Simulant chemistry for uranium and plutonium molten fuel salts: crystallographic investigation and thermodynamic modelling assessment of the NaCl–RECl₃ and NaCl-MgCl₂-RECl₃ (RE = Ce, Nd) systems

Abstract

In this study, new insights into the solid state chemistry of the systems NaCl–RECl₃ (RE = Ce, Nd) are presented, in which the intermediate compound suggested in the literature, i.e. Na₃RE₅Cl₁₈, is investigated more closely. Our studies have revealed a solubility range around the intermediate composition in the form of the stoichiometry, and have allowed us to revisit the phase diagrams of the NaCl–RECl₃ (RE = Ce, Nd) systems accordingly. Furthermore, we demonstrate that among the lanthanide chlorides, NdCl₃ is the prime simulant candidate for the melting behaviour of PuCl₃-based systems, while CeCl₃ is most suited to simulate UCl₃-based systems. This is corroborated in this work by comparing the melting profiles of the NaCl-MCl₃, MgCl₂-MCl₃, and NaCl-MgCl₂-MCl₃ (M = Ce, Nd, U, Pu) systems. In doing so, the binary systems MgCl₂-MCl₃ (M = Ce, Nd) have been re-visited based on existing data in the literature and estimated mixing enthalpies. Extrapolations to the ternary systems NaCl-MgCl₂-RECl₃ (RE = Ce, Nd) have been made and compared to the available data in the literature, showing good agreement.

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1 Introduction

Molten chloride salts are a class of materials that are central in the development of fast neutron spectrum Molten Salt Reactor (MSR) development. In this type of nuclear reactor, chloride salts can be used as both fuel and coolant. The reason for this lies in their attractive qualities, notably their high thermochemical stability and low vapour pressures, even at elevated temperatures, and their high actinide solubility.^1,2 For a safety assessment of the MSR, a thorough understanding of the thermodynamic and thermo-physical properties of the fuel salts is needed. Salt systems that have garnered interest as candidate fuels are the systems NaCl–PuCl₃,³ NaCl–UCl₃,⁴ and NaCl-MgCl₂-PuCl₃,^5–7 with this work focussing mainly on the latter fuel system. Since there is a dearth of available experimental data on the systems with PuCl₃ in general, additional data are urgently needed to assist the safety assessment of the molten chloride reactor. At this stage of MSR development, the amounts of PuCl₃ available for research are limited as it needs to be produced in special facilities due to its hazardous nature. Therefore, using an approach that does not involve the use of PuCl₃ may be desirable to reduce the number of necessary experiments. In particular, a close inspection of the (conflicting) available data in simulant systems with lanthanide elements is meaningful. In this work, we have scrutinized systems with lanthanide chlorides from La to Yb (and Y) to identify the elements whose behaviour is closest to that of the actinides in molten chloride salts, and to identify the most suitable simulant for the melting behaviour of PuCl₃-based systems. We have found that NdCl₃ and CeCl₃ are the closes surrogates for NaCl–AnCl₃, MgCl₂–AnCl₃ and NaCl-MgCl₂-AnCl₃ (An = U, Pu) systems, thereby calling for a close inspection of the corresponding rare earth chloride systems.

Experimental investigations using X-ray diffraction (XRD) have been performed to fill in important gaps that became evident after analyzing the data in the literature, i.e. related to the solid-state chemistry in the NaCl–RECl₃ systems. There is no single interpretation of the stable intermediate compounds in these systems, with some authors claiming a stoichiometry of NaRE₃Cl₁₀,^8,9 Na₃RE₅Cl₁₈^10,11 or Na_2x(Na_xRE_2−x)C₁₆,^12,13 with the latter indicating possible solid solubility. Subsequently, CALPHAD models of the binary sub-systems NaCl–NdCl₃ and NaCl–CeCl₃ have been developed. The thermodynamic models use the quasi-chemical formalism in the quadruplet approximation for the liquid solutions, and a one-lattice polynomial model for the solid solutions. Moreover, the systems MgCl₂–MCl₃ (M = Ce, Nd, U, Pu) were modelled based on the available phase diagram data in the literature, and estimated mixing enthalpy data using the method of Davis and Rice,¹⁴ as described in more detail in a previous work.¹⁵ This allowed us to consider more generally the similarities in the NaCl-MgCl₂-MCl₃ (M = Ce, Nd, U, Pu) systems.

2 Methods

2.1 Experimental techniques

2.1.1 Sample preparation. For the experiments carried out in this work, the end-members NaCl, NdCl₃ and CeCl₃ were used in their respective ultra-dry forms, as delivered by the supplier. The purity has been verified by X-Ray diffraction (XRD) and Differential Scanning Calorimetry (DSC), as shown in Table 1. No secondary impurity phases were detected, and the measured melting temperatures were found in excellent agreement with the data in the literature. 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).

Table 1 Pure compounds used in the experiments in this work

Compound	Supplier	CAS No	Reported purity	Melting point (DSC, K)	Melting point (lit., K)
NaCl	Merck	7647-14-5	99.998%	1074 ± 5	1074 ± 1^16
NdCl3	Thermo-Fischer	10024-93-8	99.99%	1031 ± 5	1030 ± 2^17
CeCl3	Alfa Aesar	7790-86-5	99.9%	1087 ± 5	1090 ± 2^17

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Weighing was carried out using a Mettler-Toledo XPE105DR balance with a 0.01 mg uncertainty. Sample preparation was conducted by mixing end-members in the appropriate stoichiometric ratios in an agate mortar inside the dry argon atmosphere in the glovebox. The sample containers were either nickel liners in stainless steel crucibles, also used in our previous works,^15,18,19 or vacuum-sealed borosilicate ampoules. Subsequently, the mixtures were subjected to a heat treatment for 48 h at T = 693 K, either in a tubular furnace under argon flow or in a chamber furnace under air.

2.1.2 Quenching experiments. The high-temperature stability of the intermediate compound in the NaCl–CeCl₃ and NaCl–NdCl₃ systems was investigated in this work using quenching experiments. The quenching samples consisted of stoichiometric 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 773 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. No difference in obtained XRD pattern was observed when quenching after 4 hours of heat treatment instead of 2.

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

2.1.3 X-ray diffraction (XRD).
Laboratory 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 of Rietveld, Loopstra and van Laar,^20,21 using the FullProf software, Version 5.10.²² Visualisation of the crystal structure based on the refined XRD data was done with the VESTA software.²³
Synchrotron XRD. In addition to XRD measurements obtained in our lab, high resolution synchrotron XRD (sXRD) measurements were performed. The resolution of synchrotron diffraction, δ d/d, is 1–2 × 10⁻³ (depending on the capillary diameter, scattering angle and excitation energy), and thus typically a magnitude better than that of the lab diffractometer. It was used to investigate small impurities or additional phases that would otherwise be invisible on an XRD. The sXRD measurements were performed at the XRD-1 station of the ROBL beamline (BM20) at the ESRF.²⁴ This station was equipped with a 6-circle diffractometer and a Eiger CdTe 500k detector (Dectris). The wavelength of the synchrotron radiation was λ = 0.76533 Å, and the beam size was 300 × 300 μm. The sample was enclosed in a 300 μm diameter glass capillary sealed with epoxy glue itself enclosed inside a Kapton tube. Data were collected in transmission mode at 296 K and reduced using the PyFAI software suite.²⁵ Data were collected from 0 ≤ 2θ ≤ 66°. Refinement of the measured XRD data was also performed by applying the method of Rietveld, Loopstra and van Laar,^20,21 using the FullProf software, Version 5.10.²²

2.2 Thermodynamic modelling

The thermodynamic modelling assessment of the molten salt systems was performed with the CALPHAD method²⁶ using the FactSage software, Version 8.2.²⁷ Both literature and experimental data obtained in this work were used to optimize the excess parameters of the Gibbs energy functions of the phases present in the systems.

