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

Am Figure 31 Calculated Np-Pu-Am isotherm at 792 K taken from Kurata,7 with phase relation observed in Nakajima et a/.87	Weight percent titanium Figure 34 Pu-Ti phase diagram taken from Okamoto.4

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,

Weight percent zirconium

Th

Atomic percent zirconium

Zr

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

Weight percent thorium 0 10 20 30 40 50 60 70 80 90 100 Figure 50 Th-Cr phase diagram taken from Okamoto.4

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.