The oxygen potential in oxides reflects the equilib­rium between oxygen in the crystal lattice and oxy­gen in the gas phase and is defined as

m(O2) = RT ln(pO2/p0) [12]

where R is the gas constant, Tis the temperature, pO2 is the partial pressure of oxygen, and p0 is the stan­dard pressure.

As the actinide dioxides are nonstoichiometric phases, the oxygen potential data strongly vary with the O/metal ratio and with temperature.

2.02.4.3.2.1 Binary solid solutions

Numerous experimental data exist on the variation of the oxygen potential for both uranium and pluto­nium oxides as a function of the oxygen to metal ratio and temperature. A critical review of these experimental data was performed by Baichi et al9 in the U-UO2 region and by Labroche et al.10 from UO2 to U3O8.

Thermochemical models were derived to describe the thermodynamic properties of uranium oxide by Blackburn,172 Besmann and Lindemer,173-175 Park and Olander,149 Gueneau et al.,8 Chevalier et al.,176,177 Yakub et al.127 and plutonium oxide by Kinoshita et al.,27 Gueneau et al.,28 Stan and Cristea,150 and Besmann and Lindemer173 that allow describing the oxygen potential data.

The most extensively used is the associate model developed by Besmann and Lindemer173-175 that describes the oxide solution as a mixture of associates U1/3, UO2, U2O45 (or U3O7 for oxygen potential higher than _266 700 + 16.5(T (K)) (Jmol_1)) for UO2 ± x, and Pu4/3O2 and PuO2 for PuO2 _ x. This model reproduces very well the available experimen­tal data on UO2 ± x PuO2 _ x, and (U, Pu)O2 ± x from the extrapolation of the binary oxides. However, this approach does not allow calculating the phase dia­grams. More recently, thermochemical models were developed using the CALPHAD method in order to describe both the phase diagram and all the ther­modynamic properties of the phases by Chevalier et al.176,177 and Gueneau et al8 for U-O, and by Kinoshita et al27 and Gueneau et al28 for Pu-O. In the model proposed by Chevalier etal.177 for U-O, the solid solution is described with a three sublattice model (U)1(O, V)2(O, V)1 where ‘V’ designates oxygen vacan­cies. The hypostoichiometric region is taken into account by introducing oxygen vacancies, and the oxy­gen-rich part with O/metal ratio >2 is described by considering interstitial oxygen atoms in the third sublattice. In the model developed by Gueneau et al.,8 the uranium dioxide is represented using a three sublattice model with ionic species (U3+,U4+, U6+)1(O2_,V)2(O2_,V)1. The third sublattice is the site for interstitial oxygen anions to describe the excess of oxygen in urania. The electroneutrality of the phase is maintained by introducing U3+ or U6+ cations on the first sublattice for, respectively, hypo — or hyperstoi­chiometric compositions of urania. The oxygen poten­tial data, as derived by Gueneau etal. for UO2±x8 and PuO2 _ да28 are presented in Figure 19(a) and 19(b), showing that the oxygen potential is lower in UO2 _ x than in PuO2 _ x.

Few measurements exist for the other actinide oxides: Ackermann and Tetenbaum178 reported data for ThO2 _ x Bartscher and Sari179 for NpO2 _ x and Chikalla and Eyring,94,180 Casalta,181 and Otobe etal.182 for AmO2 _ x solid solutions. A thermochemical model using the CALPHAD method was derived by Konishita et al.39 to reproduce the experimental data on ThO2 _x and NpO2 _x (Figure 20(a) and 20(b)). For the Np-O system, the oxygen potential data are well reproduced, but the phase diagram assessed by Kinoshita39 is not in good agreement with the experi­mental data on the solubility limit of NpO2 _ x in equilibrium with the liquid metal.

An associate model was derived by Thiriet and Konings40 to reproduce the oxygen potential data of Chikalla and Eyring94 on the AmO2 _ x solid solution (Figure 21(a)). Very recently, Besmann183 has derived a thermochemical model on AmO2 _ x using the Com­pound Energy Formalism as in Gueneau et al.28 for Pu-O. It is worth mentioning that for the Am-O system, the experimental data of Chikalla and Eyring94 and the recent measurements by Otobe etal.182 are in disagreement with the phase diagram determined experimentally by Sari and Zamorani41 that shows the presence of a miscibility gap in the fluorite phase like in the Pu-O and Ce-O systems (see Figure 21(b)). The data of Casalta181 are con­sistent with the existence of the miscibility gap but are in poor agreement with the values of Chikalla and Eyring94and Otobe et al.182 for the oxygen potential near AmO2. Otobe et al.182 pro­posed a new tentative phase diagram based on their

	(a) O/Th
-300-
-400
Figure 20 Oxygen potential data versus O/metal ratio in (a) ThO2 _x at 2400, 2500, 2600, and 2655 K; the experimental data come from Ackermann and Tetenbaum178 and (b) NpO2_x at 1473, 1573, 1673, 1773, and 1853 K according to the model derived by Kinoshita eta!.39; the experimental data come from Bartscher and Sari.179

(b) O/Pu (b) O/Np

oxygen potential measurements and an analogy with the Ce-O system. The phase diagram is in disagree­ment with the one determined by Sari and Zamorani.41 Very recently, a CALPHAD model derived by Gotcu- Freis etal42 allows to account consistently both oxygen potential data for O/Am ratios above 1.9 from Chikalla and Eyring94 and Sari and Zamorani phase diagram data. New experimental determinations on the phase diagram will be helpful to interpret these discrep­ancies and to fix the thermodynamic properties of this system.

