As (U, Pu)N were some of the most promising candidates for the first breeder reactors, they are the best studied nitride solid solution fuels. UN and PuN form a continuous solid solution, and the lattice param­eter increases with an increase in the plutonium con­tent, and is accompanied by a large deviation from Vegard’s law, as shown in Figure 7,26 suggesting the nonideality of the solution. A diagram of the calculated U-Pu-N ternary phase at 1000 °C, shown in Figure 8,1 suggests that there is a relatively narrow range of pos­sible (U, Pu)N compositions, as is the case with U-N and Pu-N binary systems. It is suggested that the sesquinitride solid solution (U, Pu)N15 exists in a sys­tem in which PuN may constitute up to 15mol%27, although this is not depicted in Figure 8.

As uranium monocarbide and plutonium mono­carbide, as well as other actinide carbides, have an NaCl-type fcc structure, actinide nitrides and acti­nide carbides form solid solutions. Some research performed on actinide nitride carbides, for example, U-N-C, Pu-N-C,28-30 have investigated the suit­ability of these carbonitride fuels and the impurities in nitride fuels after carbothermic reduction. Phase

UN NpN

NpN PuN

Composition

stability graphs of U and/or Pu-N-C, both with and without oxygen, also have been constructed in order to make pure nitride fuels.31, 2 The irradiation behav­ior of (U and/or Pu)-N-C fuels also has been reported,33 but the details of this data are out of the scope of this chapter.

As MAs are usually burnt with uranium and plu­tonium for transmutation, and as Am originally exists in Pu, (MA, U)N or (MA, Pu)N have also been well studied. As mentioned above, the vaporization behav­ior of (Pu, Am)N has been studied34, and abnormal vaporization of Pu and Am was observed. The lattice parameters of (U, Np)N and (Np, Pu)N increase with increase in Np and Pu content, and with a small deviation from ideality, as shown in Figure 7.24 Although scarcely any data for pure CmN has been obtained, X-ray diffraction data for (Cm04Pu06)N has been reported, as shown in Figure 9.24

Inert matrix fuels, where MA as well as uranium and plutonium are embedded in a matrix, are also being considered for use in ADS for transmutation. Recent research in MAs has focused on using various nitride solid solutions and nitride mixtures as inert matrix fuels. For ADS targets, matrices have been designed and selected so as to avoid the formation of hot spots and to increase the thermal stability, especially in the case of Americium nitride. Con­sidering their chemical stability and thermal conduc­tivity, ZrN, YN, TiN, and AlN were chosen as candidates for the matrix.16,35 ZrN has an NaCl-type

0.48

0 0.2 0.4 0.6 0.8 1

PuN CmN

PUO2 Composition cmO2

Figure 9 Lattice parameter of (Pu, Cm)N and (Pu, Cm)O2. Reproduced from Minato, K.; etal. J. Nucl. Mater. 2003, 320, 18-24, with permission from Elsevier.

fcc structure with а = 4.580 A and has nearly the same thermal conductivity as UN, has a high melting point, good chemical stability in air, and a tolerable dissolu­tion rate in nitric acid. Recently, abundant data have been made available for ZrN-based inert matrix fuels. It is planned that (Pu, Zr)N, with about 20-25% Pu, will be used to burn Pu in a closed fuel cycle.36 The lattice parameter of (Pu, Zr)N decreases with an increase in the Zr content, and is between that of PuN and ZrN, in accordance with Vegard’s law.24 It has also been estimated, using a model, that (Pu, Zr)N with 20-40 mol% PuN, does not melt till up to 2773 K; this is based on experimental thermody­namic data which show that U0.9Zr0 8N does not melt till up to 3073 K.37 In the case of (Am, Zr)N, it is reported that two solid solutions are obtained when Am content is over 30%24, as shown in Figure 10. The Am content of the two phases have been estimated, from the lattice parameter, to be 14.5 and 43.1 mol%. A thermodynamic modeling of a uranium-free inert
matrix fuel, for example, (Am0.20Np0.04Pu0.26Zr0.60), has also been accomplished.38

In contrast to ZrN, TiN does not dissolve MA nitrides even though TiN also has an NaCl-type fcc structure. This is explained by the differences in lattice parameter, which was estimated by Benedict.39 A mixture of PuN and TiN was obtained by several heat treatments above 1673 K, and the product, in which one phase was formed, did not contain the other phase.40 TiN, as well as ZrN, have nonstoichio­metry. It is also reported that a TiN + PuN mixture may be hypostoichiometric although (Pu, Zr)N is hyperstoichiometric.

Vapor pressures of species in the Pu-C system were reviewed by Marcon,207 Holley et al.,4 and Matzke.5 The vapor phase in equilibrium with Pu carbides is always richer in plutonium than the condensed phase is. The partial pressure of Pu(g) dominates over other gaseous species, to the point that those are almost negligible in comparison. Therefore, any vaporization study on this system should take into account segrega­tion effects in the condensed phase, and it is impossible to treat the different Pu-C compounds separately. Marcon’s results,207 summarized in the following equa­tions, were obtained with longer measurement times in order to vent out oxygen impurities, leading to vapor pressures in equilibrium with pure carbides.

18 800
T

in the Pu-PuC and PuC-Pu2C3 domain, from room

temperature to the melting point

20200 r n log pPu = — + 4.23 [49]

in the Pu2C3-C domain, between 1500 and 2000 K; 25200

log pPu = — T + 6.8 [50]

in the Pu2C3-PuC2 domain, between 2000 and 2300 K;

, 18 150 r n

log pPu =— — + 3.15 [51]

in the PuC2-C domain, between 2000 and 2500 K.

Pu(g) partial pressure over Pu-C system is higher than U(g) pressure over U-C system in the same
temperature and composition ranges (Figure 16). The partial pressure pC1of C(g) is much higher than the partial pressures of other carbon-bearing species, which can be neglected in comparison to it. In Figure 16, the partial pressure values in equilibrium with PuC(liq) were extrapolated from those in equi­librium with PuC(s) including a correction for the enthalpy of melting.

