Low-temperature heat capacity of a-UC2-x was studied by adiabatic calorimetry between 5 and 350 K,8 yielding the already reported temperature coefficient of the electronic heat capacity, and values of the Debye temperature 0D of 302 for UC190 and 304 K for UC1.94.

Assessed thermodynamic functions for a-UC194 are reported in Table 6. The randomization entropy of UC1.90 was calculated by Storms2 taking into account the disordered and incomplete sublattice: S° = 2.7J K-1 mol-1.

Heat capacity measurements at higher tempera­tures could be affected by partial decomposition of a-UC2 into UC and C below 1790 K. Results were critically assessed by Holley et a/.4 (Table 6 and Figure 15), as well as the latent enthalpy and entropy of the UC2-x a! p transition.

Fink et a/.43 proposed a value for the enthalpy of solid p-UC2-x at the melting point, H°(2720) — H°(298) « 256 kJ mol-1.

The Gibbs energy of formation values given by Holley et a/, for UC2-x are higher than those of Chevalier and Fischer.101 The expression in Table 6 is recommended here.

A complete treatment of the vapor pressures over the UC 1+x-UC2-x phase field is reported by Holley. Norman and Winchell144 proposed the following values for the enthalpy and entropy of sublimation of p-UC2-x at the average T = 2500 K: AsubH° (2500) « 774 kJ mol-1 and AsubS° (2500) « 160 kJmol-1 K-1.

The a-UC2-x low-temperature values for the average linear thermal expansion coefficients yielded by neutron diffraction spectra at temperatures between 5 and 298 K127 were aTa = (9 ± 1)x 10-6K-1 and aTc = (6± 1)x 10-6K-1. These values for a-UC2-x

were observed to increase at higher temperature, aTa = (16.6± 0.2)x 10-6K-1 and aTc = (10.4± 0.2)x 10-6K-1 between 298 and 1208 K. Neutron scatter­ing studies between 1273 and 2573 K yielded the following average coefficient of thermal expansion for quasi-isotropic a-UC2: aTa = 18×10-6K-1

(up to 2050 K) and aTa = 25×10-6K-1 for p-UC2 at higher temperature. The coefficient of average cubic thermal expansion for p-UC2-x between 298 K and the melting point was suggested by Storms[3] [4] [5] as g = 4x 10-5 K-1.

The bulk modulus of a-UC2-x was measured to be B = 216 GPa.145

2.06.3.3.1.1 Properties and preparation of UF5

UF5 was initially prepared by Ruff through the reac­tion of UCl5 with anhydrous HF. More recent studies have been made on the reaction of gaseous UF6 on UF4 as a powder:

UF4 + UF6 ^ 2UF5

However, a low temperature (T< 453 K for pUF6 < 1bar (105Pa)) is required to avoid the decomposition to U2F9. This often means a very slow transformation (several days depending on the specific surface). UF5 has a white color but with this technique a gray or black color powder is often obtained because of presence of U2F9.

Asada has more recently prepared UF5 at 643 K but under 3 bars (3 x 105Pa) UF6.53 However, corrosion problems have been experienced.

Probably the best way to obtain pure UF5 from UF4 and UF6 is to allow evaporation of UF5 at 573-673 K and condensation at ^346-408 K. Blue UF5 needles are then obtained.

UF5 is often considered a key product because it may be involved in clogging reactors (flame reactor or fluidized bed) when no excess F2 is maintained. UF5 has a tendency to polymerize. This very impor­tant property tends to explain why the reactivity of

U(V) fluorides is lower than that of U(IV). Also UF5 melts at a low temperature compared to UF4.

UF5 has two crystalline forms that are both tetrag­onal (Figure 10):

• High-temperature a-UF5 that has an I41m sym­metry with a = 6.5259(3) JA and c = 4.4717(2) JA, which was confirmed by high-resolution neutron powder diffraction data of Howard et a/.54

• Low-temperature p-UF5 that has an I42d symmetry with a = 11.469(5) JA and c = 5.215(2) 3A (a = 11.456 (2) A, c = 5.195(1) A, Z = 8).55

The transition temperature is 398 K, independent of the UF6 pressure. The a-phase is obtained from the p form when slowly raising the temperature (18 h at 458 K). The reverse transformation form a to p has not yet been achieved.

UF5 can be separated from U(VI) compounds using anhydrous acetonitrile dissolution.56 Again this property is linked to the polymerization trend of UF5.

The actinide elements pose a very interesting para­dox. Uranium and especially plutonium are materials that are very difficult to handle because of their radioactive nature, but they are among the most
extensively studied elements in the periodic table. This is of course due to the importance of these two elements in nuclear technology. The properties of the other actinides are relatively poorly known and are generally obtained from estimations. How­ever, due to the changes in the electronic properties of the 5f electrons, varying from delocalized to loca­lized, going from Th to Am, the systematics in the properties of the actinides are difficult to predict, and analogies with the 4f lanthanides are not (always) obvious. Theoretical predictions based on atomistic calculations could help to solve this, but the predic­tive potential of such calculations is still being explored. Clearly, more experimental studies are needed, particularly on the minor actinides.

In this section, the vapor pressure of a metal gas over a solid actinide nitride is summarized.

aUnder 1 atm of nitrogen. bNot available.

cCongruent melting under 1 atm of nitrogen.

The major vapor species observed over UN are nitrogen gas, N2(g), and mono-atomic uranium gas, U(g). UN(g) can also be detected in addition to U(g) and N2(g),60 but its pressure is three orders of mag­nitude lower than that of U(g); therefore, the contri­bution of UN(g) can be ignored in practice. Some data on the pressures of N2(g) and U(g) over solid UN(s) are shown in Figure 14.