The oxygen potential was measured in Cm-O by Chikalla and Eyring184 and by Turcotte et al.,185 in Bk-O by Turcotte etal.,186’46 and in Cf-O systems.187

A comparison ofthe oxygen potential data calculated at 1600 K using the thermochemical models derived by Kinoshita etal39 for ThO2 _ x and NpO2 _ x, Thiriet and Konings40 for AmO2 _ x, Gueneau etal. for UO2 ± x8 and PuO2 _ x28 is presented in Figure 22. The oxygen potential data are the lowest for ThO2 _ x, then UO2 _ x NpO2 _ x PuO2 _ x and finally AmO2 _ x for which the highest values were measured. This trend corresponds

to the order of the elements in the actinide series and to a decreasing stability of the actinide dioxides from ThO2 to AmO2 as reported in Section 2.02.4.1.1. It can also be concluded that the oxygen ions are the most strongly bonded in the ThO2 _ x lattice.

2.02.4.3.2.2 Higher-order solid solutions 2.02.4.3.2.2.1 (U, Pu)O2 ± x The available oxygen potential data on (U, Pu)O2 ± x were compiled by Besmann and Lindemer173,175 when they presented their thermochemical model on (U, Pu)O2 ± x solid
solution based on the description ofthe two subsystems U-O and Pu-O. Because of the increasing interest for mixed oxide fuels for fast breeder reactors, more recent measurements are available. Oxygen potentials were measured for (Pu03U07)O2_x by Kato eta/.188 using thermogravimetry, for (Pu02U08)O2 _ xby Kato eta/.189 by a gas equilibration method, for (Pu079U021)O2 _ x and (Pu072U028)O2 _ xby Vasudeva Rao eta/.190 using a gas equilibration technique, followed by solid-state EMF measurements.

The thermochemical model of the U-Pu-O system proposed by Yamanaka et a/.57 using the CALPHAD method allows calculating the oxygen potential in the MOX fuel, and the calculated data are compared to a limited number of experimental data. As reported in Section 2.02.4.3.1, a point defect model was recently proposed by Kato et a/.155 to represent the experimental oxygen potential data in (U0.7Pu0.3)O2 ± x and (U0.8Pu0.2P2 ± x. Recently, a thermochemical analysis was proposed by Vana Varamban et a/.191 to estimate the oxygen potential for mixed oxides. The fuel is treated as a pseudoqua­ternary solution of UO2-UcOd -PuO2-PuaOb with b = 1.5a and d = 2.25c. The values a = 2 and c = 8 were derived to represent the oxygen potential in mixed oxides with 21, 28, and 44% of plutonium.

The oxygen potential data of (U0 9Pu01)O2 ± x and (U0.7Pu0.3)O2 ± x, as derived from the model devel­oped by Besmann and Lindemer,175 are presented in Figure 23. As expected from the above reported

data on the pure oxides, the oxygen potential of (U, Pu)O2 ± x increases with the plutonium content and temperature. In the hypostoichiometric region, the oxygen potentials were analyzed considering the change of the oxidation state of Pu from 4+ to 3+ by Rand and Markin.52

2.02.4.3.2.2.2 UO2±„ Ри02_„ and (U, Pu)O2±x containing minor actinides The effect of the minor actinides Am, Np, and Cm on the oxygen potential of uranium and plutonium oxides and mixed oxides was investigated for different composi­tions as presented in Table 15.

As expected from the data for the binary oxides UO2 _ x, PuO2 _ x, and AmO2 _ x (see Figure 22), the presence of americium leads to an increase of the oxygen potential in the ternary oxides (U, Am)O2 _ x and (Pu, Am)O2 _ x (Figure 24).

According to the comparison performed by Osaka et a/.,196 for a O/metal ratio above 1.96, the oxygen potential is the highest for AmO2 _ x then (Pu0.91Am0.09)O2 _ x followed by (U0.5Am0.5P2 _ x,

(U0.685Pu0.270Am0.045)O2 _ x, PuO2 _ x, and finally

(U0.6Pu0.4)O2 _ x. The experimental data are analyzed by considering the change ofthe oxidation states ofthe actinides Am and Pu. When the O/metal ratio decreases with stoichiometry, Am is first reduced from Am4+ to Am3+, then after all Am is reduced, Pu is similarly reduced. The recent Calphad model on the Am-Pu-O system derived by Gotcu-Freis eta/.42 allows the description of the oxygen potential in the whole composition range of the (Am, Pu)O2+/_x solid solution.

