Experimental investigation and thermodynamic modelling assessment of the AECl₂–NdCl₃ (AE = Sr, Ba) systems

Abstract

The thermodynamic and thermo-physical properties of the binary salt systems AECl₂–NdCl₃ (AE = Sr, Ba) have been investigated using an experimental and modelling approach. The binary salt systems both include a single intermediate salt, i.e. Sr₉Nd₅Cl₃₃ and Ba₃Nd₂Cl₁₂, respectively. The structure of these intermediates has been investigated with X-ray diffraction (XRD). Furthermore, these systems exhibit mutual solubility of NdCl₃ in BaCl₂ and SrCl₂. The investigation of these solid solutions has been performed using quenching experiments and subsequent post-characterisation by XRD. Phase diagram equilibria have also been investigated using differential scanning calorimetry (DSC). Using the aforementioned information on phase transitions, intermediate compound formation, and solid solubility, thermodynamic assessment of the systems has been performed using the CALPHAD method. The model for the Gibbs energy of the liquid solution is the quasi-chemical formalism in the quadruplet approximation, while the model for the Gibbs energy of the solid solutions is the two-sublattice polynomial model.

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1. Introduction

The molten salt reactor (MSR) is a nuclear reactor design that was selected by the Generation IV International Forum¹ as a promising concept for the next generation of reactors. For the safety assessment of such a reactor, a comprehensive understanding and modelling of the physical and chemical properties of the nuclear fuel is necessary. Many studies have already been conducted on the topic of fluoride-based reactors because of their appealing characteristics in terms of low vapour pressure and high thermochemical stability,^2,3 but more recently chloride-based fuels have garnered attention as well.⁴ Compared to fluoride salts, chloride salts generally have a lower melting point, allowing for lower operating temperatures, and they show a higher solubility for actinides. During reactor operation, heat is generated by the fission reaction of a fissile isotope (²³⁵U, ²³³U, or ²³⁹Pu), which produces fission products. The dissolution of these fission products in the molten chloride fuel makes it a multi-component system, thereby affecting its thermochemical and thermophysical properties. In order to predict the properties of such a multi-element system, extrapolation from the constituting binary or ternary sub-systems can be used, but for this, the thermochemistry of the constituting binaries must first be comprehensively understood.

For fluoride salts, a large knowledge base of thermodynamic and thermophysical properties has been developed already in the framework of MSR development.⁵ For molten chlorides, however, the effect of fission products on properties such as melting behaviour, heat capacity, density or viscosity is less known and needs to be investigated. In particular, the effect on the thermodynamic properties of the melt of high-yield salt-soluble fission products such as barium, strontium and neodymium must be investigated. Neodymium is of additional interest, because it can also be used as a simulant for the hazardous plutonium due to its similar thermochemical behaviour in a salt mixture, as confirmed in this article. This work more specifically contributes to a better understanding of the effect of fission products in molten chlorides by modelling the thermochemical properties of the binary systems AECl₂–NdCl₃ (AE = Sr, Ba) using the CALPHAD (calculation of phase diagrams) method, based on literature and newly obtained obtained experimental data.

Experimental investigations using X-ray diffraction, quenching experiments, and differential scanning calorimetry (DSC) were first performed to solve discrepancies noticed in the literature. Using those data as input, a CALPHAD model was then developed based on the quasi-chemical formalism in the quadruplet approximation for the liquid solutions, and a two-sublattice polynomial model for the solid solutions. In this process, mixing enthalpies of the liquid solution were also estimated, as these data have not been measured experimentally to this date, but constitute a key piece of information to develop physically accurate liquid models. To conclude this work, application calculations were performed to investigate the effect of the fission products Ba and Sr on the NaCl–NdCl₃ system, which serves as an analog to the fuel system NaCl–PuCl₃.

2. Experimental techniques

2.1. Sample preparation synthesis

For the experiments carried out in this work, BaCl₂ (Alfa Aesar, ultra-dry, 99.999% trace metals basis), SrCl₂ (Alfa Aesar, ultra-dry, 99.995% trace metals basis) and NdCl₃ (Alfa Aesar, ultra-dry, 99.9% trace metals basis) were used as delivered by the supplier. Due to the sensitivity of the salts towards oxygen and water, all sample preparation was carried out inside a glove box under dry argon atmosphere (H₂O, O₂ < 5 ppm).

Weighing was carried out using a Mettler-Toledo XPE105DR balance with a 0.01 mg uncertainty. Synthesis of intermediate compounds was conducted by mixing end-members compounds in the appropriate stoichiometric ratios in an agate mortar, followed by thermal treatment in a tubular furnace under argon flow for eight to twelve hours at a temperature of 850 K (Sr₉Nd₅Cl₃₃) or 950 K (Ba₃Nd₂Cl₁₂). The samples were heated inside a tightly closed stainless steel container, with an inner nickel liner to prevent the corrosive chlorides from interacting with the stainless steel.

Phase purity was analysed using X-ray diffraction (XRD) and melting point determination by differential scanning calorimetry (DSC). Using XRD, no additional phases were detected for any of the pure end-members. Using DSC, the melting points of the end-members were determined to be (1237 ± 5) K (BaCl₂), (1147 ± 5) K (SrCl₂) and (1031 ± 5) K (NdCl₃). These values are in good agreement with the values in the literature, which are reported as (1235 ± 1) K,⁶ (1147 ± 1) K,⁶ and (1032 ± 2) K,⁷ respectively.

The intermediate products were also analysed using XRD and in case there were still unreacted end-member reactants visible, the product was subjected to further heat treatment until the intermediate phase was obtained with high purity (>99%).

2.2. X-ray diffraction (XRD)

XRD measurements were carried out using a panalytical X’pert pro diffractometer with a Cu-anode (0.4 mm × 12 mm line focus, 45 kV, 40 mA). Scattered X-ray intensities were measured with a real-time multi-step detector (X’Celerator). The angle 2θ was set to cover a range from 10° to 120°. Measurements were typically performed for 7–8 hours, with a step size of 0.0036° s⁻¹. Refinement of the measured XRD data was performed by applying the method Le Bail,⁸ using the FullProf software, Version 5.10.⁹

2.3. Differential scanning calorimetry (DSC)

The invariant temperatures in the investigated systems were measured using a Setaram multi-detector high-temperature calorimeter (MHTC-96 type) equipped with a 3D heat flux DSC module, capable of measuring up to 1673 K. Sample preparation was done by mixing end-members BaCl₂ or SrCl₂ with NdCl₃ in the desired stoichiometric ratio. The samples were contained in a nickel liner, which in turn was contained in a tightly closed stainless steel crucible.¹⁰ Equilibration of the sample was done in the calorimeter itself during the first heating cycle by heating the mixtures to a temperature above the melting points of both end members. Invariant equilibria were collected on the subsequent cycles.

The temperature was monitored throughout the experiments by a series of interconnected S-type thermocouples. The temperature on the heating ramp (10 K min⁻¹) was calibrated and corrected for the effect of the heating rate by measuring the melting points of standard high purity metals (In, Sn, Pb, Al, Ag, Au) at 2–4–6–8–10–12 K min⁻¹. The calibration procedure was performed as recommended by Höne et al.¹¹ and Gatta et al.¹² The transition temperatures in the AECl₂–NdCl₃ phase diagrams (AE = Sr, Ba) were derived on the heating ramp as the onset temperature using tangential analysis of the recorded heat flow. The liquidus temperature of mixtures was derived from the peak extremum of the last thermal event. The uncertainty on the measured temperatures is estimated to be ±5 K for pure compounds and ±10 K for mixtures.

2.4. Investigation of solid solutions

The existence and stability range of solid solutions in the investigated systems were investigated in this work using quenching experiments. The quenching samples consisted of stoichoimetric mixtures of the end-members, thoroughly mixed using a pestle and mortar before insertion inside a nickel liner in a tightly closed stainless steel crucible. During the experiments, the samples were heated to a temperature of 973 K and equilibrated at this temperature for at least two hours, after which they were dropped into a water bath to freeze the phases stable at high temperature.

