2.02.4.1 Binary Stoichiometric Compounds

The thermodynamic data on the actinide oxides are based on the critical reviews by Konings eta/.36,38 and are generally in good agreement with the CODATA Key values12 and with the NEA reviews.12 The thermodynamic properties of the binary thorium, uranium, neptunium, and plutonium oxides are well established from experimental data. For the other actinide oxides, some experimental data are missing, and some values were estimated using the analogy with the lanthanide oxides by Konings eta/.36,38

2.02.4.1.1 Actinide dioxides

2.02.4.1.1.1 Standard enthalpy of formation and entropy

For the actinide dioxides, the enthalpy data in Table 9 are well established for ThO2, UO2, NpO2, PuO2, AmO2, and CmO2 from measurements. On the con­trary, the enthalpy of formation of PaO2, BkO2, and CfO2 was never measured. For these compounds, the values were estimated from the reaction enthalpy of the idealized dissolution reaction [AnO2(c) + 4H+(aq) ! An4+(aq) + 2H2O(l)] that is assumed to vary regularly in the actinide series as the enthalpy of dissolution of the dioxides [AfH(AnO2) _ AfH(An4+)] is a function of ionic size.

The standard entropies in Table 9 were deduced from heat capacity measurements for the solid diox­ides from ThO2 to PuO2. For the other oxides, the data were estimated by Konings.43,123 For AmO2 and CmO2, the entropy was modeled as the sum of a lattice term due to the lattice vibrations and an excess component arising from f-electron excitation: S = Slat + Sexc. Slat term was assumed to be the value for ThO2, and Sexc was calculated from the crystal field energies of the compounds by Krupa and cow — orkers.124,125 A similar method was applied to esti­mate the entropies of PaO2, BkO2, CfO2, and EsO2. In absence of crystal field data, the excess term was calculated from the degeneracy of the unsplit ground state, which probably overestimates the entropy.

As shown in Table 9, the stability of the dioxides decreases with the atomic number Z. This is consis­tent with the fact that the melting points of the dioxides decrease from ThO2 to CmO2. This can explain that the heavier tetravalent dioxides are dif­ficult to prepare. Another difficulty comes from the production of daughter products leading to an increasing contamination of the oxides with time. Finally, the dioxides lose oxygen leading to the decrease of their oxygen stoichiometry with temper­ature. The least stable dioxides CmO2 and CfO2 can evolve to form Cm2O3 and Cf2O3.

2.04.2.2.1 Crystallography

2.04.2.2.1.1 Thorium monocarbide ThC

The lattice parameter of fcc ThC1±x is dependent on the C/Th ratio and the oxygen and nitrogen impu­rities. It increases linearly for pure a-Th with the dissolution of carbon in the fcc lattice, as shown in Figure 5 6,44

It was observed to decrease by ^0.2 pm per 0.1 wt% N at low nitrogen content. High-temperature lattice parameter measurements have been performed by XRD on single-phase and two-phase Th-C com­pounds. The lattice parameter of ThC varies from 534.4 pm at room temperature to 545 pm at 2273 K.45

The linear thermal expansion (/p — /0)//0 and the linear thermal expansion coefficient aT = /— 1(d//d T) (where /0 is the sample length at 293 K) were deter­mined either by dilatometry or by XRD at different temperatures (Figure 6) and carbon contents.46

In the solid solution between ThC0.67 and ThC0.98, the value of a t lower than the thermal expansion
coefficient of pure Th (aTh ffi 11.6 x 10~6K_1 at room temperature47), increases slightly with carbon content and seems to have little dependence on oxy­gen and nitrogen impurities.

2.04.2.2.1.2 Thorium sesquicarbide Th2C3

The lattice parameter of Th2C3 varies between 855.13 and 856.09 pm in a narrow homogeneity range Th2C3_j, (0 < y < 0.05). The compound synthesized and ana­lyzed by Krupka27 had a composition of Th2C2.96 with a lattice parameter of 855.13 pm, corresponding to a theoretical density p = 10.609 gcm~ .

2.04.2.2.1.3 Thorium dicarbide ThC2

Gantzel and Baldwin48 published an XRD pattern for monoclinic ThC2_x completed by Jones et a/.49 by neutron diffraction analysis. The assessed values

for the room-temperature lattice parameters are reported in Table 1. Shein and Ivanovskii50 per­formed ab initio density functional theory (DFT) calculations on a-, p-, and g-ThC2, obtaining good agreement with the experimental results, and also suggesting a C—C distance of 132.8 pm. Pialoux and Zaug42 measured the lattice parameters a, b, c, and p of a-ThC2 by XRD as a function of temperature up to 1673 K. The results are plotted in Figure 7.