Hirota et a/.201 derived a thermochemical model for the (U, Pu, Np)O2 ± x oxide using the CALPHAD method. According to these calculations and to the experimental data of Morimoto et a/.19 on (U0.58Pu0.3Np0.12)O2, it was found that Np has a small influence on the oxygen chemical potential of (U, Pu)O2 _ x.

Table 15 Oxygen potential measurements in mixed oxides with minor actinides

(U0.5Am0.5)O2_x

(Pu0.91Am0.09)O2_x

(Am0.5Pu0.5)O2_x

(Am0.5Np0.5)O2_x

(U0.65Pu0.3Np0.05)O2 (U0.58Pu0.3Np0.12)O2 (U0.685Pu0 .270Am0.045)O2_x (U0.66Pu0.30Am0.02Np0.02)O2_x

Figure 25 Oxygen potential data of (Th1 _yUy)O2 + x solid solutions at 1473 K for various values of y after Ugajin.206

0

-100

£-200

о

E

-300

CM

Q.

a.

-400

-500

1.85 1.90 1.95 2.00 2.05 2.10

(b) O/Am

Figure 24 Oxygen potential data (a) in (Am05Pu05)O2_x at 1333 K according to Otobe efa/.197and in (Am009Pu091)O2_x at 1273 and 1423 K by Osaka efa/.196; (b) in (Am05U0.5)O2 at 873-1577 K by Bartscher and Sari.195

The oxygen potentials were measured for (Uo.66Puo.3oAmo. o2Npo. o2)O2 — * at 1473-1623 K by a gas equilibration method using (Ar, H2, H2O) mix­ture by Kato et a/.189 The values were compared to the oxygen potential data in (U07Pu03)O2 _ *188 with­out minor actinides. The m(O2) data are 10 kJ mol-1 higher in the mixed oxide containing Am and Np. The increase might be due to Am content.

2.02.4.3.2.2.3 (U, Th)O2 and (Th, Pu)O2 solid solutions Oxygen potential of (UyTh1 _J)O2 + * solid solutions was measured by Anderson et a/.202 using thermogravimetry for y = 0.03, 0.063, and
0.244, by Roberts et a/203 using pressure measure­ments for y = 0.05-0.06, by Aronson and Clayton204 using electromotive force method for y = 0.3-0.9, by Tanaka et a/.205 using electromotive force method for y = 0.05-0.3, by Ugajin206 using thermogravime­try for y = 0.05-0.2, by Matsui et a/207 using thermo­gravimetry for y= 0.2-0.4, and by Anthonysamy et a/.208 for y= 0.54-0.9 using a gas equilibration method. The analysis by Ugajin206 suggests that the oxygen potential is controlled by the change of ura­nium oxidation state as shown in Figure 25.

The results show that there is a systematic increase of the oxygen potential values with increasing thorium content. The oxygen potential data were retrieved and analyzed by Schram209 using the thermochemical model of Lindemer and Besmann with a mixture of the species ThO2, UO2, and UaOb for UO2 + *

Recent experimental data on enthalpy increments and heat capacities of (U01Th09)O2, (U0 5Th0 5)O2, and (U09Th01)O2 solid solutions were measured by Kandan et a/210 using, respectively, drop calorimetry at 479-1805 K and differential scanning calorime­try at 298-800 K. The results show that the solid solutions obey the Neumann-Kopp’s rule.

Protactinium (91Pa) is one of the rarest of the natural elements. Its most important isotope is 231Pa (half­life = 3.276x 104years), but the most interesting

from an industrial viewpoint is the artificial isotope 33Pa (half-life = 27.0 days). This is an intermediate isotope in the production of fissile 2 3U in thorium breeder reactors.

Some studies on PaC and PaC2 can be found in the literature.96-99 Lonsdale and Graves98 prepared a dilute solution of Pa in ThC2 by neutron irradiation of ThO2, followed by carbothermic reduction. The monocarbide was prepared by carbothermic reduc­tion of Pa2O5 by Lorentz et a/.99 Products of reaction at 2473 K contained a second phase, possibly PaC2.

Pa metal has been prepared from PaC in the presence of iodine using the Van Arkel method.1

2.04.3.1 Properties

Lorentz et a/.99 found by room — and high — temperature XRD that PaC is isostructural with other actinide monocarbides, displaying fcc sym­metry with a = 506.08 ± 0.02 pm, corresponding to a theoretical density of 12.95 gcm-3. At the highest temperatures (^2500 K), extra lines were observed, corresponding to a tetragonal body-centered structure (CaC2 type) with a = 361 ± 1 pm and c = 611 ± 1 pm, attributed to PaC2.

Lonsdale and Graves studied, by Knudsen effusion, the vapor pressure of Pa from a dilute solution of Pa in ThC2, showing that PaC2 has stability similar to ThC2.