2.2.1 Stoichiometric compounds. The Gibbs energy function 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) (with T in K).

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 + cT⁻² + dT² + eT^1/2 (2)

The thermodynamic data for all compounds are listed in Table 2. To be consistent with previous works^{15,18,19,28–30} and the JRC Molten Salt Database,³¹ thermodynamic data for MgCl₂ were taken from the JANAF thermochemical database,¹⁶ the thermodynamic data for NaCl was taken from van Oudenaren et al.,³² and the thermodynamic data for CeCl₃ and NdCl₃ were taken from the review by Konings and Kovács.¹⁷ The thermodynamic data for PuCl₃ and UCl₃ were taken from the review by Capelli and Konings,³³ with the heat capacity of UCl₃ taken from the re-assessment by van Oudenaren et al.³² The thermodynamic model of the NaCl–MgCl₂ system was presented in a previous work¹⁸ and is used in this work as such.

Table 2 Thermodynamic functions used in the CALPHAD model in this work. Optimized values are marked in bold. Note that compounds marked with an asterisk are not stoichiometric intermediates, but rather end-members of the Na_3xRE_2−xCl₆ solid solution as specified in section 2.2.3

Compound			C p,m(T) (J K^−1 mol^−1) = a + bT + cT^−2 + dT^2 + eT^−1/2					Temperature range (K)	Source
			a	b	c	d	e
NaCl(s)	−411 260	72.15	47.72158	0.0057	−882.996	1.21466 × ·10^−5		[298–1074]	van Oudenaren et al.^32
NaCl(l)	−390 852.5	83.302	68					[298–2500]	Dumaire et al.^28
MgCl2(s)	−641 616	89.629	54.5843	0.0214213	−1 112 119	−2.3567 × 10^−6	399.177	[298–2000]	Chase et al.^16
MgCl2(l)	−601 680.1	129.236	193.4089	−0.3620139	−3 788 504	3.199871 × 10^−4		[298–660]	Chase et al.^16
			92.048					[660–2500]	Chase et al.^16
CeCl3(s)	−1 059 700	151	90.9772	0.0358123	−271 530			[298–1095]	Konings and Kovács^17
CeCl3(l)	−1 006 100	151	90.9772	0.0358123	−271 530			[298–1095]	Konings and Kovács^17
			161.05					[1095–3000]	Konings and Kovács^17
NdCl3 (s)	−1 040 900	153.5	109.084	1.6406 × 10^−2	−1 309 950			[298–1032]	Konings and Kovács^17
NdCl3(l)	−1 017 943.3	154.59	150					[1095–3000]	Konings and Kovács^17
PuCl3(s)	−959 600	161.4	91.412	0.03716		27 400		[298–1041]	Capelli and Konings^33
PuCl3(l)	−931 116	170.46	144					[298–1500]	Capelli and Konings^33
UCl3(s)	−863 700	163.9	106.967	−0.0208595	−129 994	3.6389 × 10^−5		[298–1100]	Capelli and Konings^33
UCl3(l)	−846 616	152.919	151.1					[1100–2500]	van Oudenaren et al.^32
NaMgCl3(s)	−1 063 200	156	90	0.075				[298–1000]	Chartrand et al.,^34 Alders et al.^18
Na2 MgCl4(s)	−1 486 000	211	135	0.1125				[298–773]	Chartrand et al.,^34 Alders et al.^18
Na6MgCl8	−3 148 000	481.5	340.9138	0.055621	−1 117 417	7.05 × 10^−5	399.177	[298–6000]	Alders et al.^18
Na2Mg3Cl8	−2 767 200	410	252.3333	0.059943	−2 226 887	3.17 × 10^−5	798.354	[298–6000]	Alders et al.^18
NaNd2Cl7*	−2 505 000	378.5	265.88958	0.038512	−2 620 782.996	1.21466 × 10^−5		[298–1500]	This work
NaCe2Cl7*	−2 542 000	374.15	229.676	0.0773246	−543 882.996	1.21466 × 10^−5		[298–1500]	This work
NaU2Cl7	−2 112 623	438	261.65558	−0.036019	−260 870.996	8.49246 × 10^−5		[298–1500]	Yingling et al.,^35 This work

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2.2.2 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.³⁶ which has proven to be well-adapted to molten chloride and fluoride systems. This description assumes the existence of cation–anion quadruplets in the liquid, i.e. in the form of A–X–B–Y (A,B = cations; X,Y = anions), allowing for the modelling of short-range ordering. This formalism allows for the selection of the composition of maximum short-range ordering through its coordination numbers, corresponding to the minimum of the Gibbs energy that is often found near the composition of the lowest eutectic. By fixing either the cation–cation or anion–anion coordination number, the opposite coordination number is also obtained through eqn (3), where q_i are the charges of the respective ions. In this work, we can simplify the description to the A–X–B–X quadruplet as chlorine is the only anion we consider. The coordination numbers used in the thermodynamic model presented in this work are given in Table 3.

Table 3 Non-default coordination numbers used in the CALPHAD model presented in this work

A	B	X	Z ^AAB/XX	Z ^BAB/XX	Z ^XAB/XX	Source
Na	Mg	Cl	3	6	3	18
Na	Nd	Cl	4	6	2.67	This work
Na	Ce	Cl	3	6	2.4	This work
Na	U	Cl	2	6	2	35
Na	Pu	Cl	3	6	2.4	28
Mg	Ce	Cl	3	6	1.71	This work
Mg	U	Cl	3	6	1.71	This work

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The excess parameters that are optimized are those related to the second-nearest neighbour exchange reactions as given in eqn (4). The associated change in Gibbs energy of eqn (4) is expressed in eqn (5).

(A₂X₂)_quad + (B₂X₂)_quad → 2(ABX₂)_quad Δg_AB/XX (4)

In eqn (5) the terms , and are composition-independent coefficients that may depend on temperature. The composition dependence of the Gibbs energy is apparent through χ_AB/XX 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 Table 4. Using the data for the binary systems as a basis, extrapolations to the ternary and quaternary fields were made with Kohler/Toop interpolations, due to the asymmetry of the system. In this work, MgCl₂, CeCl₃ and NdCl₃ are considered asymmetric components, as their ionic structure in the liquid (i.e. molecular species) is different from the sodium halides (i.e. ionic species). No ternary optimization terms were added, to be consistent with the work of Beneš et al.³⁷

Table 4 Excess Gibbs energy functions used in the CALPHAD model in this work for the liquid solution. Values have been optimized unless a source is listed, in which case the values have been taken from that source

AX	BX				Source
a Re-optimized from the work of Yingling et al.^35 to reproduce the same phase diagram with a different choice of end-member function for UCl3
NaCl	MgCl2	−10 200–1.6 T	660.5	−4650–1.5 T	15
NaCl	PuCl3	−8450	−3220	−5658	28
NaCl	NdCl3	−5500–8.5 T	−6000 + 6 T	−5500 + 6 T	This work
NaCl	CeCl3	−11 200–0.5 T	2000–4 T	−4000 + 2 T	This work
NaCl	UCl3	−11 000 + 3.5 T	3000–6 T	−10 000 + 2 T	This work^a
MgCl2	PuCl3	2400–0.7 T	0.3 T		This work
MgCl2	NdCl3	2000–2.8 T	2 T	4.5 T	This work
MgCl2	CeCl3	2300–1.6 T		2200–0.5 T	This work
MgCl2	UCl3	2000	2000	3000–0.5 T	This work

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2.2.3 Solid solution modelling of Na_3xRE_2−xCl₆. The thermodynamic description of solid-solutions is done using the one-lattice polynomial model to be consistent with the description of the JRC Molten Salt Database (JRCMSD).³¹ The Gibbs Energy function of the solid-solution is given in eqn (7).