The phase relation between actinide and Group IIIA metals depends upon the characteristics of the actinide metals. Table 3 summarizes the phase rela­tions for the Th-related system, which can be divided into five groups. The first group consists of the Th-Sc, Th-Y, Th-Gd, Th-Tb, and Th-Dy systems. The mutual solubility of these systems is very

Pu

good.41-43’47 These Group Ilia metals have two allo — tropes: the low-temperature a-phase (HCP struc­ture) and the high-temperature р-phase (bcc structure). On the other hand, Th has the low — temperature a-phase (fcc structure) and the high-temperature р-phase (bcc structure). The р-phase in these systems is completely soluble as well as the liquid phase. The low-temperature a-phases have a large region of mutual solid solubil­ity, although the crystal structure is different from each other. Regarding the solubility of Th in the a-phase of Sc, Y, Gd, Tb, and Dy, a systematic unlikely tendency is seen in Table 3, which possibly originates from the differences in the method of sample preparation. Figure 7 indicates the Th-Sc phase diagram as a typical example of this group quoted from Okamoto.4 The shape of the phase boundaries suggest that these systems can be mod­eled as a simple regular solution. The second group consists of the Th-La and Th-Ce systems, for which the experimental data were mainly given by Badayeva and Kuznetsova43 and Moffatt.44 Since the low — temperature phase (fcc structure) appears for La and Ce, a complete solubility even for the low — temperature fcc phase as well as the bcc and liquid phases was indicated in these previous studies. Figure 8 shows the Th-La phase diagram as a typical example shown in Kassner and Peterson.1 As for the Th-Ce system, a similar phase diagram was originally proposed by Moffatt.44 According to Okamoto and Massalski,49 however, the shape of the phase bound­aries in the Th-La system is thermodynamically
unlikely (abrupt change in phase boundary between the bcc and fcc phases shown in Figure 8). Also, the recent assessment for the Th-Ce system4 suggests that the separation of the high-temperature bcc-phase region is more likely. These conflicts are due to the difficulty in sample preparation for these systems, and further studies are necessary. The third group consists of the Th-Pr, Th-Nd, Th-Pm, and Th-Sm systems, for which the available data were reported by Moffatt,4 Badayava and Kuznetsova,4 and Norman et a/.46 The low-temperature solid phase structure for these lanthanides is DHCP instead of HCP or fcc. The liquid and bcc phases are completely soluble. The solubility of Pr, Nd, Pm, and Sm in the a-Th phase (fcc) is very large and estimated to be higher than that of the other Group IIIA metals. Figure 9 shows the Th-Pr phase diagram as a typical example quoted from Okamoto.4 The shape of the phase boundaries suggests that these systems can also be explained by the simple regular solution model. The fourth group consists of the Th-Eu and Th-Yb systems. Since Eu and Yb behave as divalent metals, these systems are predicted to be fairly immiscible even for the liquid phase, as shown in Figure 10. The fifth group consists of the Th-Ho, Th-Er, Th-Tm, and Th-Lu systems. Although these lanthanides do not have the bcc allo — trope in the unary system, the wide solid solubility for the bcc phase is seen in these systems. Figure 11 shows the Th-Er phase diagram as a typical example quoted from Okamoto.4 On observing carefully the shape of the liquidus and solidus for the Th-Group IIIa metal system, we can predict a slight positive interaction for the high-temperature solid phase (bcc) in the relation between Th and Sc, Y, or La to Sm; on the other hand, a slight negative interaction between Th and Gd to Ho, and mostly an ideal interaction between Th and Er, Tm, and Lu, can be predicted by assuming that the liquid phase behaves as an ideal solution.

Regarding the U-Group IIIa metal systems, the U-Sc phase diagram is the only exception in which several percent of mutual solid solubility and the com­plete liquid solubility were observed by Holcombe and Chapman50 and Terekhov and Sinyakova.51 Figure 12 shows the U-Sc phase diagram quoted from Okamoto.4 The unique features of the U-Sc system are a miscibility gap for the liquid phase and a steep temperature variation on the phase boundary between the a-Sc and р-Sc phases near the Sc terminal. The latter feature needs further confirmation because it is thermodynamically

Element Th Sc Y La Ce Pr Nd Pma Sm Allotrope a-Th (fcc) a-Sc (HCP) a-Y (HCP) b-La (fcc) g-Ce (fcc) a-Pr (DHCP) a-Nd (DHCP) a-Pm (DHCP) b-Sm (DHCP) b-Th (bcc) b-Sc (bcc) b-Y (bcc) g-La (bcc) S-Ce (bcc) b-Pr (bcc) b-Nd (bcc) b-Pm (bcc) g-Sm (bcc) System — Th-Sc Th-Y Th-La Th-Ce Th-Pr Th-Nd Th-Pm Th-Sm Maximum solid — ~20at.%Th ~30at.%Th Completely Completely ~18at.%Th ~18at.%Th ~18at.%Th ~20at.%Th solubility between in Sc ~60 in Y ~50 soluble soluble in Pr ~80 in Nd ~80 in Pm ~80 in Sm ~60 low-temperature at.% Sc at.%Y in Th at.%Pr at.% Nd at.% Pm at.% Sm phases in Th in Th in Th in Th in Th Maximum solid — Completely Completely Completely Completely Completely Completely Completely Completely solubility between soluble soluble soluble soluble or soluble soluble soluble soluble bcc phases miscibility gap References 41 42 43 44 45 45 44 44 4 46 Element Eu Gd Tb Dy Ho Er Tm Yb Lu Allotrope — a-Gd (HCP) a-Tb (HCP) a-Dy (HCP) a-Ho (HCP) a-Er (HCP) a-Tm (HCP) b-Yb (fcc) a-Lu (HCP) a-Eu (bcc) b-Gd (bcc) b-Tb (bcc) b-Dy (bcc) — — — g-Yb (bcc) — System Th-Eu Th-Gd Th-Tb Th-Dy Th-Ho Th-Er Th-Tm Th-Yb Th-Lu Maximum solid Immiscible ~13at.%Th ~24at.%Th ~10at.%Th ~20at.%Th ~8at.%Th in ~10at.%Th Immiscible ~25at.%Th solubility between in Gd ~60 in Tb in Dy in Ho Er ~55at. in Tm in Lu ~40 at. low-temperature at.% Gd ~60at.% ~57 at.% ~60at.% % ErinTh ~55at.% % LuinTh phases in Th Tb in Th Dy in Th Ho in Th Tm in Th Maximum solid Immiscible Completely Completely Completely ~99at.% Ho ~99at.% Er ~20at.%Th Immiscible ~6at.%Th in solubility between soluble soluble soluble in Th in Th in Tm Lu ~90at.% bcc phases ~63at.% Tm in Th Lu in Th References 43 43 47 43 47 47 44 43 48 43 aPhase relation for the Th-Pm system is estimated from the Th-Pr and Th-Nd systems.