Hayes et a/.46 have derived equations for the pres­sures of N2(g) and U(g), which were developed by fitting the data from eight experimental investigations. According to that paper, the reported data on N2(g) agree with each other, but that of U(g) over UN(s) vary somewhat. The U(g) pressure obtained by Suzuki et a/61 is a little higher than that predicted from the equation developed by Hayes et a/., but is in agreement with values given by Alexander et a/.62 It is well known that the evaporation of UN is accompanied by the precipitation of a liquid phase, where UN(s) = U(1) + 1/2N2(g) and U(1) = U(g). The reported vapor pressure of U(g) over UN(s) is close to or a little lower than that over metal U63 It is suggested that the dissolution of nitrogen and/or impurity metal from crucibles into the liquid phase could affect the observed partial pressure. Some scat­tering of the previously reported data on U(g) over UN(s) may be also caused by a reaction of the liquid phase in UN with the crucible material. From this viewpoint, it appears that the partial pressure of U(g)

Figure 14 Partial pressure of N2(g) and U(g) over UN (s) as a function of temperature. Adapted from Hayes, S. L.; Thomas, J. K.; Peddicord, K. L. J. Nucl. Mater. 1990, 171, 300-318; Suzuki, Y.; Maeda, A.; Arai, Y.; Ohmichi, T. J. Nucl. Mater. 1992, 188, 239-243;

Alexander, C. A.; Ogden, J. S.; Pardue, W. H. J. Nucl. Mater. 1969, 31, 13-24.

over UN(s) should be a little higher than that pro­posed by Hayes et a/.

The vapor species over PuN are nitrogen gas N2(g) and mono-atomic plutonium gas Pu(g). PuN(g) is not detected because PuN is more unstable than UN.64 The N2 pressure over PuN has been reported by Alexander et a/.,65 Olson and Mulford,42

Pardue eta/.,66 and Campbell and Leary.67 These data seem to agree with each other.

The vapor pressure of Pu(g) over PuN(s), as a function of temperature, is shown in Figure 15. The values reported in the different studies almost completely agree with each other.61,68,69

According to Alexander et a/.,65 the ratio Pu(g)/ N2(g) is 5.8 throughout the investigated temperature range of 1400-2400 K, which suggests that PuN eva­porates congruently; that is, PuN(s) = Pu(g) + 1/2N2(g). However, Suzuki eta/, have reported that Pu(g) over PuN(s), at temperatures lower than 1600 K, is a little higher than the values extrapolated from the high-temperature data, and that it approaches that over Pu metal with further decrease in tempera­ture. There is some possibility that a liquid phase forms at the surface of the sample during the cooling stages of the mass-spectrometric measurements, because PuN has a nonstoichiometric composition range at elevated temperatures, while it is a line compound at low temperatures.

The vapor pressure of U(g) and Pu(g) over UN(s), (U, Pu)N(s), and PuN(s) are shown in Figure 16. Table 3 gives the vapor pressures of U(g) and Pu(g) which are represented in Figure 16 in the form of logarithmic temperature coefficients. It is noteworthy that the vapor pressure of Pu(g) over mixed nitride was observed to increase with an increase in the PuN content.

Nakajima eta/.70 have measured the vapor pressure of Np(g) over NpN(s) in the temperature range of 1690-2030 K by using the Knudsen-cell effusion mass spectrometry. This data is plotted in Figure 17 as a function of temperature. The partial pressure of Np (g) can be expressed using the following equation:

logp Np(g)(Pa) = 10.26 — 22 200/T [7]

The vapor pressures of Np(g) over NpN(s) obtained by Nakajima et a/. are similar to those of Np(g) over

104/T (K-1)

liquid Np metal found by Ackermann and Rauh71; these all are shown in Figure 17. Therefore, the decomposition mechanism is considered to be the following reaction: NpN(s) = Np(1) + 1/2N2(g), Np(1) = Np(g).

Takano et al.72 have estimated the vapor pressure of Am(g) over AmN by using values of the Gibbs free energy of formation available in literature.34 The evaporation of AmN obeys the following reac­tion: AmN(s) = Am(g) + 1/2N2(g). The estimated vapor pressure of Am over AmN, expressed as a function of temperature, is

logpAm(g)(Pa) = 12.913 — 20197/T

(1623 <T(K) < 1733) [8]

The calculated vapor pressures of Am over AmN are plotted in Figure 17 as a function of temperature. The vapor pressure of Am over AmN is higher than those of other actinide vapor species over their respective nitrides.

Among the minor actinides, only carbides of ameri­cium and curium have been identified and investi­gated so far.

2.04.7.1 Americium Carbides

The two most stable isotopes of americium, 241Am (432.2 years) 243Am (7370 years), are formed by p-decay of 241Pu and 243Pu, respectively. Therefore, a certain percentage (order of 10—1 at.%) of ameri­cium is commonly present in plutonium. As a conse­quence, traces of americium carbides can be formed in plutonium or mixed carbide matrices.226

Although the Am-C phase diagram has not been investigated in any detail, the monocarbide and the sesquicarbide have been identified, prepared by carbothermic reduction and arc-melting.227 Samples of nominal composition Am104 and Am125 were thus obtained and annealed at 1273 K for 24h, and then characterized by XRD at room temperature. The main phase displayed a fcc NaCl Fm 3m lattice, with lattice parameter a = 502 pm. Although the precise
composition and the oxygen and nitrogen contents were not determined, this phase corresponded most probably to the monocarbide. Traces of a bcc phase (most likely the sesquicarbide) were also detected. Mitchell and Lam199 prepared americium sesquicar­bide Am2C3 and analyzed it by XRD at room temper­ature. The material was found to be isostructural with Pu2C3, bcc, 143d, with eight formula units per unit cell. After annealing, the lattice parameter was found to be a = 827.57 ± 0.2 pm. Holley et al4 estimated the thermodynamic functions for the formation of ameri­cium sesquicarbide: AfH° (298) = —75 ± 20kJmol— AfS° (298) = 8 ± 8kJK—1mol—1, and AfG° (298) = — 77 ± 20kJmol—1. These values were estimated by assuming that Am2C3 is similar to Pu2C3 and that the trend toward lower values of AfH and AfG with increasing atomic number continues beyond Pu2C3.

