ru and U-Rh systems, especially for the intermediate to the Pd-rich region. The solid solubility of U in Pd attains ^15 at.% U at the maximum. In the central region of the U-Pd phase diagram, two intermetallic compounds, that is, UPd and U5Pd6, only exist in the very limited temperature region. According to Okamoto,19 however, there are still some unlikely situations in the presently suggested U-Pd phase diagram, such as the liquidus shape around UPd3, the relative relation between the liquidus and solidus

near the Pd-terminal, and the crystal structure of UPd8. In case of Pu, the phase relations observed in the Pu-Ru and Pu-Rh systems are generally simi­lar to those in the Pu-Ni system with some excep­tions, such as the structure of the intermetallic compounds, the existence of the Pu19Ru, etc. The general feature of the Pu-Pd system is similar to that of the U-Pd system. Figure 65 shows the Pu-Rh phase diagram as a typical example quoted from Okamoto,4 which was redrawn from the works of Land et at21 Significant degrees of the Gibbs energy of formation for the intermetallic compounds between actinide and these noble metals are expected from a general view of the phase diagrams. From the viewpoint of the phase stability in nuclear fuels under irradiation, the intermetallic compounds mostly rich in Ru, Rh, or Pd are of particular importance among these compounds (a detailed discussion is given in other chapters). These noble metals are observed to precipitate in the irradiated nuclear fuels and possibly contain a small amount of actinide from the fuel matrix. Unfortunately, the thermodynamic quantities ofthese compounds are not known.

The actinide-Os, Ir, or Pt phase relations are expected to be similar to those in the actinide-Ru, Rh, or Pd systems. Table 19 summarizes the inter­metallic compounds in the actinide-Os, Ir, or Pt systems as well as those in the actinide-Re system. In case of Th, the general views of the phase relations of Th-Os, Th-Ir and Th-Pt are similar to those of Th-Ru, Th-Rh, and Th-Pd, respectively. Several intermetallic compounds have the same crystal struc­tures. They are predicted to be thermodynamically stable and exist even at high temperatures. A similar tendency is also expected for the U — and Pu-related systems. In the actinide-Pt systems, the number of the intermetallic compounds generally is a maximum. The thermodynamic functions for the actinide-Pt systems were evaluated in Miedema,39 Gingerich,226 Schmidt,227 Mobius,228 Peterson,225 and Mobius et at.,229 and given in Table 20, the values of which were determined mainly from EMF measurements. Although the values are scattered, the significant nega­tive deviation is confirmed for the phase relation between actinides and Pt. Similar deviation is also expected for the relation between the actinides and the other noble metals, such as Ru, Rh, Pd, Os, and Ir.

Regarding Pa, Np, Am, and Cm, there are limited experimental observations. The high stabilization for the intermetallic compounds is speculated on in the phase relations between these actinides and Pt as well as Th, U, and Pu.

aAccording to systematic similarity, other intermetallic compounds are expected in the Pa-, Np-, Am-, and Cm-related systems. NA: there is no available information.

ND: the crystal structure is not determined yet.

2.08.3.1 Melting

In the initial development stages, melting in air was used to produce nickel-copper and nickel-chromium — iron alloys. However, subsequent to the development

Cumulative high temperature heating time (h)

of Alloys X-750 and 718 as precipitation-hardened high-strength materials for aerospace applications, a vacuum melting process in addition to a double — or triple-melting process has been applied to nickel — based alloys to minimize solidification segregation and undesirable precipitation. The double — or triple­melting process is usually selected from vacuum — induction melting, electroslag remelting, and vacuum arc remelting processes, as illustrated in Figure 18 44-51

The melting process in air was mainly applied to mill-annealed Alloy 600 for SG tubes of PWRs until the 1980s. However, after the experience with IGSCC and other corrosion problems in the SG tubes of PWRs, severe quality assurance for these tubes was demanded by end users, and the melting process was changed to vacuum melting and other high-grade melting processes. Thus, TT Alloy 690 for SG tubes and other applications has been melted using the vacuum oxygen decarburization process or a double-melting process such as electroslag remelt­ing after vacuum-induction melting.44

Many critical reviews ofthe thermodynamic proper­ties of the actinide metals have been made since the 1960s. The first milestone was the review by Oetting and coworkers,27 which gave recommended values for Th to Cm. Ward et a/.28 treated the same elements but also gave recommendations for Cf and Es. In addition, the room temperature thermodynamic properties for the major actinides Th and U have been reviewed by the CODATA team for key values for Thermodynamics,29 while Th, U, Np, Pu, and Am have been reviewed by the OECD/NEA team.30-33 The most recent evaluation was made by Konings and Benes,34 with emphasis on the high-temperature properties. There are no large differences between these studies for the major actinides and it is thus clear that the recommendations given in this chapter rely heavily on these studies (Tables 3 and 4).