90 100
1600 1541°C
1755 °C
1360 °C
800
600
400
200
0 Eu	30 40 50 60 70 80 90 100 Atomic percent thorium Th
10 20
0 10 20 Sc	100 Th
80	90
Figure 10 Th-Eu phase diagram taken from Okamoto.4
Figure 7 Th-Sc phase diagram taken from Okamoto.4
Weight percent thorium 0 10 20 30 40 50 60 70 80 90 100 Figure 11 Th-Er phase diagram taken from Okamoto.4
Weight percent thorium 0 10 20 30 40 50 60 70 80 90 100 Figure 8 Th-La phase diagram taken from Okamoto.4
Weight percent uranium 0102030 40 50 60 70 80 90
Weight percent thorium 0 10 20 30 40 50 60 70 80 90 100 Figure 9 Th-Pr phase diagram taken from Okamoto.4
100
135 °C
Figure 12 U-Sc phase diagram taken from Okamoto.

unlikely.19’49 In the other U-Group IIIa metal sys­tems, an extremely limited solubility was observed even for the liquid phase. Table 4 summarizes the solubility data for the liquid phase. Generally, it may
be said that the mutual solubility between U and light lanthanides is a little larger than that between U and heavy lanthanides. As for the solid solubility, the solubility of Gd and Ho in a-U was reported to

be <0.08 and <0.2 at.%, respectively.56 Figure 13 shows the U-Ce phase diagram calculated in the present work by assuming a regular solution model for each phase. The interaction parameter is estimated to be 53 kJ mol~ by fitting the mutual solubility data.52 This preliminary estimation is prac­tically useful not only to predict the phase diagrams but also to evaluate the safe performance of metallic nuclear fuels.

As for the Np-Group Ilia metal systems, the phase relation of the Np-La, Np-Nd, and Np-Lu systems was already studied by thermal analysis.57 The melting points or the transformation tempera­tures are depressed by several degrees compared to those of the pure elements. This suggests that there is no intermetallic compound and only a small percentage of mutual solubility in these systems. Figure 14 shows the Np-La phase diagram calcu­lated in the present study by assuming a regular solution model for each phase. When the estimated interaction parameters for the liquid and bcc phases are ^42 and 52kJmol_1, respectively, the depres­sions for the melting points of Np and La, which are of the order of 4 K, and those for the transforma­tion temperature between p-La and g-La, which are of the order of 13 K, are in good agreement with the experimental observations. Considering the system­atic variation, the phase relation between Np and Y, Ce, Pr, Pm, Sm, Gd, Tb, Dy, Ho, Er, or Tm is expected to be similar to that of the Np-La system. Better miscibility is expected for the Np-Sc system from the comparison to the U-Sc system.

500

Table 5 summarizes the solubility data for the Pu-Group Ilia metal systems. The systematic varia­tion in the Pu-related system is mostly similar to that in the Th-related system, with some exceptions. As for the first group, the shape of the previously reported Pu-Sc phase diagram44 is different from that of the Pu-Y, Pu-Gd, Pu-Tb, and Pu-Dy phase diagrams.44,58,62,64 There are several similarities between the Pu-Sc and Th-Sc systems, such as the complete solubility for the liquid and bcc phases, several tens of percent of solubility even for
the low-temperature solid phase, etc. However, an intermediate Z-phase appears in the Pu-Sc phase diagram, which suggests some degree of stabilization for the mixing between Pu and Sc in the low — temperature region. On observing the phase bound­ary between the liquid and bcc phases, on the other hand, we can conclude that these phases obey the simple regular solution model. Due to this conflict, the previously reported Pu-Sc phase diagram could not be modeled with a reasonable set of thermody­namic functions.65 This indicated that some of the phase boundaries need substantial modifications.1 Regarding the P-Y system, the shape of the phase boundary near the Y terminal is different from that for Gd, Tb, and Dy. Avery thin monophase region for p-Y appears and steeply depresses with increasing Pu Concentration in the previously reported Pu-Y phase diagram.58 This feature is thermodynamically unlikely. The phase relations for the Pu-La system are quite similar to those for the Pu-Gd, Pu-Tb, and Pu-Dy systems. Figure 15 shows the Pu-La phase diagram as a typical example for this group, which is quoted from Okamoto.4 The phase diagram was orig­inally reported in Ellinger et al.59 It appears from the phase diagram that there are miscibility gaps for the liquid phase and large regions of solid solubility of Pu in the p-La (fcc) and g-La (bcc) phases (^20 at.% at the maximum). The solid solubility of La in 8-Pu (fcc) is negligibly small, and that in e-Pu (bcc) is estimated to be about 1 at.%. As for the third group, the Pu-Pr, Pu-Nd, Pu-Pm, and Pu-Sm systems have similar features,44,62,61 as well as the Th-related sys­tem. Figure 16 shows the Pu-Nd phase diagram as a typical example, quoted from Okamoto.4 The phase relations shown in the Pu-Nd system are quite similar to those in the Pu-La system, with a few exceptions. Although the crystal structures for the low-temperature solid phase are different from each other, the shape of the phase boundaries around a-La and a-Nd are quite similar. A few per­cent of solid solubility in the 8-Pu phase (fcc) was observed not in the Pu-La system but in the Pu-Nd system, although pure La does take the fcc allo — trope whereas Nd does not. Regarding the heavy lanthanides beyond Ho as well as Y, such as the Pu-Ho, Pu-Er, Pu-Tm, and Pu-Lu systems, the mis­cibility gap for the liquid phase is expected to disap — pear.44,64 Figure 17 shows the Pu-Er phase diagram as a typical example quoted from Okamoto.4 How­ever, the experimental information is limited and confirmation is necessary, for instance, by thermal arrest measurement for the high-temperature region.