Bowman et a/.40 provided the most recent experi­mental data for the lattice parameters of p-ThC2 in equilibrium with graphite and 550 ppm O2 at 1723 K: a = 422.1 ± 0.3 pm and c= 539.4 ± 0.3pm. Pialoux and Zaug42 studied the dependence of a and c on the temperature, composition, and purity of p-ThC2. While the parameter a of p-ThC2 in equilibrium with C at 1740 K seems in good agreement with the values of Bowman et a/.,40 the lattice parameter a for single­phase p-ThC2 was observed to increase from around 420 pm at 1640 K to 422 pm at 1740 K. p-ThC2 in equilibrium with ThC shows a lattice parameter a of the order of 417 pm at 1640 K, decreasing to about 414.5 pm at 1768 K. The parameter c was observed to increase with temperature for p-ThC2 in equilibrium with ThC, varying from 540 pm at 1613 K to 545 pm at 1768 K, while the value c = 541 ± 1 pm is acceptable at all temperatures at which p-ThC2 is the equilibrium as a pure phase or with graphite. 0 K DFT calculations of structural parameters by Shein and Ivanovskii50 are not in agreement with the experimental results for p-ThC2. Obviously, ideal ordering of C2 dumbbells along the c axis and exact 2.00 stoichiometry, both postulated in Shein and Ivanovskii’s model, constitute too rough hypotheses for this phase. This complex part of the phase diagram needs further assessment.

The high-temperature g-modification of ThC2 has an fcc KCN-like structure. The C2 dumbbells, centered in the (1/2, 1/2, 1/2) position, rotate freely.6,40 The lattice parameter of g-ThC2 was measured by Pialoux and Zaug 2 between 1858 and 2283 K, and observed to vary between 581.3 and 584.1 pm, respectively. The same authors observed that the lattice parameter of g-ThC2 in equilibrium with ThO2 depends on the CO partial pressure. Its value is constant and close to 570pm between 2173 and 2228 K for pCO < 10—3bar, but increases to 584 pm for higher pCo. The nearest C—C distance was estimated by Bowman et a/.40 to be 124 ± 4 pm. The p! g-ThC2 transformation is diffusionless,51 which explains why all attempts to quench g-ThC2 to room temperature failed.52

The linear thermal expansion (/T — /0)//0 and the linear thermal expansion coefficient aT were measured by dilatometry up to 1323 K53 and by XRD54 up to 1608 K for a-ThC2—x and up to 2028 K for g-ThC2—x Values are reported in Figure 6 for samples with ~-510 ppm O2.

Ganzel et a/.54 reported aT = 8.7 x 10—6K—1 for g-ThC2—x between 1813 and 2028 K.

The average volumetric thermal expansion coeffi­cient g was estimated to be 78 x 10—6K—1 between 298 and 2883 K.6

Ganzel et a/.54 estimated that the volume increase on the a! p-ThC2—x transformation was 0.8% and 0.7% for the p! g-ThC2—x transformation. Dalton et a/.55 estimated the overall volume expansion for both transformations to be 1.3%.

2.04.2.2.2 Thermodynamic properties

Heat capacity and Gibbs energy of formation data for thorium carbides are summarized in Tables 2 and 3 and Figures 8 and 9.

2.04.2.2.2.1 Thorium monocarbide ThC

The heat capacity of ThC0965 was measured by Harness et a/.56 between 1.8 and 4.2 K and by Danan57 up to 300 K. No superconductive transition was observed around 9 K, unlike the measurements of Costa and Lallement.58 The room-temperature value is Cp (298) = 45.1 ± 0.5J K—1 mol—1 The result­ing entropy difference S(298)-S(0) ffi 58 J K—1 mol—1 would give, with a randomization entropy S(0) = — R (0.97 ln 0.97 + 0.03 ln 0.03) = 1.12J K—1 mol—1, S(298) = 59.12 JK—1 mol—1, although there is a possibility that the ThC phase contains some C2 groups compen­sated by some carbon vacancies.4 The Debye tem­perature of ThC is a function of composition and varies from 170 K for ThC0063 to 308 K for ThC100, calculated by Lindemann’s formula.6

The high-temperature heat capacity of ThC, reported in Table 2, has been obtained by compari­son with UC and from the low-temperature data reported above.

Formation enthalpies, corrected for impurities, were measured by Huber eta/.59 and Lorenzelli eta/.60

The Gibbs energy of formation of ThC0.97 at its homogeneity range upper boundary was reviewed by Holley et a/.4 according to the reported heat capacity as in Table 3 and Figure 8.

Vaporization studies performed on ThC0891, ThC0.975, ThC1.007, en 2060 and

2330 K by Knudsen effusion and mass spectrometry61 yielded AfG°(ThC, s) values in fair agreement with the earlier ones. According to this study, atomic Th is the predominant species in the gaseous phase, and partial molar sublimation enthalpies are 522 kJ mol— for ThC0891, 5 5 3 kJ mol—1 for ThC0975, 660 kJ mol—1 for ThC1 007, and 578 kJ mol—1 for ThC1 074.

