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CALPHAD Modeling of the (Na,Cs,Mg,Nd,Pu)(Cl,I) System

Journal article (2026) - Dennis C. Alders, Dhivya Panneerselvam, Elisa Capelli, Karl W. Krämer, Rudy J.M. Konings, Anna L. Smith
A thermodynamic model of the molten salt system (Na,Cs,Mg,Pu,Nd)(Cl,I) has been developed in this work to assess the effect of CsI on the melting and vaporization behavior of the nuclear fuel in molten salt reactors. Investigation using X-ray diffraction (XRD) and differential scanning calorimetry (DSC) of the binary systems NdCl3–NdI3 and MgI2–NdI3, as simulant systems for the analogous Pu system, is presented for the first time. Both systems were found to be binary eutectic systems, with solid solutions NdCl3–3xI3x (hexagonal in space group P63/m) and NdCl3yI3–3y (orthorhombic in space group Cmcm) in the NdCl3–NdI3 system, and Mg1–xNdxI2+x (hexagonal in space group P 3 m1) in the MgI2–NdI3 system. Additionally, the system CsI–MgI2 was scrutinized using DSC, confirming the available experimental data in the literature. Furthermore, the investigation of the reciprocal diagonals in the systems (Na,Nd)(Cl,I), (Cs,Mg)(Cl,I), (Mg,Nd)(Cl,I), and (Cs,Nd)(Cl,I) is presented, allowing the characterization of the quaternary behavior of these salts. Based on the experimental data obtained in this work, a CALPHAD model is presented using the quasi-chemical formalism in the quadruplet approximation for the liquid solution. With the aim of modeling the complete (Na,Cs,Mg,Pu)(Cl,I) system, the binary systems NaCl–CsCl, CsCl–MgCl2, CsCl–NdCl3, NaI–CsI, and CsI–NdI3 were reassessed based on data from the literature. Furthermore, a CALPHAD model of the PuCl3 and PuI3 systems is also presented using Nd as a simulant for Pu in molten halide salts. With the developed thermodynamic models, calculations were finally performed to assess the fission product retention of Cs and I in a molten chloride environment. As opposed to their behavior in molten fluorides, the fission products are well retained in the fuel matrix up to concentrations of at least 5 mol%. ...
Journal article (2026) - Nick T.H. ter Veer, Ian M. Berkel, Indu Dhiman, Jean Christophe Griveau, Eric Colineau, Andries van Hattem, Sebastian Drange Couweleers, Rudy J.M. Konings, Anna L. Smith
The structural, thermodynamic, and magnetic properties of Na2CrCl4 have been investigated to provide fundamental insights into this ternary halide relevant to chloride-based molten salt reactor systems. Room-temperature powder X-ray and neutron diffraction confirm a monoclinic (P21/c) structure and phase purity. Neutron diffraction measurements at 4.6 K reveal additional magnetic reflections indexed with (Formula presented), indicating the onset of long-range antiferromagnetic order. Low-temperature heat capacity measurements in the range 2–300 K show a pronounced λ-type anomaly at TN = 8.5 ± 0.5 K, with an associated magnetic entropy Smag = 11.9 ± 0.4 J K–1 mol –1 consistent with antiferromagnetic ordering of high-spin Cr2+ (S = 2), a second-order phase transition. The standard molar entropy at 298.15 K, Sm°(298.15 K) = 256.8 ± 7.7 J K–1 mol –1, is slightly lower than previous CALPHAD assessments of the NaCl-CrCl2 system. Magnetic susceptibility measurements also confirm antiferromagnetic behavior, with a Curie–Weiss fit giving μeff = 5.57 ± 0.05 μB and θCW = −15.0 ± 1.0 K. Compared to the related ferromagnetic chlorides K2CrCl4, Rb2CrCl4, and Cs2CrCl4, Na2CrCl4 exhibits a distinctly lower ordering temperature and antiferromagnetic structure, likely due to variations in lattice geometry and exchange interactions. These results provide the first experimental thermodynamic parameters for Na2CrCl4, contributing to refining phase diagrams and corrosion models in chloride salt systems. ...

