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

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

Figure 23 Calculated Pu activity at 1473 K in the U-Pu system taken from Kurata,7 and the experimental data taken from Kurata et a/.89 (o) and Nakajima et a/.87 (•).

Figure 24 Calculated U-Am phase diagram taken from Kurata.7

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

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 ().

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

Figure 26 Calculated Np-Am phase diagram taken from Kurata,7 and the experimental data taken from Gibson and Haire.57

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

1500- bcc Figure 27 Calculated Pu-Am phase diagram taken from Kurata,7 and the experimental data taken from Ellinger et a/.95

Weight percent plutonium 0 1 0 20 30 40 50 60 70 80 90 1 00

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.