Nakajima et al7 have estimated the values of AfG for NpN(s). Figure 23 shows the temperature depen­dence of AfG, together with AfG for UN(s), as given

-90 E

-100

c g

I -110

-120 O)

-130

c

(D

S -140

4—

(J)

-150

by Hayes et al.46 and the AfG for PuN(s), as given by Matsui and Ohse.76 The line for NpN(s) is that of the following equation and was determined by a least — squares treatment of the data:

Af G(J mol1) = -295 900 + 89.88T

(1690 <T(K) < 2030) [16]

Nakajima et al. have evaluated these results in the temperature range of 1690-2030 K using the data of N2(g) pressure over NpN(s) + Np(1) derived upon extrapolation of the experimental data given by Olson et al. Then, Nakajima et al.85 have also carried out a mass-spectrometric study on NpN(s) co-loaded with PuN(s) in order to control the N2(g) pressure by the congruent vaporization of PuN(s). The AfG value calculated for NpN(s) almost completely agrees with that obtained from eqn [16].

Ogawa et al.34 have estimated the Gibbs free energy of formation for AmN from the partial pres­sure of Am(g) over (Pu, Am)N. Their values of AG for AmN(s) are given by the following equation:

AG(J mol-1) = -297659 + 92.054T

(298 <T(K) < 1600) [17]

Phase relationships in the U-Pu-C system have been studied extensively in Los Alamos Scientific Lab of the University of California and Argonne National Laboratory.234-237 The most recent review of the U-Pu-C system is due to Fischer.238

A few general results are commonly accepted:

1. with increasing ‘Pu’ content, the sesquicarbide becomes more stable

2. segregation occurs, resulting in a sesquicarbide phase richer in plutonium238

3. the lattice defect concentration typical of Pu-C compounds decreases with the addition of uranium

4. the melting point decreases with increasing Pu

Many properties of (U, Pu) mixed carbides can be deduced from these points.

Uranium monocarbide forms a complete solid solution with plutonium monocarbide. An isothermal section at 843 K of the ternary U-Pu-C diagram is shown in Figure 29. The (U, Pu)C phase is stoichiometric in regard to its carbon content in a composition range from 0 to 35 at.% Pu. With a further increase in Pu content, it tends to become hypostoichiometric.

The biphasic field, MC+MCi.5, exists between 50 and 60 at.% C, depending upon the Pu/U ratio. Mardon and Potter241 calculated segregation in the MC+M2C3 region at 1200 and 1800 K. Holleck242 reports segregation at 1773 K at two defined conodes: [xpJP = 0.095, x^203 = 0.172] and [xpJP = 0.17, *Mu2C3 = 0.264], indicating that the higher the pluto­nium content, the more pronounced is the plutonium segregation into two phases. This effect is reduced at higher temperature. Accordingly, the lattice para­meter trend in the pseudobinary UC-PuC1— x and U2C3-Pu2C3 systems often deviates from Vegard’s law (Figure 30). This behavior has been explained as due to the abundant lattice vacancies and the phase segregation toward the formation of the sesquicarbide in the Pu-rich composition range (>65 at.% PuC1—x). Interestingly, a clear negative deviation from Vegard’s law and from the ideal solution behavior was observed in the U-rich carbides too.235 A slightly negative deviation from Vegard’s law was also reported for the solid solution U2C3-Pu2C3.

Ohse and Capone240 studied (U08Pu02)-C in the temperature range 1773-2731 K, and the composition range, C/M = 0.95-1.4, and reported (i) MC/(MC+M2C3) phase boundaries: 2000 K for xc = 0.517, 2100 K for xc = 0.524 and 2200 K for xc = 0.532; (ii) MC/(MC+M2C3+MC2) phase bound­ary: 2300 K, xc = 0.539; and (iii) MC/(MC+MC2)

499.5

499.0

498.5

498.0

Q.

497.5

ф

I 497.0

Q.

496.5

о

496.0

495.5

495.0

494.5 __

0 10 20 30 40 50<pUCi 60 70

UC PuC

Atomic % Pu in UPuC1-x

phase boundaries: 2400 K for xc = 0.547 and 2500 K for xc = 0.551.

The (U, Pu)C10 solidus-liquidus curves are plot­ted together with experimental data in Figure 31.

The higher solidus line was calculated by assuming an ideal solution behavior of both solid and liquid (U, Pu)C. However, solidus data reported by Dalton by high-temperature XRD243 are lower, and in better agreement with the phase boundary calculated by Fischer238 using a substitutional solution model.

This confirms the nonideal behavior of the (U, Pu)C solution. The formation of a M2C3 phase in the Pu-rich part of the UC-PuC diagram explains the partial disagreement between the observed melting temperature of high-Pu mixed carbides and the peri — tectic of pure PuC1_x131,238 (cf. Figure 32(b) below).