The furnace used for quenching is an MTI split vertical quenching tube furnace (OTF-1500X-80-VTQ), which contains an electromagnet that holds the sample in the heated part of the furnace. When the sample is at the desired temperature and has reached equilibrium, the electromagnet is shut off and the sample drops into a water bath. Due to the double containment of the sample of nickel inside stainless steel, the sample stays water-free during this experiment.

3. Thermodynamic modelling

The thermodynamic modelling assessment of the molten salt systems was performed with the CALPHAD method¹³ using the FactSage software, Version 8.2.¹⁴ Both literature and experimental data obtained in this work were used to adjust the excess parameters of the Gibbs energy functions of the phases present in the systems.

3.1. Stoichiometric compounds

The Gibbs energy function (G(T), kJ mol⁻¹) for stoichiometric compounds is dependent on the standard enthalpy of formation , the standard entropy at the reference temperature of 298.15 K and the heat capacity as shown in eqn (1).

The isobaric heat capacity C_p,m is expressed as a polynomial that takes the form of eqn (2).

C_p,m(T) = a + bT + cT² + dT⁻² (2)

The compounds in the investigated systems are two end-members and two intermediates. The thermodynamic data for these are listed in Table 1. The thermodynamic functions for NdCl₃ were taken from the critical review by Konings and Kovács.⁷ The thermodynamic functions for BaCl₂ were taken from the IVTAN thermochemical database,¹⁵ to be consistent with our earlier work.¹⁶ The thermodynamic functions for SrCl₂ were taken from the JANAF thermochemical tables.⁶ A polymorphic transition is reported in the aforementioned tables for SrCl₂ with a transition enthalpy of 6 kJ mol⁻¹ that was not included in the current thermodynamic modelling assessment. This transition is a second-order transition, from a cubic structure to a slightly distorted cubic structure, that does not appear in phase equilibria measurements, as further elaborated on in 6. The thermodynamic functions of NaCl, used in the assessment of the ternary systems, were taken from van Oudenaren et al.,¹⁷ who reviewed the available thermodynamic data in their work. The heat capacity of the intermediate compounds in this work was obtained through the Neumann–Kopp rule.

Table 1 Thermodynamic functions used in the CALPHAD model in this work. Optimized values are marked in bold

Compound			C p,m (T) (J K^−1 mol^−1) = a + bT + cT^−2 + dT^2				Temperature range (K)	Source
			a	b	c	d
α-BaCl2(s)	−855 200	123.7	69.371	0.01912548	5882.698	2.499235 × 10^−9	[298–1198]	15
β-BaCl2(s)	−837 800	138.22	131				[1198–1234]
BaCl2(l)	−821 950	151.07	109				[1234–2500]
SrCl2(s)	−828 850.4	114.809	79.48261	−0.001792036	−440 859.7	1.798911 × 10^−5	[298–600]	6
			194.5439	−0.246728	−8 159 846	0.0001661617	[600–1000]
			123.0096				[1000–1147]	This work
SrCl2(l)	−812 629	128.95145858762	104.6				[1147–2000]	6
NdCl3(s)	−1 040 900	153.5	109.084	0.016406	−1 309 950		[298–1032]	7
NdCl3(l)	150						[1032–3000]
NaCl(s)	−411 260	72.15	47.72158	0.0057	−882.996	1.21466 × 10^−5	[298–1074]	17
NaCl(l)	−390 853	83.30249	68				[1074–2500]	18
Sr9Nd5Cl33(s)	−12 782 000	1800	737.36	0.91178	−14 478 000		[298–1500]	This work
Ba3Nd2Cl12(s)	−4 641 500	682	486.281	0.09018844	−2602251.9	7.2 × 10^−9	[298–1500]
Na3Nd5Cl18(s)	−6 478 000	983.845	714.332	0.042932	−7 577 460	6.56 × 10^−5	[298–1500]

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3.2. Liquid solution

The excess Gibbs energy terms of the liquid solution are modelled using the quasi-chemical formalism in the quadruplet approximation as proposed by Pelton et al.¹⁹ which has proven to be well-adapted to molten chloride and fluoride systems. This description assumes the existence of quadruplets in the liquid, allowing for the modelling of short-range ordering. This formalism allows for the selection of the composition of maximum short-range ordering through its cation–cation coordination numbers, corresponding to the minimum of the Gibbs energy that is often found near the composition of the lowest eutectic. By fixing these numbers, the anion–anion coordination number is also obtained through eqn (3), where q_i are the charges of the respective ions. The cation–cation coordination numbers used in this work are presented in Table 2.

Table 2 Coordination numbers used in the CALPHAD model presented in this work

A	B	Z ^AAB/ClCl	Z ^BAB/ClCl	Z ^ClAB/ClCl
Ba	Ba	6	6	3
Sr	Sr	6	6	3
Nd	Nd	6	6	2
Ba	Nd	6	3	1.5
Ba	Sr	6	6	3
Sr	Nd	6	6	1.9

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The excess parameters that are optimized are those related to the second-nearest neighbour exchange reaction as given in eqn (4), where the associated change in Gibbs energy (Δg_BaNd/ClCl, J mol⁻¹) is expressed as eqn (5).

(Ba–Cl–Ba) + (Nd–Cl–Nd) → 2(Ba–Cl–Nd)Δg_BaNd/ClCl (4)

In eqn (5) the terms Δg⁰_BaNd/ClCl, gⁱ⁰_BaNd/ClCl and g^0j_BaNd/ClCl are composition-independent coefficients that may depend on temperature. The composition dependence of the Gibbs energy is apparent through χ_BaNd/ClCl as these are defined as per eqn (6). In this equation X_AA is the cation–cation pair fraction, or the molar fraction of the quadruplet containing two cations A. For this binary system, {X_AA + X_AB + X_BB} is equal to one.

The Gibbs energy functions used in this work to describe the liquid solutions are given in eqn (7) and (8) for the SrCl₂–NdCl₃ and BaCl₂–NdCl₃ systems, respectively.

Δg_SrNd/ClCl = −1800 − 2.5T + (1.5T)χ_SrNd/ClCl + (−3300 + 4T)χ_NdSr/ClCl (7)

Δg_BaNd/ClCl = −6500 − 0.7T + (−7000 + 8T)χ_NdBa/ClCl (8)

3.3. Solid solution modelling

The thermodynamic description of solid-solutions is done using the two-sublattice polynomial model to be consistent with the description of the JRC Molten Salt Database (JRCMSD).²⁰ The Gibbs Energy function G(T) (J mol⁻¹) of the solid-solution is given in eqn (9).

G(T) = X_A·G⁰_A + X_B·G⁰_B + X_ART ln X_A + X_BRT ln X_B + ΔG^excess_m (9)

In the above equation, G⁰_i are the end-member molar Gibbs energies, and X_i are the site molar fractions of the end-members SrCl₂ or BaCl₂ (A) and NdCl₃ (B), respectively. The third and fourth terms in eqn (9) represent the configurational entropy. The excess Gibbs energy, present in eqn (9) as ΔG^excess_m (in J mol⁻¹), is defined as per eqn (10).

The term L^ij_AB in eqn (10) is an interaction coefficient that can be a function of temperature if necessary. The equivalent site fractions y_A and y_B are charge equivalent site fractions. In this work, these fractions are y_Ba (resp. y_Sr) and y_Nd, as defined by eqn (11) and (12):

The Gibbs energy function used in this work to describe the solid solutions in the BaCl₂–NdCl₃ system is given in eqn (13), where NdCl₃ is soluble in the high-temperature cubic phase β-BaCl₂. For the modelling of the SrCl₂–NdCl₃ system, separate solid solution descriptions were used to model the solubility of NdCl₃ in the cubic SrCl₂ (eqn (15)) and the solubility of SrCl₂ in the hexagonal NdCl₃ (eqn (14)).