The equation of state (EOS) of solid ThC was studied by Das et a/. by density functional and

tight-binding linear muffin tin orbital method (TB LMTO) calculations,16 obtaining a bulk modulus B = V-1(d2E/d V2) = 43 GPa. This differs by almost exactly a factor 3 from the value, 125 MPa, recom­mended by Gomozov et al62 In this case, the discrep­ancy might be attributed to some factor (probably dimensional) missing in the calculations. A reasonable value for B is actually around 120 MPa, also directly deduced from the elastic constants reported in Section 2.04.2.2.4.

The EOS of liquid ThC was studied starting from the significant structure theory, which takes into account the complex vaporization behavior of ThCx.63 The resulting enthalpy of melting is 35.2 kJ mol-1. This value is considerably lower than that estimated by applying Richard’s law to the accepted melting temperature.64,65 A direct measurement of

AmH (ThC) is still required to solve this discrepancy. Gigli et a/.63 obtained the following values from their EOS for liquid ThC: S° = 207.6J K-1 mol-1; Cp = 89J K-1 mol-1; Cv=50J K-1 mol-1; cubic thermal expansion coefficient a = 1.4×10-4K-1; isothermal compressibility k = V-1(dV/dP) = 3.7 x 10-11 m2N-1, plus the critical constants reported in Table 3. Liquid ThC total pressure was calculated up the critical temperature as

log p = 22.210 — 39282 T-1 — 4.2380 logT

+ 2.0313 x 10-4T [2]

with p in bar and T in K.

2.04.2.2.2.2 Thorium sesquicarbide Th2C3

The Gibbs energy of formation of Th2C3 at 1 atm estimated by Potter66 from the phase field distribu­tion of isothermal sections of the Th-Pu-C system between 1573 and 1873 K is reported in Table 3 and Figure 9.

The reported values are consistent with the inequality

AfG°(Th2C3,s) > AfG°(ThC, s)+AfG°(ThC2,s)2

8T < Tmelting [3]

which justifies the thermodynamic instability of Th2C3 at atmospheric pressure and all temperatures.

The volume change for the reaction ThC + ThC2 = Th2C3 is AV = -2.32×10-6m3mol-1. Krupka27 hav­ing estimated that AfGp = (AfG° — 2.32p) J mol-1 and that the p-AV term (in SI units) provides an excess AfG term AfG^ ffi — 7kJ mol-1, the room-temperature standard Gibbs energy of formation for Th2C3 can be extrapolated as

T (K)

Figure 8 The heat capacity of thorium carbides.

DfG298(Th2C3,s) = — 226 ± 21kJmol 1

Giorgi et al67-69 studied the electronic and magnetic properties of thorium sesquicarbide. The valence electron concentration of Th2C3 is exactly 4.0. Mag­netic susceptibility measurements show a supercon­ductive transition in ThC145 treated under high pressure. The transition temperature is 4.1 ±0.2 K, with a pressure dependence dTc/dp = —0.040 K kbar—1 between 0 and 10kbar.

Various kinds of intermetallic compound appear in the phase diagrams between Th and Group Ib or Ilb metals, like those existing in the phase diagrams between Th and Group VIII metals. A gradual decrease in the decomposition temperature for these intermetallic compounds is observed from VIII toward Group IIb metals, in general. Figures 66-68 indicate the typical examples, which compare among the Th-Pd, Th-Ag, and Th-Cd phase diagrams. These figures were given in Okamoto,4 in which they were redrawn mainly from Thomson,20 Terekhov et a/.,205 Raub and Engel,230 Baren,231 and Bates et a/.,232 Palenzona and Cirafici,233 and Dutkiewicz,234 respectively. A gradual decrease in the relative stability of these intermetallic compounds is speculated by observing the figures. Regarding the Th-Cd system, the enthalpy of solution of ThCd11 in the liquid phase, —90.5 kJ mol— , was derived from the slope of the solubility.235 A similar tendency is seen in the Pu-related systems and possibly the Np-related systems. In the case of the U-related sys­tems, the decrease in stability appears more distinctly. Figures 69 and 70 show the U-Pd and U-Ag phase diagrams given in Okamoto,4 which were redrawn

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.

mainly from Catterall et al,209 Pells,210 Terekhov et al.,238 and Buzzard et al.,239 respectively. Figure 71 shows the assessed U-Cd phase diagram for the Cd-rich region given in Kurata and Sakamura,236 based on the work of Martin et al.237 Although there are several intermetallic compounds in the Pd-rich region of the U-Pd phase diagram, there is no com­pound in the U-Ag system, and only U11Cd exists in the U-Cd system.