In the above equation, are the end-member molar Gibbs energies, and X_i are the site molar fractions of the end-members A and B, respectively. The third and fourth terms in eqn (7) represent the configurational entropy. The excess Gibbs energy, present in eqn (7) as ΔG^excess_m, is defined as per eqn (8).

The term L^ij_AB in eqn (8) is an interaction coefficient that can be a function of temperature if necessary. The terms Xⁱ_A and X^j_B are the site molar fractions of end-members A and B. To model the homogeneity range of the Na_3xRE_2−xCl₆ intermediate, the NaCl and NaRE₂Cl₇ end-members were selected in this work. It is important to note that the Gibbs energy of the NaCl end-member was also destabilised with an arbitrary enthalpic term of +5000 J mol⁻¹ to be able to reproduce accurately the phase diagram data. The corresponding Gibbs energy functions are given in Table 5.

Table 5 Optimized excess Gibbs energy functions used in the CALPHAD model in this work for the solid solution

A	B	L AB ^11
NaCl	NaCe2Cl7	−9000 + 15 T
NaCl	NaNd2Cl7	−6500 + 7.5 T

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3 Results and discussion

3.1 Simulant selection

Cerium has often been cited as actinide surrogate in the literature,^38–41 but other rare earth elements show comparable behaviour. Cerium is commonly used for the fact that its stable oxidation states (i.e. +3 and +4) mirror that of plutonium in oxide systems, where CeO₂ and Ce₂ O₃ can be used as simulant for PuO₂ and Pu₂ O₃, respectively. In a molten salt environment, Pu is mostly stable in its +3 oxidation state (i.e. PuCl₃), but can oxidize to +4 in case oxychlorides or oxides form (i.e. PuOCl₂,^42,43 PuO₂ ⁴⁴). Only a few lanthanides are stable in the +4 oxidation state, among which Ce, which is why Ce seems like the most logical choice at first glance. However, when looking at the melting behaviour and ionic radius, it may not be the most suitable lanthanide to fill the role of simulant element, as we show in this work. This observation is in agreement with the work of Goloviznina et al.,⁴⁵ who show based on DFT calculations and MD simulations that NdCl₃ is the most appropriate simulant for PuCl₃ with respect to density and viscosity in molten NaCl–MCl₃ (M = Nd, Ce, Pu) chlorides.

A comparison of the melting behaviour of different lanthanide chloride-alkali chloride systems has been made by collecting experimental liquidus data reported in the literature for the systems NaCl–MCl₃.^{8–10,35,40,46–60} The decision on which potential simulants to consider is based on the data shown in Fig. 1, which allows for a pre-selection based on similarity with Pu and U at first glance. Shown in these figures is the melting behaviour of NaCl–MCl₃ (M = La–Yb, Pu, U) mixtures as a function of x(MCl₃), i.e. the molar fraction of the MCl₃ species. The systems with NaCl were selected because NaCl is part of the base fuel salt, and there is an abundance of data in the literature.

Fig. 1 Liquidus lines of NaCl–MCl₃ systems (M = La–Yb, Y, U, Pu) reported in the literature^{8–10,35,40,46–60} (a), and selected liquidus lines for potential simulant systems (b).

As seen in Fig. 1b, the liquidus line of the NaCl–NdCl₃ system is almost perfectly overlapping with that of the NaCl–PuCl₃ system. Following the conclusion of Goloviznina et al.⁴⁵ that NdCl₃ is the prime candidate for simulating the density and viscosity of PuCl₃ in NaCl–MCl₃ molten chlorides, this work shows that it is also the best simulant with respect to the melting behaviour. Also shown in this figure is the liquidus line of the NaCl–CeCl₃ system, which has been cited as simulant for Pu and U in the literature,^38–41 but bears the closest resemblance to the liquidus in the NaCl–UCl₃ system. From this first analysis, we focused our efforts on the chemistry of the NaCl–RECl₃ and NaCl-MgCl₂-RECl₃ (RE = Ce, Nd) systems as most suitable surrogates for the corresponding AnCl₃ (An = U, Pu) systems. A number of open issues were identified for those systems, which we have explored in detail as described hereafter.

3.2 Insights into NaCl–RECl₃ (RE = Ce, Nd) chemistry

3.2.1 NaCl–NdCl₃. Experimental data have been reported in the literature on the NaCl–NdCl₃ system by Seifert et al. in 1988,⁶¹ who performed Differential Thermal Analysis (DTA) and XRD analyses. They found by XRD that an intermediate compound exists, which they assigned to Na₃Nd₅ Cl₁₈, also written as Na_0.67(Na_0.33Nd_1.67)Cl₆ (space group P6₃/m ⁶¹). Sato et al.¹⁰ also presented an experimental investigation of this system in 1998 using DTA and XRD, and they retained the intermediate compound found by Seifert et al., Na₃Nd₅Cl₁₈ in their assessment. They suggested that a homogeneity range exists at elevated temperatures, specifically between x(NdCl₃) = 0.59 and x(NdCl₃) = 0.70 and T = (573–873) K. According to the sketched phase diagram Sato et al. reported, the homogeneity range is only stable at elevated temperatures, while the room temperature composition remains Na₃Nd₅Cl₁₈. However, neither Sato et al. nor Seifert et al. reported detailed crystallographic information on the intermediate compound, notably the atomic positions in the crystal structure. Earlier DTA assessments by Igarashi et al. (1990)⁹ and Sharma et al. (1992)⁸ agreed about the existence of an intermediate, but suggested the intermediate NaNd₃Cl₁₀ instead, and indicated no homogeneity range. In view of the discrepancies between the literature studies, new investigations of the crystal structures of this compound were performed in this work to address the remaining questions.

In addition to the phase diagram studies found in the literature, single-crystal studies of the intermediate compound by Lissner et al. (1994)¹² dived more in detail into the crystal structure chemistry. They reported a structure of Na_0.698(Na_0.35Ce_1.65)Cl₆, corresponding to a general stoichiometry of (space group P6₃/m). The existence of this compound is confirmed in our work with new experimental investigations, and the description of Lissner et al. is thus retained. Moreover, the extent of the homogeneity range is scrutinized in detail for the first time. While the notation gives an insight into the crystallography (e.g. the shared Na/Nd position), in this work we will use the simpler notation Na_3xNd_2−xCl₆ or Na_2x (Na_xNd_2−x)Cl₆. Based on the atomic positions Lissner et al. reported for a sample of stoichiometry Na_0.608(Na_0.304Nd_1.696)Cl₆, we can define a general description for the Na_3xNd_2−xCl₆ phase that has been used in this work (see Table 7, Fig. 2).