Complete solubility of plutonium sesquicarbide in uranium sesquicarbide has been observed below 2033 K. The equilibrium temperature of the transfor­mation MC15 ! MC+MC2 increases with increas­ing plutonium content from 2106 K for UC15 to 2273 K for (U0.9Pu0 1)045C0.55 and 2445 K for (U0.9Pu0.2)C15. However, this decomposition reaction is not observed for (U09Pu01)0.48C0.52 as uranium — rich monocarbide can accommodate extra carbon at high temperatures.

By mass spectrometry and electron micro­probe analyses, Browning et at24 established the reaction MC2!M2C3+C for Pu/(U+Pu) = 0.575 at 2128 ± 10 K, 100 K higher than Dalton243 and Reavis
eta/.132 At high temperatures, U-rich MC2_xforms a continuous solid solution with MC, as observed for the binary U-C system. However, small amounts of plutonium get segregated as sesquicarbides phase because PuC15 is more stable than PuC2.

The compositions U0.5Pu0.5C2 and U0.5Pu0.5C1.5 undergo peritectoid decomposition and melting tran­sitions at 2018 and 2598 K, and 2018 and 2613 K, respectively. Data are not always consistent due to inaccurate determination of the C content and the presence of N and O impurities.

Udovskii and Alekseeva245 used the experimental data from the literature to construct the phase dia­gram of the U-Pu-C system. They also presented a schematic projection of the liquidus surface. Simi­larly, Mardon and Potter241 calculated phase equili­bria for isothermal sections at 2573, 2473, 2373, and 2273 K. No ternary compounds have been observed in the U-Pu-C system.242

The pseudobinary UC2-PuC2 system is little known and still controversial.9 The solidus-liquidus lines appear rather close to each other and regular between the melting points of the two end members. The cubic dicarbide phase appears to be more stable in the mixed dicarbide than it is in the pure Pu dicarbide, and the tetragonal dicarbide seems to exist for U-rich compositions only (PuC2 < 20at.%).

As a summary of the discussed results, Figure 32 (a)-32(d) show the xc = 0.60 isopleth section of the U-Pu-C ternary phase diagram proposed by

Dalton243 and the MC, M2C3, and MC2 isoplethal sections optimized by Fischer,238 respectively.

The thermal conductivity of (U, Pu)C decreases with increasing Pu content (up to 1273 K), as reported in Figure 1. The electrical resistivity increases with increasing Pu content by a factor 3 between 10 at.% PuC and pure PuC.

Sengupta et al. , observed that the thermal expansion coefficient of (U,Pu) carbides increases with Pu content. Although no creep data are available for pure plutonium carbides, Sengupta et al. observed that Pu-rich carbide fuel is harder than U-rich fuel up to 1553 K (average volumetric temperature of the

fuel pin).248

2.04.5 Summary

Research on actinide carbides is seeing a renaissance after the ‘Generation IV’ International Forum relaunched the design of nuclear plants with fast neutron spectra.1 In the last decade, early experimen­tal results have been assessed and reinterpreted in the light of recent theoretical calculations. In parallel, a few new experimental results are being produced with novel techniques. More complex geometries and interactions are also being studied, as for exam­ple, the behavior of coated carbides in fuel particles.

It appears that the properties of actinide car­bides are strongly dependent on the experimentally unavoidable oxygen and nitrogen impurities. For this reason, a deeper understanding of the behavior of these materials as a function of oxygen and nitrogen contents will be of fundamental importance. This is true for both fundamental physicochemical properties and technologically important ones, such as the mechanical parameters and the behavior under irradiation.

The thermal properties of Zr alloys are given in Table 3. The heat capacity increases with tempera­ture, about 10% for 300 K. The anisotropy in any property is indeed decreasing with temperature, as the anisotropy in thermal expansion drives the hcp cell of Zr toward the ideal c/a ratio. In addition to the anisotropy of the thermal expansion coefficient, the elastic weakening in temperature has also to be considered.

As for any alloy, an increase in temperature results in a decrease in strength, but the evolution is not uniform, and a plateau in strength is observed near 200-400 °C. Known as the dynamic strain aging (DSA), it corresponds to the interaction of oxygen atoms with the dislocations. In this temperature range, oxygen atoms diffuse at rates commensurable with dislocation glide and hinder their motion. At higher temperatures, they are too mobile to affect the creep rates drastically.

Typical creep deformation rates are expressed by equations such as

e= Asnexp

Due to the transition induced by the oxygen in DSA, large discrepancies are observed in the creep
behavior of different alloys.43 For conditions leading to strain rates below 10-9s — (i. e., low temperatures and/or stresses), a low stress coefficient is observed: n ~ 1-2. Grain boundary sliding may be the mecha­nism involved in these conditions. For high creep rates, stress exponents larger than 4-6 have been reported. The mechanisms considered are complex, with predominance of dislocation glide controlled by local climb.44 Similarly, the activation energy was measured to be as low a 40 kJ mol-1 for the low temperature regime, and 2 or 3 times larger for the high strain rates.