The effect of Np substitution on the first-order transition at low concentration ((Formula presented) 0.05)

Journal article (2026) - R. J.M. Konings, E. Colineau, J. C. Griveau, K. Popa, S. O. Vălu
The low-temperature heat capacity and temperature-dependent DC magnetic susceptibility of neptunium-doped UO2 samples (U1−y[jls-end-space/]Npy[jls-end-space/])O2 with y = 0.01, 0.03 and 0.05 were measured. A strong effect was observed on the magnetic anomaly typical for UO2[jls-end-space/], both the Néel temperature and transition entropy. By comparison with data for other (U1−y[jls-end-space/], My[jls-end-space/])O2 solid solutions, it is suggested that this effect can be explained by the lattice strain resulting from substitution on the anion sublattice, and electron spin interaction. ...

Thermodynamic modelling, experimental investigation and application calculations

In this study, new insights into the solid state chemistry and melting behaviour of the Image 1001 system are presented, building on results in the simulant system Image 1002. Our studies have revealed the solubility of U in the high-temperature β[jls-end-space/]-phase of BaCl2 (i.e Image 1003 ) and an intermediate compound, Ba3U2Cl12, which has led us to revisit or present for the first time the phase diagrams of this system accordingly. Furthermore, we present revised thermodynamic models for the systems Image 1004, Image 1005, Image 1006 and Image 1007 (AE = Sr, Ba) based on existing literature data. With the constructed multi-component database Image 1008, the effect of fission products on the melting behaviour of molten chloride salts containing uranium and thorium is investigated through higher order phase equilibria calculations. ...
Journal article (2026) - Rania Zaier, Andries van Hattem, Brandon N. de Waal, Rudy J.M. Konings, Anna L. Smith, Philippe Zeller, Christine Guéneau
A comprehensive thermodynamic assessment of the Cs-Pb system was performed with the CALPHAD method using the experimental thermodynamic and phase diagram data available in literature supplemented by density functional theory (DFT) calculations. The exact nature of the stable compounds in the phase diagrams reported in the literature is uncertain, except for CsPb and Cs4Pb9 whose crystalline structures are well known. Therefore, DFT calculations were performed to calculate the energy of formation at 0 K of different possible compounds with various crystalline structures. The enthalpies of formation of the compounds CsPb, Cs4Pb9, and CsPb4, found to be the stable ones by DFT, were then used in the CALPHAD model. The result of this process has enabled the development of a more refined phase diagram comparing to experimental ones, providing more comprehensive insights into the phase equilibria in this system. Moreover, the CALPHAD model succeeded in describing the peculiar behavior of the heat capacity of the liquid phase, by using an ionic two-sublattice model (Cs+1)P(Pb−1,Va,Pb)Q which takes into account the short-range ordering taking place at the equimolar composition CsPb, related to the formation of clusters Cs4Pb4, modelled as (Cs+1) (Pb−1). The model allows for the prediction of important thermodynamic properties, which are of interest for a range of applications, including lead-cooled fast reactors and perovskite-based photovoltaics. ...
Journal article (2026) - Andries van Hattem, John Vlieland, Eric Colineau, Jean Christophe Griveau, Rudy J.M. Konings, Anna L. Smith
The chemistry following cladding failure in Lead-cooled Fast Reactors involves the interaction between lead (Pb) coolant and the Joint Oxyde Gain (JOG)-phase, mostly composed of dicesium molybdate (Cs2MoO4). A thermodynamic analysis of coolant-JOG phase chemical interaction as studied via the scenario of Pb-Cs2MoO4 chemical interaction is reported. Measurements of the standard thermodynamic properties of α -Cs2Pb(MoO4)2 are presented. The enthalpy of formation of α -Cs2Pb(MoO4)2 is measured to be -(2570.7 ± 2.3) kJ · mol−1 using solution calorimetry, while the standard entropy is determined to be (399 ± 12) J · K−1·mol−1 using thermal-relaxation calorimetry. Thermodynamic calculations show that Cs2Pb(MoO4)2 is in several cases thermodynamically stable under conditions typical for operation of Lead-cooled Fast Reactors. This means Cs2Pb(MoO4)2 can form in cladding failure scenarios. ...