Fig. 2 Crystal structure of the Na_0.335(Na_0.168Nd_1.832)Cl₆ compound obtained in this work viewed along the c-axis, with the elements Na, Nd and Cl indicated in yellow, orange and green respectively. The corresponding atomic parameters are listed in Table 7.

Several samples were prepared in this work with varying (NaCl : NdCl₃) ratios as detailed in Section 2.1.1, with the aim of confirming the crystal structure model, and defining the limits of the homogeneity range. Mixtures were prepared within the expected homogeneity range, as well as in the two-phase domains. The mixtures were subjected to thermal treatment at T = 693 K for at least 48 hours. A few quenching experiments were also performed at compositions x(NdCl₃) = 0.60, 0.625 and 0.65 at T = 773 K. The aim of these experiments was to investigate the behaviour of this compound both at elevated temperatures and at room temperature, following the hints in the literature by Sato et al.¹⁰ and Lissner et al.¹²

Shown in Fig. 4 is the profile refinement of the composition x(NdCl₃) = 0.65, collected at room temperature using sXRD. This refinement shows that a single phase exists at this composition, with no detectable amounts of the end members NaCl and NdCl₃. The same was observed for the compositions x(NdCl₃) = 0.55, 0.6 and 0.625 in the same binary system, confirming the existence of an intermediate with a considerable homogeneity range. The Na_3xNd_2−xCl₆ phase adopts the same crystal structure symmetry as NdCl₃ (also hexagonal, in space group P6₃/m ¹³). Upon addition of sodium to the NdCl₃ structure, partial substitution of sodium on the Nd site (2c) occurs, while the rest of the sodium is located on the (0,0,0) position (2b) with an occupancy equal to x. The shared Nd/Na2 site is nine-fold coordinated (same as in the NdCl₃), while the Na1 site is six-fold coordinated. The crystal structures of Na_3xNd_2−xCl₆ and NdCl₃ are shown in Fig. 2 and 3, respectively to illustrate this. The atomic positions obtained from the refinements of the intermediates Na_3xRE_2−xCl₆ are presented in Table 7.

Fig. 3 Crystal structure of NdCl₃ as reported by Meyer et al.¹³ viewed along the c-axis, with the elements Nd and Cl indicated in orange and green respectively.

Fig. 4 Profile refinement of the sXRD (λ = 0.7653 Å) at x(NdCl₃) = 0.623 in the NaCl–NdCl₃ system, showing the single phase Na_0.335(Na_0.168Nd_1.832)Cl₆. The observed intensity (red circles) is shown alongside the calculated intensity (black line), and the difference between the two is shown (blue line). The angles at which reflections occur, i.e. the Bragg positions, are shown as well (green, vertical lines).

At composition x(NdCl₃) = 0.70, as shown in Fig. 5, the first traces of the end member NdCl₃ become apparent, showing that the limiting composition of the homogeneity range lies between x(NdCl₃) = 0.65 and x(NdCl₃) = 0.70. Similarly, the other limiting composition, i.e. that on the NaCl-rich side, was found between x(NdCl₃) = 0.50 and x(NdCl₃) = 0.55. Contrary to the assessments of Seifert et al.¹¹ and Sato et al.,¹⁰ the solid solution in this system was observed to be stable at room temperature, rather than exclusively at elevated temperatures.

Fig. 5 Profile refinement of the sXRD (λ = 0.7653 Å) at x(NdCl₃) = 0.70 in the NaCl–NdCl₃ system, with phases Na_0.304(Na_0.152Nd_1.848)Cl₆ and NdCl₃ ¹³ included in the refinement. The zoomed part of the figure shows the distinct separation of the Na_3xNd_2−xCl₆ peak (left) and the NdCl₃ peak (right). The observed intensity (red circles) is shown alongside the calculated intensity (black line), and the difference between the two is shown (blue line). The angles at which reflections occur, i.e. the Bragg positions, are shown as well (green, vertical lines).

The stability of the solid solution at elevated temperatures was moreover investigated through quenching experiments, where three samples at compositions x(NdCl₃) = 0.6, 0.625 and 0.65 were heated up to 773 K and subsequently quenched in a water bath to preserve the crystal structures stable at high temperatures. These experiments showed that at T = 773 K, the crystal structure was still that of the single-phase solid solution. Furthermore, to rule out kinetic effects that limit the formation of the solid solution, we performed a synthesis experiment at x(NdCl₃) = 0.75 with two different heating durations (48 h and 96 h). No appreciable difference was observed between the two experiments, thus we conclude that 48 h is enough time for the synthesis experiment to reach thermodynamic equilibrium.

The progression of the cell volume of the intermediate compound Na_3xNd_2−xCl₆ is shown in Fig. 7 as a function of composition, and the values are reported in Table 6. On the left side of the single-phase region (i.e. from x(NdCl₃) = 0.55–0.65), a mixture of NaCl and Na_3xNd_2−xCl₆ is found, and the solid solution reaches the volume at its limiting composition. On the right side of the solubility range, a mixture of NdCl₃ and Na_3xNd_2−xCl₆ is found, but the size of the unit cell of the intermediate keeps shrinking as the NdCl₃ fraction increases. We would expect the volume of the intermediate compound to remain constant and equal to that at the limiting composition of the homogeneity range instead. The reason for this is as of yet not known, and should be subjected to further investigation. As shown before in Fig. 4 and 5, several samples in the NaCl–NdCl₃ system were measured with synchrotron-XRD (λ = 0.7653 Å), labelled (sXRD) in Fig. 7, while others were measured by conventional laboratory XRD. The aim of the synchrotron experiments was to investigate the possible presence of end-members towards the limiting compositions, i.e. x(NdCl₃) = 0.55 and 0.7, given the higher resolution of s-XRD compared to lab-XRD, as well as obtain a high-resolution XRD of the single-phase Na_3xNd_2−xCl₆. The results of the synchrotron-XRD are very similar to the measurements carried out using lab XRD, confirming the reliability of the results.

Table 6 Refined lattice parameters of the Na_3xRE_2−xCl₆ phase in all investigated samples in the NaCl–RECl₃ (RE = Nd, Ce) systems, also shown in Fig. 7

x(RECl3)	a,b (Å)	c (Å)	Volume (Å^3)	Method
a {NaCl + Na3xRE2−xCl6}. b Single phase Na3xRE2−xCl6. c {RECl3 + Na3xRE2−xCl6}.
NaCl–NdCl 3
0.500^a	7.5343(4)	4.2326(5)	208.1(3)	XRD
0.548^b	7.5340(5)	4.2321(3)	208.0(2)	XRD
0.548^b	7.5345(4)	4.2322(5)	208.1(3)	sXRD
0.600^b	7.5385(6)	4.2294(3)	208.0(3)	XRD
0.625^b	7.5279(3)	4.2307(3)	207.6(2)	XRD
0.625^b	7.5269(4)	4.2310(5)	207.6(3)	sXRD
0.650^b	7.5210(3)	4.2300(3)	207.2(2)	XRD
0.700^c	7.5130(5)	4.2304(5)	206.8(3)	XRD
0.700^c	7.5134(4)	4.2293(5)	206.8(2)	sXRD
0.750^c	7.5069(4)	4.2291(5)	206.4(3)	XRD
NaCl–CeCl 3
0.500^a	7.5596(4)	4.3070(4)	213.2(2)	XRD
0.543^a	7.5593(4)	4.3082(4)	213.2(2)	XRD
0.588^b	7.5584(2)	4.3078(2)	213.1(1)	XRD
0.630^b	7.5550(5)	4.3057(4)	212.8(2)	XRD
0.649^b	7.5513(8)	4.3078(7)	212.7(4)	XRD
0.700^c	7.5470(4)	4.3052(4)	212.4(2)	XRD
0.750^c	7.5392(6)	4.3056(8)	211.9(3)	XRD