Most of the metallurgical parameters affect the creep rate. The effect of alloying elements on creep properties is different from their effect on tensile strength. Oxygen improves creep resistance, espe­cially at low temperatures, but its effect is small compared to improvement in yield strength at room temperature. Despite its detrimental effect on cor­rosion, tin is maintained at significant levels in Zircaloys as an efficient alloying element to im­prove creep resistance.45 For similar alloys with the same structure, creep behavior is similar; for exam­ple, Zircaloy-2 and Zircaloy-4 have similar creep strengths for the same thermomechanical processing. However, the metallurgical state of the material also influences the creep mechanisms; although SR mate­rial has higher tensile strength, its high dislocation density induces a two — to threefold increase in creep rate, compared to the RX state. Completely dissolved hydrogen increases the creep rate, while precipitated hydrides harden the alloys.46 For additions as low as 50 ppm, sulfur drastically increases the creep strength, and is now an alloying element for specific alloys.47

2.07.5.2 Hydrogen Embrittlement and Other H Effects

During oxidation of Zr alloy components in reactors or in autoclaves, the reduction of water by the Zr alloy follows the general reaction scheme:

2H2O + Zr! ZrO2 + 4H"

The reduction of the water molecules at the coolant-oxide interface releases four hydrogen atoms as radicals H". They are chemically adsorbed at the tips of the oxide pores and their evolution controls the behavior of this chemical species. Most of the H atoms recombine, creating hydrogen mole­cules that escape and dissolve into the coolant. A limited amount can ingress in the oxide and migrate to the metallic matrix, where H is soluble, or interact with Zr to form hydrides (see Chapter

5.3, Corrosion of Zirconium Alloys). The frac­tion of the hydrogen that is trapped in the Zr alloy is called the hydrogen pick-up fraction (HPUF). For Zry-2, it is in the range of 30-60%, and for Zry-4 a lower HPUF is observed (15-25%), while the Zr-Nb alloys show the lowest one (4-10%). In order to reduce H pick-up, care should be taken to avoid the alloys catalyzers of the hydrogen molecule dissociation, such as Ni and Pt. This is the main reason for suppression of that element in Zircaloy-4: on removing Ni, HPUF is generally below 15% for standard PWR fuel cladding. Due to the strong variation of the solubility of H with temperature (^200 ppm at 350 °C, but near 1 ppm at RT), hydro­gen reacts with Zr to precipitate as hydrides as the alloy is cooled down.

One of the consequences of hydrogen ingress into Zr is the delayed hydride cracking (DHC).48 This high temperature mechanism involves the ingress of hydrogen into a Zr-alloy component, its migration up the stress or thermal gradients, and its concentration in the regions of low temperature or higher tensile stress. When the local concentration exceeds the terminal solid solubility, the hydride phase precipitates.49 At operation temperatures, a quasicontinuous crack growth is observed, whose rate depends on the hydrogen content, on the struc­ture of the alloy, and on its crystallographic texture.50 The failure of CANDU pressure tubes by this mech­anism added pressure to the R&D in this field.51

At lower temperatures, corresponding to fuel handling and transport, the dissolved hydrogen pre­cipitates as 8 hydrides that have very brittle behavior. The hydrides are brittle below 200 °C and crack when the stresses are high enough; failure of the components at low temperatures occurs because of percolation of the broken hydride platelets. Depend­ing on the geometry and spatial distribution of the hydrides, very low ductilities can be observed. A slight increase in temperature would make the hydrides ductile and the mechanical behavior of the claddings returns to normal above 200 °C.52,53

Hydrogen increases the creep strength of SR Zry, whatever be the H content. However, for RX alloys, H that gets completely dissolved enhances the creep rate, while precipitated hydrides harden the alloys.54 This difference in behavior is connected to the effect of hydrides in inhibiting the thermal recovery. As described earlier, sulfur at very low concentrations drastically increases the creep strength, and even the yield strength.47,55

Hydrogen in the cladding is also claimed to increase the corrosion rate due to the presence of an outer rim of hydrides,56 and to deteriorate the behav­ior of the cladding during accident sequences, such as reactivity-induced accident (RIA), in which brittle hydrides drastically reduce the strain to failure,57-60 or loss of coolant accident (LOCA), where the clad­ding that is softened by hydrogen creeps faster and fails at lower temperatures than it would with lower hydrogen contents,61 or mixtures of these effects.

2.07.5.3 Prospectives

Although the use of Zr alloys has proven to be a good engineering solution, several properties are still sub­ject to poor scientific understanding of their origins. Among them, deformation mechanisms (critical shear stresses on the different shear and twin systems), irradiation behavior (point defects interactions with alloying elements and mobilities), and corrosion mechanisms at atomic scales clearly need further basic scientific work.

For industrial purposes, the lot-to-lot variations in properties observed in many instances require larger margins in design and consequently reduce the effi­ciency of the power plants. Detailed analysis of the origins of these variations could be highly cost effective.

Last, the current development of computational materials science is a major opportunity for in-depth understanding and forecasting of the mechanisms of irradiation damage under irradiation. In that direc­tion, multiscale modeling is particularly suited to nuclear materials. Zr alloys having no other sizable application than in the nuclear industry would strongly benefit from these new R&D techniques.