ΔG^excess_{m,cubic(Ba,Nd)} = y_Ba²y_Nd(−12 110 + 5T) + y_Bay_Nd²(7000) (13)

ΔG^excess_{m,cubic(Sr,Nd)} = y_Sry_Nd(9000) +y_Sr²y_Nd(20 000) (14)

ΔG^excess_{m,hexagonal(Nd,Sr)} = y_Sry_Nd(−4000) + y_Sry_Nd²(20 000) (15)

4. Results and discussion

The phase diagrams of the salt systems AECl₂–NdCl₃ (AE = Sr, Ba) have been investigated experimentally in this work through the use of XRD, quenching experiments and DSC. The mixing enthalpy of the systems has been estimated using the estimation method of Davis and Rice,²¹ as explained in a previous work.¹⁶ We refer the reader to the latter paper for a detailed explanation of the estimation method applied to derive the mixing enthalpies. Additionally, an assessment of Nd as a simulant for Pu is presented in Section 4.1, through the comparison with other commonly used simulant elements in Ce and U.

In the SrCl₂–NdCl₃ system, the intermediates Sr₄NdCl₁₁ (space group P2₁/m) and Sr₉Nd₅Cl₃₃ (space group R3̄), as well as a solid solution Sr_1−xNd_xCl_2+x, have been identified by Hodorowicz et al.²² Experimental measurement of invariant equilibria has been reported by Morozov et al.²³ and Vogel et al.²⁴ No intermediates have been reported in the literature on the BaCl₂–NdCl₃ system. However, Meyer et al.²⁵ have reported a compound with the chemical formula Ba₉Nd₆Cl₃₄O. This compound could correspond to the intermediate Ba₃Nd₂Cl₁₂ instead, as is the case in the analogous BaCl₂–CeCl₃ system.¹⁶ Measurements of invariant equilibria have been reported by Morozov et al.²³ and Vogel et al.²⁴

4.1. Simulant systems NaCl–MCl₃ (M = Ce, Nd, U)

To assess the potential of neodymium as a simulant for plutonium in the context of molten chlorides, a comparison between systems consisting of NaCl with NdCl₃, CeCl₃ and UCl₃ is presented in this section. Thermodynamic models for these systems have been used to calculate phase diagrams, which were then compared to the experimental phase diagram data on the NaCl–PuCl₃ system presented by Bjorklund et al.²⁶ as shown in Fig. 1.

Fig. 1 Calculated phase diagrams of the systems NaCl–NdCl₃ (solid black line), NaCl–CeCl₃ (dashed blue line) and NaCl–UCl₃ (dashed red line), compared to the experimental data on the NaCl–PuCl₃ system (open black circles) presented by Bjorklund et al.⁷

The thermodynamic model of the NaCl–NdCl₃ system was optimized based on data from the literature in this work, as detailed in 8. For the thermodynamic model of the NaCl–CeCl₃ system, we refer the reader to a previous work.¹⁶ The thermodynamic model of the system NaCl–UCl₃ was taken from Beneš and Konings,²⁷ with the addition of the intermediate NaU₂Cl₇ as suggested by Yingling et al.²⁸Fig. 1 shows that both the eutectic compositions and eutectic temperatures of the CeCl₃-system and UCl₃-system deviate significantly from the experimental data in the PuCl₃-system. Moreover, the temperature of the liquidus on the right side of the eutectic, is consistently higher than that of the NaCl–PuCl₃ system, mainly due to the difference in melting points between the compounds.

Fig. 1 also shows that the model of the NaCl–NdCl₃ system reproduces the experimental data for the NaCl–PuCl₃ system very well. The main difference between these two systems, is that the intermediate Na₃Nd₅Cl₁₈ (x(NdCl₃) = 0.625) does not have a known Pu-analog. This does not significantly influence the temperature of the liquidus, however, and therefore makes Nd an excellent simulant to describe the melting behaviour of Pu-systems. The SrCl₂–NdCl₃ and BaCl₂–NdCl₃ systems are subsequently investigated in this work, which can give insights into the melting behaviours of the SrCl₂–PuCl₃ and BaCl₂–PuCl₃ systems, respectively.

4.2. Intermediates Sr₉Nd₅Cl₃₃ and Ba₃Nd₂Cl₁₂

Both systems SrCl₂–NdCl₃ and BaCl₂–NdCl₃ contain one intermediate compound with composition Sr₉Nd₅Cl₃₃ and Ba₃Nd₂Cl₁₂, respectively. The intermediate phase Sr₄NdCl₁₁ as suggested by Hodorowicz et al.²² was not observed in any of our synthesis attempts. The intermediate Sr₉Nd₅Cl₃₃ (hexagonal in space group R3̄) was succesfully synthesised, and the profile refinement is shown in Fig. 2. The obtained refined cell parameters are compared to those presented by Hodorowicz et al. in Table 3, and these are in good agreement with each other (Fig. 3).

Fig. 2 Profile refinement of the intermediate salt Sr₉Nd₅Cl₃₃ using the structural model by Hodorowicz et al.²² The observed intensity (Y_obs, red) is plotted along with the calculated intensity from the refinement (Y_calc, black), and the difference between the two is shown (Y_obs − Y_calc, blue). The angles at which reflections occurr are shown as well (Bragg positions, vertical lines). Measurement at λ = Cu-Kα.

Table 3 Comparison between cell parameters obtained for intermediate Sr₉Nd₅Cl₃₃ (space group R3̄) in this work and in the literature

Source	a, b (Å)	c (Å)	V (Å^3)
This work	12.899(1)	24.858(2)	4136(2)
Hodorowicz et al.^22	12.908(6)	24.82(1)	4135(5)

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Fig. 3 Profile refinement of the intermediate salt Ba₃Nd₂Cl₁₂, using the structure of Ba₉Nd₆Cl₃₄O as reported by Meyer et al. as crystal structure. The observed intensity (Y_obs, red) is plotted along with the calculated intensity from the refinement (Y_calc, black), and the difference between the two is shown (Y_obs − Y_calc, blue). The angles at which reflections occurr are shown as well (Bragg positions, vertical lines). Measurement at λ = Cu-Kα.

The intermediate Ba₃Nd₂Cl₁₂ has not been reported in the literature before, but Meyer et al.²⁵ do suggest the existence of a compound with the same stoichiometric ratio of barium to neodymium, i.e. Ba₉Nd₆Cl₃₄O. In our previous work on the analogous BaCl₂–CeCl₃ system,¹⁶ we encountered a similar situation where the crystallographic information published by Meyer et al. for Ba₉Ce₆Cl₃₄O agreed very well with our synthesised compound Ba₃Ce₂Cl₁₂. We therefore conclude that the same occurs here, and the intermediate Meyer et al. identified as Ba₉Nd₆Cl₃₄O is actually the intermediate Ba₃Nd₂Cl₁₂ (tetragonal in space group I4/m) as presented in this work. The refined lattice parameters obtained in this work are shown in Table 4, and are compared to the one presented by Meyer et al.,²⁵ as well as the values reported for Ba₃Ce₂Cl₁₂ in the literature. The lattice parameters of Ba₃Nd₂Cl₁₂ are smaller than those of Ba₃Ce₂Cl₁₂, as expected since the crystal radius of Nd³⁺ is smaller than that of Ce³⁺.²⁹ There is a slight discrepancy between the values reported by Meyer et al. and those obtained in this work, particularly regarding the lattice parameter c. However, as shown in Table 4, this is also the case for the intermediate Ba₃Ce₂Cl₁₂, leading us to believe that the intermediate observed in this work is indeed an analog to Ba₃Ce₂Cl₁₂. Meyer et al. suggested the presence of an oxygen ion in this structure to satisfy charge conditions, but we believe that two chlorine ions are more likely. The reader is referred to the previously mentioned work by Alders et al.¹⁶ for further details on the crystallography of this compound.