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Table 7 Crystallographic data of the Na_3xRE_2−xCl₆ solid solution (SGR P6₃/m; RE = Ce, Nd) obtained from the refinements of the XRD data in this work. Compositions at which sXRD data was used are marked with an asterisk. The occupancy is treated as variable in this work, and is based on molar fraction of RECl₃ in the solid solution: . Marked in bold are the compositions at which only single-phase Na_3x RE_2−xCl₆ was found

x(RECl3)	Intermediate stoichiometry	Site	Element	Wyckoff position	X	Y	Z	Occupancy
All	—	Na1	Na	2b	0	0	0	x
All	—	RE1	RE	2c	⅓	⅔	¼
All	—	Na2	Na	2c	⅓	⅔	¼
RE = Nd
0.500	Na0.429(Na0.214Nd1.786)Cl6	Cl1	Cl	6h	0.3816(6)	0.2967(6)	¼	1
0.548	Na0.429(Na0.214Nd1.786)Cl6				0.3760(6)	0.2926(6)
0.548*	Na0.429(Na0.214Nd1.786)Cl6				0.3872(1)	0.3027(1)
0.600	Na0.364(Na0.182Nd1.818)Cl6				0.3783(8)	0.2937(9)
0.623	Na0.335(Na0.168Nd1.832)Cl6				0.3826(6)	0.2986(7)
0.623*	Na0.335(Na0.168Nd1.832)Cl6				0.3902(2)	0.3032(2)
0.650	Na0.304(Na0.152Nd1.848)Cl6				0.3736(7)	0.2938(7)
0.700	Na0.304(Na0.152Nd1.848)Cl6				0.3915(2)	0.3049(2)
0.700*	Na0.304(Na0.152Nd1.848)Cl6				0.3763(6)	0.2918(2)
0.750	Na0.304(Na0.152Nd0.848)Cl6				0.3752(7)	0.2903(7)
RE = Ce
0.500	Na0.379(Na0.190Ce1.810)Cl6	Cl1	Cl	6h	0.3758(6)	0.2948(6)	¼	1
0.543	Na0.379(Na0.190Ce1.810)Cl6				0.3754(6)	0.2920(6)
0.588	Na0.379(Na0.190Ce1.810)Cl6				0.3736(5)	0.2914(5)
0.630	Na0.328(Na0.164Ce1.834)Cl6				0.3737(4)	0.2908(4)
0.649	Na0.305(Na0.153Ce1.847)Cl6				0.3768(6)	0.2942(6)
0.703	Na0.305(Na0.153Ce1.847)Cl6				0.3804(6)	0.2974(7)
0.750	Na0.305(Na0.153Ce1.847)Cl6				0.3732(6)	0.2913(6)

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The phase diagram has then been optimized based on the experimental DTA data from Sato et al.,¹⁰ shown in solid black circles in Fig. 6. The data from Sato et al. largely agree with the work of Seifert et al.,⁶¹ with the exception of the peritectic equilibrium. Seifert et al. measured two sub-liquidus equilibria between x(NdCl₃) = 0.5 and x(NdCl₃) = 0.95, whereas Sato et al. only measured one. This single peritectic equilibrium was also reported by Igarashi et al.⁹ and Sharma et al.⁸ Moreover, the work of Sharma et al. and Igarashi et al. reported the eutectic equilibrium up to x(NdCl₃) = 0.8, while Sato et al. and Seifert et al. reported the eutectic up to x(NdCl₃) = 0.5 and 0.6, respectively. A possible explanation for the fact that Sharma et al. and Igarashi et al. measured the eutectic equilibrium up to higher NdCl₃ content could be a contamination (Sharma et al. report a minor NdOCl contamination), or a subcooling effect (Igarashi et al. analysed the measured cooling curves). Another explanation could be that the kinetics of formation of the solid solution is slow, meaning that if previous authors measured with high heating rates, they could potentially observe metastable phases in the system.

Fig. 6 Phase diagram of the NaCl–NdCl₃ system calculated with the thermodynamic model presented in this work. Experimental data from Sato et al.¹⁰ (closed black circles), Igarashi et al.⁹ (open blue squares), Sharma et al.⁸ (open upward green triangles) and Seifert et al.⁶¹ (open downward red triangles).

Additionally, the limits of the homogeneity range and the stability at room temperature of the intermediate Na_3xNd_2−xCl₆ have been included in the optimisation using the experimental data obtained in this work. The mixing enthalpy of this system has been measured by Gaune-Escard et al.⁶² at T = 1124 K and has been optimized based on these experimental data. The calculated mixing enthalpy of this system is presented in Fig. 9. The intermediate compound Na_3xNd_2−xCl₆ has been included in the thermodynamic model as a solid solution with NaCl and NaNd₂ Cl₇ (corresponding to Na_0.571(Na_0.286Nd_1.714)Cl₆ at x(NdCl₃) = 0.66) as end-members to account for the limiting compositions of the solubility range.

3.2.2 NaCl–CeCl₃. Similarly, the salt system NaCl–CeCl₃ has been investigated experimentally by various authors in the literature. Most authors have interpreted the system as a simple binary eutectic system,^63–66 with Storonkin et al.⁶⁷ suggesting solubility of NaCl in a hypothetical low-temperature polymorphic phase of CeCl₃. Since CeCl₃ does not have a low-temperature phase, that interpretation is discarded. Krämer and Meyer (1990)⁶⁸ and Lissner et al. (1992)¹² reported single-crystal studies of Na_0.76(Na_0.38Ce_1.62)Cl₆ and Na_0.698(Na_0.35Ce_1.65)Cl₆, respectively, again corresponding to a general stoichiometry of Na_3xCe_2−xCl₆ (space group P6₃/m). Seifert et al.¹¹ suggested, based on DTA and XRD, that a solid solution between CeCl₃ and an intermediate compound of composition Na₃Ce₅Cl₁₈ existed.

In addition to the data found in the literature, an experimental investigation of the intermediate compound Na_3xCe_2−xCl₆ was performed, like in the NaCl–NdCl₃ system, mostly to gain further insight into the composition of the intermediate and possible existence of a homogeneity range. Synthesis experiments at several compositions were performed to identify the solubility limits of this intermediate compound. A single-phase intermediate compound was found at compositions x(CeCl₃) = 0.60, 0.625 and 0.65, while NaCl was observed at compositions x(CeCl₃) ≤ 0.55 and CeCl₃ was observed at compositions x(CeCl₃) ≥ 0.70. Based on these results, we conclude that the limiting concentrations of this solid solution are between x(CeCl₃) = 0.55 and 0.60 on the NaCl-rich side, and x(CeCl₃) = 0.65 and 0.70 on the CeCl₃-rich side. The progression of the cell volume of the intermediate compound Na_3xCe_2−xCl₆, obtained from the refinements performed in this work, is shown in Fig. 7 and reported in Table 6. The compositions at which a single phase solid solution is observed obey the expected linear trend. Furthermore, like in the Na_3xNd_2−xCl₆ intermediate, the limiting composition on the left side of the solubility range shows that the cell volume reaches a maximum at compositions x(CeCl₃) ≤ 0.59. The same trend in the cell volume decreasing beyond the solubility limit of the rare earth chloride (that was also seen in the NaCl–NdCl₃ system), is observed here.

