Modelling and calculation of the phase diagrams of the LiF–NaF–RbF–LaF3 system

Computer Coupling of Phase Diagrams and Thermochemistry 31 (2007) 209–216 www.elsevier.com/locate/calphad

Modelling and calculation of the phase diagrams of the LiF–NaF–RbF–LaF3 system O. Beneˇs ∗ , J.P.M. van der Meer, R.J.M. Konings European Commission, Joint Research Centre, Institute for Transuranium Elements, P.O. Box 2340, 76125 Karlsruhe, Germany Received 15 May 2006; received in revised form 5 December 2006; accepted 7 December 2006 Available online 30 January 2007

Abstract Four ternary phase diagrams of the quaternary system LiF–NaF–RbF–LaF3 were calculated from the data of LiF–NaF, LiF–RbF, LiF–LaF3 , NaF–RbF, NaF–LaF3 and RbF–LaF3 binary phase diagrams using the Kohler symmetric and Kohler–Toop asymmetric approximation. Excess Gibbs parameters of all six mentioned binaries were optimized using the experimental results taken from the literature. For the LiF–RbF system our own data were used. In all cases very good agreement between the experimental data and our optimized values was achieved. Excess Gibbs functions for the liquid phases were obtained using the modified quasi-chemical method based on quadruplet interactions and the excess Gibbs function for the solid solution was calculated by a sublattice model. The quaternary eutectic was determined and a set of pseudo-ternary systems with fixed ratio of LaF3 was calculated in order to find the optimal composition for a molten salt fuel. c 2007 Elsevier Ltd. All rights reserved.

Keywords: Nuclear fuel; Phase diagram; Molten fluoride salt; Thermodynamics

1. Introduction The Molten Salt Reactor is based on the dissolution of fissile material (233 U, 235 U and 239 Pu) in an inorganic fluid which circulates in the primary circuit from the reactor core to the heat exchanger and back. The molten salt can be extracted for clean up in a chemical plant online or in a batch process. The first concept of a molten salt reactor was made in the 1950s and is known as the US Aircraft Reactor Experiment (ARE). In the 1960s, the Oak Ridge National Laboratory (ORNL) focused the research on civil applications of this concept and their effort culminated with the construction and operation of the Molten Salt Reactor Experiment (MSRE). This MSRE was a graphite moderated test reactor located in ORNL with an output of 7.4 MW. In the 1970s, the Molten Salt Reactor project was abandoned and nuclear science was shifted to other designs. Nowadays the Molten Salt Reactor is a subject of renewed interest, since it is a safe and efficient system with a potentially high fuel burn-up, thermal breeding and the possibility for actinide burning. It belongs to the group of Generation IV reactors. ∗ Corresponding author. Tel.: +49 7247 951263; fax: +49 7247 951566.

E-mail address: [email protected] (O. Beneˇs). c 2007 Elsevier Ltd. All rights reserved. 0364-5916/$ - see front matter doi:10.1016/j.calphad.2006.12.004

The fuel in a Molten Salt Reactor is the fissile material dissolved as a fluoride salt in a matrix of metal fluorides which have the required properties. These are: thermodynamic stability at high temperatures, low neutron-capture cross section, stability to radiation, low vapor pressure at the operating temperature, relatively low eutectic temperature and good solubility for uranium, thorium and plutonium [1,2]. In MSRE the fuel matrix was LiF–BeF2 (FLIBE) with a small concentration of ZrF4 . But for better solubility of PuF3 and other higher actinide trifluorides, when designed as an actinide burner, LiF–NaF seems to be a potential carrier. In previous work [3], the LiF–NaF–LaF3 system was thermodynamically described and in this work the effects of the addition of RbF to that system is studied. The main contribution of RbF in the overall LiF–NaF–RbF–LaF3 system is to lower the melting (eutectic) temperature, while LaF3 serves as a proxy componenet for PuF3 fuel. 2. Experimental Experimental data for the LiF–RbF phase diagram were obtained from thermal analysis, which was performed on a NETZSCH STA 449 C Jupiter apparatus using the