Rudy Konings is currently head of the Materials Research Unit in the Institute for Transuranium Elements (ITU) of the Joint Research Centre of the European Commission. His research interests are nuclear reactor fuels and actinide materials, with particular emphasis on high temperature chemistry and thermodynamics. Before joining ITU, he worked on nuclear fuel-related issues at ECN (the Energy Research Centre of the Netherlands) and NRG (Nuclear Research and Consultancy Group) in the Netherlands. Rudy is editor of Journal of Nuclear Materials and is professor at the Delft University of Technology (Netherlands), where he holds the chair of ‘Chemistry of the nuclear fuel cycle.’

Roger Stoller is currently a Distinguished Research Staff Member in the Materials Science and Technology Division of the Oak Ridge National Laboratory and serves as the ORNL Program Manager for Fusion Reactor Materials for ORNL. He joined ORNL in 1984 and is actively involved in research on the effects of radiation on structural materials and fuels for nuclear energy systems. His primary expertise is in the area of computa­tional modeling and simulation. He has authored or coauthored more than 100 publications and reports on the effects of radiation on materials, as well as edited the proceedings of several international conferences.

Todd Allen is an Associate Professor in the Department of Engineering Physics at the University of Wisconsin — Madison since 2003. Todd’s research expertise is in the area of materials-related issues in nuclear reactors, specifi­cally radiation damage and corrosion. He is also the Scientific Director for the Advanced Test Reactor National Scientific User Facility as well as the Director for the Center for Material Science of Nuclear Fuel at the Idaho National Laboratory, positions he holds in conjunction with his faculty position at the University of Wisconsin.

vi Editors Biographies

The thermodynamic data for uranium and neptu­nium oxides with oxygen/metal ratios >2 are reported in Tables 13 and 14 based on the review by Konings et a/.38

For UO3, the recommended heat capacity func­tion is based on the fit of the experimental heat

Table 12 Heat capacity function for actinide sesquiox­ides according to Konings eta/.36

Oxide Heat capacity equation for solid oxides (JK-1 mol-1)

Pu2O3 Cp = 130.6670 + 18.4357 x 10-3T — 1705300T-2 Am2O3 Cp = 115.580 + 22.976 x 10-3T — 1087100T-2 Cm2O3 Cp = 123.532 + 14.550 x 10-3T — 1348900T-2

capacity data from Popov eta/.140 and enthalpy incre­ment by Moore and Kelley.141 For U3O8 and U4O9, the equation for the heat capacity is taken from Cordfunke and Konings.142

2.02.4.2 Mixed Oxides

Carbajo et a/.84 did a review of the thermophysical properties of MOX and UO2 fuels. All the available

experimental data and equations for heat capacity and enthalpy data are given in that paper.

Recent measurements were performed by Duriez et a/.143 and by Kandan et a/.144 Duriez et a/.143 measured the heat capacity of stoichiometric (U, Pu)O2 samples with up to 15% Pu in the temper­ature range 473-1573 K using differential scanning calorimetry. Kandan et a/.14 measured enthalpy increment for MOX with 21%, 28%, and 40% Pu using a high-temperature differential calorimeter in the temperature range 1000-1780 K. The agreement between all the experimental data is good.

As reported in all these studies, the experimental results are in good agreement (within 2-3%) with the Neumann-Kopp rule:

Cp(T, U^PuyO2) = (1 — y)Cp{T; UO2)

+ yCp(T; PuO2) [10]

2.02.4.3 Nonstoichiometric Dioxides

As mentioned above, the actinide dioxides always exhibit a composition range with a deficit and an excess in oxygen where the thermodynamic proper­ties vary with both deviation from stoichiometry and temperature.

The theoretical density of a given crystal structure can be obtained from the lattice parameters if also the molecular weight is known. Using а = 534.60 pm for ThC0.98 at room temperature yields p = 10.60 gcm~3. Considering the thermal expansion, the th. d. of solid ThC at the melting point is p = 10.2 gcm~ .

The adiabatic elastic constants Cj were measured only on a ThC0063 sample by the pulse echo overlap method between 4.2 and 300 K along the [110] crys­tallographic directions.85 The resulting adiabatic bulk modulus B = 1/2(c11+2c12) = 60.49 GPa at 300 K. The adiabatic shear modulus was obtained in the Voigt approximation to be G = 31.87 GPa. Geward et a/.86,87 evaluated the isothermal bulk modulus of ThC0.8 from high-pressure XRD measurements up to 50 GPa, yielding BThC0.8 = 109 ± 4 GPa at 300 K, with dB/dTffi+3. As the direct Th-C bonding for­mation leads to a pronounced increase of structural rigidity from metal to carbide, the Th carbide bulk modulus increases with C content starting from metallic a-Th, and a value of around 120 GPa for B seems reasonable for stoichiometric ThC.