For seamless tube production, first a hot extrusion is performed in the temperature range of 600-700 °C. For pressure tube fabrication, this step is followed by a single cold drawing step and a final stress relieving heat treatment. For cladding tubes, the extrusion produces a large extruded tube (‘Trex’ or ‘shell’), of 50-80 mm in diameter and 15-20 mm in thickness, which is further reduced in size by cold rolling on pilger-rolling mills.

After each cold working step of plate or tube material, an annealing treatment is mandatory to restore ductility. It is usually performed in the range of 530-600 °C to obtain the fully recrystallized material (RX). The resultant microstructure is an equiaxed geometry of the Zr grains with the precipi­tates located at the a-grain boundaries or within the grains. The location of the precipitates at the grain boundaries is not due to intergranular precipitation but because they pin the grain boundaries during grain growth (Figure 9). These different heat treat­ments contribute to the control of the cumulative annealing parameter to be described below. For better mechanical properties of the final product, the tem­perature of the last annealing treatment can be reduced to avoid complete recrystallization. This is the stress-relieved (SR) state, obtained with final heat treatment temperature of 475 °C, which is character­ized by elongated grains and a high density of dis­locations, and by relief of the internal stresses, leading to a greater ductility than cold-worked mate­rials. It is mostly applied to the PWR claddings, while for BWRs, a complete recrystallization is performed at 550-570 °C.

2.07.3.4.1 Crystallographic texture development

Two plastic deformation mechanisms are operating during low temperature deformation of the Zr alloys: dislocation slip and twinning. As reviewed by Tenckhoff,14 the most active deformation mechanism depends on the relative orientation of the grain in the stress field.

Dislocation slip occurs mostly on prism plane with an a Burgers vector. It is referred to as the {1010} (1210), or prismatic, system. The total strain imposed during mechanical processing of the Zr alloys cannot, however, be accounted for only with this single type of slip, as the different orientations of the crystal would only give two independent shear systems. At high deformations, and as the temperature is increased, (c + a) type slip is activated on {1121} or {1011} planes. These are the pyramidal slip systems, having higher resolved shear stresses (Figure 2).

Different twinning systems may be activated depending on the stress state: for tensile stress in the c-direction, {1012} (1011) twins are the most frequent, while the {1122} (Ї123) system is observed when compression is applied in the c-direction. The resolved shear stresses of the twin systems have been shown to be higher than the one necessary for slip, but due to the dependence of the Schmid factor on orientation, twinning is activated before slip, for some well-oriented grains. Therefore, there are five independent deformation mechanisms operating in each grain, and thus the von Mises criterion for grain-to-grain strain compatibility is fulfilled.

At the large strains obtained during mechanical processing, steady-state interactions occur between the twin and slip systems that tend to align the basal planes parallel to the direction of the main deformation.15,16 For cold-rolled materials (sheets or tubes), the textures are such that the majority of the

Figure 2 The two Burgers vectors (a and c + a) for strain dislocations in Zr alloys, and the two slip planes (prismatic and pyramidal) in hcp a-Zr.

grains have their c-axis tilted 30-40° away from the normal of the foil or of the tube surface toward the tangential direction, as can be seen in the (0001) pole figure of a cladding tube (Figure 3).

During tube rolling, the spread of the texture can be reduced by action on the ratio of the thickness to diameter reductions (Qfactor): a reduction in thick­ness higher than the reduction in diameter gives a more radial texture, that is, a texture with the c poles closer to the radial direction.16

After cold processing, the (1010) direction is paral­lel to the rolling direction, and during a recrystalliza­tion heat treatment a 30° rotation occurs around the c-direction and the rolling direction is then aligned with the (1120) direction for most of the grains.

Interestingly, the lattice parameters also depend linearly on the stoichiometry in hypo — and hyper­stoichiometric actinide (mixed or not) dioxides. The variation of the volume AO/O induced by single
isolated defects may be related to the variation of the macroscopic volume A V/ V, as follows:

AV AO

/ [8l

V O M

Depending on the sign ofAO, there will be a swelling or a contraction of the volume. The evolution of the cell parameter is linear as function of stoichiometry x in UO2 + x and (U, Pu)O2 ± x (see Figure 14), with different slopes for hypo — and hyperstoichiometric dioxides from Javed,86 Gronvold26 in UO2 + x, and Markin et a/.53 in (U, Pu)O2 ± x. This is because the formation volumes AO of oxygen defects are different. Concerning the thermal expansion, the coefficients are roughly similar to each other, whatever be the stoichi­ometry considered, as can be seen in Figure 15. Such a behavior is well reproduced by MD calculations (see Watanabe eta/.87 and Yamasaki eta/.88).

The evolution of the lattice parameters as a func­tion of stoichiometry has been summarized by Kato et a/.56 in minor actinides containing MOX (see Figure 16(b)). The hypostoichiometry induces a swelling of the lattice as in UO2 + x. Such behavior has been seen in americium containing PuO2 by

Temperature (K)

Miwa eta/.90 and in pure MOX (see Arima eta/.,81 and references therein), and this is qualitatively repro­duced by MD calculations (see Figure 16(a)). The thermal expansion coefficients of hypostoichiometric dioxides (not reproduced here) simply follow the Vegard’s law (see Arima et a/.81), as evidenced in urania in the previous section.