The actinide-Cd phase diagrams are particularly important when considering the pyrometallurgical reprocessing of the spent nuclear metal fuels. Ther­modynamic evaluation on the actinide-rich region of the U-Cd, Np-Cd, and Pu-Cd systems was performed in Kurata and Sakamura.236,240 Table 21 summarizes the assessed results, in which the Gibbs energy of formation of the intermetallic compounds is determined from the activity of actinide in the liquid Cd phase. The values were evaluated from the previous EMF measurements,242,243 with the exception of U11Cd. The values for U11Cd were given by Barin241 Figures 72 and 73 show the assessed Np-Cd and Pu-Cd phase diagrams of the actinide-rich region in which the solubility data of Krumpelt etal235 and Johnson etal243 are reasonably plotted on the calculated phase boundary. The data are in good agreement with each other. Using these evaluated data, the ternary isotherm of the U-Pu-Cd

system was predicted by Kurata et al..244 Figure 74 shows the calculated ternary isotherm of the U-Pu-Cd system at 773 K with the experimental observations given in Kato et al.245 and Uozumi

et al.,246 in which the mixture of U and Pu was recovered in a liquid Cd cathode by electrolysis and then the cross section of the solidified Cd was analyzed by SEM-EDX after quick cooling. Two

or three different phases were detected in the sam­ples. The open circle in the figure indicates the average composition of the liquid Cd cathode, and the black solid circle indicates the composition of

Table 21 Assessed interaction parameters for U-Cd, Np-Cd, and Pu-Cd systems

GO(U, liq), GO(Np, liq), GO(Pu, liq), GO(Cd, liq): given in Dinsdale[10]

Gex(Cd-U, liq) = xU(1 — xU) (-22220 + 60.57T) Gex(Cd-Np, liq) = XNp(1 — XNp) (-84856 + 73.34T) Gex(Cd-Pu, liq) = xPu(1 — xPu) (-77167 + 63.387

— 30 413 (xCd — XPu))

Gform(UCd11) = -154.6 + 1.6437 — 0.327871nT

— 0.0000268872 +1328/7: given in Barin241 Gform(NpCd11)a = -175.9 + 0.1627 Gform(PuCd11)a = -192.0 + 0.1497 Gform(NpCd6)a = -106.3 + 0.0717 Gform(PuCd6)a = -164.3 + 0.1087

smaller than that for actinides, by a few orders. This may suggest that further stabilization appears in the Am-Cd or Cm-Cd systems compared to U-Cd, Np-Cd, and Pu-Cd systems. This stabilization for the Am, Cm, or lanthanides prevents not only the separation from U, Np, or Pu but also the separation among Am, Cm, and lanthanides.

The phase diagrams between actinides and Zn have features similar to those between actinide and Cd. However, the phase diagrams between actinides and Hg are completely different from those between actinides and Cd or Zn. The liquid phase is

significantly stabilized in the Hg-related system, and various intermetallic compounds decompose at very low temperatures.

Austenitic alloys have inferior hot-formability char­acteristics compared to low-alloy steels due to the lack of softening at higher temperatures. Nickel — based alloys show even less formability than austen­itic stainless steels due to their high deformation resistance at higher temperatures.

Hot-forming is basically carried out in a tempera­ture range between the solidus temperature and the temperature at which recrystallization begins. How­ever, nickel forms eutectic with various elements including chromium, molybdenum, silicon, titanium, aluminum, niobium, tungsten, phosphorus, sulfur, and carbon. Thus, in the case of nickel-based alloys that contain many alloying elements, heating at tem­peratures higher than 120 °C poses the risk of local fusion or precipitation of a secondary phase. Careful selection of the hot-forming temperature range is essential and the temperature range needs to be con­firmed by high-temperature, high-speed tensile tests, high-temperature torsion tests, forging tests, etc., prior to the hot-forming process.52 The Ugine — Sejournet extrusion process with a glass lubricant is normally applied during hot-working of tubes and pipes, such as SG tubes. This is an expansion working process using billets with machined and drilled holes for the forged or rolled bloom.

Figure 19 illustrates the typical fabrication process of hot-finished pipes for CRDM adapter

nozzles of PWRs, compared to that of cold-finished tubes for use as SG tubes.44’50

2.08.3.2 Cold Forming

Cold forming can be easily applied to nickel-based alloys, except in the case of highly strengthened alloys such as precipitation-hardened Alloys X-750, 718, etc. Under severe cold-forming conditions,
intermediate and final annealing steps are needed for the products after cold forming.

The cold-forming process for the nickel-copper Alloy 400 and for Alloys 600, 690, and 800 nickel — chromium-iron alloys is typically as follows.

The bare tubes, which are hot-formed and heat — treated, are pickled using nitric and fluoric acids to remove glass and other contaminants incorporated during the hot-working and other processes, and
then finished to the desired shape by cold drawing, cold reducing, or cold rolling at ambient temperature. This cold-forming process produces small-diameter and thin-walled tubes with excellent dimensional accuracy and a fine surface finish that cannot be obtained by hot processes. However, severe or progressive die-forming operations require heavy-duty lubricants with good surface-wetting characteristics and high film strength, such as those found in metallic soaps and chlorinated or sulfochlorinated oils. However, it is very important to remove all traces ofthese lubricants prior to any heat treatment or welding due to the danger of carbon pickup and consequent lowering of corrosion resis­tance by the formation of complex carbides. Parts formed using zinc-alloy dies should also be flash — pickled to prevent liquid-metal embrittlement during heating. In the case of the fabrication of Alloys TT600 and 690 for SG tubes and other nuclear products, lubricant treatment using an oxalate film coating is recommended for the tube-drawing process.52

The degree of work hardening is relatively large for nickel-based alloys. However, these alloys have somewhat higher strength and hence there is the need to have forming equipment with sufficient power commensurate with the mechanical character­istics of these alloys.