ThC1±x Vickers hardness increases from 50 HV for 0.02 wt% C to 850HV (with a load of 2 N) for ThC0 98 (with 1 at.% of oxygen).6

According to these results, the addition of carbon to thorium drastically reduces its cold workability. Untempered samples with C contents >6 at.% are stiff and brittle with room elongations at fracture eF = 0. Thus, tensile properties could be studied for low C content only. The 0.2% offset yield stress s0.2 varies from 165MPa for 0.10 wt% C to 250MPa for 0.20 wt% C. The yield stress, ay varies from 166MPa for 0.04 wt% C to ^370MPa for 0.22 wt% C (ThC005 in equilibrium with ThC0.67 at room temperature). The elongation at fracture eF goes from 35% for 0.04 wt% C to 11% in ThC005 in equilibrium with ThC0.67, to nearly zero for higher C contents. In the same composition range, the ulti­mate tensile strength ffu ranges between 250 and 400 MPa at room temperature and rapidly decreases with temperature (around 50 MPa at 1000 K).6

The creep and flow stress behavior in ThC alloys up to 2.83 wt% C (ThC0.54) between 4.2 and 573 K was reviewed by Kleykamp et а/6 It was found to be composed of a thermally activated and an athermal component. The first increases with carbon content and the strain rate. The 2% offset yield stress at a strain rate de/dt = 3.3×10~5s~1 was obtained as a function of temperature. At room temperature, it ranges from 50 MPa for 0.077 wt% C to 250 MPa for 2.83 wt% C. This value increases considerably at 4.2 K, where it is measured around 1.3 GPa.

2.04.2.2.4.1 Thorium dicarbide

The theoretical XRD density of monoclinic a-ThC2 is 9.14 gcm~3 and 8.80 gcm~3 for tetragonal p-ThC2 with C/Th = 1.94 at 1768 K. Fink eta/.43 estimated the density of g-ThC2 to be around 9.0 g cm~3 at the melting point.

Oikawa and Hanaoka88 give a value of Young’s modulus E = 1-2 GPa and a compressive strength suc = 20 MPa for low-density ThC2_x in equilibrium with C at room temperature. Room temperature Vickers hardness of arc-melted, two-phase a-ThC2 in equilibrium with C under a load of 2 N is 600 HV. This value is increased up to 650 HV after heat treatment to 1873 K, and it obviously depends on the oxygen-impurity content, which can make it increase up to 970 HV.6,89

Values of the bulk modulus B = V^(d2E/dV2) = V~J(dP/dV) and its pressure derivative B = dB/dP reported in Table 3 were calculated at 0K for the three ThC2_x allotropies by Shein and Ivanonvskii.50

2.04.2.2.3 Optical properties

2.04.2.2.5.1 Thorium monocarbide

Freshly broken surfaces of ThC have a shiny metallic gray color which darkens in the presence of oxygen. Optical constants of nearly stoichiometric ThC have been measured in liquid samples by Bober et a/.90 by a laser integrating sphere reflectometer between 2900 and 3900 K and l = 458, 514, 647, and 752 nm. For unpolarized light, p at the melting point (2773 K) was measured to be close to 0.45 at l = 647 nm and в = 45°, this value not being very much dependent on the angle. Optical constants are deduced from these results: the real refractive index n (between 1.6 and 2.0) and the absorption constant k (between 1.7 and 2.5). Both n and k slightly increase with wave­length and decrease with temperature.

2.04.2.2.5.2 Thorium dicarbide

a-ThC2_x crystals are transparent and look yellowish under the optical microscope. Freshly broken sur­faces of ThC2_x crystals display a very pale metallic yellowish appearance which darkens with time in the presence of oxygen.6

Grossman84 reported measurements of spectral normal emissivity e2 of ThC2_x (9.24 wt% C, <0.5% O2) for 1500K < T< 2100K, yielding an average value ei = 0.58 ± 0.03. The same author also reported an average value of the total spherical emissivity between 1800 and 2150 K, et = 0.475 ± 0.025.

The general view on the phase diagram between actinides and Sn or Pb is slightly different from that between actinides and Al or Ga. Several intermetallic compounds with the same composition between acti­nide and the Group b metal appear in those phase diagrams, although some of the crystal structures are different from each other. The crystal structure ofthe Laves phase formed between actinides and Group b metals is summarized in Table 24. In the actinide-Al or actinide-Ga systems, the typical Laves phases with the structure of AlB2 or Cu2Mg appear, with the exception of ThGa2. The Laves phase is the most stable compound in those systems and melts con­gruently. In the actinide-Sn systems, however, the Laves phase has different structures and decomposes with the peritectic reaction. In the Th-Pb and Pu-Pb systems, the phase relations are roughly similar to those in the actinide-Sn systems, although the crystal structure for the Laves phase is unknown. The gen­eral view of the U-Pb system is different from that of the Th-Pb and Pu-Pb systems, especially for the U-rich region. Figure 79 shows the U-Pb phase diagram compiled by Okamoto,4 which was based mainly on Teitel,284 Frost and Maskrey,285 and Teitel.286 There are two intermetallic compounds

aAb initio calculation.

Reference states: g-U and liq-Al.