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Table 1 Results from the DTA analysis performed on the LiF–RbF binary system xLiF

xRbF

Temp. (K)

Type of equilibrium

0.90

0.10

729.8 1079.9

Eutectic Liquidus

0.80

0.20

0.70

0.30

746.4 956.2 686.4 741.1 933.9

Eutectic Liquidus Decomposition Eutectic Liquidus

0.60

0.40

688.9 746.9 861.9

Decomposition Eutectic Liquidus

0.50

0.50

688.9 747.3 752.9

Decomposition Eutectic Liquidus

0.40

0.60

745.8

Eutectic

0.30

0.70

686.1 745.5 895.5

Decomposition Eutectic Liquidus

692.2 743.0 1005.1 735.5 1045.5

Decomposition Eutectic Liquidus Eutectic Liquidus

1076.5

Melting point

0.21

0.79

0.11

0.89

1

0

DSC detector. The temperature scale of this apparatus was calibrated using several standard materials with various characteristic temperatures. As standard material CsCl, BaCO3 , Ag2 SO4 , KClO4 , NaCl, KCl, In, Sn and Bi were used. LiF 99.98% and RbF 99.99%, both from Alfa Aesar, were used as starting material for the experimental measurements. These materials and especially RbF are very hygroscopic. Therefore they were dried in an argon atmosphere at a temperature of 523 K for 5 h before all of the measurements. Weighed mixtures (accuracy of weighing was ±0.1 mg) were put in boron nitride crucibles (AX05 grade, oxygen binder free boron nitride) with screwed caps and immediately inserted into the measuring chamber of the DSC. The atmosphere of the chamber was kept under a constant flow of argon 5.0 gas. All measured samples underwent two heating runs. The first was used to form the intermediate compound LiF·RbF and to vaporize the adsorbed moisture, which could be attracted to the crucible. In the second heating run the eutectic temperature and the LiF·RbF decomposition temperature were identified as the onset temperatures of the peak on the heat flow curve. For the liquidus determination the endset temperature of the peak was taken. The cooling ramp was not taken into account because of the shift of the characteristic temperature due to supercooling effects. Table 1 lists the results from DTA measurements of the LiF–RbF phase diagram. 3. Thermodynamic method To describe a T –X phase diagram, the Gibbs energy equations of all compounds and the Gibbs equations of mixing,

in the case of the presence of solutions, are required. If these data are not known they need to be obtained by performing a thermodynamic assessment. This was all done according to the CALPHAD method, including the critical review of all available data of interest, followed by the optimization of unknown data to get the best possible fit between calculated values and experimental data. Because the data for ternary systems are usually not known, and it was so in this case, first the binary phase diagrams need to be evaluated and then they can be extrapolated to higher order systems according to the Kohler–Toop formalism [4]. All optimizations were performed using the OptiSage module in the FactSage 5.4 software [5], which uses the Bayesian Optimization Algorithm [6]. This algorithm is based on the estimation of a probability distribution function. 3.1. Binary assessments 3.1.1. Condensed phases The Gibbs energy equation for relevant compounds is described by Eq. (1) as a contribution of the enthalpy of formation, the absolute entropy at the reference temperature and the heat capacity. G(T ) = 1 f H 0 (298.15 K) − S 0 (298.15 K)T  Z T  Z T C p (T ) C p (T )dT − T + dT. T 298.15 298.15

(1)

Eq. (1) can be written also in different form, in which the C p contribution is represented by a polynomial function of T as is shown in Eq. (2). In this equation a and b are constants. G(T ) = 1 f H 0 (298.15 K) − S 0 (298.15 K)T X + ai T i + bT ln(T ).