Journal article (2025) - N. T.H. ter Veer, W. K. de Vries, C. T.C. Heyning, T. F. Abbink, J. A. Ocádiz-Flores, A. E. Gheribi, R. J.M. Konings, A. L. Smith
The structural, thermochemical, and thermophysical properties of the AnCl4, and NaCl-AnCl4 (An = Th, U) melts were investigated using molecular dynamics (MD) simulations based on the Polarisable Ion Model (PIM). New force fields were proposed and used to compute key properties including density, thermal expansion, enthalpy of mixing, heat capacity, as well as the local structure and chemical speciation in the molten (Na, An)Clx (An = Th, U) salts. Thermodynamic models were then developed based on the CALPHAD method, using both PIM-MD and experimental data as input. Employing the modified quasichemical formalism in the quadruplet approximation for the liquid solution, the models account for the chemical speciation in the melt as calculated by MD simulations, and reproduce well phase equilibria in those systems. In particular, the models included monomeric and dimeric species to represent the physical nature of the ionic melt, which shows progressive oligomerisation with increasing AnCl4 fraction. Our studies confirm that the melt becomes highly volatile at high AnCl4 fractions, which is discussed in light of the results obtained herein. ...
Journal article (2025) - Jacobus Boshoven, Abibatou Ndiaye, Bertrand Morel, Marco Cologna, Jean François Vigier, Ramon Carlos Marquez, Rudy J.M. Konings, Karin Popa
We show that a homogeneous single-phase mixed oxide is obtained by blending and sintering commercial UO2 and nanocrystalline PuO2 powder; whereas, under the same conditions, conventional PuO2 powder obtained from oxalate precipitation and composed of platelets, yields two-phase mixed oxide. The use of nanometric PuO2 results in a larger final grain size. ...
Journal article (2025) - J. Y. Colle, J. N. Zappey, O. Beneš, M. Cologna, T. Wiss, R. J.M. Konings
The presence of CsI in nuclear fuel has long been debated. Its formation significantly decreases volatility, thereby reducing the rate at which iodine and cesium are released from the reactor core during a nuclear accident. A series of samples were investigated by Knudsen Effusion Mass Spectrometry (KEMS) in order to determine whether CsI is present in irradiated nuclear fuel. The examined samples were pure CsI, CsI exposed to gamma radiation, CsI-doped UO2 simulated fuel and irradiated LWR fuel samples. The CsI and CsI-doped samples were examined to establish boundary conditions for the detection of CsI by KEMS. These samples indicated that the presence of CsI in fuel is characterized by three mass spectrometric signals Cs+, I+ and CsI+, with a peak ratio of CsI+ and I+ of 1:0.7. The examinations of irradiated fuels showed none of these characteristics and hence no evidence that CsI is present in irradiated LWR nuclear fuel, at least after a storage period of years. ...
The thermochemistry of the quaternary molten salt system NaCl-NaI-MgCl2-MgI2 has been studied using an experimental and thermodynamic modeling approach. The binary subsystems NaCl-NaI and NaCl-MgCl2 were reassessed based on existing data in the literature. The binary subsystem NaI-MgI2 was subjected to a renewed experimental investigation, to complement and revisit the data in the literature. The subsystem MgCl2-MgI2 was investigated for the first time in this work using Differential Scanning Calorimetry (DSC). Furthermore, the phase equilibria in the pseudobinary phase diagrams of NaCl-MgI2 and NaI-MgCl2 in the quaternary system were investigated by DSC, while the condensed phases in the quaternary system were investigated using X-ray diffraction (XRD). A thermodynamic model of the quaternary system was developed using the CALPHAD (CALculation of PHase Diagrams) method with the quadruplet approximation in the modified quasichemical model for the liquid phase, and two-sublattice polynomial models for the solid solution phases. With this model, the liquidus surface of the NaCl-NaI-MgCl2-MgI2 quaternary system has been described for the first time. ...
Journal article (2025) - Dennis C. Alders, Ana Sacristán-Civera, Mädchen Wolff, Elisa Capelli, Eleanor L. Bright, Christoph Hennig, Rudy J.M. Konings, A. L. Smith
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.