Table 4 Comparison between cell parameters obtained for intermediates Ba₃RE2Cl12 (RE = Ce, Nd) (space group I4/m) in this work and the literature

Source	Compound	a, b (Å)	c (Å)	V (Å^3)
This work	Ba3Nd2Cl12	11.304(7)	21.635(3)	2765(2)
Meyer et al.^25	Ba9Nd6Cl34O	11.329(5)	21.676(7)	2782(4)
Alders et al.^16	Ba3Ce2Cl12	11.363(1)	21.547(6)	2782(2)
Meyer et al.^25	Ba9Ce6Cl34O	11.348(3)	21.729(5)	2798(2)

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4.3. Solid-solutions – Sr_1−xNd_xCl_2+x

In their investigation of the SrCl₂–NdCl₃ system, Hodorowicz et al.²² found that NdCl₃ is soluble in the cubic crystal structure of SrCl₂ (space group Fm3̄m) with a maximum of approximately 18% NdCl₃. The existence of this solid solution is confirmed in this work with quenching and post-XRD measurements. Stoichiometric mixtures of SrCl₂ and NdCl₃ of compositions x(NdCl₃) = 0, 0.05, 0.1 and 0.15 were quenched from 923 K. All mixtures showed a single phase solid solution. The profile refinements of the collected XRD data are reported in the supplementary information to this work, and the evolution of the lattice parameters in Fig. 5.

In Fig. 4, a refinement of the post-XRD at x(NdCl₃) = 0.1, quenched from 850 K, is shown, indicating a single-phase solid solution at this composition. In contrast to the findings of Hodorowicz et al., the cell volumes calculated with the refined lattice parameters from the profile refinements do not obey a decreasing linear trend, but instead seem to fluctuate around an average value, as seen in Fig. 5. Based on the DSC data obtained in this work, shown in Section 4.7.1, we are inclined to conclude that the solid solution is stable up to approximately 20% NdCl₃, as the peritectic transition observed at approximately 890 K disappears at lower concentrations. This is in line with the 18% solubility limit as reported by Hodorowicz et al.²²

Fig. 4 Profile refinement of a quenched sample with x(NdCl₃) = 0.1, showing solid solution Sr_1−xNd_xCl_2+x, quenched from 850 K. The observed intensity (Y_obs, red) is plotted along with the calculated intensity from the refinement (Y_calc, black), and the difference between the two is shown (Y_obs − Y_calc, blue). The angles at which reflections occur are shown as well (Bragg positions, vertical lines). Measured at λ = Cu-Kα.

Fig. 5 Cell volumes of the cubic Sr_1−xNd_xCl_2+x (space group Fm3̄m) phase, calculated from the profile refinements of the solid solutions quenched in the SrCl₂–NdCl₃ system for T = 923 K.

Fig. 6 Cell volumes of the cubic Ba_1−xNd_xCl_2+x phase, calculated from the profile refinements of the quenching experiments performed in the BaCl₂–NdCl₃ system at T = 973 K.

4.4. Solid-solutions – Ba_1−xNd_xCl_2+x

Solid solutions of CeCl₃ in the high-temperature cubic phase of BaCl₂ (space group Fm3̄m) have been observed previously by Alders et al.¹⁶ in the BaCl₂–CeCl₃ system. Due to the similarities between CeCl₃ and NdCl₃ (r_Ce(3+),VI = 1.01 Å, r_Nd(3+),VI = 0.98 Ų⁹), we expect a similar solid solution to also form in this system. Additionally, the invariant points measured by DSC between x(NdCl₃) = 0.05 and 0.25 (see Section 4.7.2) correspond to the formation event of a high-temperature solid solution.

Quenching experiments were performed at a temperature of 973 K, for compositions 0.1 ≤ x(NdCl₃) ≤ 0.3. These experiments confirmed the existence of a solid solution, as the cell parameters of (Ba,Nd)Cl_2+x decrease upon the addition of NdCl₃. It is, however, not possible to quantify the extent of the solid solution at this temperature based on the present quenching experiments, due to the fact that the predicted stability range at 973 K is very narrow. Moreover, the experiments performed at x(NdCl₃) = 0.1 and 0.25 show additional phases, namely α-BaCl₂ and Ba₃Nd₂Cl₁₂ respectively, which is in agreement with the expected phases based on the phase diagram in Fig. 11. The profile refinement of the experiment performed at x(NdCl₃) = 0.10 is shown in Fig. 7 and shows the phases that were expected based on the phase diagram. The other profile refinements obtained from the post-XRD analyses are reported in the supplementary information to this work.

Fig. 7 Profile refinement of a quenched sample with x(NdCl₃) = 0.10, showing both the solid solution Ba_1−xNd_xCl_2+x and α-BaCl₂, quenched from 973 K. The observed intensity (Y_obs, red) is plotted along with the calculated intensity from the refinement (Y_calc, black), and the difference between the two is shown (Y_obs − Y_calc, blue). The angles at which reflections occur are shown as well (Bragg positions, vertical lines). Measured at λ = Cu-Kα.

4.5. Solid-solutions – Nd_yAE_1−yCl_3−y (AE = Sr, Ba)

Quenching experiments and post-XRD were also carried out to investigate the solid solution on the NdCl₃-rich side of the SrCl₂–NdCl₃ system. The calculated cell volume is slightly larger than that of NdCl₃, as expected from the respective crystal radii (r_Nd(3+),VI = 1.123 Å, r_Sr(2+),VI = 1.32 Ų⁹), but the difference is within the margin of experimental error.

No quenching experiments were carried out to investigate the existence of a solid solution on the NdCl₃-rich side of the BaCl₂–NdCl₃ phase diagram. However, a small decrease of the eutectic temperature at x(NdCl₃) = 0.948 and 0.969 is observed, consistent with the formation of a solid solution in this composition range. This is also consistent with the observations of Alders et al.¹⁶ in their work on the BaCl₂–CeCl₃ system. The existence of solid solutions at the NdCl₃-rich side of the AECl₂–NdCl₃ (AE = Sr, Ba) systems is also supported by the Tamman-diagrams in Fig. 10 and 13, respectively (see Sections 4.7.1 and 4.7.2).

4.6. Phase equilibria measurements

A list of mixtures measured in this work by DSC, along with the temperatures of invariant transitions and associated invariant reactions, is presented in Tables 5 and 6 for the SrCl₂–NdCl₃ and BaCl₂–NdCl₃ systems, respectively. The phase equilibria are also shown on the optimized phase diagrams in Fig. 8 and 11, respectively.

Table 5 Equilibrium data in the SrCl₂–NdCl₃ system as measured by DSC

x NdCl3	T (K)	Equilibrium	Equilibrium reaction
a The uncertainties on compositions xNdCl3 are ±0.005. b The uncertainties on temperatures are ±5 K for pure end-members and ±10 K for mixtures.
0	1147	Congruent melting	SrCl2 = L
0.100	1123	Liquidus	Sr1−xNdxCl2+x + L′ = L
0.150	1104	Liquidus	Sr1−xNdxCl2+x + L′ = L
0.203	1075	Liquidus	Sr1−xNdxCl2+x + L′ = L
0.229	1064	Liquidus	Sr1−xNdxCl2+x + L′ = L
	897	Peritectic	Sr9Nd5Cl33 = Sr1−xNdxCl2+x + L′
0.251	1045	Liquidus	Sr1−xNdxCl2+x + L′ = L
	883	Peritectic	Sr9Nd5Cl33 = Sr1−xNdxCl2+x + L′
0.269	1037	Liquidus	Sr1−xNdxCl2+x + L′ = L
	894	Peritectic	Sr9Nd5Cl33 = Sr1−xNdxCl2+x + L′
0.359	981	Liquidus	Sr1−xNdxCl2+x + L′ = L
	894	Peritectic	Sr9Nd5Cl33 = Sr1−xNdxCl2+x + L′
	872	Eutectic	Sr9Nd5Cl33 + Nd1−ySryCl3−y = L
0.449	910	Liquidus	Sr1−xNdxCl2+x + L′ = L
	883	Peritectic	Sr9Nd5Cl33 = Sr1−xNdxCl2+x + L′
	874	Eutectic	Sr9Nd5Cl33 + Nd1−ySryCl3−y = L
0.530	885	Eutectic	Sr9Nd5Cl33 + Nd1−ySryCl3−y = L
0.570	873	Eutectic	Sr9Nd5Cl33 + Nd1−ySryCl3−y = L
0.599	919	Liquidus	Nd1−ySryCl3−y + L′ = L
	874	Eutectic	Sr9Nd5Cl33 + Nd1−ySryCl3−y = L
0.699	955	Liquidus	Nd1−ySryCl3−y + L′ = L
	875	Eutectic	Sr9Nd5Cl33 + Nd1−ySryCl3−y = L
0.899	1009	Liquidus	Nd1−ySryCl3−y + L′ = L
	874	Eutectic	Sr9Nd5Cl33 + Nd1−ySryCl3−y = L
0.948	1019	Liquidus	Nd1−ySryCl3−y + L′ = L
	868	Eutectic	Sr9Nd5Cl33 + Nd1−ySryCl3−y = L
1	1031	Congruent melting	NdCl3 = L