If uncertainties regarding the behavior of An car­bides, mostly linked to metastability and uncontrol­lable oxygen and nitrogen impurities, still represent an obstacle to the fabrication and employment of these materials as an alternative nuclear fuel to oxi­des, their higher fissile density constitutes a big advantage. Moreover, the metallic thermal conduc­tivity (Figure 3) and high melting temperature of An carbides ensure a higher conductivity integral margin to melting (CIM), defined by eqn [1], for these mate­rials with respect to the traditional UO2, UO2-PuO2, and ThO2 fuels:

Tm

1(T )dT

Top

Here, Top is the reactor operational temperature at the fuel-cladding interface (around 500 K for light water reactor (LWR), and up to 1500 K for the Generation IV very high-temperature reactors, VHTRs) and Tm is the fuel melting temperature. The better compatibility of carbides with liquid metal coolants compared to oxides is a further rea­son for making them good alternative candidates for high burnup and/or high temperature nuclear fuel.

Uranium carbide was traditionally used as fuel kernel for the US version of pebble bed reactors as opposed to the German version based on uranium dioxide.8 Among the Generation IV nuclear systems, mixed uranium-plutonium carbides (U, Pu)C consti­tute the primary option for the gas fast reactors (GFRs) and UCO is the first candidate for the VHTR.1 In the former case, the fuel high actinide density and thermal conductivity are exploited in view of high burnup performance. In the latter, UCO is a good compro­mise between oxides and carbides both in terms of thermal conductivity and fissile density. However, in the American VHTR design, the fuel is a 3:1 ratio of UO2:UC2 for one essential reason, explained by Olander.32 During burnup, pure UO2 fuel tends to oxidize to UO2+x UO2+x reacts with the pyrocarbon coating layer according to the equilibrium:

UO2+x + xC ! UO2 + xCO [IV]

The production of CO constitutes an issue in the VHTR because the carbon monoxide accumulates in the porosity of the buffer layer. The CO pressure in this volume can attain large values and, along with the released fission gas pressure, it can compro­mise the integrity of the coating layers and contribute to the kernel migration in the fuel particle (‘amoeba effect’). In the presence of UC2, the following reaction occurs rather than reaction [IV] in the hyperstoichio­metric oxide fuel:

UO2+X + XUC2 ! (1 + x)UO2 + 2xC [V]

Because no CO is produced in reaction [V], the latter is more desirable than [IV] in view of the fuel integrity.

Thanks to its fast neutron spectrum, the GFR can suit a 232Th-233U fuel concept, in the chemical form of (Th, U)C2 mixed carbides.33,34 However, the tho­rium cycle is at the moment not envisaged in Gener­ation IV systems.

The use of Pu-rich mixed carbide fuel has recently been proposed for the Indian Fast Breeder Test Reactor.35 However, pure plutonium carbides present a low solidus temperature and low thermal conduc­tivity, which are important drawbacks, with respect to pure U — or mixed carbides, for a nuclear fuel.

More details about the use and behavior of uranium carbides as nuclear fuel can be found in Chapter 3.03, Carbide Fuel.

Figures 32-34 show the Th-Ti, U-Ti, and Pu-Ti phase diagrams quoted from Okamoto,4 which were previously assessed by Murray.98 A thermodynamic calculation using the CALPHAD approach was also attempted by Murray.98 The results are summarized in Table 8. The Th-Ti phase diagram was assessed based mainly on the works of Carlson et a/.99 and Pedersen et a/, and is categorized as a typical eutectic type. The liquid phase is completely misci­ble and the solid phases do not have any detectable

Table 8 Calculated interaction parameters for actinides-Ti systems

GO(Ti, liq) = 0 GO(Th, liq) = 0 GO(U, liq) = 0 GO(Pu, liq) = 0

GO(Ti, bcc) = -16234 + 8.368T

GO(Th, bcc) = -16121 + 7.937T

GO(U, bcc) = -8519 + 6.0545T

GO(Pu, bcc) = -3347 + 3.6659T

GO(Ti, HCP) = -20585 + 12.134T

GO(U, HCP) = -16103 + 13.594T

GO(Pu, HCP) = -4477 + 8.14T

GO(Ti, fcc) = -17238 + 12.134T

GO(Th, fcc) = -18857 + 9.610T

GO(Pu, fcc) = -4477 + 5.1944T

GO(Ti, b-U) = -21 000 + 15.0T

GO(U, b-U) = -13311 + 10.627T

G°(Ti,§’-Pu) = -12 000 + 8.368T

GO(Pu, S’-Pu) = -3933 + 4.4441 T

GO(Pu, g-Pu) = -4561 + 5.3373T

GO(Pu, b-Pu) = -6402 + 9.1568T

GO(Pu, a-Pu) = -9247 + 16.3960T

GO(TiU2) = -12313 + 6.162T

Gex(Th-Ti, liq) = xTh(1 — xTh) (16798-4853(xTi-xTh))

Gex(U-Ti, liq) = xy(1 — xy) (17000- 1458(xTi-хи))

Gex(U-Ti, bcc) = xu(1 — xu) (18078-2425(xTi-xu))

Gex(U-Ti, HCP) = xu(1 — xu) (31 216+3257(xTi — xu))

Gex(U-Ti, b-U) = xu(1 — xu) (25 400)

Gex(Pu-Ti, liq) = xPu(1 — xPu) (10158)

Gex(Pu-Ti, bcc) = xPu(1 -xPu) (17559) Gex(Pu-Ti, HCP) = xPu(1 — xPu) (31 245) Gex(Pu-Ti, fcc) = xPu(1 — xPu) (16677) Gex(Pu-Ti, S’-Pu) = xPu(1 — xPu) (13730)

Source: Murray, J. L. 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 106-108, 233-238, 405-409.