UPb3 and UPb, although there is a miscibility gap for the liquid phase even at high temperature. This might suggest that the variation in the Gibbs energy of mix­ing between U and Pb is asymmetric with variations in the composition. The Gibbs energy of formation for the UPb3 and UPb was evaluated by vapor pressure287 and EMF measurements.270,288 Sheldon eta/.94 recom­mended the latter data and performed the assessment by the CALPHAD approach. Table 25 summarizes the thermodynamic properties for the U-Pb and the U-Sn systems evaluated in Sheldon et a/.94 and Chase.289 The excess term for the interaction parameter for the U-Pb system is highly asymmetric with composition, although that for the U-Sn system is modeled as a simple regular solution (symmetric). Regarding the Pu-Pb intermetallic compounds, Foltyn and Peterson290 calculated the Gibbs energy of forma­tion of PuPb3 from the distribution of Pu between liquid Pb and Zn in the temperature region between 976 and 1038 K.291 The value is —94.1 kJ mol-1.

The phase relations for the Th-Bi, U-Bi, and Pu-Bi systems have similar tendencies to the corresponding Pb-related system. The general view

of the U-Bi phase diagram is quite similar to that of the U-Pb system, although the number of interme­tallic compounds is 3 in the U-Bi system instead of 2 in the U-Pb system. Thermodynamic evaluation for the U-Bi and Pu-Bi systems was performed240 using the CALPHAD approach. Figures 80 and 81 show the calculated Pu-Bi phase diagram and the estimated variation in Pu activity with the experi­mental data points.292,293 The calculated phase

boundaries and the Pu activity are in good accor­dance with the experimental data points. This sug­gests at least that the calculated Gibbs energy of formation of PuBi2, which is the most Bi-rich com­pound, must give a reasonable value. The Pu activity in liquid Bi is extremely small, meaning that the actinide elements are stabilized by dissolving in liq­uid Bi. This phenomenon makes the separation ratio between actinide and lanthanide larger in the distri­bution using the molten salt/liquid Bi system. Table 26 indicates the assessed parameters for the U-Bi and Pu-Bi systems.240

2.05.4 Summary

The salient features of the actinide phase diagrams containing actinide elements were summarized in this chapter. The phase diagrams largely differ from each other in accuracy due to differences in experi­mental information. Nevertheless, systematic obser­vations with the periodic table and basic knowledge of the phase diagram type, as well as thermodynamic properties, still are practically useful at present.

aThe composition does not melt congruently. bDecompositon temperature is not the highest in the system. ND not determined. m. p. melting point.

Weight percent uranium 0 10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50 60 70 80 90 100

Pb Atomic percent uranium U

Figure 79 U-Pb phase diagram taken from Okamoto.

In the present chapter, some phase diagrams were estimated hypothetically using the CALPHAD approach, and these are very helpful for starting new research activities efficiently. From the viewpoints of technological applications, further research is needed particularly for the following systems.

1. Minor actinide systems: When taking the trans­mutation of minor actinides into account using a metallic fuel fast reactor, which is believed to be one of the most promising transmutation sys­tems, the experimental information on the phase diagram is insufficient for Np-, Am-, and Cm — related systems. Not only the phase diagrams between actinides, such as Pu-Am, Pu-Cm, and Np-Am, but also those between each minor acti­nide and Zr or Fe particularly are needed for the design of metallic fuels containing minor acti­nides. Zirconium is considered to be the best can­didate for the metal fuel matrix constituent, and the most urgent and important study from this point

Table 25 Thermodynamic functions for U-Pb and U-Sn systems

GO(Pb, liq) = 4800 — 7.991 T GO(Sn, liq) = 7195 — 14.244T GO(U, liq) = 16690 — 13.989T GO(Pb, fcc) = 0 GO(Sn, bct) = 0

GO(Sn, fcc) = -1966 + 6.871 T GO(U, bcc) = 7548 — 7.497T GO(U, b-U) = 2791 — 2.962T GO(U, a-U) = 0

GO(Pb3U) = -72 712 + 15.076T GO(PbU) = -64 524 + 27.456T GO(Sn2U3) = -156 530 + 27.725T GO(Sn5U3) = -233 200 + 31.864T GO(Sn3U) = -103 864 + 10.008T Gex(U-Pb, liq) = xu(1-xu) [49992 — 19.824T — 37151 (1 — 2xU) + 9 068(1 — 2xU)2 +11 778(1 — 2xU)3] Gex(U-Sn, liq) = xU(1 — xU) (3287 — 8.686T)

Source: Sheldon, R. I.; Foltyn, E. M.; Peterson, D. E. In Phase Diagrams of Binary Actinide Alloys; Kassner, M. E., Peterson,

D. E., Eds.; Monograph Series on Alloy Phase Diagrams No. 11; ASM International: Materials Park, OH, 1995; pp 202-207, 223-227.

