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been reported. Takano et a/.22 have examined the relationship between the decomposition temperature and the instantaneous coefficients of linear thermal expansion (CTE) and used it to predict the decomposition temperature of AmN. Figure 13 shows the CTE at 293 and 1273 K plotted against reciprocal decomposition temperature under 1 atm of nitrogen for some transition metal nitrides (TiN, ZrN, HfN) and actinide nitrides (UN, NpN, PuN). The data used for this is summarized in Table 26,22,25,41-43,50-59 with references. Except for the large CTE value for PuN at 293 K, a reasonable linear relationship is shown by the agreement of the broken lines. From the CTE values for AmN, determined by the high-temperature X-ray diffraction technique, the decomposition temperature of AmN under 1 atm of nitrogen was roughly predicted to be 2700 K, which is much lower than that of PuN.
O and N dissolve in monocarbide by substituting carbon or by occupying vacant C-sites in the lattice. For example, in PuC1-x, the small oxygen atoms can easily fill the vacant carbon sites, leading to a compound close to stoichiometric. PuC can accommodate more oxygen (up to 78mol% PuO) than UC (<35mol% UO), probably because of the smaller size of the Pu atoms.9
Solid compact plutonium carbide has been observed to react slowly with air between room temperature and 573 K. However, it can burn in pure oxygen at 673 K.9,224 Pu2C3 was observed to be somewhat more stable than the other Pu carbides with respect to oxidation.
The pseudobinary PuC-PuO system follows a nearly ideal solution behavior. Anselin et a/.225 measured the evolution of the PuC1-x lattice parameter (in the presence ofmetallic Pu) with the addition of oxygen. They noticed a first rapid increase (from
496.0 to 497.3 pm) between 0 and 20 mol% PuO. This behavior was explained as resulting from a change in the actual C/Pu ratio and from lattice expansion following the occupation of vacant sites. Vegard’s law was then followed for composition richer in oxygen. The lattice parameter varied from 497.3 pm at 20mol% PuO to 495.6 pm at 78mol% PuO, where the solubility limit was reached (Figure 26). Extrapolated values agree with literature data on the pure compounds.
The same investigation carried out on the pseudobinary PuC-PuO2 showed very limited variation of the lattice parameter upon oxygen addition.225
XRD and chemical analyses of the Pu-C-O system have shown that both monocarbide and ses — quicarbide of plutonium are hypostoichiometric at low oxygen content and become stoichiometric at high oxygen content (>6000 ppm oxygen). In the biphasic mixed carbide system, MCO + MC15, calculations indicate that carbon activity increases with ‘O’ substitution in the monocarbide. This carbon activity increase is, however, less pronounced than it is in U-rich fuel, due to the higher tolerance of ‘O’ substitution in PuC1-x, which also implies a lower pCO in Pu-rich fuels.
PuC and PuN form solid solutions. As in the case of the Pu-C-O system, the high vacancy concentration of PuC and the preferential formation of Pu2C3
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Figure 26 Lattice parameter of plutonium monocarbide oxides and mixed plutonium-uranium carbide-oxides. Reproduced from Holleck, H.; Kleykamp, H. In Gmelin Handbook of Inorganic Transurane Teil C: Verbindungen; Springer-Verlag: Berlin, 1972.
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    lead to important deviations from Vegard’s law in the C-rich part of the PuC-PN pseudobinary system (Figure 27).9 The PuC hypostoichiometry is curtailed at high temperature by the addition of nitrogen, especially near the PuN side. N addition increases the carbon activity and reduces the actinide activity in monocarbides. Moreover, nitrogen was observed to stabilize PuC2 below its decomposition temperature.9
Whatever the processing route followed for the production of Zr metal, the sponge or the chips obtained by scrapping out the electrodes are the base products for alloy ingot preparation. The melting of the alloys is performed using the vacuum arc remelting (VAR) process. This process is specific to highly reactive metals such as Zr, Ti, or advanced superalloys.
For industrial alloy preparation, an electrode is prepared by compaction of pieces of base metal fragments (sponge or scraps) with inclusion of the alloying elements. Typically, the elements to be added are the following: O (in the form of ZrO2 powder), Sn, Nb, Fe, Cr, and Ni to the desired composition. In addition, a strict control ofminor elements, such as C, N, S, and Si, is ensured by the producers, at concentrations in the range of 30-300 ppm, according to their requirements to fulfill the engineering properties.
A few specific impurities are strictly controlled for neutron physics reasons: Cd and Hf due to their impact on neutron capture cross-section, U for the contamination of the coolant by recoil fission fragments escaping from the free surface of the cladding, and Co for in-core activation, dissolution transport, contamination, and g-irradiation.
The compact stack is melted in a consumable electrode electric vacuum furnace with water chilled Cu crucible. Electromagnetic fields are often used for efficient stirring of the liquid pool and reduced segregations. After three to four melts, the typical dimensions of the final ingots are 0.6-0.8 m diameter and 2-3 m length, that is, a mass of 4-8 tons.
2.07.3.2 Forging
Industrial use of Zr alloys requires either tube — or plate-shaped material. The first step in mechanical processing is forging or hot rolling in the p-phase, at a temperature near 1050 °C, or at lower temperatures in the a + p range or even in the upper a range. The high oxidation kinetics of Zr alloys in air at high temperatures restricts the high temperature forging process to thick components, that is, with minimum dimensions larger than 10 cm, at least. Final dimensions after forging correspond to 10-25 cm diameter for billets and 10 cm for slabs.