Cold drawing is a cold-forming procedure for bare tubes using dies and subsequent drawing. There are several cold-drawing methods, such as plug drawing, sink drawing, mandrel drawing, and hydraulic draw­ing. Mandrel drawing and hydraulic drawing allow for a high ratio of cold-working and fine surface finishes.

Cold rolling and cold reducing are applied during tube fabrication using nickel-based alloys as one of the cold-forming methods. Cold rolling can be used for high-reduction-ratio cold forming, even for nickel-based alloys with inferior workability charac­teristics, due to compressive forming.52

Figure 19 illustrates the typical fabrication pro­cess of cold-finished tubes for SG tubes, compared with hot-finished pipes for CRDM adapter nozzles of PWRs.44,50

The low-temperature heat capacity has been mea­sured for the actinides Th through Am, in most cases showing anomalies. The origin of these anoma­lies has generally not been explained adequately35 but is likely related to ordering phenomena and f-electron promotion. The measurements for the major actinides Th, U, and Pu in the a-structure were made on gram-scale quantities, and the results should thus be of an acceptable accuracy.

However, although the low-temperature heat capacity ofplutonium was measured by a remarkably large number of authors,36-42 there is considerable scatter among the results above 100 K (see Figure 8), probably due to self-heating and radiation damage. But even the results for 242Pu samples from the same batch,40,41 which are affected less due to its much longer half-life, differ considerably. The differences in the heat capacity have a pronounced effect on the standard entropy at T = 298.15 K: 56.03J K-1 mol-1,39 56.32 J K-1 mol-1,40 54.46J K-1 mol-1,41 and 57.1 J K-1 mol-1.42 Especially, the results of Lashley et al42 indicate a very different shape of the heat capacity curve of a-Pu, rising much steeper up to T = 100 K and saturating at a lower value near room temperature. Although the relaxation method used in that study is less accurate (±1.5% as claimed by the authors) than the traditional adiabatic technique used in the other studies, the difference is significant. Lashley et al42 attributed this to the buildup of radia­tion damage at the lowest temperatures, which they tried to avoid by measuring upon cooling, and below T = 30 K by intermediate annealing at room temper­ature. However, other authors also addressed this issue. For example, Gordon et al41 performed a heat­ing run from room temperature to T = 373 K before each low-temperature run. Moreover, no substantial difference between the results for 239Pu and 242Pu was observed in that study.

The electronic Sommerfeld heat capacity coeffi­cient (ge), a property proportional to the density of states at the Fermi level, varies strongly in the actinide series (Table 5). It increases steadily up to Pu but is very low for Am. For 8-Pu the electronic heat capacity coefficient ge is even three times higher than that of a-Pu. This corresponds well with the results of photoemission spectra48 that show a-Th has a small density of states at the Fermi level com­pared with that of a-U, a-Np, and a-Pu (Figure 9). In a-Am, the valence band is well removed from the Fermi level. The low-temperature heat capacity of other modifications of plutonium has been measured recently. Specifically, the 8-structure sta­bilized by Am or Ce doping shows clearly enhanced values of the electronic heat capacity coefficient ge at

50,51

very low temperature.

The standard entropies derived from the low- temperature heat capacity data are given in Table 3,

Table 3 Recommended entropy (J K 1 mol 1) and the heat capacity (J K 1 mol 1) of actinide elements in the solid and liquid phase Phase S0 (298.15) Cp — A + B x T (K) + C x T2 (K) + D x T3 (K) + E x T-2 (K) Temperature range (K) A B C DorE Th a 51.8 ± 0.50 23.435 8.945 x 10-3 E —-1.140 x 104 298-1650 b — 15.702 11.950 x 10-3 1650-2020 Liquid — 46 2020-2500 Pa a 51.6 ± 0.80 21.6522 12.426 x 10-3 298-1443 b — 39.7 1443-1843 Liquid — 47.3 1843-2500 U a 50.20 ± 0.20 28.4264 -6.9587 x 10-3 29.8744 x 10-6 E —-1.1888 x 105 298-941 b — 47.12 941-1049 g — 61.6420 E —-33.1644 x 106 1049-1407 Liquid — 46.45 1407-2500 Np a 50.45 ± 0.40 30.132 -36.2372 x 10-3 1.1589 x 10-4 298-553 b — 40 553-850 g — 36 850-913 Liquid — 46 913-2500 Pu a 54.46 ± 0.80 17.6186 45.5523 x 10-3 298-399 b — 27.4160 13.060 x 10-3 399-488 g — 22.0233 22.959 x 10-3 488-596 s — 28.4781 10.807 x 10-3 596-741 S’ — 35.56 741-759 £ — 33.72 759-913 Liquid — 42.80 913-2500 Am a 55.4 ± 2.0 30.0399 -29.053 x 10-3 5.2026 x 10-5 D —-1.8961 x 10-8 298-1042 b — 8.4572 33.167 x 10-3 -7.587 x 10-6 1042-1350 g — 43 1350-1449 Liquid — 52 1449-2500 Cm a 70.8 ± 3.0 28.409 -4.142 x 10-4 3.280 x 10-6 298-1569 b — 28.2 1569-1619 Liquid — 37.2 1619-2500 Source: Konings, R. J. M.; Bene;;, O. J. Phys. Chem. Ref. Data 2010, 39, 043102.