Graphical abstract: 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 ...

Material selection, fabrication and thermoelectric effect demonstration

Journal article (2025) - Jean François Vigier, Daniel Freis, Rudy J.M. Konings, Jérémie Manaud, Philippe E. Raison, Patrick Lajarge, Sebastien Gardeur, Sorin Octavian Vălu, Jean Christophe Griveau, More authors...
This work provides an in-depth analysis of the extensive research and development activities on americium-based ceramics for space applications, particularly as heat source for radioisotope power generation. Our pioneering efforts focus on synthesizing and characterizing various americium ceramics with fluorite, monazite, perovskite, zircon, and pyrochlore structures, and assessing their potential for use in Radioisotope Power Systems (RPSs). This study identifies uranium-stabilised cubic americium oxide as the best candidate among the ceramic forms analysed, due to its superior stability and performance under extreme conditions relevant to space missions. The review emphasises the unique facilities and methodologies employed, including remote-handling techniques and advanced material characterization, to overcome the challenges posed by the high radiation dose and specific activity of 241Am when working with gram quantities. ...
Journal article (2025) - D.C. Alders, D.J. Cette, R. Konings, A.L. Smith
Correction for ‘Experimental investigation and thermodynamic modelling assessment of the AECl2–NdCl3 (AE = Sr, Ba) systems’ by D. C. Alders et al., Phys. Chem. Chem. Phys., 2024, 26, 24041–24057, https://doi.org/10.1039/D4CP01784F.

The reference list in the originating article was incorrect. The correct list of references is shown here.