A p-quenching is usually performed at the end of the forging step. This heat treatment allows complete
 dissolution of the alloying elements in the p-phase and their homogenization above 1000 °C, followed by a water quench. During the corresponding bainitic p to a transformation, the alloying elements are redistributed, leading to local segregations: O and Sn preferring the middle of the a-platelets, while the TMs (Fe, Cr, and Ni) and Nb are being rejected to the interface between the platelets.13 These segregations lead to plastic deformation strains highly localized at the interplatelet zones for materials having a p-quenched structure (heat-affected zones, welds, or p-quenched without further thermomechanical processing). As described later, this p-quench controls the initial size distribution of the precipitates in Zircaloy, and further recovery heat treatments should be performed below the p-a transus only.
Few binary, ternary, and quaternary mixed actinide dioxides have been investigated experimentally. The cell parameters at room temperature along the mixed oxides solid solutions usually follow the Vegard’s law quite well — that is, a linear evolution between the end members of the solid solution.
  ![Подпись: [7]](/img/1185/image065_2.png "image065")  
This has been evidenced for Th _ xUxO2 by Bakker et a/.59 on the basis of collected experimental data (see Figure 12) and observed later by Yang et a/.78
According to experimental work by Tsuji et a/.,79 Lyon and Bailey,48 and Markin and Street,53 Vegard’s law applies for Ui _ xPuxO2 too (see Figure 12), and this trend is nicely reproduced by MD calculations by Terentyev80 and Arima et a/.81 (see Figure 13). MD calculations are consequently currently used for more complex mixed dioxides, for example, by Kurosaki et a/.82 on the ternary mixed dioxides
U0.7 _ xPu0.3AmxO2.
Recently, experimental measurements done by Kato et a/.56 showed that the Vegard’s law is valid for ternary and quaternary mixed dioxides. The evolution of the lattice parameter a in U1 _ z _y_y’PuzAmyNpy’O200 for low contents of Am, Pu, and Np obeys quite well the following linear relation with the ionic radii rU, rPu, rAm, rNp, and rO and the composition:
l!! ,
z _ y _ У ) + rpuZ
+ ГАшУ + tNpy" + To]
Kato eta/.56 tried to extract the valence of americium in U1 _ z _JPuzAmyO2 00, from the evolution of the cell parameter as a function of the americium
content. They deduced that americium is +4 rather than +3 for the U1 _ z _y _y’PuzAmyNpy/O2 00 solid solution, owing to the fact that the ionic radii depend on both the nature and the valence of the element.
The thermal expansion of mixed actinide dioxides NpxPu1_xO2 has been measured by Yamashita eta/.71 The thermal expansion coefficients are so similar to each other along the mixed oxide solid solution (see Table 3) that Carbajo et a/.84 recommended in
their review a single equation for the whole solid solution. The thermal expansion coefficients as a function of neptunium and thorium composition in UO2 have been measured by Yamashita et a/.,83 and by Anthonysamy et a/.85 The data are reported in Tables 4 and 5. In the UxTh1 _ xO2 solid solution, the evolution of those coefficients b; (0 < i< 3, eqn [3]) follows a quadratic relation with the composition, as shown by Anthonysamy et a/.85 or Bakker et a/.59 But in many cases, the simple Vegard’s law is applied to the evolution of lattice parameters as a function of composition and temperature. Results obtained by MD calculations show that such a simplification works well in the MOX (see Arima et a/.81 in Figure 13 or Kurosaki et a/82 for ternary mixed (U, Pu, Am)O2).
The composition versus temperature phase diagram constitutes the most basic information for each carbide system, fundamental to correlate thermophysical, thermodynamic, and chemical data ofcompounds in a consistent way. Thus, phase stability data are first given for each actinide carbide system, followed by a review ofthe available information on physicochemical data.
Although the general properties have been assessed, especially for the most studied systems, Th-C, U-C, and Pu-C, doubts still remain about the effective stability or ‘meta’-stability of certain crucial phases (e. g., UC2 at room temperature). The current phase diagrams, often completed with newer data and assessed by more recently developed thermodynamic optimization methods (CALPHAD), seem to generally, but not always, confirm the data obtained in the 1950s-1960s with traditional thermal analysis techniques. The discrepancies are sometimes linked to the deviation of the samples investigated from an ideal behavior, mostly due to oxygen and nitrogen contamination, a well-known and common issue related to carbides.
A short discussion of the most common actinide carbide oxides and carbide nitrides is, therefore, presented, with the goal of providing a hint of the main effects ofoxygen and nitrogen additions on the physicochemical properties of pure carbides.
2.04.1.2.2 Preparation
Actinide mono — and dicarbides for research purposes are preferentially prepared by arc-melting a mixture of metal and graphite in the right proportions. This process is normally performed under ^1bar of helium or argon. Special care is needed to avoid oxygen, nitrogen, and water impurities in the furnace.
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2
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 Th
Figure 2 DFT calculations of (a) 1 — charge density map and 2 — charge density profiles along the Th-C and Th-Th bonding lines in the (100) plane of face-centered cubic ThC (reproduced from Shein, I. R.; Shein, K. I.; Ivanovskii, A. L. J. Nucl. Mater. 2006, 353, 19-26). (b) Charge density map in the (110) plane of tetragonal p-ThC2 (reproduced from Shein, I. R.; Ivanovskii, A. L. J. Nucl. Mater. 2009, 393, 192-196).
The preparation of oxygen and nitrogen-free carbides is hardly possible.