---

Table 6 Equilibrium data in the BaCl₂–NdCl₃ system as measured by DSC

x NdCl3	T (K)	Equilibrium	Equilibrium reaction
a The uncertainties on compositions xNdCl3 are ±0.005. b The uncertainties on temperatures are ±5 K for pure end-members and ±10 K for mixtures.
0	1235	Congruent melting	β-BaCl2 = L
	1198	α–β transition	α-BaCl2 = β-BaCl2
0.06	1234	Liquidus	Ba1−xNdxCl2+x + L′ = L
	1134	Solidus	α-BaCl2 + Ba1−xNdxCl2+x = Ba1−xNdxCl2+x
	941	Eutectoid	α-BaCl2 + Ba3Nd2Cl12 = Ba1−xNdxCl2+x
0.148	1202	Liquidus	Ba1−xNdxCl2+x + L′ = L
	939	Eutectoid	α-BaCl2 + Ba3Nd2Cl12 = Ba1−xNdxCl2+x
0.207	1172	Liquidus	Ba1−xNdxCl2+x + L′ = L
	1020	Peritectic	Ba3Nd2Cl12 = Ba1−xNdxCl2+x + L′
	939	Eutectoid	α-BaCl2 + Ba3Nd2Cl12 = Ba1−xNdxCl2+x
0.249	1153	Liquidus	Ba1−xNdxCl2+x + L′ = L
	1023	Peritectic	Ba3Nd2Cl12 = Ba1−xNdxCl2+x + L′
	939	Eutectoid	α-BaCl2 + Ba3Nd2Cl12 = Ba1−xNdxCl2+x
0.265	1132	Liquidus	Ba1−xNdxCl2+x + L′ = L
	1024	Peritectic	Ba3Nd2Cl12 = Ba1−xNdxCl2+x + L′
	938	Eutectoid	α-BaCl2 + Ba3Nd2Cl12 = Ba1−xNdxCl2+x
0.305	1113	Liquidus	Ba1−xNdxCl2+x + L′ = L
	1031	Peritectic	Ba3Nd2Cl12 = Ba1−xNdxCl2+x + L′
0.370	1045	Liquidus	Ba1−xNdxCl2+x + L′ = L
	1018	Peritectic	Ba3Nd2Cl12 = Ba1−xNdxCl2+x + L′
0.380	1043	Liquidus	Ba1−xNdxCl2+x + L′ = L
	1017	Peritectic	Ba3Nd2Cl12 = Ba1−xNdxCl2+x + L′
0.391	1039	Liquidus	Ba1−xNdxCl2+x + L′ = L
	1019	Peritectic	Ba3Nd2Cl12 = Ba1−xNdxCl2+x + L′
	893	Eutectic	Ba3Nd2Cl12 + Nd1−yBayCl3−y = L
0.405	1035	Liquidus	Ba1−xNdxCl2+x + L′ = L
	1015	Peritectic	Ba3Nd2Cl12 = Ba1−xNdxCl2+x + L′
	894	Eutectic	Ba3Nd2Cl12 + Nd1−yBayCl3−y = L
0.41	1018	Peritectic	Ba3Nd2Cl12 = Ba1−xNdxCl2+x + L′
	908	Eutectic	Ba3Nd2Cl12 + Nd1−yBayCl3−y = L
0.431	896	Eutectic	Ba3Nd2Cl12 + Nd1−yBayCl3−y = L
0.498	1010	Liquidus	Ba3Nd2Cl12 + L′ = L
	910	Eutectic	Ba3Nd2Cl12 + Nd1−yBayCl3−y = L
0.55	989	Liquidus	Ba3Nd2Cl12 + L′ = L
	912	Eutectic	Ba3Nd2Cl12 + Nd1−yBayCl3−y = L
0.600	924	Liquidus	Nd1−yBayCl3−y + L′ = L
	899	Eutectic	Ba3Nd2Cl12 + Nd1−yBayCl3−y = L
0.674	912	Eutectic	Ba3Nd2Cl12 + Nd1−yBayCl3−y = L
0.753	962	Liquidus	Nd1−yBayCl3−y + L′ = L
	902	Eutectic	Ba3Nd2Cl12 + Nd1−yBayCl3−y = L
0.850	1000	Liquidus	Nd1−yBayCl3−y + L′ = L
	915	Eutectic	Ba3Nd2Cl12 + Nd1−yBayCl3−y = L
	899	Unknown	—
0.948	1026	Liquidus	Nd1−yBayCl3−y + L′ = L
	904	Eutectic	Nd1−yBayCl3−y = L
	897	Solidus	Ba3Nd2Cl12 + Nd1−yBayCl3−y = Nd1−yBayCl3−y
0.969	1030	Liquidus	Nd1−yBayCl3−y + L′ = L
	970	Solidus	Nd1−yBayCl3−y = Nd1−yBayCl3−y + L′
	894	Solidus	Ba3Nd2Cl12 + Nd1−yBayCl3−y = Nd1−yBayCl3−y

---

4.7. Thermodynamic models

4.7.1. SrCl₂–NdCl₃. With the thermodynamic descriptions of the parameters in the system as described in eqn (1), (7) and (15), the phase diagram and mixing enthalpy of the system were calculated. The optimized phase diagram is shown in Fig. 8, and the enthalpy of mixing is reported in Fig. 9. The invariant equilibria calculated with this CALPHAD model are presented, and compared with the available experimental data in Table 7.

Fig. 8 Phase diagram of the SrCl₂–NdCl₃ binary system, as calculated with the optimized thermodynamic model. Data from Morozov et al.²³ (empty blue triangles), Vogel et al.²⁴ (empty red squares) and this work (filled black circles). The compositions and temperatures at which quenching experiments have been performed are marked with black crosses.

Fig. 9 Mixing enthalpy of the SrCl₂–NdCl₃ binary system at T = 1273 K, as calculated with the thermodynamic model. The mixing enthalpy data were obtained with the mixing enthalpy estimation method presented by Davis and Rice,²¹ highlighted in a previous work.¹⁶

Table 7 Calculated invariant equilibria in the SrCl₂–NdCl₃ system, as well as experimentally measured values of these invariants from Morozov et al.,²³ Vogel et al.²⁴ and this work (DSC). The numbers in parentheses are the respective compositions of the eutectic

x NdCl3	T (K)				Equilibrium	Invariant reaction
	CALPHAD	Morozov et al.^23	Vogel et al.^24	This work (DSC)
0	1146	1142	1151	1147 ± 5	Congruent melting	SrCl2 = L
0.357	890	893	873	894 ± 10	Peritectic	Sr9Nd5Cl33 = Sr1−xNdxCl2+x + L′
0.535	878 (0.530)	872 (0.560)	853 (0.420)	885 ± 10 (0.535)	Eutectic	Sr9Nd5Cl33 + Nd1−ySryCl3−y = L
1	1030	1016	—	1031 ± 5	Congruent melting	NdCl3 = L

---

The CALPHAD model presented in Fig. 8 was optimized to fit the experimental data obtained in this work by DSC. There is, however, a significant discrepancy between the calculated liquidus between x(NdCl₃) = 0.2 and x(NdCl₃) = 0.6 when comparing to the data from Morozov et al.²³ and Vogel et al.²⁴ Given the fact that the data from these sources are not in agreement with each other, and that the actual liquidus we measure is in between the reported sets of data, we are confident in the accuracy of our experimental measurements and model in this composition range. The calculated mixing enthalpy has been optimized to fit the estimation obtained using Davis' method, as presented in Fig. 9. The temperature and composition of the eutectic is in good agreement with the values measured in this work by DSC, as well as the values of Morozov et al. The eutectic data from Vogel et al. deviate greatly from the other two sources, and give us reason to not retain their data. The eutectic composition calculated by the model is in good agreement with the predicted composition from the Tammann-diagram in Fig. 10, where the heat flow area of the eutectic transition is plotted against composition.