and the variation along the actinide metal series is shown in Figure 10. The entropies of the elements Th to Am are close to the lattice entropies of the corresponding lanthanides, showing the absence of magnetic contributions. The entropies of the other actinide elements must be derived from estimations, as experimental studies do not exist. To this pur­pose Ward et al28 suggested a general formula by correlating the entropy with metallic radius (r), atomic weight (M), and magnetic entropy (Sm):

Su (298.15K) = Sk(298.15K)- + ^ ln M [2]

rk 2 Mk

where u refers to the unknown (lanthanide or actinide) element and k refers to the known element. Sm is taken equal to Sspin = (2J + 1), where J is the total angular momentum quantum number. The entropy of Cm thus obtained is significantly higher than that of the preceding elements, showing its magnetic character.

The heat capacity of the actinide metals from room temperature up to the melting temperature has been reported for Th, U, and Pu with reasonable accuracy and for Np for the a-phase only. The values for the other metals are based on estima­tions. For example, Konings52 estimated the heat capacity of americium metal from the harmonic, dilatation, electronic, and magnetic contributions, Cp = Char + Cdil + Cele + Cmag, whereas the heat capac­ity of g-americium was obtained from the trends in the 4f and 5f series. The high-temperature heat capac­ity data for the actinide metals was analyzed in detail by Konings and Benes,34 who gave recommendations for the elements Ac to Fm. The results for the elements Th to Cm are summarized in Table 3.

Figure 11 shows the variation of the sum of the transition entropies from the crystalline room temperature phase to the liquid phase for the lantha­nide and actinide series. This value is about constant in the lanthanide series but shows large variation in the actinide series, particularly for the elements U-Np-Pu. The deviation from the baseline

correlates well with the atomic volume of the metals that is also anomalous for these elements, indicating that the itinerant behavior of the 5f electrons and the resulting lowering of the room temperature crystal symmetry require additional entropy to reach a similar disordered liquid state.

In general, the thermal conductivity decreases with departure from stoichiometry. This has been seen in AmO2 _ x by Nishi et al..254 and in UO2 ± x by Watanabe et a/.87 and also by Yamashita et a/.88

Lucuta et al. 255 found a linear relation between the thermal conductivity and the stoichiometry x in UO2 + x for 0 < x< 0.10 (see Figure 32): A(x) = 0.0257 + 3.34x and B(x) = (2.206 _ 6.86x).

Amaya et al.256 proposed a somewhat different and more complicated expression, but valid for 0.0 < x< 0.20:

where 10 = 1/(A + BT), в = Dp2x10, and D = D0 exp(DT).

The fit performed by Amaya et al.256 leads to A = 3.24 x 10"2KmW_‘, B = 2.51 x 10-4mW_1, C = 5.95 x 10-11 Wm_1 K_4, D0 = 3.67 m1/2 K1/2 W_1/2, and D1 = —4.73 x 10-4K_1. 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 a/.257: A = 29.3 x 10-2mKW_1 and B = 5.39 x 10-4mW_1.

For U1 _JPuyO2 _ x with a low amount of Pu, Duriez et a/.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 eta/.143 found an electronic contribution to the thermal conductivity at high temperature. The para­meters (of eqn [17]) are A(x) = 2.85x + 3.5 x 10_2 KmW_1, B(x) = (—7.15x + 2.86) 10_4 mW_1, C = 1.689 x 109 WK_1m, and D = 1.3520 x 104K.

As an example for the evolution of the thermal conductivity as a function of temperature and stoichiometry, we show the figure from Duriez et a/.143 for a sample containing 15% urania (Figure 34).

For higher amount of plutonium (0.15 <y < 0.30), Inoue238 obtained a somewhat different dependence (qualitatively reproduced by MD calculations by Arima eta/.81): A(x) = 0.06059 + 0.2754px KmW-1, B = 2.011 x 10-4 m W-1, C = 4.715 x 109 WK^’m, and D = 1.6361 x 104K.