Probably the most used method for industrial applications is the carbothermic reaction of AnO2, based on a reaction of the type:
UO2 + 3C! UC + 2CO [I]
normally performed under vacuum (1.25 x 10~5bar) at 1700-1850 K for 4 h.
Other possible preparation methods are reaction of An hydrides with carbon, aluminothermic reaction of AnF4, pyrolytic reaction of AnCl4 with CH4, and An-Hg amalgam distillation in a hydrocarbon atmosphere. Single crystals have been obtained by electron-beam melting, quenching, and annealing of polycrystalline samples. Potter25 showed that carbothermic reduction of PuO2 cannot yield oxygen — free Pu monocarbide, because the very high Pu pressures corresponding to the Pu2C3-PuC!_xOx equilibrium would lead to the formation of Pu2O3 or Pu2C3 in equilibrium with PuC1_x.
The preparation ofsesquicarbides is more complicated. Th2C3 and U2C3 have been obtained with complex experimental procedures, whereas the preparation of Pu2C3 is rather straightforward, thanks to the high thermodynamic stability of this phase. Th2C3 was successfully synthesized by Krupka and coworkers26,27 starting from arc-melted 57-67 at.% C alloys then sintered in a belt-type high pressure die under a pressure of 2.8-3.5 GPa between 1323 and 1623 K for 1 h.
The preparation of U2C3 is extremely difficult and it commonly requires a long (~1 day) annealing of a two-phase UC + UC2 metastable starting material in a narrow temperature range, between approximately 1720 and 1900 K. The annealing time can be reduced to a few minutes under particular conditions, for example, under high pressure or in a suitable atmosphere. Several ways of preparing U2C3 have been successfully explored. They can be regrouped in two main categories: those employing the ‘synthetic reaction’
UC + UC2 ! 2U2C3 [II]
and those based on the ‘decomposition reaction’
2UC2 ! U2C3 + C [III]
Several methods based on the synthetic reaction are available in the literature. For example, Matzke and Politis5 obtained U2C3 by annealing cast UC15 two-phase samples at 1720 K for 20 h under high vacuum. U2C3 was also obtained by Krupka28 at 1220 K under a pressure of 15 kbar for 2.75 min. In the light ofthis latter work, it seems difficult to believe that the application ofmechanical strain has no influence on the synthesis of U2C3, as proposed by a few researchers.29,30 The work of Henney et al.31 showed that even a high content of oxygen impurities can have an important influence on the U2C3 synthesis rate. Starting from a UC158 sample with 2900 ppm of oxygen, these authors obtained almost pure U2C3 after annealing for 74 h at 1773 Kunder vacuum. The extra carbon reacted with oxygen to form CO and CO2, fostering the formation of the sesquicarbide.
Producing or quenching cubic fcc-KCN-like actinide dicarbides to room temperature is virtually impossible due to the martensitic nature of the cubic! tetragonal transformation and its extremely fast kinetics. Tetragonal dicarbides, on the other hand, are easily quenched even when they are not in a thermodynamically stable phase at room temperature (as in the case of a-UC2).
The rate of oxidation of PuC and ThC in air is much higher than that of UC and (Th, U)C and (U, Pu)C solid solutions, whereas it is much lower in sesquicarbides.
The oxidation of actinide carbides occurs sometimes with the formation of flames (pyrophoricity), especially in samples with large specific surface (fine powders).
Actinide carbides tend to hydrolyze in water and even on exposure to laboratory air, where they exfoliate, increase in weight, and produce final hydrolysis products.
Regarding the phase relation between Th and other actinides, the Ac-Th and Th-Pa systems were predicted to be soluble completely.5 Figure 19 shows the Th-U phase diagram quoted from Peterson.69 The key literature sources for the assessment are Carlson,70 Bentle,71 Murray,72 and Badayeva and Kuznetsova.73 The general feature of the Th-U phase diagram looks similar to that for the Pu-light lanthanide phase diagrams. There is a miscibility gap for the liquid phase. The solid solubility of U in Th attains 12 at.% at the maximum, whereas that of Th in U is
extremely low. There is no intermetallic compound. Regarding the width of the miscibility gap for the liquid phase, there is conflict between two experimental data.70,72 Results given by Badayeva and Kuznetsova73 agree well with the latter. The assessment for the Th-Pu system was also performed by Peterson69 based on previous data.7 The assessed Th-Pu phase diagram is shown in Figure 20, which is quoted form Okamoto.4 The diagram is dominated by the high solid solubility of Pu in Th, whereas that of Th in Pu is relatively small. The system has a single intermetallic compound, named Z, which is formed by a peritectic reaction with the liquid and e-Pu phases. As for the composition of the Z-phase, several values
were reported previously.74,75,78,79 The composition
of Th3Pu7 was determined by Portnoff and Calais78 by microanalysis and by Marcon and Portnoff79 by measuring the cell dimension and density, respectively, the latter value taken from Peterson.69 As for the peri — tectic temperature, the value obtained by Poole et a/.74 of 888 K was selected by Peterson.69 A partial phase relations near the Pu terminal was also assessed by Peterson69 based on the work of Elliott and Larson.76 Slight stabilization of 8-Pu (fcc structure) by mixing with Th is seen. Due to the difficulty of preparing the samples and measuring the transition temperatures for the Th-rich region, the phase boundaries for p-Th and liquid or a-Th still possibly could have large experimental errors. Nevertheless, it is predicted from the general feature of the Th-Pu phase diagram that the Gibbs energy ofmixing for each phase slightly deviates to negative direction from the Raoult’s law. There is no available data for the Th-Np and Th-Am systems. The partial solid solubility, possibly of the order of several percent, and the complete liquid solubility are predicted for the Th-Np system based on the
systematic similarity with the Th-U and Th-Pu systems. Better miscibility is also speculated for the Th — Am system based on the systematic similarity with the Th-lanthanide systems.