(2)

There are ten condensed phases in the studied LiF–NaF– RbF–LaF3 system. These are LiF, NaF, RbF, LaF3 and six intermediate phases of 3RbF·LaF3 , 2RbF·LaF3 , RbF·LaF3 , RbF·2LaF3 , LiF·RbF and NaF·LaF3 . The thermodynamic data for LiF, NaF, RbF, LaF3 are known and were taken from an internal report [7], and in the case of RbF from [8]. The data for all six intermediate compounds were not available and had to be obtained by optimization. NaF·LaF3 was indeed assessed in [3], but for the reason of remodelling of the NaF–LaF3 system, this was not considered in our work. The heat capacity of NaF·LaF3 was taken from [9], while the data for the heat capacity of the LiF·RbF compound were taken from [10]. According to Eq. (1), the enthalpy of formation, the absolute entropy at the reference temperature and the heat capacity are necessary to calculate thermodynamic equilibrium. It was assumed, following the Neumann–Kopp rule, that the data for C p of the intermediate phases could be obtained as a proportional contribution of the pure compounds, while the data for enthalpy and entropy needed to be assessed. The thermodynamic data of the condensed phases that were used in this work are summarized in Table 2. In the case of binary non-ideal solutions, the Gibbs energy function is defined by Eq. (3) as the weighted average of the

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Table 2 1 f H 0 (298.15 K) (kJ mol−1 ), S 0 (298.15 K) (J K−1 mol−1 ) and C p data for the pure components and intermediate compounds of the system LiF–NaF–RbF–LaF3 Comp.

1 f H 0 (298.15)

S 0 (298.15)

a

bT

LiF(l)a NaF(l)a RbF(l)a LaF3 (l)a LiF(cr)a NaF(cr)a RbF(cr)a LaF3 (cr)a,b LiF·RbF(cr)c 3RbF·LaF3 (cr)c,b 2RbF·LaF3 (cr)c,b RbF·LaF3 (cr)c,e RbF·2LaF3 (cr)c,f NaF·LaF3 (cr)d

−598.654 −557.730 −542.370 −1633.920 −616.931 −576.650 −559.700 −1669.500 −1177.711 −3373.181 −2793.656 −2246.555 −3900.200 −2245.597

42.962 52.755 85.103 97.639 35.660 51.210 77.70 106.980 111.773 342.542 281.732 182.560 296.660 161.200

64.183 72.989 71 135.00 43.309 47.63 42.343 122.119 85.652 249.2 206.8 140.4 286.6 132.61

1.6312E−02 1.479E−02 2.6024E−02 −2.2467E−02 4.2336E−02 5.5600E−02 2.9580E−02 2.6000E−02 −1.8912E−02 −2.9109E−02

c T2

d T −2

5.0470E−07

−5.6912E+05 −4.643E+05

−4.69E+04 −1.6309E−05 5.0470E−7 −1.6309E−5 −1.6309E−5

−2.1714E+06 −6.1602E+05 −2.3121E+06 −2.2652E+06

3.2619E−5 3.4332E−05

−4.3897E+06 −4.6607E+05

a b c d

Data taken from an internal report [7]. An extra term in the C p function: 2.8175E−08T 3 . Obtained by assessment with modified Quasi-Chemical model. Heat capacity data taken from [9]. The entropy had to be slightly lowered compared to experimental value [9], to make the compound stable in the temperature range 298.15–1058 K. e Data for heat capacity taken from [10]. f An extra term in the C function: 5.6349E−08T 3 . p

Gibbs energies of the pure components plus the contribution of ideal mixing plus the excess Gibbs energy.

Table 3 Cation–cation coordination numbers of the liquid

G(T ) = x1 G 1 (T ) + x2 G 2 (T ) + x1 RT ln x1 + x2 RT ln x2 + ∆xs G.