The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers. ...
Journal article (2025) - A. van Hattem, L.M.T. de Geus, A. Sacristán Civera, B.J.R. Dankelman, S.D. Couweleers, Christoph Hennig, Jean Christophe Griveau, R. Konings, A.L. Smith, More authors...
The detailed crystal structure as well as the heat capacity at low temperature and standard entropy of Ba2MoO5 are reported for the first time. High-resolution X-ray and neutron diffraction were employed to reveal the structural features of this compound. Ba2MoO5 has a six-coordinated Mo and a strongly negative excess volume with respect to the binary oxides. X-ray absorption near edge structure (XANES) spectroscopy at the Mo K-edge shows Mo to be in the oxidation state 6+. The pre-edge peak in the XANES spectrum indicates a distorted octahedral environment, in line with the results from diffraction studies and FDMNES calculations. The standard entropy and heat capacity of Ba2MoO5 at 298.15 K, determined with a thermal-relaxation technique, are calculated to be respectively 223.2 ± 7 and 184.7 ± 5 J·K–1·mol–1. The obtained thermodynamic properties are discussed in the context of the literature reports on molybdate compounds. ...
Journal article (2025) - Jacobus Boshoven, Jean François Vigier, Philipp Pöml, Abibatou Ndiaye, Bertrand Morel, Rudy J.M. Konings, Karin Popa, Marco Cologna
We compare typical reductive sintering conditions for U, Pu mixed oxides (4 h at 1700 °C in Ar/6 % H2 + 1200 ppm H2O) with lower temperature and mildly oxidative conditions (2 h at 1200 °C in CO/CO2 = 1/9) and report on the resulting microstructures and homogeneity. We show that lower temperature and mildly oxidative conditions, without cover gas change, can give close-to stoichiometric, crack-free MOX pellets with a relative density of ∼ 95 %, and we propose ways to improve the homogenisations of PuO2 and UO2 and increase the grain size. ...
Journal article (2025) - Evangelia D. Mooren, Walter Bonani, Karin Popa, Stefaan Van Winckel, Rafael Alvarez-Sarandes, Rudy J.M. Konings, Glenn Beersaerts, Sonja Schreurs, Wouter Schroeyers
We present a two-step procedure for treating contaminated liquid waste generated during the processing of uranium, specifically residual uranium-contaminated liquid after precipitation. After precipitating U(IV) as sodium diuranate under alkaline conditions, the resulting solution was solidified by immobilising it in an alkali-activated material. Static leaching tests indicated excellent material stability in water. Exposing the material to aggressive chemical conditions (nitric acid) resulted in slow and incomplete dissolution of uranium (and of structural elements) from a thin superficial layer with further passivation. Characterisation of the solid phase was performed to assess the stability of the alkali-activated material under the tested conditions. ...
Journal article (2024) - D.C. Alders, D.J. Cette, R. Konings, A.L. Smith
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. ...
The thermodynamic and thermo-physical properties of the molten salt system [Formula presented] have been investigated using an experimental and modelling approach. This molten salt system includes a single intermediate compound [Formula presented], whose structure has been investigated using X-ray and neutron diffraction. Furthermore, this system exhibits solubility of [Formula presented] in [Formula presented] at high temperatures up to a concentration of around 25% [Formula presented] at 1060 K. Additionally, our measurements show solubility of [Formula presented] in [Formula presented] up to about 5% [Formula presented] at 973 K. The investigation of these solid solutions has been performed using quenching experiments and subsequent post-characterisation by X-ray diffraction (XRD). Phase diagram equilibria have also been investigated using differential scanning calorimetry (DSC). Using the aforementioned information on phase transitions, intermediate compound formation, and mutual solid solubility, a thermodynamic assessment of the system 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 a two-sublattice polynomial model. ...
Journal article (2024) - Milena Milich, Hunter B. Schonfeld, Konstantinos Boboridis, Davide Robba, Luka Vlahovic, Rudy J.M. Konings, Jeffrey L. Braun, John T. Gaskins, Niraj Bhatt, More authors...
We measure the thermal conductivity of solid and molten tungsten using steady state temperature differential radiometry. We demonstrate that the thermal conductivity can be well described by application of Wiedemann-Franz law to electrical resistivity data, thus suggesting the validity of Wiedemann-Franz law to capture the electronic thermal conductivity of metals in their molten phase. We further support this conclusion using ab initio molecular dynamics simulations with a machine-learned potential. Our results show that at these high temperatures, the vibrational contribution to thermal conductivity is negligible compared to the electronic component. ...
Journal article (2024) - Andries van Hattem, Robert Dankelman, Eric Colineau, Jean-Christophe Griveau, Kathy Dardenne, Jörg Rothe, Sebastian Couweleers, Rudy J.M. Konings, Anna L. Smith
A combined experimental and modelling study into the Pb-Mo-O system has been conducted in view of the safety analysis for lead-cooled nuclear systems. The thermal expansion and low-temperature heat capacity of the ternary compounds PbMoO4 and Pb2MoO5 have been determined experimentally, as well as the melting enthalpy of PbMoO4. Moreover, XANES measurements have confirmed the hexavalent oxidation state of Mo in PbMoO4 and Pb2MoO5.

A thermodynamic model of the ternary system including the ternary phases PbMoO4, Pb2MoO5 and Pb5MoO8 has also been developed in this work based on the CALPHAD methodology. For the first time, an ionic two-sublattice model is used for the liquid phase, while the compound energy formalism is used for the solid phases. ...