Regarding the phase relation between U and other actinides, the Pa-U system was predicted to be soluble completely.5 As for the phase relation among U-Np-Pu-Am, thermodynamic evaluation was performed by the CALPHAD approach.7 Figure 21 indicates the U-Np phase diagram, which was calculated based on the work of Mardon and Pearce.80 The calculated results agree well with the experimental data points, with the exception of the low- temperature region around a-Np. Kurata estimated,7 the Gibbs energy for the intermediate 8-phase from the hypothetical transformation temperatures obtained by enlarging the related phase boundaries to the Np or U terminal. The temperature dependence, therefore, has some degree of error. This might be a major reason for the inconsistency for the phase relations around a-Np. The shape of the liquidus and the solidus in the U-Np system suggests that U and Np can be mostly ideally soluble in both liquid and bcc phases. The 8-phase was proposed to be isomorphous with the Z-phase appearing in the Pu-U system.80 Regarding the U-Pu system, the phase diagram was previously assessed by Peterson and Foltyn,81 which was constructed mainly from the works of Calais eta/.,77 Ellinger eta/.,82 and AEC Research and Development Report.83 According to the criteria proposed by Okamoto,84 several thermodynamically unlikely
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features are present in the previous U-Pu phase diagrams. For example, when extrapolating some phase boundaries to the U or Pu terminal, a two-phase field does not close without introducing abrupt changes in the slope of its phase boundaries. A thermodynamically likely phase diagram was then proposed based on the CALPHAD method.85 A modified U-Pu phase diagram was then proposed by Okamoto,19 in which, however, there are many differences between the assessed phase boundaries and the experimental data points given in the previous studies. A reassessed U-Pu phase diagram was proposed by Kurata,7 in which the other new data for the phase boundary86 were also taken into consideration. The assessed phase boundaries give a better fit even for the previous experimental studies, with the exception of the low-temperature Pu-rich region. Figure 22 shows the reassessed U-Pu phase diagram. In the previous model,85 the liquid phase was assumed to be an ideal solution. Kurata,7 on the other hand, takes into consideration the Pu activity evaluated from vapor pressure measurements,87,89 in which a slight negative deviation was observed for the Gibbs energy of mixing for the liquid phase. Figure 23 shows the calculated Pu activity in the U-Pu system at 1473 K along with the experimental data points. Although the data points are rather scattered, the negative variation from the Raoult’s law is clearly observed. When evaluating a multielement phase diagram, for instance, the U-Pu-Zr ternary system
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Figure 24 Calculated U-Am phase diagram taken from Kurata.7
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discussed later in this chapter, the assessment for the binary subsystems using thermodynamic information, such as vapor pressure, electromotive force, etc., is extremely important to increase the accuracy not only for the assessment of the binary subsystems but also of the multielement system. The U-Am phase diagram was previously shown by Okamoto90 based on the theoretical evaluation of Ogawa91 A similar tendency with the Th-U phase diagram is observed: for instance, there are several percent of mutual solid solubility. According to the experimental observation,68 however, the solubility between U and Am is extremely low. For instance, the solubility of Am in U is of the order of ~1at.% even in the quenched sample from the liquid phase, which was prepared by the arc-melting method. The interaction parameter of the liquid phase in the newly assessed U-Am phase diagram is estimated to be 50 kJ mol-1 based on these experimental observations.7 Figure 24 shows the newly assessed U-Am phase diagram.
The Np-Pu phase diagram was previously redrawn by Okamoto4 based on the work of Mardon eta/.92 and Poole eta/.93 Figure 25 shows the calculated Np-Pu phase diagram.7 The calculated phase boundaries are in reasonable agreement with the experimental data points, with some exceptions around the low-temperature Np-rich region. The Np-Pu phase diagram has a unique feature. Almost all parts in the phase diagram consist ofthe one-phase region and the width of the two-phase region is very narrow, with the exception of the p-Np and p-Pu phase
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Figure 25 Calculated Np-Pu phase diagram taken from Kurata,7 and the experimental data taken from Mardon et a/.92 () and Poole et a/.93 ().
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boundaries. Sheldon et a/94 pointed out that the extremely high solubility of Np in the low-temperature Pu allotropes, such as the a-Pu and p-Pu phases, is an especially unique feature ofthis system, although the phase boundaries are quite uncertain. These suggest that the difference in the Gibbs energy of each phase for both Np and Pu, especially for the low- temperature allotropes, is rather small. Consequently, this small difference in the Gibbs energy makes it difficult to get an accurate assessment by the CALPHAD approach, because any small deviations on the interaction parameters may follow
the significant variations in the phase boundaries. Apparently, this difficulty appears clearly in the p-Np and p-Pu phase boundaries, as shown in Figure 25. Nevertheless, the assessed interaction parameters are practically very useful when evaluating the multielement systems, which are discussed later. The Np-Am phase diagram was given previously by Okamoto90 based on the theoretical evaluation by Ogawa,91 in which the phase relation against a-Am was neglected. Thermal analysis was performed,57 and six different thermal arrests were observed in the 54% Np-46% Am alloy samples, which indicated the depression of melting points and transformation temperatures. Furthermore, experimental observation indicates that the solubility of Np in Am is 2-3 at.% but of Am in Np it was 5-7 at.% for a 60% Np-40% Am sample that was quickly cooled from the arc-melted liquid phase.68 The interaction parameters are assessed based on these experimental observations, which for the liquid phase, for instance, was estimated to be 20 kJ mol-1.7 Figure 26 shows the newly assessed Np-Am phase diagram, in which the depressions of melting point and transformation temperature agree reasonably well with calculations.