A

B

A Z AB

B Z AB

Li Na Rb La Li Li Li Na Na Rb

Li Na Rb La Na Rb La Rb La La

6 6 6 6 6 6 2 6 2 2

6 6 6 6 6 6 6 6 6 6

(3)

3.1.2. Liquid solutions The G 1 and G 2 terms in Eq. (3) are the Gibbs energy functions of the pure compounds that the liquid solution consists of and can be calculated using the thermodynamic data of these compounds following Eq. (1), resp. Eq. (2). Because the heat capacity of these compounds (LiF, NaF, RbF, LaF3 ) is, for the liquid phase, constant, the G 1 and G 2 functions in Eq. (3) can be written as shown in Eq. (4). 0 0 G 1,2 (T ) = 1 f H1,2 (298.15 K) − S1,2 (298.15 K)T   T + C p1,2 (T − 298.15) − T C p1,2 ln . (4) 298.15

For the description of the excess Gibbs energy for liquids, the modified quasi-chemical model based on a quadruplet approximation proposed by Chartrand and Pelton [11,12] was used. The parameters of this model are the Gibbs energy changes ∆g AB/ X for the second nearest neighbor pairexchange reaction: (A − X − A) + (B − X − B) = 2(A − X − B)∆g AB/ X

(5)

where A and B represent the cations and X the anion. Since there is only one type of anion in our work (F − ), we could directly use the model to treat cation–cation interaction on the cation sublattice. The ∆g AB/ X parameter from reaction (5) can be expanded as a polynomial such as X ij j i ∆g AB/ X = ∆g 0AB/ X + g AB/ X χ AB/ (6) X χ B A/ X (i+ j)=1

ij

where ∆g 0AB/ X and g AB/ X are composition independent coefficients (although possibly temperature dependent) obtained from the optimization of the experimental data for binary AX − B X solutions. The χ AB/ X term is a composition variable and is defined as   X AA (7) χ AB/ X = X A A + X AB + X B B where X A A , X AB and X B B represent the cation–cation pair mole fractions. It can not be ignored that this model requires A , the definition of cation–cation coordination numbers Z AB B . The chosen values for each pair were taken resp. Z AB from [13] and are listed in Table 3. It is likely that the cation–cation coordination numbers differ with composition, nevertheless the chosen values correspond to the composition of maximum second nearest neighbor short range ordering in A, B − X binary subsystem [11] and therefore are composition independent. The optimized excess Gibbs terms for the modified quasichemical model are listed below keeping the same notation as

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Fig. 1. A comparison between the experimental data of mixing enthalpies [10] and the modelled values for the LiF–LaF3 , NaF–LaF3 and RbF–LaF3 systems. M results for RbF–LaF3 system at T = 1097 K, ◦ results for NaF–LaF3 system at T = 1183 K,  results for LiF–LaF3 system at T = 1183 K. Filled signs correspond to liquid–solid equilibrium, not taken into account in this work.

proposed by Chartrand and Pelton [13–15]. In [14] the LiF–NaF system was modelled but these assessed values together with the thermodynamic data of the compounds that we used did not reproduce the phase diagram correctly, so they were neglected and the system has been remodelled. The Gibbs energy equation of formation of the Li–F–Na pairs was found to be ∆gLiNa/FF = −2307.47 + 0.4281T J mol−1

(8)

and the excess equations for the other possible quadruplet interactions are listed below: ∆gLiRb/FF = −4217.10 − 1442.58χRbLi − 452.22χLiRb J mol−1

(9)

∆gLaLi/FF = −3711.58 − 0.6200T − 7871.99χLaLi J mol−1

(10)

∆gNaRb/FF = 301.86 − 323.56χRbNa + 367.33χNaRb J mol−1

(11)

∆gNaLa/FF = −13 374.91 + 0.541T − 14 439.7χLaNa − 579.59χNaLa J mol−1

(12)

∆gRbLa/FF = −31 587.27 + 9.4800T + (10 973.95 − 7.8668T )χRbLa + (33 334.0 − 45.2400T )χLaRb J mol−1 .

(13)

Fig. 2. The calculated diagram of LiF–NaF. M results by Holm [18].