Fig. 10 Tammann-diagram showing the heat flow area of the eutectic transition versus composition, obtained in this work on the SrCl₂–NdCl₃ system. The intersection of the linear fits (dashed lines) is the predicted composition of the eutectic in this system, and the diagram matches with the composition of the intermediate.

The composition of the intermediate that we identified is also different from that reported by Morozov et al. and Vogel et al. report, but its existence is supported by the XRD data obtained in this work, as well as the work of Hodorowicz et al.²² It is also consistent with the limiting composition obtained at x = 0.357 in the Tammann diagram. The existence of mutual solid solubility of NdCl₃ and SrCl₂ was suggested previously by Vogel et al. and Hodorowicz et al., which our data corroborate. Moreover, there is solubility of SrCl₂ in NdCl₃ up to 5% SrCl₂ at 900 K. This is again in line with the Tammann diagram in Fig. 10 where the area of the eutectic peak goes to zero at approximately x(NdCl₃) = 0.95, indicating that there is a solid solution at higher compositions.

4.7.2. BaCl₂–NdCl₃. With the optimized parameters as described in Table 1 and eqn (8) and (13), the phase diagram and mixing enthalpy of the system were calculated. The phase diagram is shown in Fig. 11, and the enthalpy of mixing is reported in Fig. 12. The invariant equilibria calculated with this CALPHAD model are presented and compared with the available experimental data in Table 8.

Fig. 11 Phase diagram of the BaCl₂–NdCl₃ binary system, as calculated with the optimized thermodynamic model. Data from Morozov et al.²³ (empty blue triangles), Vogel et al.²⁴ (empty red squares) and this work (filled black circles). The compositions and temperatures at which quenching experiments have been performed are marked with black crosses.

Fig. 12 Mixing enthalpy of the BaCl₂–NdCl₃ binary system at T = 1273 K, as calculated with the thermodynamic model presented in this section. The mixing enthalpy data were obtained with the mixing enthalpy estimation method presented by Davis and Rice,²¹ highlighted in a previous work.¹⁶

Table 8 Calculated invariant equilibria in the BaCl₂–NdCl₃ system, as well as experimentally measured values of these invariants from Morozov et al.,²³ Vogel et al.²⁴ and this work (DSC). The numbers in parentheses are the respective compositions of the eutectic

x NdCl3	T (K)				Equilibrium	Invariant reaction
	CALPHAD	Morozov et al.^23	Vogel et al.^24	This work (DSC)
0	1198	1200	1199	1197 ± 5	α–β transition	α-BaCl2 = β-BaCl2
	1234	1243	1239	1235 ± 5	Congruent melting	β-BaCl2 = L
0.2	935			939 ± 10	Eutectoid	α-BaCl2 + Ba3Nd2Cl12 = Ba1−xNdxCl2+x
0.4	1017	1011	1020	1015 ± 10	Peritectic	Ba3Nd2Cl12 = Ba1−xNdxCl2+x + L′
0.676	906 (0.676)	902 (0.710)	901 (0.620)	912 ± 10 (0.674)	Eutectic	Ba3Nd2Cl12 + Nd1−yBayCl3−y = L
1	1030	1016	—	1031 ± 5	Congruent melting	NdCl3 = L

---

The CALPHAD model displayed in Fig. 11 was optimized to fit the measured invariant points, as well as the estimated mixing enthalpy as shown in Fig. 12. The DSC data between 0.05 ≤ x(NdCl₃) ≤ 0.3 at T = 935 K that were not observed by Morozov et al.²³ or Vogel et al.²⁴ are explained rather well by the addition of a solid solution phase Ba_1−xNd_xCl_2+x, stable only at elevated temperatures. The temperature of the peritectic, as well as the temperature and composition of the eutectic, are reproduced accurately by the model. While both Morozov et al. and Vogel et al. reported an intermediate of composition Ba3NdCl9 to be stable in this system, the absence of a eutectic event at compositions x(NdCl₃) ≤ 0.39 indicates that the intermediate Ba₃Nd₂Cl₁₂ is more likely, as is corroborated by the XRD analysis presented in this work, and the limiting composition of x = 0.4 in the Tammann diagram, as seen in Fig. 13.

Fig. 13 Tammann-diagram calculated from the DSC data obtained in this work on the BaCl₂–NdCl₃ system. The intersection of the linear fits (dashed lines) is the predicted composition of the eutectic in this system. the limiting compositions are x = 0.4 (intermediate Ba₃Nd₂Cl₁₂) and x = 0.96 (solid solution Nd_1−yBa_yCl_3−y).

There is good agreement between the literature and our experimental data on the temperatures of the eutectic and peritectic equilibria, as seen in Table 8, as well as with the Tammann-diagram presented in Fig. 13, which shows the recorded heat flow area of the eutectic transition versus temperature. Solid solubility of NdCl₃ in BaCl₂ was already suggested by Vogel et al., and the data in the Tammann diagram in Fig. 13 indicate that there is a narrow solid solution on the NdCl₃-rich side as well, with a limiting composition of 96% NdCl₃.

To further cement the potential of neodymium as a simulant for plutonium in the context of molten chlorides, a comparison is drawn between the systems AECl₂–NdCl₃ (AE = Sr, Ba) and the corresponding AECl₂–PuCl₃ system. In the case of the BaCl₂–PuCl₃ system, the model from our previous work on the BaCl₂–CeCl₃ system is included in the comparison.

As seen in Fig. 14, the liquidus line and eutectic of the SrCl₂–PuCl₃ system is approximated very well by the thermodynamic model of the SrCl₂–NdCl₃ system. The comparison of the BaCl₂–MCl₃ systems shown in Fig. 15 shows that the liquidus line of the PuCl₃-system is very similar to the one calculated with the model of the BaCl₂–NdCl₃ system, and that it deviates slightly from the CeCl₃-system, owing to the higher melting point of CeCl₃. Fig. 14 and 15 both show that, like in the systems NaCl–MCl₃ shown in Section 4.1, neodymium is a very accurate simulant for the melting behaviour of plutonium in molten chlorides.

Fig. 14 Calculated phase diagram of the SrCl₂–NdCl₃ system (solid black line) compared to the experimental data on the SrCl₂–PuCl₃ (open black circles) system presented by Johnson et al.³⁰

Fig. 15 Calculated phase diagram of the BaCl₂–NdCl₃ system (solid black line) compared to the model of BaCl₂–CeCl₃ from a previous work (dotted red line) and experimental data on the BaCl₂–PuCl₃ (open black circles) system presented by Johnson et al.³⁰

4.8. Ternary systems NaCl–SrCl₂–NdCl₃ and NaCl–BaCl₂–NdCl₃

Neodymium is a good candidate to act as a simulant for plutonium in chloride systems due to its similar melting behaviour and structural properties, the former being exemplified by the very similar liquidus equilibria in the NaCl–NdCl₃ and NaCl–PuCl₃ systems shown in Section 4.1. We believe that the investigations of the SrCl₂–NdCl₃ and BaCl₂–NdCl₃ systems as presented in this work can give valuable insights into the liquidus equilibria of the SrCl₂–PuCl₃ and BaCl₂–PuCl₃ systems too, which are more challenging to investigate experimentally. Moreover, they can be used to predict the melting behaviour of the molten salt fuel NaCl–PuCl₃ (some MSR designs rely on using the eutectic composition of this system) upon addition of the fission products Sr and Ba. To this end, thermodynamic calculations were performed in the ternary systems NaCl–SrCl₂–NdCl₃ and NaCl–BaCl₂–NdCl₃ as simulant systems to the equivalent PuCl₃-based systems. For this, the binary subsystems NaCl–SrCl₂, NaCl–BaCl₂ and NaCl–NdCl₃ were also modelled, which is presented in 7. The extrapolation to the ternary system is solely based on the constituting binary systems, and no ternary excess terms were added. The liquidus projections of these ternary systems are shown in Appendix C.