mutual solubility. The eutectic point is at 1463 K with 57.5 at.% Th. Thermodynamic calculation for the Th-Ti system was attempted by assuming that the solid phases are completely immiscible, and then the calculated liquidus curve was found to fit reasonably well with the experimental data. Never­theless, Murray98 pointed out that the mutual solid solubilities should be reexamined using high-purity Ti. The Pu-Ti phase diagram was assessed based mainly on the works of Elliott and Larson,76 Poole eta/.,93 Kutaitsev eta/.,1 1 and Languille.1 2 The peri — tectic reaction among p-Ti, e-Pu, and liquid phases dominates this system. The mutual solid solubilities in the Pu-Ti system are far larger than those in the Th-Ti system. The peritectic point is at 1041 K, and the composition for the p-Ti, e-Pu, and liquid phases is 19, 72, and 82.5 at.% Pu, respectively. There is a miscibility gap for the bcc phase (p-Ti, e-Pu), the critical point of which is thought to lie above the peritectic temperature. There are six other invariant reactions in the lower temperature region. The high­est one is supposed to be the eutectoid reaction among the a-Ti, p-Ti, and e-Pu phases, the eutectoid point of which is at 876 K, and the composition for the a-Ti, p-Ti, and e-Pu phases is 2, 15, and 84 at.% Pu, respectively. Due to the lack of experimental data, the other five invariant reactions have large uncer­tainties. A detailed study around the 8′-Pu phase was carried out by Elliott and Larson.76 A ‘self-plating’ effect was noted by these authors,76 in which reaction with oxygen causes Ti to be depleted in the bulk of the sample and to form an oxide layer on the surface. This phenomenon makes it difficult to determine precisely the phase boundaries near the Pu terminal. Thermodynamic calculation of the Pu-Ti system was attempted only for the phase relation among the liquid, a-Ti, p-Ti, and e-Pu phases in the tem­perature region above 773 K. The U-Ti phase dia­gram was assessed mainly based on the works of Udy and Boulger,103 Knapton,104 and Adda et a/.105 The general feature is different from the Th-Ti and Pu — Ti systems. The bcc phase (g-U, p-Ti) is completely miscible as well as the liquid phase, and there is a U2Ti intermetallic compound. The invariant tem­peratures and phase boundaries were determined by optimizing the Gibbs energy functions.98 The U2Ti phase transforms congruently to the bcc phase at 1171 K. Three eutectoid reactions appear in the system. The assessed eutectoid points are at 938 K, 15 at.% U; at 993 K, 93 at.% U; and at 941 K, 98 at. % U. Regarding the crystal structure for the U2Ti phase, the AlB2-type, which is thought to be an ordered hexagonal structure,98 was recommended. The difference in the general features for the Th-Ti, U-Ti, and Pu-Ti phase diagrams suggests that the miscibility in the actinide-Ti system is qual­itatively in the order U-Ti > Pu-Ti The interaction parameters for each system are slightly shifted to the negative direction. The previous thermodynamic assessments were carried out using only the phase boundary data of each system, and therefore, the assessed values possibly are relatively shifted depending upon the systems. Further studies might be required to evaluate the variation in the chemical potentials for these systems. According to systematic considerations, the Np-Ti is speculated to be ordered between the U-Ti and Pu-Ti and Am-Ti after Th-Ti. The shape of the phase relations for the Np-Ti and Am-Ti systems is speculated only preliminarily.

Figure 35 shows the Th-Zr phase diagrams quoted from Okamoto,4 which was constructed from the works of Gibson et a/.106 and Johnson and Honeycombe.107 Complete miscibility for the bcc phase is observed as well as for the liquid phase. There is a miscibility gap for the bcc phase in the central region between 46 and 60 at.% Zr concentration, the critical temper­ature of which is 1228 K. The liquidus and the solidus shift to the lower temperatures, and the bcc phase (p-Th, p-Zr) congruently melts at 1623 K (^46 at.% Zr). These facts suggest that the bcc phase is to be modeled as a simple regular solution and the interaction parameter slightly deviates to the positive direction from Raoult’s law. Although a large solid solubility of Zr in a-Th (fcc structure) is observed near the Th terminal, that of Th in a-Zr (HCP struc­ture) is negligibly small. Regarding the U-Zr system,

Table 9 Calculated interaction parameters for U-Zr systems

GO(U, liq), GO(U, bcc), GO(U, b-U), GO(U, a-U): given in Dinsdale67

GO(Zr, liq), GO(Zr, bcc), GO(Zr, HCP): given in Dinsdale67 GO(U, HCP) = 5000 + GO(U, a-U)

GO(Zr, b-U), GO(Zr, a-U) = 5000 + GO(Zr, HCP)

GO(S-UZr2) = -13394 + 21.484T Gex(U-Zr, liq) = xZr(1 — xZr) (81 206 — 57.494T)

Gex(U-Zr, bcc) = xZr(1 — xZr) (57 907 — 45.448T-6004.2

(Xu — XZr))

Gex(U-Zr, HCP) = xZr(1 — xZr) (23559)

Gex(U-Zr, b-U) = xZr(1 — xZr) (24972)

Gex(U-Zr, a-U) = xZr(1 — xZr) (25 802) [6] [7]

and (2) the low-temperature к-phase (PuZr2) trans­forms eutectoidally from the 8-Pu and a-Zr at ^74at.%Zr116 or transforms congruently to the fcc phase near the stoichiometric composition.117 How­ever, a later study indicated that the к-phase is only found as an oxygen-stabilized phase.118 Annealing tests using the к-phase composition sample were attempted at 625 K for 8 days, but the к-phase was not found.1 The congruent transformation between the fcc and

GO(Pu, liq), GO(Pu, bcc), GO(Pu, S’-Pu), GO(Pu, S-Pu): given in Dinsdale67

GO(Zr, liq), GO(Zr, bcc), GO(Zr, HCP): given in Dinsdale67 GO(Pu,HCP) = 5000 + GO(Pu, S-Pu)

GO(Zr, S’-Pu), GO(Zr, S-Pu) = 5000 + GO(Zr, HCP) Gex(Pu-Zr, liq) = xZr(1 — xZr) (16156 — 12.622T) Gex(Pu-Zr, bcc) = xZr(1 — xZr) (5730.0 — 3.4108T + 2759.7

(XPu — XZr))

Gex(Pu-Zr, HCP) = xZr(1 — xZr) (1145.9)

Gex(Pu-Zr, S’-Pu) = xZr(1 — xZr) (3000)