3.1.3. Solid solution For the studied LiF–NaF–RbF–LaF3 system it was assumed that the only solubility in the solid state occurs in the LiF–NaF system. The lithium ion, a small cation compared to sodium, is dissolved in NaF creating the solid solution of the basic formula Lix Na1−x F. To describe the thermodynamic behavior of this solid solution Eq. (3) is used. The G 1 (T ) and G 2 (T ) terms are the Gibbs functions of the LiF resp. NaF compounds. The excess Gibbs energy has been optimized using the sublattice model described in [16], which deals with vacancies that are formed after mixing two cations on one sublattice that have different oxidation states. Nevertheless in the case of Lix Na1−x F solid solution no vacancies were formed, because both cations have the same oxidation state. From this fact we could assume that the solution is clearly substitutional and is created only from the LiF and NaF species. As can be seen in Fig. 2, the solid solution is not miscible over the complete range and therefore we had to optimize the enthalpy of formation of the hypothetical endmember LiFss . The optimized values of LiFss and excess Gibbs energy of mixing are listed below in Eqs. (14) and (15). 0 1 f HLiF (298.15 K) = −597 084.8 J mol−1 ss   x + J mol−1 . ∆xs G = 6.6565 Li xF−

(14) (15)

The terms xLi+ and xF− in Eq. (15) represent mole fractions of the Li+ cation, resp. F− anion, in solution.

The Gibbs energy equations of formation of Li–F–La and Na–F–La pairs differ from what was published in [3]. That is due to the fact that in our work we considered additional experimental data [10]. The comparison between these measured enthalpies of mixing and our modelled values was made for LiF–LaF3 , NaF–LaF3 and RbF–LaF3 systems and is shown in Fig. 1. The Gibbs energy equations of formation of Li–F–Na pairs were also published in [3], but since we now considered the Lix Na1−x F solid solution, which was neglected in [3], the data have been reoptimized.

3.2. Ternary assessment After the binary phase diagrams are evaluated, the ternary phase diagrams can be extrapolated according to the Kohler symmetric, respectively Kohler–Toop asymmetric, formalisms [4]. The LiF–NaF–RbF system was treated as symmetric, because all cations are alkali metals with similar properties and they all have the same, highly ionic bonding. The other three ternaries were treated as asymmetric systems, where the asymmetric component has different chemical properties compared to the other two. In all three cases it was most reasonable to select LaF3 as the asymmetric component.

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In the case of LiF–NaF–RbF and LiF–NaF–LaF3 systems, small ternary interactions were introduced in order to reproduce the eutectic temperature which was found experimentally by Barton et al. [17] and by van der Meer et al. [3], respectively. The ternary terms are listed below in Eqs. (16) and (17). 001 ∆gLiNa(Rb)/FF = −6125.5 J mol−1

(16)

001 ∆gLiNa(La)/FF = −9565.5 J mol−1 .

(17)