The Pu-Am phase diagram was previously introduced by Okamoto4 based on the work of Ellinger et al95 Figure 27 shows the calculated Pu-Am phase diagram,7 in which the calculated phase boundaries more or less overlap with the experimental data points with the exception of the Am terminal. The Pu-Cm phase diagram was also introduced by Okamoto4
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Figure 26 Calculated Np-Am phase diagram taken from Kurata,7 and the experimental data taken from Gibson and Haire.57
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based on the work of Shushanov and Chebotarev,96 as indicated in Figure 28. The general feature looks similar to the phase diagram between Pu and heavy lanthanides. The a’-Cm is a faulted fcc structure, differing from the a-Cm (HCP) structure. However, the allotropy of Cm is still under discussion.
Table 7 summarizes the interaction parameters for the phase relation among the U-Np-Pu-Am system given by Kurata,7 in which some parameters are empirically estimated. Using the assessed interaction parameters, multielement phase diagrams can be reasonably predicted. A few examples are introduced here. The first example is a ternary relation of the U-Np-Pu system. According to Mardon and
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1500-
bcc
Figure 27 Calculated Pu-Am phase diagram taken from Kurata,7 and the experimental data taken from Ellinger et a/.95
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Calculated interaction parameters for the U-Np-Pu-Am system
 GO(U, liq), GO(U, bcc), G°(U, p-U), G°(U, a-U): given in Dinsdale67 GO(Np, liq), G°(Np, bcc), G°(Np, b-Np), G°(Np, a-Np): given in Dinsdale67
G°(Pu, liq), GO(Pu, bcc), GO(Pu, S’-Pu), GO(Pu, fcc), G°(Pu, g-Pu), G°(Pu, b-Pu), G°(Pu, a-Pu): given in Dinsdale67 GO(Am, liq), G°(Am, bcc), G°(Am, fcc), G°(Am, DHCP): given in Dinsdale67 G°(U, b-Np) = 260.4 + G°(U, b-U)
G°(U, a-Np) = 2814.7 + G°(U, a-U)
G°(U,8′-Pu), G°(U, fcc), G°(U, DHCP) = 5000 + G°(U, bcc)
G°(U, g-Pu), G°(U, b-Pu), G°(U, a-Pu) = 5000 + G°(U, a-U)
G°(U, z) = 118.7 + G°(U, b-U)
G°(U, Z) = 337.8 + G°(U, bcc)
G°(Np, b-U), G°(Np, a-U) = 792 + G°(U, b-Np)
G°(Np, S’-Pu), G°(Np, fcc), G°(Np, DHCP) = 5000 + G°(Np, bcc)
G°(Np, g-Pu) = 2000 + G°(Np, b-Np)
G°(Np, b-Pu) = 80.8 + G°(Np, b-Np)
G°(Np, a-Pu) = 187.2 + G°(Np, a-Np)
G°(Np, z) = 153.2 + G°(U, b-Np)
G°(Np, Z(S)) = 227.1 + G°(U, b-Np)
G°(Pu, b-U) = 209.6 + G°(Pu, S’-Pu)
G°(Pu, a-U) = 652.7 + G°(Pu, b-Pu)
G°(Pu, b-Np) = 575.1 + G°(Pu, S’-Pu)
G°(Pu, a-Np) = 1248.6 + G°(Pu, a-Pu)
G°(Pu, DHCP) = 5000 + G°(Pu, fcc)
G°(Pu, z) = 51.1 + G°(U, fcc)
G°(Pu, Z) = 500 + G°(U, b-Pu)
G°(Am, j) = 5000 + G°(Am, DHCP): j means b-U, a-U, b-Np, a-Np, S’-Pu, g-Pu, b-Pu, a-Pu, z, and Z Gex(Np-U, liq) = Xu(1 — Xu) (0)
Gex(Np-U, bcc) = xU(1 — xU) (796.8)
Gex(Np-U, b-U) = Xu(1 — Xu) (753.3)
Gex(Np-U, a-U) = xU(1 — xU) (-5310.1 + 6.92T)
Gex(Np-U, b-Np) = xU(1 — xU) (-1392.3 + 2.88T)
Gex(Np-U, a-Np) = xU(1 — xU) (3652.9)
Gex(Np-U, S’-Pu), Gex(Np-U, fcc), Gex(Np-U, g-Pu), Gex(Np-U, b-Pu), Gex(Np-U, a-Pu), z = xU(1 — xU) (5000) Gex(Np-U, Z) = xu(1 — Xu) (-4268.5 + 5.14T + (-2467.7 + 2.80T) (xNp — Xu) + (14 741 — 15.48T) (xNp — Xu)2) Gex(Pu-U, liq) = xU(1 — xU) (32231 — 31.465T-8980.2(xPu — xU))
Gex(Pu-U, bcc) = xU(1 — xU) (19374 — 17.250T-4939.5(xPu — xU))
Gex(Pu-U, b-U) = Xu(1 — Xu) (5287.3)
Gex(Pu-U, a-U) = xU(1 — xU) (6176.5)
Gex(Pu-U, b-Np), Gex(Pu-U, a-Np) = xU(1 — xU) (5000)
Gex(Pu-U, S’-Pu) = xU(1 — xU) (495.4)
Gex(Pu-U, fcc) = xU(1 — xU) (723.8)
Gex(Pu-U, g-Pu) = xU(1 — xU) (4342.7)
Gex(Pu-U, b-Pu), Gex(Pu-U, b-Pu), Gex(Pu-U, DHCP) = xU(1 — xU) (5000)
Gex(Pu-U, z) = xU(1 — xU) (4049.1 — 1.52T + (-617.4 — 3.41 T) (xPu — xU))
Gex(Pu-U, Z) = xU(1 — xU) (-6336.9 + 10.45T + (-19 997 + 24.65T) (xPu — xU) + (12 364 — 7.84T) (xPu — xU)) Gex(Am-U, j) = xU(1 — xU) (50000): f means all related phases.