Regarding U-Sn system, the reference state for U is bcc instead of a-U.

of view is to solve the conflicts in the Np-Zr system. The certification of the phase relation for the Am-Fe and Cm-Fe systems is also valuable for evaluating the eutectic interaction between minor actinides and the stainless steel cladding. Since the eutectic interaction between Am and Fe was found in the irradiated U-Pu-Zr fuel, research on the Am-Fe system is helpful for designing not only the transmutation fuels but also the standard metallic fuels in which the minor actinides are not contained initially. From the viewpoint of modeling the eutectic

interaction, thermodynamic and phase relation data are very important. For instance, the temper­ature dependence on the Gibbs energy of forma­tion of intermetallic compounds between Pu, Np, Am, or Cm and Fe is extremely valuable. The modeling of these actinide phase diagrams is prac­tically helpful for the modeling of oxide, nitride, or carbide systems based on the CALPHAD approach.

2. Thorium systems: When taking the Th cycle into consideration, the metallic form would be a

Table 26 Thermodynamic functions for U-Bi and Pu-Bi systems

GO(Bi, sol), GO(Bi, liq), GO(U, liq), GO(Pu, liq): given in

Dinsdale67

GO(Bi2U)a = -186780 + 99.785T GO(Bi4U3)a = -482700 + 245.74T GO(BiU)a = -120710 + 55.66T GO(Bi2Pu)a = -223750 + 72.741 T GO(BiPu)a = -204380 + 58.181T Gex(Bi-U, liq) = Xu(1-Xu)

[-5445.6 + 3.8377T + (-66562 + 5.0193T) (1 -2хи)]
Gex(Bi-Pu, liq) = xPu(1 — xPu) [-194370 + 3.1201 T — 54753

(1-2xpu)]

aReference state is liquid.

candidate for the fuel. In general, the experimental data for the Th-related systems are limited and scattered compared to the U — or Pu-related sys­tems. Also, the phase diagram types between Th and other metals often are widely different from those between U or Pu and other metals. A systematic study for the Th-related systems is needed, especially for Th-lanthanides, Th-noble metals, Th-Zr, Th-Fe, etc. These data are also available for the basic modeling of oxide systems containing Th.

3. Noble metal systems: Under irradiation, the behavior of noble metal fission products in the metallic fuel is completely different from that of the oxide fuel due to the large differences in the oxygen potential. In the oxide fuel, noble metals condense as fine inclusions, which are the so — called nonsoluble residues. In a metallic fuel, on the other hand, the noble metals react with the actinide metals and form intermetallic compounds, such as UPdx, PuRhx, PuRux, etc. Possibly, these intermetallic compounds are soluble in each other, or at least partially soluble, and form multielement compounds. These intermetallic compounds are considered to be thermodynamically very stable. As the burnup of the fuel becomes higher, the amount ofthese intermetallic compounds becomes larger, which changes the composition and mor­phology of the fuel matrix. Regarding the actinide — noble metal systems, not only the phase diagrams but also thermodynamic data for the intermetallic compounds are necessary to evaluate the fuel performance.

4. Multielement systems: In the metallic fuel, the behavior of each fission product is largely different from that in the oxide fuel. It is necessary for suffi­cient understanding to accumulate experimental information regarding the multielement systems, including actinide metals. The thermodynamic database is practically useful from this point of view. In the Al-, Fe-, Ni-, Ti-, Zr-based alloy systems, the thermodynamic databases have already been prepared with sufficient accuracy. In the case of metallic fuels, the base alloy will be U-Zr or U-Pu-Zr. This database would be helpful when considering the behavior of the fission products in nitride or carbide fuels. Various approaches have been attempted for modeling the redistribution of fuel constituents or fission products under a tem­perature gradient. The thermodynamic database will be a practically useful tool for evaluating the driving force.

5. Liquid metal systems: In the various methods of pyrometallurgical processing of spent nuclear fuels, liquid metal is used as a solvent. The candi­dates are Al, Bi, Cd, Pb, Zn, etc. Phase diagrams between these liquid metals and actinides are needed for process design. Especially, the cur­rently available solubility and thermodynamic data for Am and Cm are insufficient.

The machinability of nickel-molybdenum and nickel-chromium-iron alloys is inferior to that of austenitic stainless steels. When very close tolerances are required for nickel-based alloys, grinding or machining is the preferred method. Grinding wheels must be selected carefully. Tungsten carbide and ceramic-tipped tools are recommended for machin­ing nickel-based alloys. High-speed steel tools can also be used, although their machinability is not very good. During machining, some nickel-based alloys work-harden rapidly, generating large amounts of heat during cutting, and may weld to the cutting — tool surface, thus offering high resistance to metal removal due to their higher shear strength compared to austenitic stainless steels.52

Sufficient power and rigidity of the machine, avoiding vibration during machining, sharpness of the tools, low cutting speeds, higher feed rates, and a water-based cutting-oil lubricant should all be used for machining nickel-based alloys.

2.08.3.4 Welding

For welding nickel-based alloys, cleanliness of the weld joint is the most important parameter for producing a sound weld. Lack of thorough cleaning has accounted for most of the problems associated with welding encountered in industry, including cracking, porosity, and accelerated corrosion. The contaminants to watch out for prior to welding are carbon, oxides, sulfur, lead, phosphorous, and other elements that form low — melting-point eutectics with nickel such as arsenic, antimony, bismuth, and tin.54 These contaminants may come from a variety of sources, including supple­mentary materials such as markers, tools, oils, etc.