Element Pu Sca yb La Ce Pr Nd Pmc Sm Allotrope S-Pu (fcc) a-Sc (HCP) a-Y (HCP) p-La (fcc) g-Ce (fcc) a-Pr (DHCP) a-Nd (DHCP) a-Pm (DHCP) p-Sm (DHCP) £-Pu (bcc) p-Sc (bcc) p-Y (bcc) g-La (bcc) S-Ce (bcc) p-Pr (bcc) p-Nd (bcc) p-Pm (bcc) g-Sm (bcc) System — Pu-Sc Pu-Y Pu-La Pu-Ce Pu-Pr Pu-Nd Pu-Pm Pu-Sm Maximum solid — ~48at.% Pu ~15at.%Pu ~19at.% Pu ~34at.% Pu ~29at.% Pu ~27 at.% Pu ~28at.% Pu ~29at.% Pu solubility between in Sc in Y ~0at. in La ~0at. in Ce in Pr ~2 at. in Nd ~2 at. in Pm ~2 at. in Sm ~2 at. low-temperature ~22at. % Y in Pu % La in Pu ~24at. % Pr in Pu % Nd in Pu % Pm in Pu % Sm in Pu phases % Sc in Th % Ce in Pu Maximum solid — Completely ~17at.%Pu ~20at.%Pu ~18at.% Pu ~30at.% Pu ~33at.% Pu ~35at.% Pu ~33at.% Pu solubility between soluble in Y ~0at. in La ~1 at. in Ce in Pr ~2 at. in Nd ~2 at. in Pm ~2at. in Sm ~2 at. bcc phases % Y in Pu % La in Pu ~15at. % Pr in Pu % Nd in Pu % Pm in Pu % Sm in Pu % Ce in Pu References 44 58 59 60 61 61 44 61 Element Eu Gd Tb Dy Ho Er Tm 62 Yb Lu Allotrope — a-Gd (HCP) a-Tb (HCP) a-Dy (HCP) a-Ho (HCP) a-Er (HCP) a-Tm (HCP) p-Yb (fcc) a-Lu (HCP) a-Eu (bcc) p-Gd (bcc) p-Tb (bcc) p-Dy (bcc) — — — g-Yb (bcc) — System Pu-Eu Th-Gd Th-Tb Th-Dy Th-Ho Th-Er Th-Tm Th-Yb Th-Lu Maximum solid Immiscible ~28at.% Pu ~28at.%Pu ~28at.%Pu ~28at.% Pu ~20at.% Pu ~20at.% Pu Immiscible ~20at.% Pu solubility between in Gd ~0at. in Tb ~0at. in Dy ~0at. in Ho ~0at. in Er ~0at. in Tm ~0at. in Lu ~0 at. low-temperature % Gd in Pu % Tb in Pu % Dy in Pu % Ho in Pu % Er in Pu %Tm in Pu % Lu in Pu phases Maximum solid Immiscible ~30at.% Pu ~30at.%Pu ~30at.%Pu ~0at.% Pu in ~0at.% Pu ~0at.% Pu in Immiscible ~0at.% Pu in solubility between in Gd ~2 at. in Tb ~2at. in Dy ~2 at. Ho ~2 at. in Er ~2at. Tm ~2at. Lu ~2at. bcc phases %Gd in Pu % Tb in Pu % Dy in Pu % Ho in Pu % Er in Pu %Tm in Pu % Lu in Pu References 63 44 44 44 44 44 44 44 44 64 64 62 64 64 64 64 64 aPhase relation for the Pu-Sc system need substantial modification.65 bPhase boundary of p-Y in the Pu-Y system shows thermodynamically unlikely feature. cPhase relation for the Pu-Pm system is estimated from the Pu-Pr and Pu-Nd systems.

Weight percent plutonium 0 10 20 30 40 50 60 70 80 90 100 Figure 15 Pu-La phase diagram taken from Okamoto.4
Figure 18 Calculated Pu-Ce phase diagram, and experimental data taken from Selle and Etter.60 Data from Shirasu, N.; Kurata, M. Private communication.
Weight percent plutonium 60 70
Table 6 Calculated interaction parameters for the Pu-Ce system GO(Pu, liq), GO(Pu, bcc), GO(Pu, fcc): given in Dinsdale67 GO(Ce, liq), GO(Ce, bcc), GO(Ce, fcc): given in Dinsdale67 GO(U, HCP) = 5000 + GO(U, a-U) GO(Zr, b-U), GO(Zr, a-U) = 5000 + GO(Zr, HCP) GO(S-UZr2) = -13394 + 21.484T Gex(Ce-Pu, liq) = xPu(1 — xPu) (15080 + 0.2T-1000 (XCe — Xpu)) Gex(Ce-Pu, bcc) = xPu(1 — xPu) (16483 — 1595(xCe-xPu)) Gex(Ce-Pu, fcc) = xPu(1 — xPu) (10076 + 6.0T + (5745 — 7.744T) (xCe — xPu))
Figure 16 Pu-Nd phase diagram taken from Okamoto.4
Weight percent plutonium 10 20 30 40 50 60 70 80
90	Source: Shirasu, N.; Kurata, M. Private communication. Note: other allotropes for Pu are neglected.
	100
system shows a unique feature near the Pu termi­nal.60 The solid solubility of Ce in 8-Pu (fcc struc­ture) is far larger compared to the other lanthanides and attains 24 at.% at the maximum. Also, the 8-Pu region is enlarged at lower temperature. This feature is observed in the Pu-Al or Pu-Ga system. Although La also has a p-La phase with fcc structure, this stabilization of 8-Pu phase was observed only in the Pu-Ce system among the Pu-lanthanide systems. Figure 18 indicates the Pu-Ce phase diagram calcu­lated by the CALPHAD approach,66 in which only the liquid, bcc, and fcc phases were modeled and other phases were omitted. Experimental data points, however, fit reasonably well with the calculated values when using the assessed interaction para­meters indicated in Table 6.
In the Pu-Eu and Pu-Yb systems, the mutual solu­bility is considered to be very low. The solid solubility of Pu in Eu was reported to be 0.74 at.%, and vice versa <0.02 at.%.63 The phase relation in the Pu-Ce

Regarding the Am-Group Ilia metal systems, wide regions for the solid solubility were expected from the experimental observation by Kurata,68 in which the phase relation of an annealed alloy con­taining U, Pu, Zr, Np, Am, Y, Ce, Nd, and Gd was studied by scanning electron microscopy/wavelength dispersive X-ray (SEM/WDX). Two and three phases were observed in the samples annealed at 973 and 773 K, respectively. These phases were identified: (1) A bcc phase rich in U, Pu, Zr, and Np and (2) a rare-earth phase rich in Pu, Am, Y, Ce, Nd, and Gd were detected in the samples annealed at 973 K; and (3) the Z — and (4) 8-phases rich in U, Pu, Zr, and Np and (5) the rare-earth phase rich in Pu, Am, Y, Ce, Nd, and Gd were detected in the samples annealed at 773 K. The Pu and Am con­centrations in those rare-earth phases were roughly 8 and 30 at.%, respectively, at both temperatures. The Pu concentration agrees reasonably well with the phase diagrams described earlier. Perhaps the Cm- related system systematically has features similar to those of Am.

2.08.2.2.1 Chemical compositions, physical properties, and mechanical properties

The chemical compositions of typical nickel — chromium-iron and nickel-chromium-iron — molybdenum alloys are shown in Table 3, together with those of other nickel-based alloys.

As described earlier, nickel is a very versatile corrosion-resistant metal. The addition of chromium confers resistance to sulfur compounds and also pro­vides resistance to oxidizing conditions at high tem­peratures or in corrosive solutions, with the exceptions of nitric acid and chloride solutions. In addition, chromium confers resistance to oxidation and sulfidation at high temperatures.

Alloy 600 consists of about 76% nickel, 15% chromium, and 8% iron. The alloy is not precipitation- hardenable and can only be hardened and strengthened by cold-working. It has excellent resistance to hot halogen gases and has been used in processes involv­ing chlorination. It has excellent resistance to oxida­tion and chloride SCC. It is widely applied as a structural material in many industrial fields owing to its strength and corrosion resistance.10

The thermal expansion coefficient of Alloy 600 is smaller than those of austenitic stainless steels and somewhat larger than those of ferritic steels, as shown in Table 7. It is also highly resistant to sensitization in heat-affected zones during welding. The alloy and its weld metals such as Alloys 82, 132, and 182 have there­fore been widely used for dissimilar metal weld joints to reduce residual stresses and strains after welding.