Gex(Np-Pu, liq) = xPu(1 — xPu) (0)
Gex(Np-Pu, bcc) = xPu(1 — xPu) (961.3)
Gex(Np-Pu, b-U), Gex(Np-Pu, a-U) = xPu(1 — xPu) (5000)
Gex(Np-Pu, b-Np) = xPu(1 — xPu) (-1617.8 + 2.73T)
Gex(Np-Pu, a-Np) = xPu(1 — xPu) (-1307.6)
Gex(Np-Pu, S’-Pu) = xPu(1 — xPu) (-2569.8)
Gex(Np-Pu, fcc) = xPu(1 — xPu) (-2475.3)
Gex(Np-Pu, g-Pu) = xPu(1 — xPu) (1108.5)
Gex(Np-Pu, b-Pu) = xPu(1 — xPu) (226.2)
Gex(Np-Pu, a-Pu) = xPu(1 — xPu) (-2722.9)
Gex(Np-Pu, z) = xPu(1 — xPu) (596.9)
Gex(Np-Pu, Z) = xPu(1 — xPu) (5000)
Gex(Am-Np, liq) = XNp(1 — XNp) (20000)
Table 7 Continued
Gex(Am-Np, bcc) = xNp(1 — xNp) (38000 — 7T)
Gex(Am-Np, fcc), Gex(Am-Np, b-Np), Gex(Am-Np, a-Np), Gex(Am-Np, DHCP) = xNp(1 — xNp) (38000) Gex(Am-Np, j) = xNp(1 — xNp) (40 000): j means the other phases.
Gex(Am-Pu, liq) = xPu(1 — xPu) (5495.9 — 7.787)
Gex(Am-Pu, bcc) = xPu(1 — xPu) (7528.6)
Gex(Am-Pu, fcc) = xPu(1 — xPu) (-22 630 + 26.377)
Gex(Am-Pu, j) = xPu(1 — xPu) (5000): j means the other phases
Source: Kurata, M. In Proceedings of Actinides 2009, San Francisco, CA, July 12-19, 2009.
 
Pearce,80 the structure of the 8-phase is isomorphous with the Z-phase appearing in the U-Pu system. Thus, these two phases are treated as the same as the one by Kurata.7 The ternary U-9at.%Np-26 at.% Pu alloy was annealed at 923 K for a few days and then quickly cooled by Nakajima et a/.87 Energy disperse X-ray microscope (EDX) analysis detected three phases in the sample. Figure 29 indicates the calculated phase relation for the U-Np-Pu isotherm, with the average composition of each phase detected in the annealing test. The phase separation between the 8-(U, Np) and Z-(U, Pu) phases is shown in the diagram. According to Nakajima eta/.,87 phase separation was also observed in the annealed U-Pu-Am and Np — Pu-Am samples annealed at 897 and 792 K, respectively. Figures 30 and 31 indicate the calculated U-Np-Am and U-Pu-Am ternary isotherms, respectively, as another example. The experimental data for the annealing test are also shown in the figures, such as the average composition of each phase detected in the annealing test. The results agree reasonably well with the experimental data points. A similar evaluation was performed by Dupin.97 Reasonable phase diagrams among actinides were also shown, although the assessed phase boundaries in both estimations7,97 are slightly different from each other. This happens usually with the semiempirical methods used.
2.08.2.3.1 Chemical compositions, physical properties, and mechanical properties
The chemical compositions of typical nickel — molybdenum-iron, nickel-molybdenum-chromium — iron, and nickel-chromium-molybdenum-iron alloys are shown in Table 3, along with those of other nickel — based alloys.
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350 0C WOL-type specimens
K1 (MPaVm) K1 (MPaVmi)
Figure 14 Stress corrosion tests in deaerated sodium hydroxide 350 °C on fracture mechanics-type specimens: comparison of Alloys 600 and 690 behavior effect of heat treatment at 700 °C for 16 h.
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Figure 16 The effect of molybdenum content on corrosion resistance of nickel-molybdenum alloys in boiling 10% hydrochloric acid solution.
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  corrosion rates.29 It is seen that the corrosion rate in 10% hydrochloric acid dramatically decreases with increasing molybdenum content. Commercial nickel-molybdenum alloys include about 30% molybdenum.
Alloy B (UNS N10001) (nickel-based 28% molybdenum-5% iron) is one of those rare materials which is resistant to corrosion in hydrochloric acid up to its boiling point. The alloy shows excellent corrosion resistance in reducing and oxidizing chloride solutions. However, because of its lack of chromium
content, care must be taken to avoid using this alloy in oxidizing environments.
