Polarizable Ion Model Research Articles

Computing the solubility of argon and xenon in molten sodium chloride and potassium chloride salts

Molten salt reactors (MSRs) offer significant advancements in nuclear reactor safety and efficiency by operating at higher temperatures and lower pressures compared to traditional reactors. A critical aspect of MSR operation involves understanding the solubility of fission byproducts, particularly noble gases, in the molten salts used. This study employs molecular dynamics (MD) simulations to compute Henry’s law constants and enthalpies of solvation for argon and xenon in molten sodium chloride (NaCl) and potassium chloride (KCl). We developed a new pairwise potential for the noble gas and salt interactions based on first principles calculations. We then used this potential to calculate Henry’s law constants of the two gases in the molten salts, which were modeled using both a rigid ion model (RIM) and a polarizable ion model (PIM). The solubility calculations, performed using the Widom insertion method, show qualitative agreement with limited experimental data, highlighting the temperature dependence and greater solubility of both gases in KCl compared to NaCl. Additionally, free volume analysis elucidated the role of available space within the molten salts in governing solubility trends. Our findings suggest that PIM trajectories provide more reliable predictions for noble gas solubility than RIM due to their accurate density representation. These results enhance understanding of gas solubility in MSR environments, and the methods can be readily extended to other systems.

Analysis of the Transport Properties of Alkaline-earth Halides MX<sub>2</sub> (M = Ca, Sr, Ba, and X = F, Cl, Br) by Simulation with a Polarizable Ion Model

Analysis of the Transport Properties of Alkaline-earth Halides MX<sub>2</sub> (M = Ca, Sr, Ba, and X = F, Cl, Br) by Simulation with a Polarizable Ion Model

Structural and transport properties of the molten salt NaCl-KCl-UCl3 using the polarizable ion model

Molecular dynamics simulations are a powerful tool for predicting the properties of molten salts at conditions sometimes challenging to achieve experimentally. Here, they are applied within the framework of the polarizable ion model (PIM) for the investigation of the NaCl-KCl-UCl3 molten salt at two different compositions and for a temperature range between 1000 and 1400 K. This allowed us to understand the impact of sodium and potassium ions on the structure of the solvation shell of uranium ions, as well as predicting their density, viscosity, self-diffusion coefficients and heat capacity at different conditions.

Mechanisms of like-charge attraction in many-body systems

The physics of like-charge attraction in a collinear binary system of N particles has been investigated via a polarizable-ion model. It was found that like-charge attraction between an array of (N−1) type-A particles on the left and a single type-B particle on the right is conditional upon a sufficient degree of dissimilarities between the two types of particles. By assuming that (1) the particles of one type are strongly polarizing (but weakly polarizable) such that the Coulomb fields they produce are dominant all over other electric fields, and that (2) the particles of the other type are strongly polarizable (but weakly polarizing) such that their Coulomb-field-induced dipoles are the only polarization effects worth considering, a good agreement between our approximate analytic theory and exact numerical solutions has been obtained. Our analytic results show that the attractive components of the electrostatic force between the two types of particles could be thought of as arising from imaginary charges induced in the polarized particle(s) by the polarizing ones, resulting in a screening of the real charge(s) in the polarized particle(s). Like-charge attraction occurs if the field contributions from the imaginary charges collectively outweigh the field contribution(s) from the real charge(s).

Capturing the interactions in the BaSnF4 ionic conductor: Comparison between a machine-learning potential and a polarizable force field.

BaSnF4 is a prospective solid state electrolyte for fluoride ion batteries. However, the diffusion mechanism of the fluoride ions remains difficult to study, both in experiments and in simulations. In principle, abinitio molecular dynamics could allow to fill this gap, but this method remains very costly from the computational point of view. Using machine learning potentials is a promising method that can potentially address the accuracy issues of classical empirical potentials while maintaining high efficiency. In this work, we fitted a dipole polarizable ion model and trained machine learning potential for BaSnF4 and made comprehensive comparisons on the ease of training, accuracy and efficiency. We also compared the results with the case of a simpler ionic system (NaF). We show that contrarily to the latter, for BaSnF4 the machine learning potential offers much higher versatility. The current work lays foundations for the investigation of fluoride ion mobility in BaSnF4 and provides insight on the choice of methods for atomistic simulations.