Finally, the thermal conductivity continues to decrease as a function of plutonium content, as shown by Sengupta et a/.259 in Pu0 .44U0.66O2.

Morimoto et a/.258 have investigated the effect of hypostoichiometry on the thermal conductivity

of U0.68Pu0.30Am0.02O2.00 — x (0.00 < x < °.°8). Both

parameters A(x) and B(x) (of eqn [17], C = D = 0) depend on the stoichiometry x as follows: A(x) = 3.31x + 9.92 x 10-3KmW-1 and B(x) = (-6.68x + 2.46)10-4 mW-1.

Lemehov et a/.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 — x and (Am, Np, U)O2 — 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 eta/.43 are A = 36.29 x 10-2mKW-1 and B = 1.78 x 10-4mW-1.

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.

Many studies have been performed on the system U-O-N in the 1960s-1970s.8 We summarize here some essential results limited to low N contents.

The U-C-N ternary system is characterized by the complete miscibility between UC and UN in the solid state (Figure 23).

Three invariant points limit the three-phase equi­librium domains: UC1_xNx + U2N3 + C (point 1), UC1_xNx + UC2 + C (point 2), and UC1_xNx + U2C3 + UC2 (point 3). Their composition depends mostly on temperature and nitrogen partial pressure.8

UC1_xNx is the only ternary compound known in this system. It crystallizes as NaCl-like fcc (group Fm 3m). Its lattice parameter varies continuously from а = 496 pm for UC to а = 488 pm for UN. A slight deviation from Vegard’s law in the positive direction was observed by Cordfunke,188 who studied the complex behavior of the lattice parameters of a — and p-UC2 in equilibrium with UC1_xNx between 1773 and 2273 K by high-temperature XRD. Increasing nitrogen content and temperature were observed to lead to shrinkage of the lattice, attributed to the formation of nonstoichiometric carbide nitrides where nitrogen atoms substitute either CN groups or C2 pairs.

Benz189 obtained maxima in the solidus tempera­ture for (C + N)/U ratios close to one in the UC-UN pseudobinary plane. UC0 .25N0. 75 was observed to melt at 3183 K, higher of both UC (2780 K) and UN (3103 K). This result is consistent with a slightly nega­tive deviation of UC1_xNx from the ideal solution behavior for intermediate values of x, confirmed by activity calculations performed at various N2 partial pressures190 and similar anomalies in other physical properties such as Young’s modulus191 and the creep behavior.192 Young’s modulus extrapolated at zero porosity was observed to be highest at approximately UC0.2N08 (280 GN m~ ), whereas the compressive creep rate was reported to have a maximum near the composition UC075N0.25 (2х10~п_1 with a load of 4kgmm~2 at 1773 K) and a minimum near the

composition UC0.75N0.25 (2×10-2h-1 with a load of 4kgmm-2 at 1773 K). Padel eta/.191 observed a maxi­mum even in the Debye temperature (around 300 K) near UC0 .20N0 80, corresponding to an optimal filling of the binding molecular orbital 6d-2p.

The thermal conductivity of UC1_xNx was observed to decrease upon addition of nitrogen to pure UC for 300 K < T< 900 K,193 this trend being less and less marked at increasing temperature and even inversed for T> 1000 K approximately.

The electrical resistivity of UC1_xNx with x > 0.5 increases with decreasing temperature, and particu­larly below room temperature, due to localized mag­netic moments.8

The electronic coefficient of the low-temperature heat capacity slightly increases with nitrogen content, and has a maximum for UC013N0 87.

The coefficient of linear thermal expansion of UC078N021O001 was measured between 298 and 2400 K, obtaining values (9.5×10-6K-1 at 298 K and 13.8 x 10-6 K-1 at 2400 K) lower than those ofpureUC.8

The carbon self-diffusion coefficient changes little for small additions of nitrogen to UC, but can decrease by several orders of magnitude for N/(N + C) > 0.5.

The total hemispherical emissivity et of UC0 55N045 was reported to be 0.21 ± 0.03 between 1300 and 1700 K.8 This value, indicating a strongly metallic behavior, should be confirmed by further investigation.

2.06.4.1 Gaseous Uranium Hexafluoride

2.06.4.1.1 Molecular structure and physical properties

The gaseous UF6 was studied extensively in the 1950s and 1960s. Gas-phase electron diffraction,77 Raman, and infrared studies78 have established the octahedral structure, Oh, of the gaseous UF6 and the molecular and vibrational parameters (Table 6). The U-F distance is 2.00 A. From the molecular and vibrational parameters, the entropy can be cal­culated accurately.

In the gas phase, the density of UF6 can be described according to an equation which is similar in form to the ideal gas law.

p = 4291P/(T (1 — 1.3769.106 P/T3))

where p is in kgm-3, P in atm, and T(K).15

The viscosity and thermal conductivity have been measured by Llewellyn.9

We report that:

p = 2.1.10-4 P at 100°C

l = 8.10-3 W K-1m-1 at 105°C

2.06.4.1.2 Thermodynamic properties

The values recommended by Grenthe et a/24 and updated by Guillaumont et a/.39 are presented in Table 7.