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 a/.84 and Inoue238) where the electronic conductivity increases at high temperatures. Any defect (point defect, grain boundary, void, porosity, impurity, etc.; see, e. g., Buyx23 ), as referred to the ideal perfect lattice, may contribute to decrease the thermal conductivity by phonon scattering (see, e. g., Millet et a/.240). The thermal conductivity l may consequently be expressed as

_ 1 C D

= a + в x t + T2 expv-T [17]

The last term, that is dependent upon C and D parameters, is related to the electronic conductivity (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 a/.242 Indeed, as irradiations pro­duce significant amounts of defects and impurities, they will contribute to the modification of A (see, Ronchi et a/.,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 1TD of the fully dense material:

l = Itd (1 — P)x [18]

P is the porosity and x is related to the shape of the closed pores; in the spherical case, x= 1.5. Bakker et a/.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 /я/t/o 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 eta/.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 a/.,64 Uchida et a/.,65 Kurosaki et a/.,247 or models based on approxi­mated phonon spectra by Sobolev67-69 and Lemehov

et al248) 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.

An overview of the ternary uranium-plutonium and uranium-thorium carbides is given later in this chap­ter. Here, a short introduction to uranium carbide oxides and carbide nitrides is presented. Ternary species of this kind form relatively easily in UCx in contact with air.

T (K)

Figure 19 The spectral emissivity of UC2 at two different wavelengths. Reproduced from De Coninck, R.; De Batist, R.; Gijs, A. High Temp. High Press. 1976, 8,167-176.

2.04.4.2.6.1 Uranium carbide oxides

The oxidation of uranium carbide is a complex process dependent on temperature, the O2 partial pressure, the separation of the reaction products, and the process state. A comprehensive review on the oxidation of uranium carbides can be found in Le Guyadec.172 In this paper, two mechanisms for UC ignition between 413 and 473 K are proposed, shown in Figure 20, based on the nature of the oxide layers or bilayers formed (UCO solid solution and UO2 oxide) and on the sudden or progressive fracture of these layers. The formation of U3O8 was instead observed above 573 K.

Earlier, Camagni eta/.173 had shown that the oxide layer formed on UC in air can have a passivating effect, hindering further bulk oxidation.

Many studies have been carried out in the U-C-O system, not only motivated by the usual presence of oxygen impurities in uranium carbides, but also because the oxycarbide themselves can be suitable for nuclear applications.32 In the technological con­text of the TRISO fuel development, the system U-C-O has been recently reviewed both from the viewpoint of the oxygen-impurity contamination of uranium carbide fuel174 and the interaction of UO2 fuel with the pyrolytic graphite buffer layer.175,176 The only real ternary compound is the solid solution UC1±xOj, (or U(C, O)), besides the slight solubility of oxygen in UC2 with the resulting dicarbide stabilization. Henry177 measured the composition of UC1±xOj, in equilibrium with UO2 and metal as UC066O0 34 at 1973 K, with a fcc NaCl lattice parame­ter a = 494.8 ± 0.1 pm. These measurements are in fair agreement with more experimental data assessed by

Holleck and Kleykamp,8 and were essentially used by Gueneau eta/.174 in their thermodynamic study. Up to 5% vacancies can be formed in the nonmetal sublattice of U(C, O). The phase diagram U-C-O is illustrated through the isothermal sections given in Figure 21.174

These isothermal sections of the ternary sys­tem U-C-O were constituted from thermodynamic functions of the U-O, U-C, and C-O binary sys — tems.101,178 The thermodynamic functions of both UC1±xOj, and UC2—xOx were evaluated from Henry’s data177 and the free energy of formation estimated by Potter.179 For UC1±xOj, a (C1,C2,O, Va)1(U)1 sub­lattice model was used, allowing to take into account a U/(C + O) ratio different than 1. For the dioxycarbide, a similar model (C1,C2,O, Va)1(U)1 was chosen, assuming an ideal solution between UC2 and UO2. A solubility of several percents of oxygen in UC2 was obtained. It was reported by Heiss180 that up to 6% of carbon atoms can be replaced by oxygen in the anion sublattice of a-UC2. However, the temperature of formation of the ternary phase UC2—xOx in U-O-C is not known. Only uncertain experimental data exist for T< 1573 K, where more calculations have recently
been compared with some mass spectroscopy data.175 Blum eta/.181,182 observed at 1390 K the ternary eutec­tic of the U-C-O system. The eutectic of the pseudo­binary UC-UO2 system was reported at 2523 K.183