Gex(Pu-Zr, S-Pu) = xZr(1 — xZr) (-7620.0 — 1.9961T +15833 (xPu — xZr) — 5974.7(xPu — xZr)2)

Source: Kurata, M. In Proceedings of Actinides 2009, San Francisco, CA, July 12-19, 2009.

bcc phases was also confirmed by Suzuki et al.119 as observed by Bochvar et al.116 The liquidus and the solidus were calculated by Leibowitz et al.120 based mainly on the experimental data of Marples117 by assuming that the liquid phase is an ideal solution. Figure 38 shows the reassessed Pu-Zr phase diagram given by Okamoto4’19 based on the experimental data of Bochvar et al.,75 Marples,117 Suzuki et al.,119 and Tayler121 and the calculations by Leibowitz et al.120 Later, the vapor pressure of Pu in the Pu-Zr system was measured at 1473 and 1823 K as well as the liqui­dus and the solidus.122 Thermodynamic evaluation was performed again for the Pu-Zr system7 by addi­tionally taking into consideration the data of Maeda et al.,122 in which a slight positive deviation from Raoult’s law was shown for the liquid phase. Table 10 summarizes the results. The newly calcu­lated results reasonably overlap with the liquid, bcc,

Zr

fcc, and HCP phase boundaries, as indicated in Figure 39, although the phase relations for the low — temperature phases were not assessed because of the lack of the thermodynamic data around the 0-phase. Figure 40 shows the activity diagram with the experi­mental data of Maeda et al.122 The slightly positive deviation is clearly seen in the figure. As for the

Table 11 Calculated interaction parameters for Np-Zr systems

GO(Np, liq), GO(Np, bcc), GO(Np, p-Np), GO(Np, a-Np): given in Dinsdale[8]

GO(Zr, liq), GO(Zr, bcc), GO(Zr, HCP): given in Dinsdale67 GO(Np, HCP) = 5000 + GO(Np, bcc)

GO(Zr, b-Np), GO(Zr, a-Np) = 5000 + GO(Zr, HCP) Gex(Np-Zr, liq) = xZr(1 — xZr) (16000 — 13T)

Gex(Np-Zr, bcc) = xZr(1 — xZr) (9000 — 3T)

Gex(Np-Zr, HCP) = xZr(1 — xZr) (15000)

Gex(Np-Zr, b-Np), Gex(Np-Zr, a-Np) = xZr(1 — xZr) (15000)

isotherms for the solid phase relation in the tem­perature region 773-973 K have been reported.126 Calculated ternary isotherms were given by Kurata7 based on thermodynamic modeling for the U-Pu, U-Zr, and Pu-Zr binary subsystems described above. Figures 43-45 compare both results at vari­ous temperatures. The experimental observations agree reasonably well with the calculation: for instance, the width of the miscibility gap for the bcc phase (g-U, Pu, Zr) at 973 K, the decomposi­tion of Z-phase at around 943 K, the phase relation between the g — and 8-phases at around 868 K, etc. Figures 46 and 47 indicate the calculated liquidus and solidus of the U-Pu-Zr alloy along with the measured values shown in Leibowitz and Blomquist113 and Harbur et a/.127 The calcu­lated values coincide with the measured one within ±20 K variation. By introducing the thermo­dynamic data as well as the phase boundary data for the evaluation of the binary subsystems, reason­able accuracy of the calculated isotherms for the ternary is achieved. In order to solve the conflict for the Np-Zr system described above, the ter­nary information for the U-Np-Zr system may be useful. The similarity of the features between the U-Pu-Zr and the U-Np-Zr systems was shown by Rodriguez eta/.12

Regarding the actinide-Hf systems, the Th-Hf, U-Hf, and Pu-Hf phase diagrams were given by Okamoto.4 These phase diagrams have many simila­rities to those for the actinide-Ti and actinide-Zr

systems, although the experimental data are still not sufficient. The Th—Hf phase diagram is categorized as eutectic type, although a larger mutual solid solu­bility is observed compared to the Th-Ti phase diagram.106 The U-Hf phase diagram shows that the liquid and bcc phases are completely soluble and a miscibility gap exists in the central region of

the bcc phase.128 The Pu-Hf phase diagram looks quite similar to that of Pu-Ti.58

The very limited solid solubility and the miscibil­ity gap even for the liquid phase are speculated on the Am or, possibly, Cm and Group IVa metal systems, which are concluded from the expected similarity with Ce and Ti, Zr, or Hf systems.2,

Due to the difficulty of the experimental study because of the high melting point of Group Va metals, such as V, Nb, and Ta, the experimental data points in these systems sometimes are rather scattered. Nine phase diagrams between Th, U, or Pu and V, Nb, or Ta were summarized by Okamoto.4 The Th—V, Th—Nb, and Th-Ta phase diagrams are categorized as eutectic type. The key references for these systems

are Carlson etal,99 Pedersen eta/.,100 Palmer eta/.,130 Bannister and Thomson,1 1 Smith et a/.,1 McMasters and Larsen,133 Ackermann and Rauh,134,135 and Saroja eta/.136 Their eutectic reactions appear to be more at high temperature and with high Th concentra­tion, as given in Table 12. The thermodynamic functions were evaluated from the liquidus curve for the Th-V and Th-Ta systems by Smith eta/.132