Alloy 601 has a higher chromium content (about 23%) than Alloy 600 and about 1.4% aluminum. The alloy is resistant to high-temperature oxidation and has good resistance to aqueous corrosion. Oxidation resistance is further enhanced by its aluminum con­tent. The alloy has been applied to the muffles of heat-treatment furnaces and in catalytic convertors for exhaust gases in automobiles.11

Alloy X-750 contains titanium, aluminum, and niobium, and is hardened by precipitation of the g0 phase as Ni3(Ti, Al, Nb).12 Alloy 718, on the other hand, contains niobium, molybdenum, titanium, and aluminum, and is hardened by the precipitation of both the g0 phase as Ni3(Ti, Al, Nb) and the g00 phase as Ni3Nb.13 These alloys were developed as high creep-strength and high creep-rupture-strength materials for jet-engine blades and vanes in the 1940s. These precipitation-hardened materials have also been used in industrial gas-turbine materials. In addition, Alloy X-750 has been used as a bolting material and Alloy 718 has been applied to bellows, springs, etc. for industrial products.

Alloy 690 (UNS N06690) was developed in the late 1960s and has a higher chromium content (about 30%) than Alloys 600 and 601. It exhibits excellent resistance to many corrosive aqueous media and high-temperature atmospheres. The properties of Alloy 690 are useful in a range of applications involv­ing nitric or nitric/hydrofluoric acid production, and as heating coils and tanks for nitric/hydrofluoric solutions used in the pickling of stainless steels, for

14

example.

Alloy 800 (UNS N08800) is an iron-based nickel — chromium alloy. This alloy has been compared to Alloys 600 and 690 from the view point of its corrosion resistance in many environments. It was introduced for industrial use in the 1950s as an oxidation-resistant alloy and for high-temperature applications requiring optimum creep and creep — rupture properties. Alloy 800 has been widely used as an oxidation-resistant material and is suitable for high-temperature applications due to its high resis­tance to а-phase embrittlement after heating in the range of 650-870 °C.15

Alloy 825 (UNS N08825) was developed from alloy 800 by the addition of molybdenum (about 3%), copper (about 2%), and titanium (about 0.9%) for improved aqueous corrosion resistance in a wide vari­ety of corrosive media. In this alloy, the nickel content confers resistance to chloride-ion SCC. Nickel in con­junction with molybdenum and copper gives outstand­ing resistance to reducing environments such as those containing sulfuric and phosphoric acids. Molybde­num also enhances its resistance to pitting and crevice corrosion. In both reducing and oxidizing environ­ments, the alloy resists general corrosion, pitting, crev­ice corrosion, intergranular (IG) corrosion, and SCC. Some typical applications include various components used in sulfuric acid pickling of steel and copper, com­ponents in petroleum refineries and petrochemical

<i CO <i oJ <i CO CO <i CO <i Ц1) CO <i CO <i CO <i —

plants (tanks, valves, pumps, agitators), equipment used in the production of ammonium sulfate, pollution con­trol equipment, oil and gas recovery, and acid production.

Alloy A-286 (UNS S66286) is an iron-based nickel-chromium alloy with added molybdenum

and titanium. The alloy is age-hardenable to achieve superior mechanical properties. It maintains good strength and oxidation resistance at temperatures up to about 700 °C.16

The mechanical and physical properties of typical nickel-chromium-iron and nickel-chromium-iron — molybdenum alloys are shown in Tables 4 and 5, respectively, together with those of other nickel — based alloys.

The lattice parameters of actinide oxides are usually measured in glove boxes because of radioactivity and chemical hazards. In fact, the radioactive decay may drastically modify the cell parameters with

characteristic time of months (see measurements on (Pu, Am)O2 by Jankowiak et a/.,62 on CmO2 in the review by Konings,43 and on sesquioxides by Baybarz et a/.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 a/.64 on UO2 and PuO2, and by Uchida et a/.65 on AmO2). The method is slightly different when ab initio calculations are performed (see, e. g., the work of Minamoto et a/.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).

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 2. They are

In fact, the recommended values77 for UO2 are as follows:

For 273K < T < 923K: a(T) = a273(9.9 7 3 x 10-1 + 9.082 x 10-6T — 2.705 x 10-10T2 + 4.391 x 10-13T3) [4]

For 923K < T < 3120K: a(T)

= a273(9.96 72 x 10-1 + 1.179 x 10-5T — 2.429 x 10-9T2 + 1.219 x 10-12T3) [5]

indeed (almost) linearly dependent upon the ionic radius of the actinide cations (see Figure 11). It is noteworthy that the cell parameters reported may be significantly affected by self-irradiation, as men­tioned, for example, in CmO2 by Konings43 based on measurements by Mosley.70

A first review of the linear thermal expansion of stoichiometric actinide dioxides has been done by Fahey et al.75 in the 1970s. This has been updated by Taylor76 in the 1980s and later by Yamashita etal.71 and Konings43 in the 1990s. In the simple case of cubic crystals (such as actinide dioxides; see below), the evolution of the cell parameter as a function of temperature is fitted using a polynomial expression up to the third (sometimes fourth) degree as follows:

a(T)=b0 + hT + Ьг T2 + b3 T3 [3]

Selected values ofthe parameters obtained are shown in Table 2. Overall, the values reported for the b1 parameters are of the same order of magnitude.

Sobolev and coworkers67-69 recently proposed an alternative approach for determining the thermal expansion of actinide dioxides from experimental data. It is based on the evaluation (from experiments) of the specific heat CV from the phonon spectra at the expense of some approximations. The thermal expan­sion aP is then deduced using the following relation:

Ус Cv (V, T) Bt (V, T)V

The thermal expansion coefficient aP depends upon the bulk modulus BT, the heat capacity CV and the Griineisen parameter gG. The results obtained by Sobolev (see figures in Sobolev and coworkers67-69) reproduce quite well the available experimental data and allow the extrapolation to temperatures higher than the measurements.

Carbides are chemical compounds in which carbon bonds with less electronegative elements. Depending on the difference in electronegativity and the valence state of the constituting elements, they exist as differ­ent bonding types. Accordingly, they are classified as salt-like compounds (in which carbon is present as a pure anion and the other elements are sufficiently electropositive), covalent compounds (SiC and B4C), interstitial compounds (with transition metals of the groups 4, 5, and 6 except chromium), and ‘intermedi­ate’ transition metal carbides.14

In general, carbides display metallic properties, and they are mostly refractory (high melting). Their more specific properties depend on the constituting elements.