Alloy B-2 (UNS N10665) is an advanced version of Alloy B. It has superior corrosion resistance in weld-heat-affected zones compared to Alloy B, due to reduced carbon and silicon contents and a restricted range of iron content.
Alloy B-3 (UNS N10675) was developed to minimize problems associated with the fabrication of B-2 alloy components. Alloy B-3 has excellent resistance to hydrochloric acid at all concentrations and temperatures.30 It also withstands sulfuric, acetic, formic, and phosphoric acids, as well as other nonoxidizing media. Alloy B-3 has a special chemistry designed to achieve a level of thermal stability superior to that of Alloy B-2. It has been applied to similar components as Alloy B-2, but cannot be used in environments containing ferric or cupric salts because these salts may cause rapid corrosion failure.
Alloy C (UNS N10002) (nickel-based 18% chromium-16% molybdenum-5% iron-4% tungsten) is also an advanced version of Alloy B. It has superior corrosion resistance to oxidizing environments compared to Alloy B due to the added chromium. However, Alloy C is degraded after heating in the temperature range 650-1090 °C due to the precipitation of M6C carbides and of m phase along grain boundaries. Solution heat treatment is therefore necessary after welding in the case of this alloy.
Alloy C-276 (UNS N10276) improves upon this weakness by using reduced carbon (<0.01%) and silicon (<0.08%) contents compared to Alloy C. The alloy can be used in most cases in the as-welded state (without solution heat treatment after welding).31
Alloy C-4 (UNS N06455) improves upon the long-range aging characteristics of Alloy C-276 by the addition of titanium and a reduction in the iron
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content.
Alloy C-22 (same as Alloy 22) (UNS N06022) shows improved corrosion resistance in oxidizing environments due to increased chromium content (about 22%) compared to Alloy C-276 and maintains its corrosion resistance in reducing environments.33
Alloy 625 (UNS N06625) was originally developed as a gas-turbine material. It is a typical nickel- chromium-molybdenum-iron alloy as well as a solid-solution-hardenable alloy. It has high creep — rupture strength at high temperatures, due to the added molybdenum and niobium, and high resistance to corrosion and pitting in oxidizing environments such as nitric acid due to its higher chromium (about 22%) and lower molybdenum (about 9%) content compared to Alloy C-276.34 However, the corrosion resistance of the alloy in reducing environments such as hydrochloric acid and sulfuric acid is inferior to that of Alloy C-276. Alloy 625 is used where welding is required, based on the stabilization of carbon by niobium addition (about 3.5%) for preventing sensitization. Also, the alloy shows excellent SCC resistance to chloride solutions and seawater, due to its high nickel content.
Alloy 625 LCF (UNS N06626), a modified Alloy 625, shows improved low-cycle fatigue properties and cold formability for bellows applications.
Alloy 686 is very similar in composition to Alloy C-276 but where the chromium level has been increased from 16 to 21% while maintaining molybdenum and tungsten at similar levels. Alloy 686 is used for resistance to aggressive media in chemical processing, pollution control, pulp and paper manufacture, and waste management applications. This alloy contains chromium, molybdenum, and a tungsten content of around 41%. To maintain its singlephase austenitic structure, this alloy has to be solution-annealed at a high temperature of around 1220 °C followed by rapid cooling to prevent precipitation of intermetallic phases.35
Alloy 59 has high chromium and molybdenum content with low iron content. This alloy has excellent resistance to general corrosion, SCC, pitting, and crevice corrosion in aggressive corrosive environment. The alloy is a nickel-chromium-molybdenum alloy without the addition of any other alloying element. This purity and balance ofnickel-chromium — molybdenum is mainly responsible for its thermal stability.36
Alloy 825 (UNS N08825) was developed from alloy 800 with the addition of molybdenum (about 3%), copper (about 2%), and titanium (about 0.9%) for providing improved aqueous corrosion resistance in a wide variety of corrosive media. In this alloy, the nickel content confers resistance to chloride-ion SCC. Nickel in conjunction with molybdenum and copper gives outstanding resistance to reducing environments such as those containing sulfuric and phosphoric acids. Molybdenum also aids resistance to pitting and crevice corrosion. In both reducing and oxidizing environments, the alloy resists general corrosion, pitting, crevice corrosion, IG corrosion, and SCC. Some typical applications include various components used in sulfuric acid pickling of steel and copper, components in petroleum refineries and petrochemical plant (tanks, valves, pumps, agitators), equipment used in the production of ammonium sulfate, pollution control equipment, oil and gas recovery, and acid production.37
The mechanical and physical properties of typical nickel—molybdenum—iron, nickel-molybdenum— chromium-iron, and nickel—chromium—molybdenum— iron alloys are shown in Tables 4 and 5 respectively, along with those of other nickel-based alloys.
2.08.2.3.2 Applications to nuclear power industrial fields
Alloy 625, as a typical nickel-chromium— molybdenum—iron alloy, has been investigated for its SCC resistance in high-temperature water as an alternative material to austenitic stainless steels, from the view point of preventing sensitization. The alloy has also been studied for corrosion resistance in highly caustic solutions as a candidate material for components of supercritical light water-cooled reactors. Alloy 625 is one of the candidates for reactor — core and control-rod components in water-cooled reactors and a candidate component material for supercritical water-cooled reactors, due to its high strength, excellent general corrosion resistance, SCC resistance, and pitting resistance in high-temperature water. The alloy is also being considered in advanced high-temperature reactors because of its high allowable design stress at elevated temperatures, especially between 650 and 760 °C.