Table 12 Phase relation in actinide-Group Va metal System Th-V Th-Nb Th-Ta U-V U-Nb U-Ta Pu-V Pu-Nb Pu-Ta Phase diagram type Eutectic Eutectic Eutectic Eutectic Solid solution Peritectic Eutectic Eutectic Peritectic monotectoid Invariant temperature 1708 ± 10K 1708K 1953±2 K 1313 ± 5 K 920 K 1433 K 898 K 903 K 931 K 79.7 at. 84 at. 98 at. 82 at. 30 ± 2 at. 97 at. 99.4 at. 99.5 at. 99.2 at. %Th %Th %Th %U %U 86.7at.% U %U %Pu %Pu %Pu References for phase 130 99 133 137 138,139 135 17 140 11 relation 100 134 141 136 140 131 135 142,143 144 145 145 146 [75Smi] 136 147 148 Reference for 132 — 149 — 150 149 151 — 151 thermodynamic modeling

and Krishnan et al.,149 respectively. The Pu-V, Pu-Nb, and Pu-Ta phase diagrams are categorized as eutectic or peritectic type. However, the eutectic or peritectic point is very close to the Pu terminal like that in the Th-Ta system. The key references for the Pu-V system is Konobeevsky17 and Bowersox and Leary.145 Thermodynamic modeling was performed by Baxi and Massalski151 based on both the experi­mental data and semiempirical estimation.40 Since the shape of the Pu-V is quite simple, the thermody­namically calculated phase boundaries fit reasonably well with the experimental data points. However, the measurement of thermodynamic data is still necessary for more accurate evaluation. Also, in the Pu-V sys­tems, a metastable amorphous phase possibly forms in spite of the high degree of immiscibility for the solid phases.152 The Pu-Nb system looks quite similar to the Pu-V system.140,145 The general shape of the Pu-Ta system is slightly different from the other systems. The invariant reaction is changed to peritec — tic from eutectic. However, the peritectic point is comparable to the eutectic points of the Pu-V and Pu-Nb systems. The thermodynamic modeling for the Pu-Ta system was performed in a similar manner to the Pu-V system.151 Regarding the U-related sys­tem, the U-V and U-Ta phase diagrams have mostly similar shapes. The eutectic point appears at 1313 ± 5 K with 82 at.% of U in the U-V system137 as does the peritectic point at 1433 Kwith ^97 at.% of U in the U-Ta system.135,136,144,148 However, the solid solubilities in the U-V and U-Ta systems attain several percent at the maximum, which suggests that the mis­cibility in the U-related system is slightly better than that in the Th — and Pu-related systems. Figure 48 shows the Pu-Nb phase diagram as a typical example
for the relation between the actinide and Group Va metals. The only exception is the U-Nb system, in which g-U and g-Nb (bcc structure) are completely soluble and the general feature for the phase relations is rather similar to that in the U-Zr phase diagram. Figure 49 shows the U-Nb phase diagram quoted from Okamoto.4 The key sources for the system are Pfeil etal.,138 Rogers etal.,139 Peterson and Ogilvie,141 Fizzotti and Maspereni,142 Terekhov,143 and Romig.147 There is a miscibility gap in the bcc phase and an invariant monotectoid reaction at 920 K.150 The solid solubility of Nb in a-U and p-U attains a few percent at the maximum. A couple of reports indicated the formation of the 8-phase in the Nb-rich region during annealing of a diffusion couple between pure U and Nb.141,147 The 8-phase was observed only in the diffu­sion couples but not in the homogenized bulk speci­men. This suggests that the 8-phase is metastable. Poor miscibility between Am, or possibly Cm, and Group Va metals is speculated from the phase relations between Ce and Group Va metals.4

The phase relation between actinides and Group Via metals, such as Cr, Mo, and W, is mostly similar to that between actinides and Group Va metals. They are categorized in the simple eutectic — or peritectic — type phase diagram with the exception of the U-Mo system. Figure 50 shows the Th-Cr phase diagram as a typical example for the actinide-Group Via metal system, which is quoted from Okamoto.4 The phase diagram is redrawn from the assessment of Venkatra- man et al.153 The Th-Mo, Th-W, U-Cr, and Pu-Cr phase diagrams reveal a similar tendency on the phase relations, although the eutectic point is shifted toward the actinide terminal in the case of the W-related system due to the high melting point of

pure W. In the case of Pu-Mo and Pu-W systems, it is difficult to identify whether the invariant reaction is eutectic or peritectic, because the invariant points are very close to the Pu terminal. In the U-W system, the peritectic reaction appears instead of the eutectic reaction.1 4 These phase relations are summarized in Table 13. A simple thermodynamic evaluation for the Cr-related system was carried out153 by assuming that the liquid phase behaves as an ideal solution. Their estimated eutectic temperature for the Th-Cr and U-Cr systems is roughly a few hundred kelvin lower than the experimental observations. This might sug­gest the slightly positive deviation from Raoult’s law for the liquid phase in these systems. The Ac-Cr, Np-Cr, Am-Cr, and Cm-Cr systems were also roughly evaluated by Venkatraman et a/.153 by assuming the liquid phase in the same manner. The U-Mo system shows some differences with respect to the other systems. The U-Mo phase diagram was proposed originally by Brewer,3 in which the solid solubility of Mo in U attains ^40 at.% at the maximum. However, a conflict was pointed out by Massalski eta/.2 as follows. According to Lundberg,163 the MoU2 com­pound exists up to at least 1525 K. The crystal structure for MoU2 was reported to be MoSi2-type tetragonal and different from that of TiU2, which is AlB2-type hexagonal,1 although they have the same composition. Further study is needed to resolve the conflict. Figure 51 shows a tentatively assessed U-Mo phase diagram.164 Regarding the Mo-related systems, the eutectic type of the Np-Mo phase diagram was pre­dicted from thermodynamic modeling.3 Probably, the features of the Np-W system are similar to those for the Np-Mo system. Poor miscibility between Am, or possibly Cm, and Group Via metals is speculated from the phase relation between Ce and Group Via metals.