Molecular dynamics study of fission product behaviour in molten [formula omitted]-[formula omitted] salt

The solvation of fission products in fuel salts and the effects due to their accumulation are important factors to understand in molten salt reactor design. In this contribution, we use ab initio Molecular Dynamics (AIMD) and polarizable ion model (PIM) based MD to study the structural and dynamic characteristics of the fission products (Cs, I and Xe) in the model fuel salt ThF4-LiF with different compositions at the infinite dilution limit. We first develop or refine existing PIM potentials to better reproduce the results of AIMD simulations. The AIMD and PIM-MD results are then compared in terms of the structures present in the salt, and the dynamics of their coordination. The results of this study indicate that, at 1200 K and 1400 K the fission products studied here have weak interactions with all composition ranges of fuel salt. This is evident, as first coordination shell associations being generally short-lived, as determined by cage correlation times. The diffusion coefficients determined through PIM-MD match the AIMD results reasonably well. The three fission products studied here are diffuse at similar rates; however, the Cs+ diffusion is slightly lower likely due to its more tightly bound associated F−. With all solutes, the diffusion coefficients decrease with a greater ThF4 fraction. Additionally, the behaviour of these solutes was studied at finite concentration ranges, up to 4 atom %. Here, it was found that the presence of Cs+ has little effect on the density, heat capacity and viscosity. However, these properties were affected by higher I+ and Xe concentrations.

Mechanisms of like-charge attraction in three-body systems

The physics of like-charge attraction in three-body systems has been investigated via a polarizable-ion model. It was found that like-charge attraction is possible for two configurations of a collinear binary system with regular interparticle spacings. For the mirror-symmetric configuration ABA, the dominant mechanism of like-charge attraction between the type-B particle and each type-A particle is the polarization of each type-A particle by the type-B particle. For the mirror-asymmetric configuration AAB, the dominant mechanism of like-charge attraction between the type-B particle and the pair of type-A particles is either the polarization of the pair of type-A particles by the type-B particle, or vice versa. For either configuration, the occurrence of like-charge attraction is conditional upon the presence of dissimilarities in net charge or polarizable volume between the two types of particles, as in the case of a two-particle system. The findings point to a new direction for manipulating interactions of polarizable particles at the micro- or nano-scale.

Computing the Liquidus of Binary Monatomic Salt Mixtures with Direct Simulation and Alchemical Free Energy Methods.

We describe and validate a free-energy-based method for computing the liquidus for binary solid-liquid phase diagrams in molecular simulations of monatomic salts. The method is demonstrated by calculating the liquidus for LiCl-KCl and MgCl2-KCl salt mixtures with the polarizable ion model (PIM). The free-energy-based method is cross-validated with direct coexistence simulations. Both techniques show excellent agreement with one another. Though the predictions of the PIM disagree with experiments, we use our free-energy-based approach to decouple the contributions of liquid mixture nonidealities and pure component solid-liquid equilibrium to the phase diagram. In both mixtures, the PIM accurately reproduces the liquid phase nonidealities but fails to predict the liquidus because it does not accurately predict the pure component melting temperature of LiCl or MgCl2.

Coupled structural-thermodynamic modelling of the molten salt system NaCl-UCl3

Molten chloride salts are ionic liquids in which the anions and cations exhibit network formation. An attractive salt system for use in molten salt reactors is NaCl-UCl3, an ionic liquid with complex non-ideal thermodynamic behaviour due to the formation of short-range order. The relationship between local structure and thermodynamic properties is investigated in this work, in which molecular dynamics simulations using the Polarizable Ion Model (PIM) and thermodynamic modelling by means of the CALPHAD method are combined. The system is simulated for a wide range of temperatures and compositions and various properties are derived derived from molecular dynamics data: density/molar volume, thermal expansion, heat capacity and excess properties including excess molar volume, mixing enthalpy and excess heat capacity. Generally, there is good agreement with previously published experimental data. An in depth analysis of the local structure of the liquid is performed for multiple temperatures. This analysis demonstrates the transition from a molecular liquid consisting of primarily Na+, Cl−, UCl63-/UCl74- at low UCl3 content to a polymeric liquid at high UCl3 content, manifesting itself in the formation of species like U2Cl126-, U3Cl178-, U4Cl2210- etc. Exceeding 40% UCl3, the liquid consists of a three-dimensional network of corner or edge-sharing uranium polyhedra. The output of the MD simulations and experimental data are incorporated into a coupled structural-thermodynamic model for the NaCl-UCl3 system based on the quasi-chemical formalism in the quadruplet approximation, that provides a physical description of the melt and reproduces (in addition to the thermodynamic data) the chemical speciation of uranium polymeric species predicted from the simulations.