The formation of Gibbs energy for PaC was esti­mated to be

AfG(PaC) ffi 182.5 — 0.0841 T(kJmol-1) [5]

Enthalpy, entropy, and Gibbs energy of formation of PaC and PaC2 are reported in Table 4 as estimated by assuming that the thermodynamic functions for Pa carbides lie between those of Th and U carbides.4 The considerable uncertainties stem from the large lack of data.

2.06.3.1 UF6: Uranium Hexafluoride

2.06.3.1.1 Properties

UF6 is solid at room temperature with a signifi­cant vapor pressure (P = 105mbar (1.05 x 104Pa) at 298 K). The triple point is 337 K for p = 1.5 bar, as shown on the P(UFg) = f (T) diagram (Figure 3).

The vapor pressure equations are detailed in Section 2.06.4.1.2.

The critical temperature was found between 513 and 518 K.9

Many other physical, thermodynamic, and crys­tallographic properties can be found, respectively, by Llewellyn,9 Settle et al.,10 and Hoard and Stroupe.1

What can be noted about UF6 is the large dif­ference between the density of the liquid and that of the solid at the triple point (4830 kgm — vs. 3630 kgm — ). If liquid UF6 solidifies in a process pipe, care must be taken during heating because of the swelling. The recommended equations for the density of solid and liquid UF6 are12

pS = 5200 — 5.77(T — 273)

pL = 3946 — 4.0628(T — 273) — 1.36102(T — 273)2 where p is in kilogram per cubic meter.

The viscosity of liquid UF6 is close to that of water (0.8 cps at 90 °C): 0.91, 0.85, 0.80, and 0.75 cps at, respectively, 70, 80, 90, and 100 °C.13 Liquid UF6 usually flows by gravity to fill the 48Y containers. A 48Y is a container that contains approximately 12.5 tonnes UF6.

Liquid UF6 has a dielectric constant e = 2.18 at 65 °C typical of a nonpolar solvent. The solubility of ionic compounds is low.14

A review of thermal conductivity for UF6 in the solid and liquid forms can be found in Lewis eta/.15

Our recommended values are:

k = 1.1Wm-1oC4 at 55°C

k = 0.16Wm-1oC-1 at 90°C

UF6 is thermally stable up to 1000 K. However, it is very difficult to study the stability above 700 K due to rapid corrosion of the metal reactors. Also, UF6 can be easily dissociated under UV source.16

UF6 -! UF5 + 0.5 F2

The average U-F binding energy in UF6 is 515 kJ mol-1, lower than H-F or Si-F but higher then C-F

or As-F.17

However, the first dissociation energy of UF6 is as low as 286 kJ mol — , yielding UF5. When the poly­merization energy of UF5 (153 kJmol-) is sub­tracted, one obtains an energy of 134 kJ mol-1, close to the dissociation energy of fluorine (153 kJ mol-1).

All these properties show that UF6 will act as an oxidative/fluorinating agent. It will not act as a reduc­ing agent due to its high ionization potential of 14 eV.

UF6 is therefore a stronger oxidizing agent than MoF6 or WF6. A lot of publications have been
devoted to various reactions of UF6 in organic chemistry18 or mineral chemistry.19

Two reactions are of industrial importance because of the need to convert the depleted UF6 back into U3O8.

• Hydrolysis of UF6 with water:

UF6 + 2H2O! UO2F2 + 4HF

In the presence of a large excess of UF6, other oxi — fluorides can be formed such as UOF4 or U3O5F8.20

• Reduction with H2:

UF6 + H2 ! UF4 + 2HF

Apart from oxidative properties, UF6 is also consid­ered a Lewis acid and will react with Lewis bases such as KF, which is usually present in the F2 used to produce UF6. NaF also forms Na2UF8 complexes that have been used to purify reprocessed UF6 from fission products.

2.06.3.1.1.1 Crystal structure

The structure of solid UF6 was determined by Hoard et a/.21 from X-ray single-crystal data. UF6 is orthorhombic, space group Pnma (D^h) with a = 9.00(2) A, b= 8.962(2) A, and c= 5.207(2) .A (Figure 4). This structure was confirmed by single­crystal neutron diffraction at 293 K by Taylor eta/.22 with a = 9.924(10) A, b = 8.954(9) A, and c = 5.198(5) A and by Levy eta/.23 with a = 9.92(5)A, b = 8.97(5)A, and c = 5.22 A.

2.08.4.1 In Air and in Water

Nickel does not lose its metallic brightness and does not discolor indoors, but it does slightly discolor outdoors, and a thin adhesive sulfate corrosion film is formed.