4. Results and discussion 4.1. Binary subsystems Six binary subsystems were assessed: LiF–NaF, LiF–RbF, LiF–LaF3 , NaF-RbF, NaF–LaF3 and RbF–LaF3 . The LiF–LaF3 and NaF–LaF3 systems were assessed using the quasichemical model with quadruplet approximation and the results were described by van der Meer et al. [3]. Nevertheless these two systems were reassessed in this work taking into account additional experimental data [10]. LiF–LaF3 is a single eutectic system, with the eutectic at T = 1043 K and X LaF3 = 0.17, whereas NaF–LaF3 contains a eutectic (1008 K; 0.28 X LaF3 ) and a peritectic (1058 K; 0.34 X LaF3 ), where the intermediate compound NaLaF4 decomposes. LiF–NaF is a single eutectic system (921 K; 0.39 X NaF ) with the solid solubility at the NaF rich side. Experimental data by Holm [18] and data on the enthalpy of mixing at 1360 K by Hong and Kleppa [19] were used for the optimization. The assessment of the LiF–RbF system was based on our experimental data and on the data by Barton et al. [20]. The Gibbs energy equation for the intermediate compound LiRbF2 , for which decomposition in the solid phase was derived from the experimental data, was optimized in the assessment. The NaF–RbF diagram, a simple eutectic system, was measured by Holm [18], whose data were used in the assessment. The assessment of the RbF–LaF3 system was based on the experimental data made by Abdoun et al. [10] and Filatova et al. [21]. The enthalpies of mixing measured by Abdoun et al. [10] were also considered. The eutectic temperature of the system was calculated to be T = 890 K at X LaF3 = 0.21, which is slightly higher than what was found in [10], but the composition is in perfect agreement. This system contains four peritectic points and all of them are in excellent agreement with the results in [10,21]. The first peritectic, where Rb3 LaF6 decomposes, was found at T = 909 K and X LaF3 = 0.247, while the second peritectic was found at T = 946 K and X LaF3 = 0.28. Here Rb2 LaF6 decomposes. In the third peritectic RbLaF4 decomposes and it was found to be at T = 1013 K and X LaF3 = 0.34. The last peritectic was found at T = 1100 K and X LaF3 = 0.40. Here RbLa2 F7 decomposes. The decision to consider this compound in our paper was based on the work of Fedorov [22] and Filatova et al. [23] and it has a narrow temperature field of stability like Rb2 LaF7 . It is realized that rather large values are needed for the excess coefficients for the RbF–LaF3 system, especially in the T -terms. However, it appeared that a satisfying result could

Fig. 3. The calculated diagram of LiF–RbF. • present experimental data; M results by Barton et al. [20].

Fig. 4. The calculated diagram of NaF–RbF. M results by Holm [18].

Fig. 5. The calculated diagram of RbF–LaF3 . M results by Abdoun et al. [10], • results by Filatova et al. [21].

not be reached with less or with smaller coefficients. Figs. 2–5 show the calculated phase diagrams of, respectively, LiF–NaF, LiF–RbF, NaF–RbF and RbF–LaF3 . Table 4 lists the calculated invariant binary equilibria. 4.2. Ternary subsystems Using the data from the binary subsystems, the four ternary subsystems were extrapolated: LiF–NaF–LaF3 , LiF–NaF–RbF,

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Table 4 Invariant equilibria in LiF–NaF, LiF–RbF, NaF–RbF, LiF–LaF3 , NaF–LaF3 and RbF–LaF3 , calculated using the quasi-chemical model in quadruplet approximation Equilibrium

T (K)

Mole fraction

Eutectic Max. in solid sol.

921 921

0.394NaF/(LiF + NaF) 0.926NaF/(LiF + NaF)

Eutectic Decomposition

747 680

0.540RbF/(LiF + RbF) 0.500RbF/(LiF + RbF)

Eutectic

938

0.320NaF/(RbF + NaF)

Eutectic

1043

0.170LaF3 /(LiF + LaF3 )

Eutectic Peritectic

1008 1058

0.280LaF3 /(NaF + LaF3 ) 0.34LaF3 /(NaF + LaF3 )

Eutectic Peritectic Peritectic Peritectic Peritectic

890 909 946 1013 1100

0.210LaF3 /(RbF + LaF3 ) 0.247LaF3 /(RbF + LaF3 ) 0.280LaF3 /(RbF + LaF3 ) 0.340LaF3 /(RbF + LaF3 ) 0.400LaF3 /(RbF + LaF3 )

LiF–RbF–LaF3 and NaF–RbF–LaF3 . The ternary subsystem LiF–NaF–LaF3 was indeed described in previous work [3], but for the consideration of the solid solution in the LiF–NaF binary system and because of the reassessment of the LiF–LaF3 and NaF–LaF3 systems, it had to be recalculated. There are two invariant points in this system. The ternary eutectic was calculated for 853 K with composition of X LaF3 = 0.144, X LiF = 0.421 and X NaF = 0.434 and the peritectic, where the NaLaF4 decomposes, was found for 867 K and X LaF3 = 0.158, X LiF = 0.441, X NaF = 0.401. These values are in excellent agreement with the results published previously in [3] (in [3] the E = 853 K and P = 862.3 K). The LiF–RbF–LaF3 system contains five invariant points, a ternary eutectic at T = 745 K and X LaF3 = 0.010, X RbF = 0.543, X LiF = 0.446 and four peritectics. In the NaF–RbF–LaF3 system, there are four peritectics and two eutectics, whereas the ternary eutectic was found at T = 840 K and X LaF3 = 0.237, X RbF = 0.556, X NaF = 0.207. The last system LiF–NaF–RbF is the simplest with only one ternary eutectic at the temperature of T = 708 K