2.04.1.1 General Properties of Actinide Carbides

Actinides are known to form three main types of stoichiometric carbides (Table 1): monocarbides of the type AnC, sesquicarbides of the type An2C3,

and dicarbides of the type AnC2 (sometimes called ‘acetylides’). Mono — and dicarbides have been observed for protactinium, thorium, uranium, neptunium, and plutonium. Sesquicarbides have been identified for thorium, uranium, neptunium, plutonium, ameri­cium, and, recently, curium.

Other types of actinide carbides such as CmC3 and Pu3C2 have been observed.

Data for mixed U-Th and U-Pu carbides, briefly summarized and discussed in the last section of this chapter, have mostly been indigenously collected from the few nuclear plants using this kind of fuel.15

2.04.1.2.1 Structure of the matter

In general, actinide carbides are of the ‘salt-like’ type. In these compounds, carbon is present as single anions, ‘C4-’ in the monocarbides; as two atom
units, ‘C2_’ in the acetylides; and as three atom units,‘C3 in the sesquicarbides. This model, useful for a first visual description of these materials, is physically inconsistent with their essentially metallic properties. The An-C bonds are certainly more cova­lent than ionic, as recently confirmed.16 Actinide compounds are characterized by a peculiar elec­tronic structure, where the extended nature of the 5f electron wave functions yields a unique interplay between localized and band electrons. This feature leads, in particular, to properties associated with covalent bonding in these compounds, which show crystal structures normally associated with ionic bonding.5

Monocarbides AnC1±x (An = Th, Pa, U, Np, Pu, Am) crystallize in the NaCl-type space group Fm3m — No. 225 (Table 1). The elementary cell is

Table 1 Synopsis of the known actinide carbides

Compound and lattice Composition and Space group Structure

parameters temperature range ^ — Actinide; ® — C

Other actinide carbides with little information: PaC2, NpC2, probably isostructural to CaC2, Pu3C2, stable between 300 and 800 K, but unknown structure; Cm3C with fcc Fe4N-like lattice with a = 517.2 ± 0.2 pm.

represented by four formula units. The lattice param­eter is dependent on the C/An ratio, and the oxygen and nitrogen impurities. The lattice parameter of pure monocarbides increases with the dissolution of carbon in the ideal face-centered cubic (fcc) lattice in an essentially linear manner.

The sesquicarbides of Th, U, Np, Pu, Am, and Cm have been identified to be body-centered cubic (bcc) of the 143d type, with eight molecules per unit cell
(Table 1). This structure is more complex than that of the mono — and dicarbides, and is often difficult to form. Thus, Th2C3 was observed only under high pressure (2.8—3.5 GPa), and U2C3 is produced by a complex preparation procedure. Both decompose into a mixture of mono — and dicarbides at high tem­peratures. The situation is different in the case of Pu2C3, which is the most stable among the Pu car­bides and forms easily at temperatures ranging from

room temperature to the melting point. Unlike the fcc modifications of mono — and dicarbides, sesquicar — bides can hardly accommodate lattice defects; there­fore, they essentially exist as line compounds.

Actinide dicarbides AnC2_x have been observed in a larger variety of allotropes (Table 1). At inter­mediate temperatures, generally between 1700 and 2050 K, Th, U, Pu, and probably, Pa and Np, form tetragonal dicarbides of the type CaC2 (I4mmm — Group 139). Th also forms a monoclinic C2/c (No. 15) substoichiometric dicarbide that is stable from room temperature to 1713 K. The high-temperature form of actinide dicarbides has been observed to be fcc of the type KCN, which belongs to the same symmetry group as NaCl, Fm 3m. Such structure, clearly estab­lished for g-ThC2, was observed with more difficulty by high-temperature X-ray diffraction (XRD) for p-UC2 and p-PuC2. The lattice transition between tetragonal and cubic fcc dicarbide (a! p for U and Pu, p! g for Th) is diffusionless of the martensitic type. It occurs very rapidly despite its important enthalpy change, mostly due to the lattice strain contribution. For this reason, the high-temperature cubic modification is impossible to quench to room temperature, hence the difficulty in investigating its properties. fcc allotropies of mono — and dicarbides are mostly miscible at high temperature, and for uranium and thorium, they can be considered as a single high-temperature cubic phase with a wide nonstoichiometry range. In fact, this solid solution can easily accommodate interstitial excess carbon atoms and lattice vacancies. The first ensure the existence of a broad hypostoichiometry range of the dicarbides, where most of the excess carbons form C2 dumbbells in the (^,0,0), (0,^,0), and (0,0,^) positions as in the KCN lattice (see Table 1). The second are responsible for the existence of hypostoichiometric monocarbides An1_x, extending to the pure metal for thorium but only to a narrow UC1_x domain for uranium. The situation is different for Pu carbides due to the high stability of Pu2C3 up to its melting point and to the fact that fcc plutonium monocarbide exists only in a vacancy-rich hypostoichiometric form, with 0.74 < C/Pu < 0.94. This originality, common to other Pu compounds, is certainly related to the pecu­liar behavior of the six 5f electrons of plutonium, which exhibit behavior on the limit between valence and conduction, and can follow one or the other (or both) in different compounds.

The electronic (band) structure of actinide car­bides has been studied rather extensively, both exper­imentally (by low-temperature calorimetry and X-ray
photoelectron spectroscopy, XPS) and theoretically (by tight-binding methods and, more recently, by density functional theory techniques). These com­pounds are, in general, good electronic and thermal conductors, with a nonzero density of electronic states at the Fermi level (Figure 1).

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

(c) Energy (eV) ef
which tend to be more localized or more itiner­ant according to the actinide and the compound involved. Thus, Pu carbides have much higher elec­trical resistivity than Th and U carbides. Similarly, mono — and dicarbides are better electronic conduc­tors than sesquicarbides are. Magnetic transitions have been observed at low temperatures in sesqui — carbides, and Np and Pu monocarbides.