Fig. 7 Cell volumes calculated from the profile refinements carried out in this work in the NaCl–RECl₃ (RE = Ce, Nd) systems. The data are both from synchrotron XRD and lab XRD, and the results obtained with these techniques are in good agreement with each other. A linear trend is visible in the single-phase solid solution following the insertion of the Na cation in the interstitial sites of the Na_3xRE_2−xCl₆ crystal structure. The refined values are also given in Table 6.

The NaCl–CeCl₃ thermodynamic model was optimized based on the DTA data from Seifert et al.¹¹ The measurement of the eutectic equilibrium past x(CeCl₃) = 0.55 in the other sources could be due to contaminations. Kojima et al.⁶⁶ and Nishihara et al.⁶⁵ report CeCl₃ purities ≤98%, and Storonkin et al.⁶⁷ measured what they interpret as a polymorphic transition in CeCl₃, which is an indication that they also had impurities in their CeCl₃ batch. Baev et al.⁶³ and Korshunov et al.⁶⁴ do not specify their measurement method or end-member purity, so it is difficult to say what could have gone wrong.

The extent and stability of the intermediate compound Na_3xCe_2−xCl₆ along with its solubility range was optimized based on the experimental data obtained in this work. The phase diagram of this system is presented in Fig. 8. The mixing enthalpy of this system was optimized based on the experimental data from Papatheodorou et al.,⁶⁹ and is shown in Fig. 9. Like in the NaCl–NdCl₃ system, the intermediate compound Na_3xCe_2−xCl₆ has been included in the thermodynamic model as a solid solution between NaCl and NaCe₂Cl₇ end-members, with again an arbitrary destabilization term of the NaCl end-member of +5000 J mol⁻¹.

Fig. 8 Phase diagram of the NaCl–CeCl₃ system calculated with the thermodynamic model presented in this work. Experimental data from Seifert et al.¹¹ (closed black circles), Baev et al.⁶³ (open blue squares), Storonkin et al.⁷⁰ (open upward green triangles), Kojima et al.⁶⁶ (open downward red triangles), Korshunov et al.⁶⁴ (open gold diamonds) and Nishihara et al.⁶⁵ (grey pluses).

Fig. 9 Calculated mixing enthalpies of the NaCl–MCl₃ (M = Ce, Nd, U, Pu) systems at T = 1125 K using the thermodynamic model presented in this work (NaCl–NdCl₃ and NaCl–CeCl₃), by Yingling et al.³⁵ (NaCl–UCl₃) and by Dumaire et al.²⁸(NaCl–PuCl₃). Experimental data from Gaune-Escard et al.⁶² (NaCl–NdCl₃, open black circles) at T = 1124 K, Papatheodorou et al.⁶⁹ (NaCl–CeCl₃, open downward green triangles) at T = 1118 K and Matsuura et al.⁷² (NaCl–UCl₃, open blue upward triangles) at T = 1113 K. Data of the NaCl–PuCl₃ system (open red squares) were estimated using the method of Davis and Rice.¹⁴

3.2.3 Simulant chemistry in NaCl–MCl₃ systems. Before an assessment of the simulant representativeness can be made, the melting behaviour of the systems NaCl–UCl₃ and NaCl–PuCl₃ must be addressed. The system NaCl–UCl₃ has been investigated experimentally by Kraus et al.,⁷¹ Sooby et al.⁴⁰ and Yingling et al.³⁵ The former reported the use of thermal analysis to obtain their results without further specifying their measurement method, whereas Sooby et al. and Yingling et al. used DSC. Both Kraus et al. and Sooby et al. interpret this system as a simple binary eutectic system. Yingling et al., however, suggest that an intermediate compound with the composition NaU₂Cl₇ (or Na₃U₅Cl₁₈) exists at elevated temperatures, based on their XRD measurements. Yingling et al. fit their thermodynamic model to the liquidus and eutectic equilibria of Kraus et al. and Sooby et al., rather than those they measured themselves. Given the results obtained in this work in the NdCl₃ and CeCl₃ systems, we hypothesize that a similar homogeneity range could exist (i.e. Na_3xU_2−xCl₆), although it might be stable only at high temperatures to match with the DSC data. Complementary studies are needed to verify this hypothesis. In this work, the assessment of Yingling et al. is largely retained, with a slight re-optimization to account for a difference in the end-members thermodynamic functions: Yingling et al. use both UCl₃ and U₂Cl₆ as end-members, which is not the case in this work.

The available experimental data for the NaCl–PuCl₃ system is much less abundant than for the other NaCl–MCl₃ systems (M = Ce, Nd, U). Bjorklund et al.⁵³ used a combination of thermal analysis (TA) and DTA to investigate the system, and concluded that it is a simple binary eutectic system with no intermediates or solid solubility. Dumaire et al.²⁸ presented a thermodynamic assessment of this system using the same formalism as used in this work. Their assessment of this binary system is therefore retained here as well. However, given the similarities between the NdCl₃ and PuCl₃ systems, the existence of a similar intermediate (Na_3xPu_2−xCl₆) needs to be explored by dedicated experiments.

The representativeness of the selected simulants in the NaCl–MCl₃ systems is shown in Fig. 10. In section 4.2, this study will be expanded by adding the comparison with the MgCl₂–MCl₃ (M = Ce, Nd, U, Pu) systems. Fig. 10 shows that the liquidus of the NaCl–PuCl₃ system is very close to that of the NaCl–NdCl₃ system. The systems NaCl–CeCl₃ and NaCl–UCl₃ show a similar slope of the liquidus to the PuCl₃ and NdCl₃ systems, but the difference in melting point between these simulants and PuCl₃ leads to a significant deviation of the melting temperature. The observed eutectic composition is similar for all four systems, as shown in Table 8. The eutectic composition and temperature of the NaCl–NdCl₃ system is closest to that of the NaCl–PuCl₃ system, though the latter can be once more explained by the aforementioned difference in melting point of the end-members.

Fig. 10 Calculated phase diagrams of the systems NaCl–NdCl₃ (solid black line) and NaCl–CeCl₃ (dashed blue line), for which the thermodynamic models were developed in this work, and NaCl–UCl₃ (dashed red line) using the thermodynamic model of Yingling et al.,³⁵ slightly altered to account for the different end-members. The models are compared to the experimental data on the NaCl–PuCl₃ system (open black circles) presented by Bjorklund et al.⁵³

Table 8 Eutectic equilibria in the NaCl–MCl₃ (M = Ce, Nd, U, Pu) systems as calculated with the thermodynamic models presented in this chapter

System	x 1	T 1 (K)	Source
PuCl3	0.385	725	Dumaire et al.^28
NdCl3	0.355	718	This work
CeCl3	0.303	778	This work
UCl3	0.337	794	This work

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4 Modelling NaCl-MgCl₂-MCl₃ (M = Ce, Nd, U, Pu) systems

4.1 Binary systems

As mentioned previously, the thermodynamic model of the NaCl–MgCl₂ system was taken from a previous work.¹⁸ The thermodyamic models of the systems MgCl₂–MCl₃ (M = Ce, Nd, U, Pu) are presented in this section, and were optimized based on the available data in the literature.