The enthalpy of sublimation was evaluated by third-law analysis of experimental vapor pressure data.

The thermal functions of UF6(g) are calculated from the molecular parameters given in the compre­hensive paper of Aldridge et a/.79

2.06.4.1.2.1 Enthalpy of formation

The enthalpy of formation of the gaseous uranium hexafluoride was investigated at the same time as for the crystalline UF6 by fluorine bomb calorimetry by Seattle et a/.10 and then by Johnson.80 As for the crystal, a difference of 11 kJ mol-1 was found between the two authors. The enthalpies of formation can be obtained from the analyses of the vapor pres­sure measurements that have been performed and such data have been derived in the NEA-TDB series.

2.06.4.1.2.2 Vapor pressure

Several works were devoted to measure the vapor pressure above the solid and liquid uranium hexa­fluoride.24 The agreement between the authors is excellent (Figure 16).

The vapor pressure equation based on the experi­mental data above the solid and liquid uranium hex­afluoride is, respectively:

, , , 2562.46± 3.64 ,

log P(Pa)=- t +(12.7767 ± 0.01235)

[230 — 337 K]

Table 7 Thermodynamic properties of the gaseous uranium hexafluoride

AfH0 (UF6, g, 298.15 K)

(kJ mol-1)

S0 (UF6, g, 298.15 K)

(J K-1 mol-1)

Cp (UF6, g, 298.15)

(J K-1 mol-1)

Cp (UF6, g, T) (JK-1 mol-1) 137.373 + 3.9605 x 10-2T

2.178^ x 10-5T2

AsubH0(UF6, 298.15 K)

(kJ mol-1)

, , , 1490.27 ± 6.56 ,

log P(Pa) = — j +(90.60167 ± 0.01862)

[337 — 370 K]

A comprehensive source of vapor pressure data has been published by Oliver eta/.81

The phase diagram of the uranium-oxygen system, calculated by Gueneau et a/.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 UO167 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 ± 20 K. The melting temperature decreases with departure from the stoichiometry. The experimental data on solidus/liquidus temperature for UO2 + x from Manara eta/.,11 reported in Figure 1(b), are significantly lower than those reported in Baichi et a/.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 eta/.12 and considered as a metastable phase by Gueneau et a/8

The most reliable standard thermodynamic function data for PuN are those reported by Matsui and Ohse.76 Matsui et al. have calculated the thermal functions of PuN(s) using the recommended

equations for Cp and the H—H298 values of Oetting75, and setting S298 to be 64.81Jmol—1 K—1 these are summarized in Table 5. The values of Cp and H—H298 higher than 1600 K are extrapolations of the data reported by Oetting.75

The values of AfG for PuN were calculated with AH298 set at —299 200J mol—1(83) and the thermal functions for plutonium84 and nitrogen.82 The values of entropy S, the free energy function —(G—H298)/T and Gibbs free energy of formation AfG of PuN(s) are also given in Table 5.

The AfG of PuN is expressed with the following equation:

AfG(Jmol—1) = —3.384 x 105 + 152.0T — 0.03146T2 — 5.998 x 10—6T3 + 6.844 x 106/T (298 <T(K) <3000) [14]

The temperature dependencies of the AfG for PuN are shown in Figure 22. The values of AfG are close to those derived from the precise vapor pressure mea­surements by Kent and Leary,68 with a difference of around 1 kJ mol—1 at 1000 K and 6 kJ mol—1 at 2000 K.

2.03.3.4.1 Uranium and plutonium mononitride

The standard thermodynamic function data for (U0.8Pu0.2)N were determined using an ideal-solution model. Matsui et al. have estimated the entropy at 298 K (S298) for (U0.8Pu0.2)N to be 67.07J mol-1 K-1

Temperature (K)

from S298 values for UN (62.43 J mol-1 K-1) and PuN (64.81 J mol-1 K-1) coupled with an entropy of mixing term, assuming an ideal solution. The values of the thermal functions for (U0 8Pu02)N have been calcu­lated by Matsui et al. and are summarized in Table 6. The enthalpy of formation for (U0.8Pu0.2)N was esti­mated to be -296.5 kJ mol — , on the basis of an ideal-solution model with AH298(UN) = -295.8 kJ mol-1 and AH298(PuN) = -299.2 kJ mol-1. The values of entropy S, free energy function -(G-H298)/T and Gibbs free energy of formation AfG of (U0 8Pu0.2)N(s) are also given in Table 6. The equation of AG for (U0.8Pu0.2)N is given as

AfG(Jmol-1 ) =-2.909 x 105 + 67.56T + 0.007980T2 — 1.098 x 10-6T3 — 7.455 x 105/T (298 <T(K) < 3000) [15]