The electronic structure dependence on defect and impurity concentrations has been studied in a number of cases. For example, in ThC1_x, the density of states (DOS) increases with increasing carbon vacancy concentration. Auskern and Aronson17 showed by thermoelectric power and Hall coefficient measurements that a two-band conductivity model can be applied for ThC1_x: the bands overlap more and the number of carriers increases with decreasing C/Th ratio. The valence bands have mainly a carbon 2p and a thorium 6dg character, while the Th-6de character dominates the conduction bands. Also, the increase of the DOS at the Fermi level with vacancy concentration is due to the 6d thorium electronic states. In stoichiometric ThC, the 6d Eg states are hybridized with the 2p states of carbon and are split between low-energy bonding and high-energy antibonding states. In hypostoichiometric ThC1_x, the 6d Eg dangling bonds contribute to an increase of the DOS in the vicinity of the Fermi level.18

For uranium carbides, it was shown that, following the general rules of Hill19 that imply that U—U dis­tance is <3.54 A, these compounds exhibit a metallic electronic structure due to the overlaps of f-orbitals. This rule applies to uranium monocarbide for which the U—U distance is 3.50 A, as shown by experimental measurements as well as by ab initio calculations.20, For hyperstoichiometric uranium carbides, the metal­lic character persists and the C—C bonds are covalent as in graphite. In an X-ray and ultraviolet photoelec­tron spectroscopy (XPS and UPS) study of sputtered UCx thin films (0 < x < 12), Eckle et a/.22 showed that the U-4f core levels do not change strongly with increasing carbon content, and demonstrated the pre­dominantly itinerant character of U-5f electrons. Similarly, valence region spectra show three types of carbon species for different UCx films, which are differentiated by their C-2p signals. A strong hybri­dization between C-2p and U-5f states is detected in UC, while the C-2p signal in UC2 appears only weakly hybridized, and for higher carbon contents, a p-band characteristic of graphite appears.

Calculated charge distribution maps for stoichio­metric fcc ThC and tetragonal p-ThC223 are shown in Figure 2, giving an idea of the covalent or ionic nature of the different bonds in these structures.

The analysis by Shein et a/.23 revealed that bonding in ThC2 polymorphs is of a mixed covalent-ionic-metallic character. That is, the cova­lent bonding is formed due to the hybridization effects of C-C states (for C2 dumbbells) and C2-Th states. In addition, ionic bonds emerge between the thorium atoms and C2 dumbbells owing to the charge transfer Th! C2, with about 1.95 electrons redistrib­uted between the Th atoms and C2 dumbbells. The metallic Th-Th bonds are formed by near-Fermi delocalized d and f states. Similar charge distributions have been calculated for uranium carbides.24

Dworkin50 measured the enthalpy increment of UF4 from room temperature up into the liquid phase. These results are in very good agreement with unpub­lished results obtained by Cordfunke and reported by Fuger37 (Figure 9).

Based on the results from both studies, the enthalpy is expressed as:

HT — H298(kJ mol-1) = -35.058 + 0.1145T + 10.27745 10-6T2 + 4.13159 10-3T-1 (298 — 1309 K) in solid state

HT — H298(kJmol-1) = -39.413 + 0.166Г

(1309 — 1400 K) in liquid state with T(K)

Dworkin deduced from his measurements the entropy and enthalpy of fusion at the fusion temperature

Tfus = 1309 K AfusH° = 46986 J mol 1 Af = 35.98 JK—1 mol-1

This enthalpy of fusion is higher than the approximate value calculated by Khripin5 from the differential ther­mal analysis in the UF3-UF4 binary system (AfusH0(UF4,s, 1309 K = 43 514 ± 2kJ mol-1).

The experimental data of Dworkin for the enthalpy of fusion has been recommended by Guillaumont et al. in their review, although the vapor pressure data for UF4(cr, l) are more consistent with a smaller value (36 kJ mol-1).39

2.06.3.2.3 Preparation

Two ways are industrially used to obtain UF4 from UO2 powder:

• the precipitation of UF4 in HF aqueous solution,

• the reaction of UO2 with gaseous HF at 573-773 K: UO2 + 4HF! UF4 + 2H2O.

As a consequence, the impurities in UF4 are usually oxygen based, such as UO2F2, UO2, or H2O.

The large density variation between the fluoride and the oxide tends to hinder the reaction because swelling occurs and the porosity is easily blocked dur­ing the conversion. The kinetics of hydrofluorination will then depend much on the specific surface of the

UO2. A model has been developed that takes into account the grain and pellet sizes.51 Impurities such as sodium can also be detrimental because they may favor the sintering. The NaF-UF4 eutectic melts close to 893 K.

UF4 can be obtained in a rotating furnace, in a fluidized bed, or in a moving bed reactor where the UO2 has been pelletized as described in Harrington and Ruenhle.33 If the hydrofluorination temperature is maintained below 750 K, the effect of sodium is light.

2.06.3.2.4 Uses

UF4 can be used to produce UF6 (see previous section) or U metal using magnesium reduction in a bomb:

2Mg + UF4 ! U + 2MgF2

In all cases, the oxygen residual level in UF4 will be very important. It will affect the conversion rate to U metal or UF6.

Mixtures of fluoride salts with UF4 are candidates as fuel carrier of molten salt reactors52 (see Chapter 3.13, Molten Salt Reactor Fuel and Coolant).

2.06.3.2 UFx (4 <X< 6) — Intermediate Fluorides

Pressure is expected to drive the atoms in the crystal lattice closer to each other, forcing the electrons to

~ 30 T_

О

20 E

10 0

participate in the binding (delocalization),6 which particularly affects the heavy actinides with loca­lized f-electron behavior at ambient pressure. Recent studies using diamond anvil cells coupled to synchrotron radiation have provided strong evi­dence for that. As discussed by Heathman et a/.,7 americium shows a remarkable decrease in volume with increasing pressure (at ambient temperature) with three transitions up to 100 GPa (Figure 3). Its structure changes from hcp (Am-I) through fcc (Am-II) to orthorhombic (Am-III and Am-IV), indi­cating the appearance of the itinerant character 5f electrons. This behavior is also observed in curium, with a puzzling supplementary magnetically stabi­lized Cm-III structure at 40-60 GPa.8 Uranium shows a comparatively straightforward behavior and the a-structure is stable up to 100 GPa, with a much smaller volume decrease.6 A similar behavior has been found for protactinium, its a-form being stable up to
80 GPa. This is clearly reflected in the isothermal bulk modulus (Table 2), which is around 100 GPa for the elements Pa to Np but around 30-40 GPa for Am and Cm. The Am-IV phase shows a large bulk modulus (more similar to that of uranium), as expected for a metal with appreciable 5f-electron character in its bonding. This is also evident from the comparison of the actinide and lanthanide metals (Figure 4).

Uncertainty still exists about the bulk modulus of a-plutonium. As discussed by Ledbetter et a/.,12 the published B0 values at ambient range show a large variation, as do the theoretical calculations. The most accurate results for the isothermal bulk modulus vary between 51(2) GPa13 and 43(2) GPa.14

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 law — type equation

D = D"exK_;w 1131

where D0 is the prefactor, Emig. is an effective migra­tion energy, kB is the Boltzmann constant, and Tis 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 ofthe 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 eta/.219 and Sabioni et a/.220). Thus, the reliability of the diffusion measurements is related to the control/measurement of the stoichiometry and microstructure.