Nickel-copper alloys also maintain metallic brightness, but they turn into a charcoal color and form an adhesive corrosion film in the presence of

Table 10 Filler metal of nickel-based alloys Marks Chemical compositions (%) Ultimate tensile strength at R. T. (MPa) Elongation Applicable mother metal C Mn Fe P S Si Cu Ni Cr Mo Nb + Ta Co Al Ti W Others AWSA5.14 ERNiCr-3 40.10 2.5-3.5 43.0 40.03 40.015 40.50 40.50 467.0 18.0­ 22.0 — 2.0-3.0 — — 40.75 — 40.50 4552 430 Alloy 600 ERNiCrFe-5 40.08 41.0 6.0­10.0 40.03 40.015 40.35 40.50 470.0 14.0­ 17.0 — 1.5-3.0 — — — — 40.50 4552 430 Alloy 600 ERNiCrFe-6 40.08 2.0-2.7 418.0 40.03 40.015 40.35 40.50 467.0 14.0­ 17.0 — — — — 2.5-3.5 — 40.50 4552 430 Alloy 600 ERNiCrFe-7 40.04 41.0 7.0­11.0 40.02 40.015 40.50 40.30 a 28.0­ 31.5 40.50 40.10 — 41.10 41.0 — 40.50 4552 430 Alloy 690 ERNiCrMo-3 40.10 40.50 41.0 40.02 40.015 40.50 40.50 458.0 20.0­ 23.0 8.0­ 10.0 3.15­ 4.15 — 40.40 40.40 — 40.50 4720 430 Alloy 625 ERNiCrMo-2 0.05­0.15 41.0 17.0­20.0 40.04 40.030 41.0 40.50 a 20.5­ 23.0 8.0­ 10.0 — 0.50­ 2.5 — — 0.20­ 1.0 40.50 — Alloy X ERNiCrMo-4 40.02 41.0 4.0­7.0 40.04 40.030 40.08 40.50 a 14.5­ 16.5 15.0­ 17.0 — 42.5 — — 3.0­ 4.5 40.50 4690 430 Alloy C-276 ERNiFeCr-2 40.08 40.35 a 40.015 40.015 40.35 40.30 50.0­ 55.0 17.0­ 21.0 2.80­ 3.30 4.75­ 5.50 41.00 0.20­ 0.80 0.65­ 1.15 B 4 0.006 41138 Alloy 718 aAs remainder.

Table 11 Shielded metal arc welding electrode Marks C Mn Fe P S Si Cu Ni Cr Mo Nb + Ta Co Al Ti W Others Ultimate tensile strength at R. T. (MPa) Elongation Applicable mother metal AWSA5.11 ENiCrFe-1 =0.08 =3.5 = 11.0 =0.03 =0.015 ІІЛ p Ol ІІЛ 0 01 о ^62.0 13.0­ 17.0 — 1.5­ 4.0 — — — — =0.50 ^552 ^30 Alloy 600 ENiCrFe-2 =0.10 1.0­ 3.5 = 12.0 =0.03 =0.02 =0.75 =0.50 ^62.0 13.0­ 17.0 0.50­ 2.50 0.5­ 3.0 — — — — =0.50 ^552 ^30 Alloy 600 ENiCrFe-3 =0.10 5.0­ 9.5 = 10.0 =0.03 =0.015 = 1.0 =0.50 ^59.0 13.0­ 17.0 — 1.0­ 2.5 — — = 1.0 — =0.50 ^552 ^30 Alloy 600 ENiCrFe-7 =0.05 =5.0 7.0­ 12.0 =0.03 =0.015 =0.75 =0.50 a 28.0­ 31.5 =0.50 1.0­ 2.5 — =0.50 =0.50 — =0.50 ^552 ^30 Alloy 690 ENiCrMo-3 =0.10 = 1.0 =7.0 =0.03 =0.020 =0.75 =0.50 ^55.0 20.0­ 23.0 8.0­ 10.0 3.15­ 4.15 — — — — =0.50 ^724 ^30 Alloy 625 ENiCrMo-4 =0.02 = 1.0 4.0­ 7.0 =0.040 =0.030 =0.2 =0.50 a 14.5­ 16.5 15.0­ 17.0 — =2.5 — — 3.0­ 4.5 =0.50 ^690 ^30 Alloy C-276 ‘As remainder.

sulfur pollutants outdoors and into a green-gray color when near a beach.

Nickel-chromium, nickel-chromium-iron, nickel — molybdenum, and nickel-chromium-molybdenum alloys do not lose their metallic brightness, and do not discolor indoors or outdoors.

Nickel has excellent corrosion resistance in natu­ral and distilled water. Nickel and nickel-clad steels have been used for household water tanks, due to their very low corrosion rates, <0.0005 mm year — .

Nickel-copper alloys also show excellent corrosion resistance in natural water and distilled water. These alloys have been applied as seamless tubes in feed water economizers in fossil-fuel electric power plants.

The thermopower (S) has been reported for the ele­ments Th to Pu in the cryogenic range and up to 300 K.74 Figure 19 shows the values and the sign of S for the a-phase of these actinide elements. It can be observed that it varies from Th to Pu and depends strongly on temperature range. As no carrier is avail­able at 0 K, S is reduced when approaching very low temperatures. The thermopower of U and Np at high temperature shows discontinuities at the structural phase transition (a-p and consecutive).65 The high — temperature thermopower of Pu is not well known and is very sensitive to impurities. Experimental

results indicate that the actinide metals have thermo­power values close to those of the lanthanides75 but larger than the transition metals. This essentially can be related to large band structures and a huge density of states at the Fermi level.