Highly disordered ionic distribution in α‐dicalcium silicate for structure relaxation

AbstractDicalcium silicate, which is found in steelmaking slag for dephosphorization, exists as the hexagonal α phase at high temperatures. The α‐dicalcium silicate forms a solid solution with tricalcium phosphate in the entire composition range, although the reason for high solubility of phosphorus remains unclear in view of the crystal structure. It has previously been reported that the crystal structure of α‐dicalcium silicate consists of a symmetric arrangement of Ca2+ ions and SiO44− tetrahedra, although other polymorphs exhibit asymmetric arrangements. However, because the occupation probability of each atomic site in the α polymorph is not limited to unity, it has not been qualified how these ions are exactly arranged. In this study, the ionic distribution in the α polymorph of dicalcium silicate was evaluated by first‐principles calculation based on density functional theory (DFT), as well as by molecular dynamics (MD) simulation with a polarizable ion model optimized by DFT calculation. The results indicated that the completely symmetric ionic arrangement, as reported for the α phase, is the most unstable. Electronic‐state calculation and MD simulation indicated that a highly disordered ionic arrangement spontaneously forms in the α‐phase crystal for structure relaxation when held at high temperatures, or when phosphorus is incorporated.

Experimental and Computational Exploration of the NaF-ThF4 Fuel System: Structure and Thermochemistry.

The structural, thermochemical, and thermophysical properties of the NaF–ThF4 fuel system were studied with experimental methods and molecular dynamics (MD) simulations. Equilibrium MD (EMD) simulations using the polarizable ion model were performed to calculate the density, molar volume, thermal expansion, mixing enthalpy, heat capacity, and distribution of [ThFn]m− complexes in the (Na,Th)Fx melt over the full concentration range at various temperatures. The phase equilibria in the 10–50 mol % ThF4 and 85–95 mol % ThF4 regions of the NaF–ThF4 phase diagram were measured using differential scanning calorimetry, as were the mixing enthalpies at 1266 K of (NaF/ThF4) = (0.8:0.2), (0.7:0.3) mixtures. Furthermore, the β-Na2ThF6 and NaTh2F9 compounds were synthesized and subsequently analyzed with the use of X-ray diffraction. The heat capacities of both compounds were measured in the temperature ranges (2–271 K) and (2–294 K), respectively, by thermal relaxation calorimetry. Finally, a CALPHAD model coupling the structural and thermodynamic data was developed using both EMD and experimental data as input and a quasichemical formalism in the quadruplet approximation. Here, 7- and 8-coordinated Th4+ cations were introduced on the cationic sublattice alongside a 13-coordinated dimeric species to reproduce the chemical speciation, as calculated by EMD simulations and to provide a physical description of the melt.

Computational Modelling of Ceria-Based Solid Oxide Fuel Cell Electrolyte Materials