All systems MgCl₂–MCl₃ (M = Ce, Nd, U, Pu) modelled in this section are simple binary eutectic systems, with no reported intermediates or solid solubility. The MgCl₂−NdCl₃ system has been investigated experimentally by Vogel et al.⁷³ using DTA. Sun et al.⁷⁴ measured the MgCl₂−CeCl₃ system using thermal analysis, without further specifying their measurement technique. The system MgCl₂−UCl₃ has been investigated by Desyatnik et al.⁷⁵ using differential thermal analysis (DTA), and they did not detect any solid solubility using XRD. Finally, the MgCl₂−PuCl₃ system has been modeled based on the experimental investigation by Johnson et al.⁷⁶ In the absence of experimental mixing enthalpy data for any of the systems, the mixing enthalpy of these systems has been estimated with the method of Davis and Rice.¹⁴

The systems MgCl₂−UCl₃ and MgCl₂−PuCl₃ have been modelled previously by Beneš et al.³¹ and are incorporated in the JRCMSD.³¹ In order to have our thermodynamic model agree with the estimated mixing enthalpy data, these systems have been reoptimized in this work. The phase diagrams of the systems MgCl₂−CeCl₃, MgCl₂−UCl₃, MgCl₂−NdCl₃ and MgCl₂−PuCl₃ are presented in Fig. 11, 12, 13 and 14, respectively. The calculated mixing enthalpies of these systems are given in Fig. 15, along with the estimated data using the method of Davis and Rice. The CALPHAD model reproduces the experimental phase diagram data well, as well as the estimated mixing enthalpies for the systems.

Fig. 11 Phase diagram of the MgCl₂−CeCl₃ system, calculated with the thermodynamic model presented in this work and compared to the experimental data from Sun et al.⁷⁴

Fig. 12 Phase diagram of the MgCl₂−UCl₃ system calculated with the thermodynamic model presented in this work, compared to the experimental data from Desyatnik et al.⁷⁵

Fig. 13 Phase diagram of the MgCl₂−NdCl₃ system, calculated with the thermodynamic model presented in this work and compared to the experimental data from Vogel et al.⁷³

Fig. 14 Phase diagram of the MgCl₂−PuCl₃ system calculated with the thermodynamic model presented in this work, compared to the experimental data from Johnson et al.⁷⁶

Fig. 15 Mixing enthalpy of the MgCl₂–MCl₃ systems (M = Ce, Nd, U, Pu) calculated at T = 1123 K, compared to data estimated using the method of Davis and Rice.¹⁴

4.2 Simulant chemistry in MgCl₂–MCl₃ systems

With the optimized phase diagrams in Fig. 11–14, we can continue the assessment of the simulant of choice in this work. Fig. 16 shows the comparison between the experimental data for the MgCl₂–PuCl₃ system, and the thermodynamic models for the MgCl₂–MCl₃ (M = Ce, Nd, U) systems, like in section 3.2.3 for the NaCl–MCl₃ (M = Ce, Nd, U, Pu) systems. Similar to the aforementioned systems with NaCl, the difference in melting point of the MCl₃ (M = Ce, U) end-member causes a difference in melting behaviour compared to the PuCl₃ system on the MCl₃-rich side of the phase diagram, which is not the case for the NdCl₃ system. The eutectic compositions and temperatures of the MgCl₂–MCl₃ systems are given in Table 9. This table shows that while the eutectic temperature of the CeCl₃ system is marginally closer to that of the PuCl₃ system, the composition of the NdCl₃ system is almost identical to that of the PuCl₃ system.

Fig. 16 Calculated phase diagrams of the systems MgCl₂−NdCl₃ (solid black line), MgCl₂−CeCl₃ (dashed blue line) and MgCl₂−UCl₃ (dashed red line) compared to the experimental data on the MgCl₂−PuCl₃ system (open black circles) presented by Johnson et al.⁷⁶

Table 9 Eutectic equilibria in the MgCl₂–MCl₃ (M = Ce, Nd, U, Pu) systems as calculated with the thermodynamic models presented in this chapter

System	x 1	T 1 (K)
PuCl3	0.382	922
NdCl3	0.383	906
CeCl3	0.308	934
UCl3	0.285	953

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4.3 Ternary systems

From the assessed binary systems, extrapolations to ternary systems NaCl-MgCl₂-MCl₃ (M = Ce, Nd, U, Pu) have been made without the addition of ternary excess parameters. This was done because there are no experimental data in the ternary systems available to the best of our knowledge, and to be consistent with the JRCMSD.³¹ The projected liquidus surface of the ternary systems NaCl-MgCl₂-NdCl₃ and NaCl-MgCl₂-PuCl₃ are presented in Fig. 17 and 18, respectively.

Fig. 17 Projected liquidus surface of the NaCl-MgCl₂-NdCl₃ system, calculated with the thermodynamic model presented in this work. Phases A–H listed on the ternary diagram are the primary crystallization phases. Phases listed are NaCl (A), Na₆MgCl₈ (B), Na₂MgCl₄ (C), NaMgCl₃ (D), Na₂Mg₃Cl₈ (E), MgCl₂ (F), NdCl₃ (G) and Na_3xNd_2−xCl₆ (H). The calculated ternary eutectic equilibria are presented in Table 10.

Fig. 18 Projected liquidus surface of the NaCl-MgCl₂-PuCl₃ system, calculated with the thermodynamic model presented in this work. Phases A–G listed on the ternary diagram are the primary crystallization phases. Phases listed are NaCl (A), Na₆MgCl₈ (B), Na₂MgCl₄ (C), NaMgCl₃ (D), Na₂Mg₃Cl₈ (E), MgCl₂ (F) and PuCl₃ (G). The calculated ternary eutectic equilibria are presented in Table 10.

As seen in Fig. 17 and 18, the projected liquidus surface of the NaCl-MgCl₂-NdCl₃ and NaCl-MgCl₂-PuCl₃ systems are similar. This is also seen in Table 10, in which the ternary equilibria are presented. Table 10 also shows that the number of ternary invariant compositions found using our thermodynamic model are different compared to those of Beneš et al. This is because in our model of the NaCl–MgCl₂ system, we used four intermediate compounds (Na₆MgCl₈, Na₂MgCl₄, NaMgCl₃ and Na₂Mg₃Cl₈), whereas Beneš et al. used two (Na₂MgCl₄ and NaMgCl₃). However, the compositions and temperatures of the ternary invariant equilibria predicted by Beneš et al. are close to compositions at which our thermodynamic model also predicts invariant equilibria.