Fig. 6. Calculated liquid surface of LiF–NaF–RbF. Isotherms are labeled in K with interval of 25 K.

and X LiF = 0.418, X NaF = 0.138, X RbF = 0.444. All four ternary phase diagrams are shown in Figs. 6–9 as a polythermal projection of the liquidus line. Table 5 lists the calculated ternary invariant points. 5. Discussion In the introduction it was mentioned that the main purpose of the thermodynamic investigation of the LiF–NaF–RbF–LaF3 system is the evaluation of its use as a molten salt fuel, where La is used as a proxy of Pu. It was also stated that it is necessary to have the lowest melting point of the fuel salt as possible to reduce the risk of the system ‘freezing’. In [24], the typical entering temperature of the fuel into the reactor was mentioned to be 838 K (565 ◦ C). A safety margin of 67 K (the same margin as in Molten Salt Breeder Reactor design) was kept in our work and the temperature of 771 K was taken as our reference point to predict whether the eutectic temperature is suitable for the molten salt fuel. Regarding to the composition of the fuel

Table 5 Invariant equilibria in LiF–NaF–RbF, LiF–RbF–LaF3 , NaF–RbF–LaF3 and LiF–NaF–LaF3 systems System

Equilibrium

T (K)

X LiF

X NaF

X RbF

X LaF3

LiF–NaF–RbF LiF–RbF–LaF3

Eutectic Eutectic Peritectic Peritectic Peritectic Peritectic Eutectic 1 Eutectic 2 Peritectic Peritectic Peritectic Peritectic Eutectic Peritectic Eutectic Peritectic

708 745 818 843 905 990 840 845 843 890 918 990 853 867 907 942

0.418 0.446 0.388 0.244 0.470 0.133 0 0 0 0 0 0 0.421 0.441 0.534 0.558

0.138 0 0 0 0 0 0.207 0.147 0.198 0.379 0.356 0.128 0.434 0.401 0.399 0.304

0.444 0.543 0.504 0.583 0.347 0.558 0.556 0.667 0.564 0.348 0.346 0.540 0 0 0 0

0 0.010 0.108 0.173 0.183 0.309 0.237 0.186 0.238 0.273 0.298 0.333 0.144 0.158 0.067 0.138

NaF–RbF–LaF3

LiF–NaF–LaF3 LiF–NaF–LaF3 a a Data from previous work [3].

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Fig. 7. Calculated liquid surface of LiF–RbF–LaF3 . Isotherms are labeled in K with interval of 25 K.

Fig. 8. Calculated liquid surface of NaF–RbF–LaF3 . Isotherms are labeled in K with interval of 25 K.