After the Group VIIa of metals in the periodic table, it is observed that various types of intermetallic compounds are formed by reaction with actinides. This means that the interaction between the actinide and metals after the Group Vila deviates to a large degree in the negative direction from the ideal solu­bility. The phase diagrams of actinide-Group VIIa metals, such as Mn, Tc, and Re, were summarized in Okamoto,4 in which the phase relations between acti­nide and Tc are speculated from that between the actinide and Re based on the similarity expected in the relations between Tc and Re.165 Figure 52 shows the U-Mn phase diagram as a typical example of the actinide-Group VIIa metal relation quoted from Okamoto.4 The phase diagram is constructed based mainly on the works of Wilhelm and Carlson.54 There are two types of intermetallic compounds, U6Mn and UMn2, and two kinds of eutectic reaction in both the U-rich and Mn-rich regions. The phase relation in the U-Mn system looks similar to that in the U-Fe system to be shown later. This supposes that the order of the Gibbs energy of formation of these U-Mn compounds might be comparable to those in the U-Fe compounds, although the Gibbs energy of formation of U6Mn and UMn2 has not been reported yet. In the actinide-transition — metal relations, a MgCu2-type compound with a cubic structure often appears. According to Lawson et a/.,166 p-UMn2 of the MgCu2-type transforms to g-UMn2 of the orthorhombic structure at about 230 K in the U-Mn relation. The crystal structure of U6Mn is the same as that of U6Fe. In the Th-Mn and Pu-Mn systems, the U6Mn-type compound disappears and the decomposition temperature ofthe MgCu2-type compound decreases.17,167 This suggests a decrease in the degree of the negative deviation on mixing in these systems with respect to the U-Mn system. Figure 53 shows the U-Re phase diagram as a typical example of the phase relation between acti­nide and Re. The phase diagram was assessed from Jackson et a/.,168 Garg and Ackermann,155 and Chandrasekharaish et a/.161 The Re-rich side of the phase diagram shows similarity to that in the U-Mn system. However, the crystal structure of URe2, that is, MnZn2-type, is different from the other typical structure, that is, MgCu2-type. The decomposition temperature of URe2 decreases more than that of UMn2 compared to that in the U-Fe system. On the U-rich side, U2Re appears instead of the U6Mn-type compound and the solid solubility of Re in U attains 8.8 at.%, which is significantly larger than that in the U-Mn system. In the U-Re system,

System Th-Cr Th-Mo Th-W U-Cr U-Mo U-W Pu-Cr Pu-Mo Pu-W Phase diagram type Eutectic Eutectic Eutectic Eutectic Peritectic Peritectic Eutectic Eutectic? Eutectic? Peritectic? Peritectic? invariant 1509 K 1653± 12 K 1968 K 1133K 1557±2 K >1408 K 893 K 913 K 913K temperature 75at. 86 ± 0.5 at. 98.8 at. 81 at. 60 at. 99 at. 99.16 at. ~100at.% Pu ~100at.% Pu %Th %Th %Th %U %U %U %Pu References for 16 155 134 137 155 135 76 145 11 phase relation 135 156 29 136 116 37 157 158 144 145 159 160 161 140 162 Reference for 153 3 154 153 — 154 153 3 154 thermodynamic modeling

the negative deviation from the ideal solubility is speculated to be smaller than that in the U-Mn system based on these observations. In the Th-Re and Pu-Re systems,146’155 the MnZn2-type com­pounds, such as ThRe2 and PuRe2, are the only compounds and the U2Re-type does not appear. This suggests that the negative deviation from the ideal solution between Th-Re and Pu-Re becomes smaller than that in the U-Re as well as the tendency observed in the Mn-related system. Regarding the Np — related systems, the formation of NpMn2 and NpRe2, which have the MgCu2-type and MgZn2-type struc­tures, respectively, was reported.169 Poor miscibility between Am, or possibly Cm, and Group Vila metals is speculated from the phase relation between Ce and Group VIIa metals.

2.08.2.4.1 Chemical compositions, physical properties, and mechanical properties

The chemical compositions of other nickel-based alloys not already described in the previously men­tioned categories are shown in Table 3, along with those of the alloys mentioned above.

Alloy G (UNS N06007) has excellent corrosion resistance to hot sulfuric acid and hot phosphoric acid. The alloy has superior corrosion resistance to oxidizing environments compared to Alloy C-276, due to its higher chromium content (about 22%) than that of Alloy C-276 (about 18%). On the other hand, Alloy G has inferior corrosion resistance to reducing environments such as sulfuric acid com­pared to Alloy C-276, due to its lower molybdenum content (about 6.5%) than that of Alloy C-276 (about 18%). A copper content of ^2% is included in Alloy G to improve its corrosion resistance in sulfuric acid. Alloy G can be welded because of its niobium content, which stabilizes carbon. However, the alloy is highly susceptible to hot cracking during welding.

Alloy G-3 (UNS N06985) is improved in terms of the bending characteristics of welded joints due to a reduced carbon and niobium content. This alloy has a lower susceptibility to hot cracking during welding.

Alloy G-30 (UNS N06030) was originally devel­oped to improve corrosion resistance in wet phosphoric acid. This alloy shows excellent corrosion resis­tance to oxidizing acids, such as nitric acid, and also to oxidizing halogen-ion-containing environments such as nitric and fluoric acid, due to its increased chromium content (about 30%).38

The chromium content in this alloy leads to delete­rious effects in molten fluoride. However, Alloy N shows excellent corrosion resistance to molten fluoride due to its reduced chromium content (about 7%).3

Alloy 230 (UNS N06230) shows excellent resis­tance to oxidation and nitriding as well as high strength at high temperatures. This alloy has been applied as a heat-resistant material in industrial fur­naces and gas turbines.40

Alloy X (UNS N06002) is a solid-solution-hardened alloy owing to the presence of molybdenum. This alloy has high strength at high temperatures and good resistance to oxidation in high-temperature air.41

Alloy XR was originally developed as a structural material for high-temperature gas-cooled reactors (HTGR) and is a modified version of Alloy X. It is produced by vacuum double melting with optimized contents of manganese, silicon, and boron as inten­tional additives, while minimizing the aluminum, titanium, and cobalt content, as these are undesirable

42

impurities.

The mechanical and physical properties of the above alloys are shown in Tables 4 and 5, respectively, together with those of other nickel-based alloys.