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A.L. Smith

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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) - 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 (2026) - Troy Munro, Randall Chiu, Melissa A. Rose, Sara Mastromarino, Anna L. Smith, J. A. Ocádiz Flores, Sean Scott, John Vlieland, More Authors
The development, operation, and regulation of nuclear reactors that utilize molten salts as fuel or as heat transfer media require knowledge of the thermal properties of the salt systems and quantification of the corresponding uncertainties. Knowledge of molten salt properties is also necessary for applications in material synthesis, processing, separations, solar thermal power generation, and energy storage. A round robin was conducted with national laboratory and university participants from twenty-one laboratories in five countries to compare property measurements, to better understand uncertainties, and to identify possible best practices. Two salt mixtures, each from a common batch, were distributed to participants for evaluation: equimolar NaCl-KCl and 45.0LiF-13.7NaF-41.3KF mol % (FLiNaK). Measurements were performed to determine the major constituent composition, oxygen content, density, thermal expansivity, melting point, and thermal conductivity. Error analysis was performed on each measurement for uncertainty quantification for each type of property that was explored. The resulting discussion of the methodologies used in this work is meant to lay the groundwork for the development of standard methods and reference materials for future high-temperature property measurements on halide melts. ...
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) - 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. ...

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 (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. ...
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. ...

Prioritizing standardisation needs and bridging gaps

Journal article (2025) - A. Jenet, P. Souček, K. F. Nilsson, A. Caverzan, E. Capelli, P. Paviet, M. Rose, D. Holcomb, A. Smith, More Authors...
This article outlines key standardisation needs for specific topics related to molten salt reactors (MSR), namely measurements of thermo-physical properties, safety evaluation, qualification of fuels and fuel cycles, and codes & standards for materials and components. It also explores strategies for bridging gaps in international standardisation, harmonisation and collaboration, and raises the importance of building MSR prototypes and investing in testing facilities. This article is based on a survey and direct inputs from a Putting Science into Standards workshop held on 18 and 19 March 2024 and organised by the European Commissions’ Joint Research Centre (JRC) and European Committee for Standardization (CEN) and European Committee for Electrotechnical Standardization (CENELEC). The workshop gathered 100 experts from research, industry and policy making to discuss the development and standardisation of MSR technologies. By working together at European and international levels, standardisation will be a key instrument to enable the development and commercialisation of mature MSR technologies to support the European Union's goal of achieving fully functioning small modular reactors by 2030. ...
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 ...
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) - 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) - Isabelle Morlaes, Stefano Lorenzi, Sophie Deanesi, Anna L. Smith, Dirk C. Visser, Evzen Losa, Jaén A. Ocádiz Flores, Elisa Capelli, Sylvie Delpech, More authors...
Molten Salt Reactors (MSR) are Generation IV nuclear systems in which the fuel is dissolved in a molten salt circulating through the primary system. There is growing interest in this advanced technology in Europe, but also in the US, China, South Korea, Japan and Russia, due to their inherently high safety level, flexibility, reliability, load-following capabilities, and potential for multi-recycling of materials contained in light-water reactors’ spent nuclear fuels. These advantages could position MSRs as ideal complements to other decarbonized energy sources in a future sustainable energy mix. In this respect, it is probably one of the most promising advanced technologies and, at the same time, the least mature and studied one. Two ongoing EURATOM-funded projects, MIMOSA and ENDURANCE projects are exploring molten salt reactors’ safety and performance features, as well as fuel cycle aspects, in order to assess and demonstrate their potential for future deployment in Europe. The MIMOSA and ENDURANCE projects have the common objective of improving the maturity of MSR technology. The MIMOSA project develops and analyses multi-recycling strategies for the European Union based on the use of MSR and demonstrates several key aspects of their technical feasibility and performance by both calculations and experimental investigations. The ENDURANCE project supports the safe operation and the development of Critical Technology Elements by connecting design developers and industry with universities and research centres while ensuring alignment with regulatory requirements. Whereas ENDURANCE is in its starting phase, MIMOSA has already delivered important results. ...
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. ...
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. ...
Journal article (2024) - Kaifeng Zheng, Nicholas Marcella, Anna L. Smith, Anatoly I. Frenkel
Thermal properties of actinides in molten salts are linked to the strongly disordered local environment of actinide ions. We illustrate both the limitations of the commonly used fitting method for analysis of extended X-ray absorption fine structure (EXAFS) spectra in molten UF4 and a possible solution using an “objective neural network-EXAFS” (ONNE) method. ONNE provides both extraction of the pair distribution function, as validated by its application to the EXAFS spectra calculated on molecular dynamics trajectory, and the EXAFS data reconstruction. The ONNE analysis of the molten UF4 has revealed reduction of the first nearest neighbor U-F coordination number, expansion of the U-F bond length, and smaller contribution to the second shell compared to current molecular dynamics models. This method is therefore an attractive alternative to conventional EXAFS analysis and molecular dynamics simulations for studies of disordered environment of actinides in molten salts. ...
Lithium-based fluoride salts are one of the leading options as fuel matrix in Molten Salt Reactors. The understanding of their thermodynamic behavior, e.g. chemical stability, activity, as well as heat transfer properties, in the reactor’s environment is crucial for the safety assessment. In this work, the chemical equilibria of lithium fluoride with two important fission products dissolved in the salt matrix, namely barium fluoride and zirconium fluoride, are considered. The phase diagrams of the binary systems LiF-BaF2, LiF-ZrF4 and BaF2-ZrF4, as well as the ternary system LiF-BaF2-ZrF4 are assessed by the CALPHAD (CALculation of PHase Diagram) method using the quasichemical model in the quadruplet approximation for the liquid solution. These models are based on literature and new experimental data, and provide a good overview of the stability of intermediate compounds formed in the various systems and of the liquid solution. ...
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) - T. Dumaire, O. Walter, O. Beneš, J. C. Griveau, E. Colineau, R. J.M. Konings, A. L. Smith
This work examines the thermochemistry of the chromium difluoride CrF2 corrosion product in the molten [Formula presented] fuel salt system. Through a combination of experimental investigations and thermodynamic modeling assessment, the study elucidates the thermodynamic properties, phase diagram equilibria, and overall thermodynamic behavior of CrF2 corrosion product, following dissolution from a structural material to the molten salt fuel environment. In this work, two different synthesis methods were developed for pure CrF2, further allowing to experimentally measure the phase equilibria in the [Formula presented], [Formula presented], and [Formula presented] systems. Then, thermodynamic models were developed using the CALPHAD method based on the quasichemical model in the quadruplet approximation. ...
Journal article (2023) - Andries van Hattem, Jean Christophe Griveau, Eric Colineau, Anton J.E. Lefering, Rudy J.M. Konings, Anna L. Smith
The heat capacities of CsPbI3, Cs4PbI6, and Cs3Bi2I9 were studied using low-temperature thermal relaxation calorimetry in the temperature range of 1.9-300 K. The three compounds are insulators, with no electronic contribution to the heat capacity. None of them show detectable anomalies in the studied temperature window. Thermodynamic properties at standard conditions are derived. Previously reported results on Cs3Bi2I9 are not fully consistent with the present findings. Moreover, the magnetic susceptibilities of the three title compounds were measured. ...