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another criterion had to be fulfilled. That was the concentration of LaF3 (PuF3 ). This will depend on the reactor design and strategy, but realistically it should not exceed 10 mol%. Note, that here the LaF3 is a proxy for the actinide trifluorides, which can be justified on a basis of our previous results [3] that show very close melting temperatures in the LiF–NaF–MF3 systems (M = La and Pu). The composition of the eutectic in the NaF–RbF–LaF3 system contains nearly 24 mol% of LaF3 , which is too much. Moreover the eutectic temperature of this system is 69 K above our reference value and is not acceptable. Similarly in the LiF–NaF–LaF3 system the concentration of LaF3 corresponding to the eutectic point and its temperature are too high (T = 853 K, X LaF3 = 0.144). The last LiF–RbF–LaF3 system has a low eutectic temperature (T = 745 K) with the LaF3 concentration fulfilling our criteria (X LaF3 = 0.010), but extremely low. This system could only be used for reactor designs with very frequent fuel cleanup, where the actinide concentration can be kept at low amounts. In order to find out whether the liquidus in the LiF–NaF–RbF–LaF3 system is below our reference point while containing higher concentrations of LaF3 , further investigation has been performed. Firstly the quaternary eutectic, the lowest melting point, of the LiF–NaF–RbF–LaF3 system was determined. It was found to be at 707 K (434 ◦ C) at the composition of X LiF = 0.403, X NaF = 0.136, X RbF = 0.450, X LaF3 = 0.010. Here the concentration of LaF3 is same as it is in case of the LiF–RbF–LaF3 system. However the melting temperature is very low and could be increased in order to include more LaF3 . Therefore a set of pseudo-ternary systems with constant amounts of LaF3 = 3, 5, 7, 10 mol% at T = 771 K were calculated. In all four cases the liquid region appears below our reference point, moreover the liquid region at T = 771 K for X LaF3 ≤ 7 mol% is significantly wide. This is very important for a safety of the reactor. It avoids solid precipitation when changing the composition slightly. One of the pseudoternary phase diagrams containing 5 mol% of LaF3 is shown in Fig. 10. 6. Conclusion

Fig. 9. Calculated liquid surface of LiF–NaF–LaF3 . Isotherms are labeled in K with interval of 25 K.

Thermodynamic assessments have been performed on the six binary subsystems of LiF–NaF–RbF–LaF3 . To obtain the excess Gibbs parameters, for liquids the modified quasi chemical model was used, for the solid solution the sublattice model was used. The higher order systems were approximated according to the Kohler symmetric or Kohler–Toop asymmetric method, respectively. The quaternary eutectic temperature was determined to be 707 K, low enough to use the material as a molten salt fuel, with corresponding concentration X LaF3 = 0.010. From the pseudo-ternary calculations it was concluded that from a thermodynamic point of view the LiF–NaF–RbF matrix is a very good solvent for actinide trifluorides, when used as nuclear fuel. Additional investigation of other relevant physical properties, such as viscosity, heat capacity and thermal conductivity, must be performed to establish the suitability of the LiF–NaF–RbF matrix for a plutonium fuel.

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Fig. 10. Pseudoternary plot of the LiF–NaF–RbF–LaF3 system with constant amount of LaF3 = 5 mol% at T = 771 K. Phases: (1) RbLaF4 + NaLaF4 + LiF–NaFss ; (2) RbLaF4 + LiF–NaFss + Rb3 LaF6 ; (3) RbF + LiF–NaFss + Rb3 LaF6 ; (4) L + LiF–NaFss + RbF + Rb3 LaF6 ; (5) L + RbF + Rb3 LaF6 ; (6) L + Rb3 LaF6 ; (7) L + LiF–NaFss + Rb3 LaF6 ; (8) L + LiF–NaFss ; (9) L + LiF + LiF–NaFss ; (10) L + LiF; (11) L + LiF+Rb3 LaF6 ; (12) L+RbLaF4 +LiF; (13) L+LiF+RbLaF4 +Rb3 LaF6 ; (14) RbLaF4 + LaF3 + NaLaF4 + LiF; (15) RbLaF4 + LiF–NaFss + NaLaF4 + LiF; (16) L + LiF–NaFss + RbLaF4 + LiF; (17) L + RbLaF4 + LiF–NaFss ; (18) L + LiF–NaFss + RbLaF4 + Rb3 LaF6 ; L — liquid.

Acknowledgements O.B. acknowledges the European Commission for support given in the frame of the program “Training and Mobility of Researchers”. The authors want to thank one of the referees for his suggestions for additional references. References [1] W.R. Grimes, D.R. Cuneo, Reactor Handbook, in: Materials, vol. I, Interscience Publishes Inc, New York, 1960, p. 425 (Chapter 17).

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