Alloy C-22 has been investigated for corrosion resistance in highly caustic solutions and concentrated chloride solutions as a candidate material for high — level radioactive waste-disposal storage containers, due to its excellent corrosion resistance in oxidizing and reducing environments.
Detailed studies show that the crystal lattice of most actinide metals expands with increasing temperature
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Figure 4 The isothermal bulk modulus (B0) of the actinide elements (o) compared with that of the lanthanides (•).
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Figure 5 The thermal expansion of Pu. Made after Schonfeld, F. W.; Tate, R. E. Los Alamos National Laboratory, Technical Report LA-13034-MS; 1996.
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and evolves to a simple cubic arrangement close to their melting temperature, similar to the lanthanide elements. (For numerical data on the thermal expansion, see Section 2.01.4.1) As the atoms move away from each other, the electrons in the 5f metals tend to favor a localized state. As discussed by Vohra and Holzapfel,15 this is particularly important for Np and Pu, which are on the threshold of localization/ itinerancy. The case for plutonium is much more complex, as shown in Figure 5. The crystal lattice of plutonium expands for the a-, p-, g-, and e-phases, and the g — to 8-transition has a positive expansion. The 8- and 8′-phases have negative thermal expansion and the 8- to 8′- and 8′- to s-transitions show a negative volume change, as is the case upon melting. Dynamic mean field calculations show that the monoclinic a-phase of Pu is metallic, whereas fcc 8 is slightly on the localized side of the localization — delocalization transition.16
Moreover, the stability of the crystalline state of the actinide metals varies significantly. The melting temperature is high for thorium, similar to that of the transition metals in group IVB, and low for Np and Pu (Figure 6).
When applying high temperature as well as high pressure to the actinides, phase changes can be suppressed, as is shown in Figure 7. For example, the triple point for the a—p—g equilibrium in uranium is found at about 1076 K and 31.5 kbar; above this pressure, orthorhombic a-U directly transforms in fcc g-U.17 In plutonium, the g-, 8-, and 8′-phases disappear at relatively low pressure and are replaced by a new phase designated Z- In contrast to the other actinides, plutonium shows a negative slope for the liquidus down to the p-Z-liquid triple point (773 K, 27 kbar) reflecting the increase in density upon melting.17
As mentioned above, the microscopic mechanisms of oxygen diffusion vary as a function of stoichiometry in the actinide dioxides. A schematic view of the (simplified) possible mechanisms has been reported in Table 18. Dorado eta/.232 combining both experimental and theoretical approaches identified the oxygen migration as an interstitialcy mechanism.
For x < 0in MO2 _ x (hypostoichiometric dioxides), the dominant defects in urania and plutonia are the oxygen vacancies. Hence, the migration energy could
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Figure 29 Oxygen self-diffusion coefficient in PuO2_x as a function of stoichiometry from Stan etal.153 Symbols are experimental data. © Elsevier, reprinted with permission.
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Figure 30 Comparison between the experimental self-diffusion coefficients of oxygen in hyperstoichiometric UO2 + x and the calculated ones at 1073 K. From Andersson, D. A.; Watanabe, T.; Deo, C.; Uberuaga, B. P. Phys. Rev. 2009, 806, 060101.
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be reduced to the activation energy for oxygen vacancy migration Eact: ( V") as reported in the Table 18.
In fact, Stan eta/.150’152 have shown that the point defects in hypostoichiometric plutonia PuO2 _ x do not reduce to oxygen vacancy. They determined (from a point defect model) that five different defects are at work in PuO2 _ x and hence contribute to the formation of oxygen vacancies. According to them, the prefactor D0 (eqn [13]) can then be written as a function of (i) a stoichiometry-dependent correlation factor from Tahir-Kheli233 and (ii) the formation energy of oxygen vacancy (determined using the point defect model). The results of such a model are reported in Figure 29.
Recently Kato et а/23 have studied the oxygen diffusion in hypostoichiometric MOX, and they
concluded that the diffusion coefficient of oxygen linearly depends upon the concentration of Pu in MOX.
For x > 0 in MO2 + x (hyperstoichiometric dioxides), two recent studies evidenced that the oxygen interstitials are not the only contribution to oxygen diffusion. Experimental data obtained by Ruello et a/.229 in UO2 + x show the important role of the Willis clusters. Theoretical calculations based on coupled ab initio/kinetic Monte Carlo done by Andersson et a/.168 have shown also that the diinterstitial cluster of oxygen may contribute to the oxygen diffusion for highly hyperstoichiometric UO2 + x. In fact, the diffusion of oxygen in hyperstoichiometric dioxides is due to the diffusion of interstitial oxygen and to the (counteracting) contribution of more complex oxygen clusters. Hence, the diffusion coefficient increases with stoichiometry, reaches a maximum, and decreases as may be seen in Figure 30.
Recently, Stan et a/.153 proposed a semiempirical relation between the diffusion coefficient D and the stoichiometry for UO2 + x that includes a maximum:
D(T, x) = xDo exp ^_Y°^j exp(_0x) [14]
In this expression, D0 = 1.3 x 10-2 cm2 s_1, E0 = 1.039 eV, and в = 6.1. The last term of the product corresponds to the blocking effect of the complex oxygen clusters. Such a semiempirical model reproduces the experimental data fairly well (see Figure 31), up to x < 0.1. For higher values of x (0.0 < x< 0.2 from 300 up to 1800 K), Ramirez eta/.151 established a somewhat different semiempirical relation.
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