The significant advances in materials development for solid oxide fuel cells (SOFCs) and modelling techniques have challenged researchers to develop streamlined methodologies aiming at faster and more reliable fabrication of highly efficient cells. Instead of adopting a trial-and-error technique to discover the optimal composition of fuel cell component materials, alternative tools and techniques should be developed for predicting the likely best compositions in a cost-effective and timely manner. Many formulations have been studied for application as SOFC electrolytes over the years and doubly-doped ceria materials have been of considerable recent interest.Here, a simulation methodology to calculate the lattice parameter and the oxygen ion migration energy of ceria-based electrolyte formulations was developed, and the results were analysed and benchmarked against corresponding results obtained experimentally in order to verify the efficacy of the simulation methodology. To this end, a supercell consisting of 2 x 2 x 2 ceria unit cells doubly-doped with samarium and gadolinium was modelled and simulated using molecular mechanics force field methods using the CP2K computational chemistry suite. Two compositional series were modelled with the general formula Ce32-(x+y)SmxGdyO64-(x+y)/2 where x and y are the number of samarium and gadolinium dopant atoms per supercell respectively. The first compositional series, Series One, had equal amounts of dopants but different total dopant concentration with values of x = y = 1, 2, 8, or 16. Series Two had a fixed total dopant concentration (x + y = 8) but different amounts of each dopant in each structure such that x had integer values from 0 to 8 (x = 0 ... 8) and y = 8 - x. Moreover, two doping strategies were simulated for each compositional series depending on how the dopant atoms and resulting vacancies were distributed throughout the crystal. The first doping strategy places one dopant atom in two or more of the eight minicubes comprising the 2 x 2 x 2 supercell for Series One structures and, for Series Two structures, one dopant atom is placed in each minicube starting with one gadolinium atom in each minicube and then progressively replacing one gadolinium atom with one samarium atom in each of the subsequent structures of this series until there is one samarium atom in each minicube. The second doping strategy places the dopants exclusively in the four minicubes that let the dopants be as far as possible from each other. In all cases, the oxygen vacancies are chosen to be the nearest neighbours, i.e., in the nearest lattice positions, to the dopant atoms.For each structure, the lattice parameter was calculated using a cell optimisation technique utilizing the conjugate gradient method where the soft particle mesh Ewald (SPME) sums method and the DIPole Polarizable Ion Model (DIPPIM) for the long- and short-range potentials respectively. To estimate the activation energies associated with hopping of an oxygen ion from a specific site to a neighbouring site in the structures studied, the following steps were applied: The positions of the dopant atoms in the pure crystal were assigned.The at a distance within 3.0 Å was generated.The climbing image nudged elastic band (CI-NEB) method was applied to determine all the activation barriers of the doped crystal.The average energy barrier was calculated. The results obtained for the lattice parameter were comparable to those observed experimentally and exhibited the same linear trends satisfying Vegard's law, albeit the trend for the fixed dopant concentration series had a slight negative slope. Simulation-derived values of the activation energy showed the same trends as those observed experimentally. The simulations also produced transition state curves showing the saddle point and energy minima for each structure; information that could not be obtained experimentally and that can shed some light on the mechanism of ionic conduction. It was found that the position of oxygen vacancies within the crystal structure play a key role in determining the activation energy of ion hopping, and that the different patterns of doping do not affect the overall trends in lattice parameter and activation energy. They do however produce different patterns in the energy profiles contributing to the energy barriers to ion hopping within the crystal structure.This work demonstrates that computational simulations of SOFC electrolyte materials provide results comparable with those obtained experimentally and could also provide insights into the mechanisms of ionic conduction. The incongruence of the computational and experimental results was attributed to the limitations of the molecular mechanics force field methodology utilised, with the expectation that an ab initio density functional theory (DFT) calculation would yield closer conformance. Figure 1

New insights and coupled modelling of the structural and thermodynamic properties of the LiF-UF4 system

LiF-UF4 is a key binary system for molten fluoride reactor technology, which has not been scrutinized as thoroughly as the closely related LiF-ThF4 system. The phase diagram equilibria in the system LiF-UF4 are explored in this work with X-ray diffraction (XRD) and differential scanning calorimetry (DSC). The short-range ordering in the molten salt solution is moreover surveyed with Extended X-ray Absorption Fine Structure spectroscopy (EXAFS) and interpreted using a combination of standard fitting of the EXAFS data and Molecular Dynamics (MD) simulations with a Polarizable Ion Model (PIM) potential. The density, excess molar volume, thermal expansion, heat capacity, and enthalpy of mixing are extracted from the MD simulations across a range of temperatures and compositions; the behavior is non-ideal, with reasonably good agreement with the experimental data. Also calculated is the distribution of heteropolyanions in the liquid solution, and modelled using the quasi-chemical formalism in the quadruplet approximation taking into account the existence of the single-shell complexes [UF7]3−, [UF8]4−, and the dimeric species [U2F14]6−. Subjecting the optimization of the excess Gibbs energy parameters of the liquid solution to the constraints of the phase diagram data and local structure of the melt as derived from the EXAFS and coupled MD simulations, a CALPHAD-type assessment is proposed, linking structural and thermodynamic properties, with a rigorous physical description of the melt.