In the Pu-N system, as shown in Figure 5,15 there is only one structure for the mononitride, PuN: an NaCl-type face-centered cubic (fcc) structure with а = 4.904 A. PuN is a line compound with little non­stoichiometry, and is reported not to congruently melt up to 25 bar nitrogen pressure.16 However, there is a study on the safety assessment of fuels on the basis of vaporization behavior in which the melt­ing temperature of Pu-N is given as 2993 K under a nitrogen pressure of 1.7 x 104Pa.17

2.03.2.2 Thorium Nitride

Though thorium is a fertile material, recent research on thorium and its compounds as nuclear fuel is scanty. The Th-Th3N4 phase diagram, reported in 196618, is shown in Figure 6. There are two solid compounds in this system, ThN and Th3N4; the former is an NaCl-type cubic structure with

1750

а = 5.169 A,18 and the latter is a rhombohedron with а = 9.398 JA and a = 23.78°.19 The congruent melting point is 2820 °C at nitrogen pressure of

2 atm. Hypo — and hyper-ThN appear above 1350 °C. Th3N4 decomposes to ThN in vacuum above 1400 °C with the formation of a small amount of oxide.20 As ThN oxidizes more easily than UN it is important to consider the temperature and nitrogen and oxygen pressures during the preparation of ThN by thermal decomposition of Th3N4.21

Hypostoichiometric plutonium monocarbide crystal­lizes in the rock-salt fcc (Fm3m) structure like the other known actinide monocarbides. The lattice constant of PuC1-x was studied by Rosen et a/.20 Its value for PuC074 was measured to be a = 495.4 ± 0.2 pm for samples quenched to room temperature from 673 K < T< 908 K. This value was observed to remain constant for compositions richer in Pu, whereas it increases up to 497.3 ± 0.1pm at the C-rich boundary in equilibrium with bcc Pu2C3. Based on those data, Rosen et a/. proposed the follow­ing formula to interpolate lattice constant data in the homogeneity domain of PuC1-x (Figure 25):

a(PuC1—x) = 498.13 — 11.50(1 — C/Pu) pm [46]

Of course, these data are affected by oxygen and nitrogen impurities.

The number of valence electrons per Pu atom in PuC is between 4 and 4.5,2 , 2 with a complex Fermi level occupancy of 5f electrons.2 1 C/Pu var­iations in PuC1— x are also reflected in the mag­netic ordering temperature. It was observed that PuC1— x at the C-rich limit undergoes a magnetic phase transition at «100 K, leading to a simple anti­ferromagnetic structure with Pu moments along the (0, 0, 1) direction.213

Haines et a/214 provided the most recent set of low-temperature (10 K < T< 300 K) heat capacity experimental data for PuC0.865, PuC0.89, and PuC0.9. The three samples showed a broad peak in the heat capacity curve between 75 and 95 K, certainly con­firming the antiferromagnetic transition observed by Green eta/213 with neutron diffraction. The resulting room-temperature thermal functions suggested by Holley et a/.4 for PuC0.84 are reported in Table 8.

The heat capacities of plutonium carbides increase very sharply with carbon content in the nonstoichiometric composition range of plutonium monocarbide, where available data are not always consistent. Oetting215 measured enthalpy increments of PuC0.82 and reported a sharp increase in heat capacity at ^950 K, not observed by Kruger and Savage216 in PuC0 87. The heat capacity of plutonium monocarbide is slightly lower than that of UC, prob­ably due to hypostoichiometry and higher O and N impurities, resulting in a nearly stoichiometric Pu-C-O-N lattice.

Holley et a/.4 interpolated the low-temperature data with the high-temperature data of Kruger and Savage and Oetting. The resulting equation is given in Table 9 and plotted in Figure 14. This trend differs slightly from the data of Kruger and Savage, which are, however, recommended for the calculation of the heat capacity of mixed monocarbides (U, Pu)C

497.5

Q.

497.0

4)

I 496.5

ra

CL

496.0

о

495.5

495.0

494.5

494.0

34 36 38 40 42 44 46 48 50 52 54 56

Atom % carbon

Figure 25 The lattice constant of plutonium monocarbide as a function of carbon content. Reproduced from Holleck, H.; Kleykamp, H. In Gmelin Handbook of Inorganic Chemistry Transurane Teil C: Verbindungen; Springer-Verlag: Berlin, 1972.

by the Newman-Kopps’ rule. In fact, the data of Kruger and Savage are closer to the values of hypo­thetical, vacancy free, PuC. They are well interpo­lated between 425 and 1295 K by

Cp(PuCKS) =54.76 — 4.79 x 10-4T — 1.353 x 106T-2 (Jmol-1K-1) [47]