Table 10 Calculated ternary invariant equilibria in the NaCl-MgCl₂-MCl₃ systems (M = Nd, Pu)

x(NaCl)	x(MgCl2)	x(MCl3)	T (K)	Invariant equilibrium
NaCl-MgCl 2 -NdCl 3 – This work
0.419	0.328	0.252	782	MgCl2 + NdCl3 + Na3xNd2−xCl6
0.499	0.336	0.165	714	MgCl2 + Na3xNd2−xCl6 + Na2Mg3Cl8
0.635	0.121	0.244	702	NaCl + Na6MgCl8 + Na3xNd2−xCl6
0.569	0.275	0.156	692	Na2Mg3Cl8 + NaMgCl3 + Na3xNd2−xCl6
0.596	0.236	0.167	688	NaMgCl3 + Na2MgCl4 + Na3xNd2−xCl6
0.585	0.257	0.158	688	Na2MgCl4 + Na6MgCl8 + Na3xNd2−xCl6
NaCl-MgCl 2 -PuCl 3 – This work
0.487	0.405	0.107	724	MgCl2 + PuCl3 + PuCl3
0.608	0.125	0.267	700	NaCl + Na6MgCl8 + PuCl3
0.554	0.310	0.136	692	Na2Mg3Cl8 + NaMgCl3 + PuCl3
0.570	0.282	0.148	687	NaMgCl3 + Na2MgCl4 + PuCl3
0.580	0.255	0.165	688	Na2MgCl4 + Na6MgCl8 + PuCl3
NaCl-MgCl 2 -PuCl 3 – Beneš et al. ^37
0.632	0.171	0.196	697	NaCl + PuCl3 + Na2MgCl4
0.582	0.295	0.124	706	NaMgCl3 + Na2MgCl4 + PuCl3
0.521	0.389	0.090	722	MgCl2 + PuCl3 + NaMgCl3

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Furthermore, the liquidus projections of the ternary systems NaCl-MgCl₂-CeCl₃ and NaCl-MgCl₂-UCl₃ are presented in Fig. 19 and 20, respectively. The ternary invariant equilibria shown on the liquidus projections in these figures are also listed in Table 11, along with the predicted invariant equilibria by Beneš et al.³⁷ Like in Table 10, the difference in the number of invariant equilibria found by Beneš et al. and our model is explained by the different amount of intermediate compounds present in the models. Again, like in the NaCl-MgCl₂-PuCl₃ system, the invariant equilibria calculated by Beneš et al. agree with our thermodynamic model. Additionally, when comparing the liquidus surfaces of all NaCl-MgCl₂-MCl₃ (M = Ce, Nd, U, Pu) systems, it reinforces the notion that Nd is more accurate as a simulant for Pu than either Ce or U. The behaviour of CeCl₃ in the molten salt systems presented in this chapter is closer to that of UCl₃, hence Ce could be used as a simulant for U instead.

Fig. 19 Projected liquidus surface of the NaCl-MgCl₂-CeCl₃ system, calculated with the thermodynamic model presented in this work. Phases listed A–H on the ternary diagram are the primary crystallization phases at that composition. Phases listed are NaCl (A), Na₆MgCl₈ (B), Na₂MgCl₄ (C), NaMgCl₃ (D), Na₂Mg₃Cl₈ (E), MgCl₂ (F), CeCl₃ (G) and Na_3xCe_2−xCl₆ (H). The calculated ternary equilibria are presented in Table 11.

Fig. 20 Projected liquidus surface of the NaCl-MgCl₂-UCl₃ system, calculated with the thermodynamic model presented in this work. Phases listed A–H on the ternary diagram are the primary crystallization phases at that composition. Phases listed are NaCl (A), Na₆MgCl₈ (B), Na₂MgCl₄ (C), NaMgCl₃ (D), Na₂Mg₃Cl₈ (E), MgCl₂ (F), UCl₃ (G) and NaU₂Cl₇ (H). The calculated ternary eutectic equilibria are presented in Table 11.

Table 11 Calculated ternary invariant equilibria in the NaCl-MgCl₂-MCl₃ systems (M = Ce, U)

x(NaCl)	x(MgCl2)	x(MCl3)	T (K)	Invariant equilibrium
NaCl-MgCl 2 -CeCl 3 – This work
0.417	0.490	0.093	787	MgCl2 + CeCl3 + Na3xCe2−xCl6
0.645	0.261	0.095	733	MgCl2 + Na3xCe2−xCl6 + Na2Mg3 Cl8
0.499	0.462	0.039	730	NaCl + Na6MgCl8 + Na3xCe2−xCl6
0.570	0.394	0.036	710	Na2Mg3Cl8 + NaMgCl3 + Na3xCe2−xCl6
0.599	0.359	0.042	708	NaMgCl3 + Na2MgCl4 + Na3xCe2−xCl6
0.588	0.374	0.038	706	Na2MgCl4 + Na6MgCl8 + Na3xCe2−xCl6
NaCl-MgCl 2 -UCl 3 – This work
0.639	0.260	0.101	735	MgCl2 + UCl3 + NaU2Cl7
0.500	0.481	0.020	733	MgCl2 + NaU2Cl7 + Na2Mg3Cl8
0.568	0.402	0.029	711	NaCl + Na6MgCl8 + NaU2Cl7
0.597	0.360	0.043	709	Na2Mg3Cl8 + NaMgCl3 + NaU2Cl7
0.596	0.361	0.042	707	NaMgCl3 + Na2MgCl4 + NaU2Cl7
0.587	0.378	0.036	707	Na2MgCl4 + Na6MgCl8 + NaU2Cl7
NaCl-MgCl 2 -UCl 3 – Beneš et al. ^37
0.637	0.251	0.112	719	NaCl + UCl3 + Na2MgCl4
0.578	0.356	0.066	720	NaMgCl3 + Na2MgCl4 + UCl3
0.520	0.433	0.047	731	MgCl2 + UCl3 + NaMgCl3

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5 Summary

We demonstrate in this work, by comparing the phase diagrams of the NaCl–MCl₃ and MgCl₂–MCl₃ systems (M = Ce, Nd, U, Pu), that NdCl₃ is the most suitable simulant for the melting behaviour of multicomponent systems containing PuCl₃, while CeCl₃ is most adapted for UCl₃-based systems.

Furthermore, a structural investigation of the intermediate compounds in the NaCl–NdCl₃ and NaCl–CeCl₃ systems has been performed. The existence of the intermediate compound Na_3xRE_2−xCl₆ (RE = Ce, Nd) has been found as well as the solubility limits. This solid solubility has been included in the re-assessment of the thermodynamic models. This solid solution is not included in the existing models for the systems NaCl–UCl₃ and NaCl–PuCl₃ by Yingling et al.³⁵ and Dumaire et al.,²⁸ respectively, but further experimental investigation is recommended to investigate the possible intermediate compounds Na_3xAn_2−xCl₆ (An = U, Pu) in view of the strong similarities between the actinide and lanthanide systems discussed here.

Moreover, the models for the simple binary eutectic systems MgCl₂–MCl₃ (M = Ce, Nd, U, Pu) have been optimized based on the experimental data reported in the literature, as well as the estimated mixing enthalpies using the method of Davis and Rice. Finally, ternary extrapolations to the systems NaCl-MgCl₂-MCl₃ (M = Ce, Nd, U, Pu) have been made and compared to values reported in the literature, showing a good agreement between the two, confirming that in these higher order systems, NdCl₃ and CeCl₃ are the most suitable simulants for PuCl₃ and UCl₃ based salts, respectively.

Conflicts of interest

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

Data availability

The experimental and computational data obtained in this work has been reported in the main text in Tables 2–11 and Fig. 1–20, as well as Fig. B.1–B.8 of the Appendix.

Supplementary information (SI) is available. See DOI: https://doi.org/10.1039/d5dt01486g.

Acknowledgements

The authors of this paper gratefully acknowledge financial support from the ORANO group, as well as the help of L. M. T. de Geus and N. T. H. ter Veer with the synchrotron-XRD experiments. We acknowledge the European Synchrotron Radiation Facility (ESRF) for provision of synchrotron X-ray radiation facilities under proposal number MA-6356.

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