Fig. 16 shows the pseudo-binary phase diagram {0.95 (NaCl + NdCl₃) + 0.05SrCl₂}, and Fig. 17 shows the pseudo-binary phase diagram {0.95 (NaCl + NdCl₃) + 0.05BaCl₂} to investigate the addition of 5% SrCl₂ or BaCl₂ to a NaCl–PuCl₃ mixture respectively. In this calculation, the addition of 5% fission product (Ba or Sr) is based on the order of magnitude of the fission yield of Ba (9.5%) and Sr (5.48%).³¹ In an actual reactor operation scenario these percentages will be lower, as it is contingent upon the initial Pu-concentration. The observed the effect of the addition of these fission products is therefore an amplification.

Fig. 16 Phase diagram of the {0.95NaCl + 0.05SrCl₂} and {0.95NdCl₃ + 0.05SrCl₂} pseudo-binary section of the NaCl–SrCl₂–NdCl₃ ternary system. The labelled phases are NaCl + L′ (A), NaCl + Sr_1−xNd_xCl_3−x + L′ (B), NaCl + Sr_1−xNd_xCl_3−x (C), NaCl + Sr_1−xNd_xCl_3−x + Sr₉Nd₅Cl₃₃ (D), NaCl + Sr₉Nd₅Cl₃₃ + L′ (E), NaCl + Sr₉Nd₅Cl₃₃ + Na₃Nd₅Cl₁₈ (F), Na₃Nd₅Cl₁₈ + L′ (G), Sr₉Nd₅Cl₃₃ + Na₃Nd₅Cl₁₈ + L′ (H), Na₃Nd₅Cl₁₈ + Nd_1−ySr_yCl_2+y + L′ (I), Nd_1−ySr_yCl_2+y + L′ (J), Na₃Nd₅Cl₁₈ + Nd_1−ySr_yCl_2+y + Sr₉Nd₅Cl₃₃ (K), Nd_1−ySr_yCl_2+y + Sr₉Nd₅Cl₃₃ + L′ (L). The lines in red correspond to the phase diagram of the system NaCl–NdCl₃.

Fig. 17 Phase diagram of the {0.95NaCl + 0.05BaCl₂} and {0.95NdCl₃ + 0.05BaCl₂} pseudo-binary section of the NaCl–BaCl₂–NdCl₃ ternary system. The labelled phases are NaCl + L′ (A), NaCl + BaCl₂ + L′ (B), NaCl + BaCl₂ + Na₃Nd₅Cl₁₈ (C), BaCl₂ + L′ (D), BaCl₂ + Ba₃Nd₂Cl₁₂ + L′ (E), Ba₃Nd₂Cl₁₂ + L′ (F), Ba₃Nd₂Cl₁₂ + Na₃Nd₅Cl₁₈ + L′ (G), BaCl₂ + Na₃Nd₅Cl₁₈ + L′ (H), Na₃Nd₅Cl₁₈ + L′ (I), NdCl₃ + L′ (J), Ba₃Nd₂Cl₁₂ + Na₃Nd₅Cl₁₈ + Nd_1−yBa_yCl_3−y (K), Ba₃Nd₂Cl₁₂ + Nd_1−yBa_yCl_3−y + L′ (L), Na₃Nd₅Cl₁₈ + Nd_1−yBa_yCl_3−y + L′ (M), Ba₃Nd₂Cl₁₂ + Na₃Nd₅Cl₁₈ + BaCl₂ (N). The lines in red correspond to the phase diagram of the system NaCl–NdCl₃.

The calculated phase diagram in Fig. 16 shows that the addition of 5% SrCl₂ leads to a small decrease in the eutectic temperature (10 K). This indicates that the addition of the fission product Sr has no negative effect on the melting temperature of the fuel.

By contrast, the calculated phase diagram in Fig. 17 shows that the addition of 5% of BaCl₂ could cause the melting temperature of the eutectic to rise significantly. The primary crystallization phase above the eutectic composition of the NaCl–NdCl₃ system is BaCl₂, indicating that BaCl₂ could precipitate out of the melt at high concentrations. This result would have significant consequences for the operation of the reactor, as the presence of precipitates could lead to clogging. This hypothesis should be assessed with experimental investigations and thorough modelling in the ternary system, including necessary ternary excess parameters.

5. Summary

Thermodynamic modelling assessments of the molten salt systems AECl₂–NdCl₃ (AE = Sr, Ba) are presented in this work using the CALPHAD method with the quasi-chemical formalism in quadruplet approximation for the liquid solution. The system SrCl₂–NdCl₃ is characterised by: (i) a single eutectic, (ii) a peritectic decomposition of the intermediate Sr₉Nd₅Cl₃₃, (iii) a Sr_1−xNd_xCl_2+x (cubic) solid solution in the composition range x(NdCl₃) = [0–0.2], (iv) a Nd_1−ySr_yCl_3−y (hexagonal) solid solution in the composition range x(NdCl₃) ≥ 0.95. The structure of the intermediate Sr₉Nd₅Cl₃₃ has been characterised with XRD, and the solid solution Sr_1−xNd_xCl_2+x has been investigated with quenching experiments and post-XRD characterisation. Extrapolation to the ternary NaCl–SrCl₂–NdCl₃, used here as simulant for the NaCl–SrCl₂–PuCl₃ system, shows no adverse effects on the melting point of the eutectic upon addition of 5% SrCl₂.

The system BaCl₂–NdCl₃ is similarly characterised by: (i) a single eutectic, (ii) a peritectic decomposition of the intermediate Ba₃Nd₂Cl₁₂, (iii) a Ba_1−xNd_xCl_2+x (cubic) solid solution in the composition range x(NdCl₃) = [0–0.2], stable only at temperatures above 940 K, (iv) a Nd_1−ySr_yCl_3−y (hexagonal) solid solution in the composition range x(NdCl₃) ≥ 0.95. The structure of the intermediate Ba₃Nd₂Cl₁₂ has been determined using XRD, and the solid solution Ba_1−xNd_xCl_2+x has been investigated with quenching experiments and post-XRD characterisation. Extrapolation to the ternary NaCl–BaCl₂–NdCl₃, used here as simulant for the NaCl–BaCl₂–PuCl₃ system, shows that the addition of 5% BaCl₂ could potentially increase the melting point of the eutectic and lead to BaCl₂ precipitation in the melt. This would have implications for the safety assessment of the reactor, and should be confirmed in complementary investigations of the ternary system.

Data availability

Most of the experimental data obtained in this work has been reported in the main text in Tables 1–6 and Fig. 1–7, 9, 10, 12 and 13. Further supporting data have been included as part of the ESI.†

Conflicts of interest

The authors declare to have no competing financial interests or personal relationships that influence the work reported in this paper.

Appendices

 

Appendix A: thermodynamic functions SrCl₂

The end-member SrCl₂ undergoes a second order transition from a cubic structure, to a slightly distorted cubic structure in the temperature range 900–1100 K, as evidenced by the gradual bump in the enthalpy increment data of Dworkin and Bredig³² presented in Fig. 18. In previous works, such as that of Chartrand et al.,³³ this transition was incorporated in the model as a step-wise transition with an associated transition enthalpy of 6 kJ mol⁻¹. However, because this transition is not measured as an invariant equilibrium, in this work the α–β transition of SrCl₂ was not incorporated in the thermodynamic model. The thermodynamic functions from Chartrand et al.³³ were retained for the low-temperature α-phase, however.

Fig. 18 Enthalpy increment data of SrCl₂ as measured experimentally by Dworkin and Bredig,³² compared to the calculated values using the thermodynamic functions from this work.

Appendix B: modelling of binary systems with NaCl

In order to perform calculations in the ternary systems NaCl–SrCl₂–NdCl₃ and NaCl–BaCl₂–NdCl₃, the binary systems NaCl–SrCl₂, NaCl–BaCl₂ and NaCl–NdCl₃ were modelled based on the data presented in the literature. The cation–cation coordination numbers used in these models are the same as in Table 2, with the additional coordination numbers involving Na given in Table 9.