The Gibbs free energy of formation of Pu monocar­bide reported in Table 8 from 298 K to the peritectic temperature (Figure 15) is based on the reviews of Holley eta/4 and Fischer.131

Natural zirconium has an atomic mass of 91.22 amu, with five stable isotopes (90Zr : 51.46%, 91Zr: 11.23%, 92Zr: 17.11%, 94Zr: 17.4%, and 96Zr: 2.8%). The depletion of the most absorbing isotope (91Zr, with oa ~ 1.25 x 10-28m2) would increase further the inter­est of using Zr alloys in reactors, but would clearly be economically inefficient. The cross-section for elastic interaction with neutrons is normal, with respect to its atomic number (o^ff ~ 6.5 barn). Despite its high atomic mass, the large interatomic distance in the hcp crystals lead to a limited specific mass of 6.5 kg dm-3.

The thermophysical properties correspond to stan­dard metals: thermal conductivity ~22Wm-1K- and heat capacity ~-280J kg-1 K — , that is, close to 3R per mole.

Below 865 °C, pure Zr has an hcp structure, with a c/a ratio of 1.593 (slightly lower than the ideal 1.633). The lattice parameters are a = 0.323 nm and c = 0.515 nm.3 The thermal expansion coefficients show a strong anisotropy, with almost a twofold differ­ence between the aa and ac coefficients (respectively

5.2 and 10.4 x 10-6 K-1).4 This anisotropic behavior of the thermal expansion induces internal stresses due to strain incompatibilities: After a standard heat treat­ment of 500 °C, where the residual stresses will relax, cooling down to room temperature will result in inter­nal stresses in the range of 100 MPa, depending on grain-to-grain orientations. The modulus of elasticity is also anisotropic, but with lower differences than for thermal expansion (Ea = 99GPa, and Ec = 125 GPa).5 For industrial parts, the values recommended are close to a ~ 6.5 x 10-6K-1 and E ~ 96 GPa. The tem­perature evolution of the elasticity constants is unusual: the elasticity is strongly reduced as the tem­perature increases (~5% per 100 K).6,7 This abnormal behavior is specific to the hcp metals of the IV-B row of the periodic table.8

At 865 ° C, Zr undergoes an allotropic transforma­tion from the low temperature hcp a-phase to the bcc p-phase. On cooling, the transformation is usually bai — nitic, but martensitic transformation is obtained for very high cooling rates (above 500 Ks-1). The bainitic transformation occurs according to the epitaxy of the a-platelets on the old p-grains, as proposed by Burgers9,10: (0001)a // {110} p and (1120)a // (111)p. Among the 12 different possible variant orientations of the new a-grains, only a few are nucleated out of a given former p-grain during this transformation to minimize the internal elastic strain energy. This pro­cess leads to a typical ‘basket-weave’ microstructure (Figure 1). As a result, a p-quenching does not completely clear out the initial crystallographic texture that had been induced by the former thermomechani­cal processing.11,12 Although the alloying elements present in the Zr alloys change the transformation temperatures, with a 150 °C temperature domain in which the a — and p-phases coexist, the crystallographic nature of the a-p transformation is equivalent to that of pure Zr. Specific chemical considerations (segregations and precipitations) will be described later.

The melting of pure Zr occurs at 1860 °C, sig­nificantly above the melting temperature of other structural alloys, such as the structural or stainless steels. At high pressures, (P> 2.2 GPa) a low-density hexagonal structure is observed, known as the rn-phase.

Isothermal sections of the U—Pu—0 phase diagram in the oxide-rich region are available only at 300, 673, 873, and 1073 K according to the review by Rand and Markin52 which is mainly on the basis of the

experimental investigation by Markin and Street.53 The isothermal section at room temperature was later slightly modified by Sari et a/.54 The fluorite-type structure of the mixed oxide (U, Pu)O2 has the ability to tolerate both addition of oxygen (by oxidation of the uranium) and its removal (by reduction of the pluto­nium only), leading to the formation of a wide homo­geneity range of formula MO2 ± x. Thus, at high temperature, the solid solution is a single phase that extends toward hypo — and hyperstoichiometry. But the extent of the single-phase domain is not well known at high temperature.

At low temperature, as shown in Figure 7(b) (redrawn in Konings et a/.55 from Rand and Markin,52 Markin and Street,53 and Sari et a/.54), the oxide-rich part of the U-Pu-O phase diagram is complex:

• Region with O/metal ratio <2

The mixed oxide (U10o — yPuy)O2 _ x withy < 20 at.