Those experimental issues lead to a very large scatter of data (see, e. g., Sabioni et a/.,2 0 Belle and Berman,2 1 Sabioni et a/.22 ), and hence complemen­tary ab initio and MD calculations by Terentyev,80 Stan and Cristea,150 Stan,154 Andersson et a/.,168 Vincent-Aublant et a/.,2 9 and Kupryazhkin et a/.22 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 eta/.,2 , 2 Mendez eta/.,225 Korte eta/.,226 Sali eta/.,227 Arima eta/.,228 Ruello eta/.,229 Kato eta/.230 and Garcia eta/231 and references therein. In the following, we will limit ourselves to report some semiempirical equations in known cases.

Thermodynamic functions of uranium carbides have been extensively reviewed by Holley etal.4 and, more recently, by Chevalier and Fisher.10 Numerical data are reported in Tables 5 and 6 and plotted in Figures 14 and 15.

A few authors measured the heat capacity of UC from low to high temperature. Holley et al4 assessed
the temperature coefficient g of the electronic heat capacity (18.9 ± 1mJ K-2 mol — ), the Debye temper­ature 0D = 328 K, and the high-temperature behavior for 298 K < T< 2780 K.

Most ofthe U and Pu carbides show steep increase in heat capacities at temperatures above 0.6 T11, attributed to the formation of defects.4

The 0 K randomization entropy is zero for stoi­chiometric UC, but an additional term S(0) = Rxln x should be added for nonstoichiometric UC1+x compositions. The formation enthalpy of stoichio­metric UC was also assessed by Holley et al4 Its value is composition-dependent and slightly decreas­ing in the hypostoichiometric carbide, as suggested by the uranium vaporization study by Storms128 and the carbon activity measurements of Tetenbaum and Hunt.129 The UC room-temperature Gibbs energy of formation was calculated from the enthalpy and the standard entropy, and the value AfG (UC, s, 298) = -98.89 kJ mol-1 was proposed by Holley et al. for the reaction U + C = UC. The error affecting this value was estimated to be around 2.1 kJ mol-1 from the uncertainty in the U and C activities, strongly

Table 5 The heat capacity Cp of uranium carbides at atmospheric pressure (in J K 1 mol 1)

Compound T < 10K 10K < T < 300K T > 300K

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

T (K)

dependent on composition and oxygen impurities. Sheth et al.130 proposed DmH°= 48.9k. JmoP1 for the enthalpy of fusion and the following data for liquid UC up to 4800 K:

Cp(UC, liquid) =49.887 + 7.794

x 10~3T (JK^moP1) [8]

H°(T) — H°(298)(UC, liquid) = 51362 + 49887T + 3.987 x 10~3T2(Jmol1) [9]

The recently assessed and optimized Gibbs energy data gave excellent fit with both thermodynamic properties and phase diagram data. Therefore, Gibbs energies of formation of binary compounds of both

U—C and Pu-C systems can be calculated using Gibbs energy functions given by Chevalier and Fischer10 and Fischer,131 respectively. To recalculate the Gibbs energy of formation of the compounds here, the free energy of the pure elements, in their stable reference state at a given temperature, is subtracted from that of the compounds. The following expression can be retained for UC from 298.15 K to the melting point:

Af G°(UC)( Jmol-1) =-31465.6 — 499.228T

+ 64.7501 Tln(T) — 7984166/ T — 0.0144T2 [10]

This temperature dependence of AfG (UC) is shown in Figure 15 and compared with the ones of other ura­nium and plutonium binary carbides.

The partial pressures of the actinide species play an important role in the redistribution of actinides and the restructuring of fuel elements during burnup (Figure 16).

In the case of U-C system, gaseous UCn molecules with n = 1-6 have been detected by mass spectrome­try.8 The partial pressure equations of UC2(g), C1(g), C2(g), and C3(g) are derived from the Gibbs energies
of formation and the activities of uranium and car­bon.4,132-134 In the composition range, C/U = 0.92­1.10, the partial pressure of U(g) is almost equal to the total pressure, the next predominant species being C1(g). The following equations4 can be used to calcu­late the U sublimation enthalpy in single-phase regions on the complete U-C system at 2100 K: 2.34 exp(29x) + 1 exp(- 10(x — 1)) + 1

[11]

exp(40x)+1 — 192.56x + 58.6exp(-100(x — 0.86)2) [12]

x = C/U — 1. The partial pressure of uranium decreases with increasing C/U, showing a steep change in the UC1+x phase field. Correspondingly, the U enthalpy of vaporization increases with C/U up to 711.62 kJ mol-1 at C/U ~ 1.08. The congruent vaporiz­ing composition was recommended as UC1n at 2300 K and UC184 at 2100 K.101 At the melting point,

the sublimation enthalpy is AsubH(UC, 2780) = 661 kJ mol, and the vaporization enthalpy AvapH (UC, 2780) = 611 kJ mol-1. The UC total pressure at the melting point is 2.8 x 10-5 bar.8 Sheth and Leibowitz133 and Joseph eta/.135 calculated the high-temperature vapor pressures of different species over liquid regions of UC1+x and MC + M2C3 systems. Sheth and Leibowitz calculated their values from fusion enthal­pies and Gibbs energies of formation for condensed and vapor species, whereas Joseph et a/. used a semi­empirical method based on the Principles of Corresponding States (PCS).135 They calculated the critical parameters of the compounds and the total vapor pressure over the liquid up to ~9000 K. Interest­ingly, the partial pressures of metal species dominate the vapor phase at low temperatures, but at very high temperatures, T> 4000 K, the partial pressures of carbon-bearing species prevail. Finn eta/.136 provided the following expression to estimate the total pressure (in bar) above liquid UC between 2800 and 10 000 K:

31704

log p = 6.110 — t + 0.197logT [13]

Ohse et a/.137 obtained the boiling point of UC by extrapolation of the vapor pressure curve to 4700 K. Gigli eta/.138 calculated the isotherms and isochores in the pressure-internal energy coordinates between 5200 and 13 600 K, proposing the following critical quantities: Tc = 8990K; pc = 1580bar; pc = 1.3159g cm-3. Thermal expansion of crystalline UC results from the lattice expansion and, at very high tempera­tures, the generation of Schottky defects.8 The follow­ing expression for the linear thermal expansion coefficient aT = /—1(d//dT) (/0 = sample length at 298 K) is a slight modification of an earlier one,139 which underestimated the values measured by Richards at 2773 K140:

aT = 10.08 x 10-6 + 5.802 x 10-9

(T — 273.16)(T inK) [14]

It can be useful to note that, as UC displays a higher thermal conductivity than does U2C3, there can be internal stresses for a two-phase mixture of UC + U2C3. This factor should be taken into account in multiphased samples.