Table 9 Additional coordination numbers used in the CALPHAD models presented in this section

A	B	Z ^AAB/ClCl	Z ^BAB/ClCl	Z ^ClAB/ClCl
Na	Na	6	6	6
Na	Nd	4	6	2.666
Na	Sr	3	6	3
Na	Ba	6	6	4

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The thermodynamic model for the system NaCl–NdCl₃ was optimized using the phase diagram data presented by Sharma et al.³⁴ and Igarashi et al.³⁵ in the quadruplet approximation in the modified quasichemical formalism, as used throughout this work. The excess Gibbs energy function obtained through optimization of this binary is given in eqn (16), and the calculated phase diagram is shown in Fig. 19. The calculated mixing enthalpy is compared to experimental data in Fig. 20.

Δg_NaNd/ClCl = −9000 − 5.5T (16)

Fig. 19 Calculated phase diagram of the NaCl–NdCl₃ system modelled in this work. Experimental data were presented by Sharma et al.³⁴ (open red squares) and Igarashi et al.³⁵ (open blue circles).

Fig. 20 Calculated mixing enthalpy of the NaCl–NdCl₃ system at T = 1273 K, modelled in this work. Experimental data were reported by Gaune-Escard et al.³⁶

The thermodynamic models for the NaCl–SrCl₂ and NaCl–BaCl₂ have already been presented by Chartrand et al.³³ However, since Chartrand et al. used different thermodynamic descriptions for the end-members, these systems were reassessed based on the experimental data available in the literature.

The system NaCl–SrCl₂ was optimized based on the experimentally determined phase diagram data by Vortisch et al.,³⁷ Scholich et al.³⁸ and Bukhalova et al.³⁹ The mixing enthalpy of the system was measured by Østvold et al.⁴⁰ The optimized phase diagram is shown in Fig. 21, and the calculated mixing enthalpy is given in Fig. 22. The excess Gibbs energy function is given in eqn (17).

Δg_NaSr/ClCl = −1119.3 + 0.4175T + χ_NaSr/ClCl(−1067.8) + y_SrNa/ClCl(−996.4 + 1.3T) (17)

Fig. 21 Calculated phase diagram using the model presented in this work of the NaCl–SrCl₂ system. Experimental data from Vortisch et al.³⁷ (empty black circles), Scholich et al.³⁸ (empty red squares) and Bukhalova et al.³⁹ (empty blue triangles).

Fig. 22 Mixing enthalpy of the NaCl–SrCl₂ system calculated with the model presented in this work. Experimental data from Østvold et al.³⁶

The thermodynamic model of the NaCl–BaCl₂ system was optimized based on the experimental phase diagram data presented by Gemsky et al.⁴¹ and Zakharchenko et al.⁴² No experimentally determined mixing enthalpy data are available in the literature, and therefore the mixing enthalpy estimation method presented by Davis and Rice,²¹ also used for the systems SrCl₂–NdCl₃ and BaCl₂–NdCl₃ in this work, was used. The optimized phase diagram is shown in Fig. 23, and the calculated mixing enthalpy is shown in Fig. 24. The excess Gibbs energy function used in the model is given in eqn (18).

Δg_NaBa/ClCl = 2800 − 3T + y_BaNa/ClCl(−3T) (18)

Fig. 23 Calculated phase diagram using the model presented in this work of the NaCl–BaCl₂ system. Experimental data from Gemsky et al.⁴¹ (empty black circles) and Zakharchenko et al.⁴² (empty red squares).

Fig. 24 Mixing enthalpy of the NaCl–BaCl₂ system caulculated with the model presented in this work. Mixing enthalpy data estimated using the estimation method by Davis and Rice.²¹

Appendix C: Ternary field investigations

In Section 4.8, the pseudo-binary systems {0.95NaCl + 0.05AECl₂}–{0.95NdCl₃ + 0.05AECl₂} (AE = Sr, Ba) have been presented, equivalent to the binary NaCl–NdCl₃ upon addition of 5% SrCl₂ or BaCl₂. The pseudo-binary phase diagram of NaCl–NdCl₃ upon addition of 1% and 9.5% BaCl₂ are presented here in Fig. 25 and 26 respectively. Fig. 27 and 28 show the projected liquidus surfaces of the ternary systems NaCl–SrCl₂–NdCl₃ and NaCl–BaCl₂–NdCl₃.

Fig. 25 Phase diagram of the {0.99NaCl + 0.01BaCl₂}–{0.99NdCl₃ + 0.01 BaCl₂} pseudo-binary system of the NaCl–BaCl₂–NdCl₃ ternary. The labelled phases are NaCl + L′ (A), NaCl + BaCl₂ + L′ (B), NaCl + BaCl₂ + Na₃Nd₅Cl₁₈ (C), Ba₃Nd₂Cl₁₂ + Na₃Nd₅Cl₁₈ + L′ (G), BaCl₂ + Na₃Nd₅Cl₁₈ + L′ (H), Na₃Nd₅Cl₁₈ + L′ (I), NdCl3 + L′ (J), Ba₃Nd₂Cl₁₂ + Na₃Nd₅Cl₁₈ + Nd_1−yBa_yCl_3−y (K), Ba₃Nd₂Cl₁₂ + Nd_1−yBa_yCl_3−y + L′ (L), Na₃Nd₅Cl₁₈ + Nd_1−yBa_yCl_3−y + L′ (M).

Fig. 26 Phase diagram of the {0.905NaCl + 0.095BaCl₂} and {0.905NdCl₃ + 0.095BaCl₂} pseudo-binary section of the NaCl–BaCl₂–NdCl₃ ternary system. The labelled phases are NaCl + L′ (A), NaCl + BaCl₂ + L′ (B), NaCl + BaCl₂ + Na₃Nd₅Cl₁₈ (C), BaCl₂ + L′ (D), BaCl₂ + Ba₃Nd₂Cl₁₂ + L′ (E), Ba₃Nd₂Cl₁₂ + L′ (F), Ba₃Nd₂Cl₁₂ + Na₃Nd₅Cl₁₈ + L′ (G), BaCl₂ + Na₃Nd₅Cl₁₈ + L′ (H), Na₃Nd₅Cl₁₈ + L′ (I), NdCl3 + L′ (J), Ba₃Nd₂Cl₁₂ + Na₃Nd₅Cl₁₈ + Nd_1−yBa_yCl_3−y (K), Ba₃Nd₂Cl₁₂ + Nd_1−yBa_yCl_3−y + L′ (L), Ba₃Nd₂Cl₁₂ + Na₃Nd₅Cl₁₈ + BaCl₂ (N). The lines in red correspond to the phase diagram of the system NaCl–NdCl₃.

Fig. 27 Liquidus projection of the NaCl–SrCl₂–NdCl₃ system as calculated with the models presented in this work. No ternary excess terms were added.

Fig. 28 Liquidus projection of the NaCl–BaCl₂–NdCl₃ system as calculated with the models presented in this work. No ternary excess terms were added.

The liquidus projection of the NaCl–SrCl₂–NdCl₃ system shown in Fig. 27 indicates that the melting point of the eutectic of the NaCl–NdCl₃ binary is lowered slightly upon addition of small amounts of SrCl₂, as it approaches a ternary eutectic composition.

Fig. 25 shows that the addition of 1% of BaCl₂ has no significant effect on the melting behaviour of the binary NaCl–NdCl₃, with the eutectic being approximately the same as in the pure system. Upon further addition of BaCl₂, as shown in Fig. 17 and 26, the eutectic temperature increases, and precipitation becomes more likely. The primary crystallization phase at the eutectic composition is BaCl₂. The liquidus projection in Fig. 28 shows that the addition of very small amounts of BaCl₂ (≤1%) does not influence the melting point of the eutectic in a significant way. Further addition of BaCl₂, however, does quickly lead to an increase of the eutectic temperature.

Acknowledgements

The authors of this paper gratefully acknowledge financial support from the ORANO group, as well as fruitful discussions with Dr Elisa Capelli.

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Footnote

† Electronic supplementary information (ESI) available: Experimental investigations and modelling of the thermochemistry of the AECl₂–NdCl₃ (AE = Sr, Ba) molten salt systems. See DOI: https://doi.org/10.1039/d4cp01784f

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