% of Pu is a single phase. The hypostoichiometric
oxide is in equilibrium with (U, Pu) alloy. At T< 900 K, the mixed oxides (U100 _yPuy)O2 _ x with a plutonium content y > 20at.% enter a two-phase region that leads to the decomposition into two fcc oxide phases with two different stoichiometries x and x1 in oxygen, MO2 _ x and MO2 _ xl. This is consistent with the existence of a miscibility gap in the fcc phase in the Pu-O system. This phase separation was recently observed in mixed oxides (U, Pu)O2 with small addi­tion of Am and Np by Kato and Konashi.56 For higher Pu contents (y > 50at.%), the mixed oxide can enter other two-phase regions [MO2 _ x + M2O3 (C)] and [MO2 _ x + PuO162]. The existence of these two-phase regions comes from the complex phase relations encountered in the Pu2O3-PuO2 phase diagram at T< 1400 K (Figure 2(b)). The isothermal sections at 673, 873, and 1073 K in Rand and Markin52 show that the extent of the two-phase regions decreases with temperature. The existence

of a single phase region M2O3 (C) was reported along the Pu2O3-UO2 composition line.

• Region with O/metal ratio > 2

At room temperature, the oxidation of mixed oxides with a Pu content lower than 50% results in either a single fcc phase, MO2 + x with a maximum O/M ratio of 2.27, or in two-phase regions [MO2 + x + M4O9], [M4O9 + M3O8] and [MO2 + x + M3O8]. The M4O9 and M3O8 phases are reported to incorporate a significant amount of plutonium. However, the exact amount is not known.

Yamanaka eta/.57 developed a CALPHAD model on the U-Pu-O system that reproduces some oxygen potential data in the mixed oxide (U, Pu)O2 ± x and allows calculating the phase diagram. This model pre­diets the two-phase region [MO2 _ x + PuO162] but does not reproduce the existence of the miscibility gap in the fcc phase. This region was recently reinves­tigated by Agarwal et a/.58 using a thermochemical model. The resulting UO2-PuO2-Pu2O3 phase dia­gram is presented in Figure 8. The extent of the mis­cibility gap in the fcc phase is described as a function of temperature, Pu content, and O/metal ratio. This description of the phase diagram is not complete as it does not take into account the existence of the PuO152 and PuO161 phases that may lead to the formation of other two-phase regions involving the fcc phase.

In conclusion, no satisfactory description of the U-Pu-O system exists. Both new developments of models and experimental data are required.

Recent studies on MA-containing fuels have measured the thermal expansion of various Np-Pu — Am-Cm-N compounds (shown in Figure 3498), as well as those of NpN and AmN (Figure 32). As shown in Figure 32, the thermal expansion of AmN is the same as that of PuN; however, the thermal expansion of NpN is smaller than PuN and AmN, but is the same as that of UN. The thermal expansion of Np-Pu-Am-Cm-N fuels decreases with a decrease in Np content, as shown in Figure 34. The thermal expansion of ZrN inert matrix fuels also decreases due to the low thermal expansion of ZrN. Molecular dynamics (MD) calculations have also predicted the thermal expansion of some MA nitrides; these are shown in Figure 35 9

The lack of data on MA nitrides, especially the nitrides of pure transuranium elements, is due to the difficulty in obtaining and treating bulk samples. There have been some attempts to calculate the

Temperature T (K) Temperature T (K) Temperature T (K)

Figure 35 Temperature dependence of calculated linear thermal expansion of minor actinide nitrides. Reproduced from Kurosaki, K.; Adachi, J.; Uno, M.; Yamanaka, S. J. Nucl. Mater. 2005, 344, 45-49, with permission from Elsevier.

mechanical properties of these actinide nitride samples. One such attempt combined the calculations for longitudinal velocity and porosity.100 In the method employed, a newly proposed correlation between Pois­son’s ratio and the ultrasonic longitudinal velocity was utilized, and the elastic properties of uranium nitride as well as uranium dioxide were estimated from the porosity and longitudinal velocity derived from ultra­sonic sound velocity measurements; these had been previously used to determine mechanical properties of actinide materials. Another method estimated frac­ture toughness from the Young’s modulus, hardness, the diagonal length and the length of micro cracks. Except for Young’s modulus, all the other properties were obtained by an indentation method.101 In this study, not only was the fracture toughness reported, but its load dependence, in the case of UN, was also reported.

2.03.2 Summary

In this chapter, various properties of actinide nitrides have been discussed. As nitride fuels have some advantages over the oxide fuels, thermal and thermo­dynamic properties of UN, PuN and their solid solu­tions have been thoroughly studied. On the other hand, some properties (especially physical) need bulk samples for measurements, especially the trans­uranium elements such as NpN, AmN, and CmN;

these are difficult to obtain and handle and are scarce. Some properties of the inert matrix fuels such as (An, Zr)N solid solution and AnN and TiN mixture have been obtained through recent studies on the targets for transmutation in an ADS. Recent progress in experimental procedures and estimation methods, which are supported by developments in model cal­culation, have also been discussed.

The progress made in experimental techniques and calculation science has brought about growth in the understanding of the behavior of these nitrides. However, we need to accumulate more data, espe­cially in the thermal and mechanical properties around 1673 K, in-reactor temperature, and the vari­ation of those with burnup, in order to accurately predict the in-reactor behavior of these fuels (see Chapter 3.02, Nitride Fuel).