The enthalpy of formation of UC1—xOx was measured184 by combustion calorimetry:

AH°f(298 K) = —90.8-454x kJ mol—1 up to x = 0.84 (well beyond the oxygen solubility limit). In the same work, the heat capacity of UC1—xOx between 313 and 643 K was also measured by adiabatic calorimetry, obtaining

Cp = 58.4 + 0.00134 T — 799 000T—2JK—1mol—1) [45]

The standard entropy of UC1—xOx at 298 K was esti­mated to be S°(298 K) = 47.3 + 2.97-x J K—1mol—1. More thermodynamic data can be found else­where.174-176

The equilibrium CO partial pressures in the UO2-UC2-C section of the U-C-O system were critically assessed by Gosse et a/.176 Figure 22(a) shows the CO pressure values for the monovariant equilibrium UO2—x + UC2 + C in the temperature range 1473-2140 K and Figure 22(b) reports the

equilibrium CO partial pressure on a line U-CO in the ternary phase diagram at increasing oxygen

174

content. ‘

The thermal conductivity of ternary UC1_xOx samples decreases with x, this effect being well visible even for x = 0.02. This phenomenon is mitigated at high temperature because of the thermal expansion (Figure 1).185

The electrical resistivity of UC1_xOx samples decreases with x as measured between 80 and 1200 K by Larin and Vlasov186 and reported in Figure 18.

All these data indicate how the metallic character of uranium carbides is gradually lost with the addi­tion of oxygen, already starting at some atomic per­cent of oxygen. This trend has been observed also on the spectral emissivity.187

2.06.3.4.1 Preparation

Uranium trifluoride is most conveniently prepared by reduction of UF4 with finely powdered uranium. Three methods of preparation of uranium fluoride have been investigated: (1) Palmer67 reported the reduction of uranium tetrafluoride by hydrogen at 1000 °C in molybdenum boats using stainless-steel tubes (UF4(s) + 1/2H2 $ UF3(s) + HF), (2) treat­ment of uranium trichloride with hydrogen fluo — ride,68 and (3) reduction of uranium tetrafluoride with uranium. Uranium trifluoride was prepared by the reaction of uranium tetrafluoride with a stoi­chiometric amount of uranium hydride (obtained by a hydrogenation and dehydrogenation cycle of uranium metal repeated several times) in a slow stream of argon at temperatures that slowly increase from 700 to 900 K during 5 h. Tantalum carbide crucibles were used as containers. After cooling in argon, the sample was transferred to a glove box and homogenized.47

U(turnings) +|H2 ! UH3
U + 3UF4 ! 4UF3

Uranium trifluoride is a gray to black solid.

2.06.3.4.2 Properties

As compared to other uranium(III) compounds, the trifluoride is remarkably stable on air at room tem­perature. At higher temperatures, UF3 oxidizes and at 1173 K, it is quantitatively converted into U3O8. Contrary to the other trivalent uranium halides, UF3 is not hygroscopic.

The compound is thermally unstable even in an inert atmosphere and disproportionates to UF4 and U at about 1273 K and to a smaller extent (0.1% per hour) also at 1073 K.69

2.06.3.4.2.1 Crystal structure

UF3 has a LaF3-type structure but the symmetry is reported to be either trigonal (space group P3c1, Djd) or hexagonal (space group P63cm, C36v). The uranium atom in UF3 is 11-coordinate68,70

a1 = (4.138 ± 0.03) A and a3 = 7.333 ± 0.004 A

for in agreement with

a1 = (4.13 ± 0.01) A and a3 = (7.33 ± 0.01) A
Other crystallographic data can be found elsehwere.69

Table 5 Thermodynamic properties of the crystalline uranium trifluoride compound

-(1501.4 ± 4.7)24

129.2 ± 0.51

95.1 ± 0.424

106.539 + 7.05 x 10-4T — 1035500 x T-2 (298.15-1768 K)39 17681 36.81 (298.15-1768) is the temperature range for which the Cp(T) function is valid.

The calculated density value with two molecules of UF3 per unit cell varies between 8.99 and 8.9571 compared to the experimental one of 9.18.68

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 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.

The Gibbs free energy (G) for UN has been reported by Hayes et a/.46 On the basis of the equations for Cp and H H298, they have determined other thermal functions of UN(s) in the temperature range of 298-2628 K. They have then calculated the values of the thermal functions from their equations for heat capacity, setting S298 to be 62.68J mol-1 K — ; these are given in Table 4. The values of Gibbs free energy of formation AfG for UN were thus calculated from the values of AH29876 and thermal functions of uranium81 and nitrogen.82 The values of entropy S, free energy function — (G-H298)/T and Gibbs free energy of formation AfG of UN(s) are also given in Table 4.