For welding nickel-based alloys, matching filler metals have been used. However, nickel has a thermal expansion coefficient intermediate between that of aus­tenitic stainless steels and low-alloy steels. Thus, nickel — chromium-iron Alloys 82, 182, 132, 52, and 152 have been used for dissimilar metal weld joints to minimize the residual stress and strain in the weld joints.

Shielded metal arc welding (SMAW), metal inert gas welding (MIG), submerged arc welding (SAW), metal active gas welding (MAG), flux cored arc weld­ing (FCAW), gas tungsten arc welding (GTAW), laser beam welding (LBW), and electron beam welding (EBW) have all been applied to nickel-based alloys.

Rods for SMAW and the flux for SAW must always be used in a dry state during welding to avoid form­ing blow holes in the deposited weld metal. Filler metals for GTAW, MIG, MAG, and FCAW must be checked for contaminants such as stains, oils, paints, etc. to avoid blow holes and hot cracking.

2.08.3.7.1 Weldability

Nickel-based alloys are relatively easy to weld, being similar to austenitic stainless steels in that respect. However, the hot-cracking susceptibility of nickel — based alloys is greater than that of austenitic stainless steels and the fluidity of the melted metal is inferior to that of both austenitic stainless steels and carbon steels. It has been reported that the hot-cracking susceptibility of nickel-based alloys is affected by alloying elements such as niobium, titanium, and aluminum and by minor elements such as sulfur, silicon, manganese, phosphorus, etc., as shown in Figures 20 and 21.55,56

The heat capacity and standard entropy for the ideal gas can be calculated from the atomic energy levels up to about 2000 K with reasonable accuracy using statistical thermodynamic methods34 from the atomic energy levels. As discussed in detail by Brewer,55 the electronic states of the gaseous actinide elements are complete (through experiments and estimations) to about 15000 cm — . The energies of the lowest elec­tronic states for the elements Th to Cm are listed in Table 6. Figure 13 shows a schematic representation of the atomic spectra of the actinide elements, based on the most recent assessments.56,57

The derived room temperature values for the entropy and the high-temperature heat capacity equations are shown in Table 7 and are taken from the assessment by Konings and Benes.34

The vapor pressure has been measured for all acti­nide metals except Md, No, and Lr. The majority of the results deal with the elements Th-Am. Measurements have also been made for Ac58 but they are of a very approximate nature. The vapor pressure measure­ments for Es59 and Fm60 have been made on samples containing 10~5-10~7at.% of the actinides in rare earth alloys in combination with Henry’s law for dilute solutions. These measurements have been carefully reviewed by Konings and Benes34 and the recom­mended enthalpies of sublimation derived from these studies are listed in Table 7. The assessed vapor pres­sure curves (ln(p) vs. 1/T) are shown in Figure 14, indicating that the vapor pressure of the actinide metals varies strongly within the series. It roughly increases with the atomic number but with prominent excep­tions. For example, americium is much more volatile than the neighboring Pu and Cm.

The enthalpies of sublimation of the actinides are plotted in Figure 15 together with the values

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£ 20000

10000

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Figure 13 Schematic representation of the atomic spectra of the actinide elements.

for lanthanide metals. The trend in the latter series shows a typical pattern, with La, Gd, and Lu forming an approximate linear baseline from which the others systematically deviate. This trend can be understood from the electronic states of the condensed and gas­eous atoms, as discussed by Nugent et al61 These authors argued that the values for La, Gd, and Lu are almost identical, due the fact that they have the same number of valence electrons in the ground states of the gaseous metal atom and the crystal. In between, the enthalpy of sublimation decreases regularly because of a corresponding increase in sta­bility of the divalent ground states in the gaseous metal atoms. A similar explanation can be applied to the actinide series, although Th, Pa, U, Np, and Pu deviate from this trend due to unusually large cohesive ener­gies of the crystalline metals, resulting from the large number of valence electrons in the metal.

2.03.1 Introduction

Uranium nitride UN not only has the same isotropic crystal structure as uranium dioxide UO2 but also has a higher melting point, higher metal atom density, and higher thermal conductivity, compared to UO2. UN thus has advantages as a nuclear fuel compared to UO2, is well studied, and many of its material proper­ties have been known for a long time. However, UN has some disadvantages as a nuclear fuel because of its low chemical stability and the problem of 14C.

Plutonium nitride and thorium nitride have been also well studied, mainly with regard to their suitabil­ity as nuclear fuels. Other actinide nitrides with higher atomic number are also important as potential nuclear fuels but the data on these fuels are insuffi­cient because they are difficult to obtain and handle.

In this section, the physicochemical properties of the actinide nitrides, mainly uranium nitrides and plutonium nitride, are discussed. First of all, phase stability and crystal structures of the nitrides are described. Then, their thermal, thermodynamic, and mechanical properties which are relevant to their suitability as nuclear fuels, are discussed. Character­istics of their preparation and irradiation as nuclear fuels are described in Chapter 3.02, Nitride Fuel.