The values of AfG at various temperatures were fitted to a polynomial function of temperature using the least-squares method. The AfG of UN was thus expressed as the following equation:

Af G(Jmol-1) =-2.941 x 105 + 80.98T — 0.04640 T2 + 3.085 x 10-6T3 — 1.710 x 106/T (298 <T(K) <2628) [13]

Matsui and Ohse76 have also reported AfG values for UN. The temperature dependences of AfG for UN are shown in Figure 21. The UN AfG values of these two studies agree well with each other below 1800 K, but there seems to be some discrepancy between them at higher temperatures. It should be noted that the values of AfG for UN contain some uncertainty due to the inaccuracy of the data on the H-H298 values. The values of AfG, as estimated by Matsui and Ohse have a large range of error because the calculation was performed by extrapolating the values of H-H298. Thus, the data for the A fG of UN, as reported by Hayes eta/., are considered to be the reference standard at the present.

Holleck and Kleykamp8 assessed the solubility of actinide mono — and dicarbides (Figure 28).

(a)

Figure 28 The solubility of pseudobinary actinide monocarbides (a) and dicarbides(b). +, complete solubility demonstrated and (+), 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.

The zirconium alloys in use today for nuclear applica­tions are limited in number: besides pure Zr, only four alloys are currently listed in the ASTM standards for Zr ingots for nuclear applications (ASTM-B350). Those are shown in Table 1. The first three are used for cladding and structural materials, such as guide tubes and channel boxes in PWRs and BWRs and structural materials in CANDU reactors, while grade R 60904 is used exclusively in pressure tubes for CANDU reac­tors. For cladding tubes, only Zircaloy-2 and -4 are listed in the applicable standard (ASTM B-811).

Alloys of more recent use such as ZIRLO®, M5®, E110, or E635 are now of common use in light water reactor cladding, but are not considered for ASTM designation in the near future. Due to the limited market of cladding tubes for nuclear reactors, and the small number of tube producers or fuel vendors, the exact chemistry, processing routes, or mechanical properties are usually agreed mutually between the contracting parties.

Historically, the first Zircaloy was conceived in the United States as a 2.5% Sn alloy. Owing to its poor long-term corrosion behavior, the tin content was reduced roughly by a factor of 2. A fortuitous
contamination of one melt by stainless scraps showed the drastic improvement induced by small additions of Fe, Cr, and Ni, the constituents of the austenitic stainless steels. Systematic composition variations to optimize the alloy introduced the Zircaloy-2. The capture of a significant amount of hydrogen by the alloy during corrosion was attributed to the presence of nickel. Its replacement by an equivalent amount of iron and chromium led to the Zircaloy-4.34

Zr-Nb alloys were developed in Canada, Russia, and the United States, with initial high Nb concen­trations (up to 4%). For the claddings of BWRs, they showed poor behavior and the Zr-Nb alloys development was stopped soon in the United States. Zr-2.5Nb was quite satisfactory for the pressure tubes, due to its low hydrogen pick-up during opera­tion, and the engineering optimization of this alloy was continued in Canada and Russia. It remains the reference alloy for pressure tubes, in CANDUs. Zr-1% Nb has been developed for cladding in these countries and behaved very satisfactorily in VVER. A renewal of interest in such alloys in the western world in the 1990s led to the development of a Zr-1% Nb alloy, with controlled additions of Fe and

S. The M5® alloy is now of regular use in PWRs, with excellent corrosion resistance, compared to the former Zry-4.35

‘Quaternary’ alloys were conceived as a mixture of the Zircaloys and the Zr-Nb alloys, hoping to con­serve the specificity of each of them in addition to the different alloying elements:

• Niobium for the resistance to hydrogenation during corrosion

• Tin for the corrosion resistance by reducing the dependence on deleterious impurities

• Iron also for corrosion resistance by mitigating the dependence on the coolant temperature.

The results appear to be in-line with the expectations for these alloys, which can be considered as variants

of the composition: Zr—1% Nb—1% Sn-TM alloys. The multicomponent alloys, namely, E635 and Zirlo® are, respectively, used in the cores of VVER and PWR.36,37 Both show low corrosion and very limited irradiation growth. Irradiation growth refers to the dimensional changes at constant volume of an unstressed material under irradiation.38 The growth phenomenon is induced by the anisotropic clustering or disappearance of the point defects created by irradiation. The stability under irradiation of the precipitates present in these alloys appears to be the origin of such good dimensional stability (Chapter 4.01, Radiation Effects in Zirconium Alloys).3