Thermal and Transport Properties of Molten Chloride Salts with Polarization Effect on Microstructure

Molten chloride salt is recognized as a promising heat transfer and storage medium in concentrating solar power in recent years, but there is a serious lack for thermal property data of molten chloride salts. In this work, local structures and thermal properties for molten chloride salt—including NaCl, MgCl2, and ZnCl2—were precisely simulated by Born–Mayer–Huggins (BMH) potential in a rigid ion model (RIM) and a polarizable ion model (PIM). Compared with experimental data, distances between cations, densities, and heat capacities of molten chloride slats calculated from PIM agree remarkably better than those from RIM. The polarization effect brings an extra contribution to screen large repulsive Coulombic interaction of cation–cation, and then it makes shorter distance between cations, larger density and lower heat capacity. For NaCl, MgCl2, and ZnCl2, PIM simulation deviations of distances between cations are respectively 3.8%, 3.7%, and 0.3%. The deviations of density and heat capacity for NaCl between PIM simulation and experiments are only 0.6% and 2.2%, and those for MgCl2 and ZnCl2 are 0.7–10.7%. As the temperature rises, the distance between cations increases and the structure turns into loose state, so the density and thermal conductivity decrease, while the ionic self-diffusion coefficient increases, which also agree well with the experimental results.

Comparison of fixed charge and polarizable models for predicting the structural, thermodynamic, and transport properties of molten alkali chlorides.

Results from extensive molecular dynamics simulations of molten LiCl, NaCl, KCl, and RbCl over a wide range of temperatures are reported. Comparison is made between the "Polarizable Ion Model" (PIM) and the non-polarizable "Rigid Ion Model" (RIM). Densities, self-diffusivities, shear viscosities, ionic conductivities, and thermal conductivities are computed and compared with experimental data. In addition, radial distribution functions are computed from ab initio molecular dynamics simulations and compared with the two sets of classical simulations as well as experimental data. The two classical models perform reasonably well at capturing structural and dynamic properties of the four molten alkali chlorides, both qualitatively and often quantitatively. With the singular exception of liquid density, for which the PIM is more accurate than the RIM, there are few clear trends to suggest that one model is more accurate than the other for the four alkali halide systems studied here.

SEM-Drude Model for the Accurate and Efficient Simulation of MgCl2-KCl Mixtures in the Condensed Phase.

There is a long history of models that to different extents reproduce structural and dynamical properties of high-temperature molten salts. Whereas rigid ion models can work fairly well for some of the monovalent salts, polarizability is fundamentally important when small divalent or multivalent cations are combined with significantly polarizable anions such as Cl- to form networked liquids that display a first sharp diffraction peak. There are excellent polarizable ion models (PIMs) for these systems, but there has been little success with the less expensive Core-Shell type models, which are often described as unwieldy or difficult to fit. In this article, we present the Sharma-Emerson-Margulis (SEM)-Drude model for MgCl2/KCl mixtures that with the same ingredients used in the latest and most accurate PIM models overcome the aforementioned obstacles at significantly less computational cost; structural and dynamical properties are for all practical purposes very similar to what we obtain from the PIM but typical simulations can be more than 30 times faster. This has allowed us not only to expand our recent studies on the temperature and composition dependence of intermediate range order in MgCl2/KCl mixtures but also to access transport properties that were simply too costly to properly sample in our recently published studies.

Molecular dynamics simulations of structural and transport properties of molten NaCl-UCl3 using the polarizable-ion model

Molten chlorides are a good choice for fast-spectrum molten salt reactors, but many of their thermophysical and transport properties are not available. In this work we use classical molecular dynamics simulations based on the polarizable-ion model to investigate the structural and transport properties of NaCl-UCl3 at various U3+ mole fractions. Molar volume, coordination structure and number, network structure, heat capacity, diffusivity, and ion conductivity have been simulated. We find strong variation of the second coordination shells (U-U and Cl-Cl) with U3+ mole fraction. This is consistent with the increasing network formation or oligomerization of UCl63− and UCl74− units via shared Cl− ions. The movement of Cl− is strongly coupled with U3+ as the U-Cl network structures become dominant in the mixture when the mole fraction of UCl3 is >0.25. Evaluation of a heat-transfer figure-of-merit suggests that 0.20 to 0.30 is an optimal mole fraction of UCl3 to achieve both lower operating temperatures and better heat transfer.

A new approach for coupled modelling of the structural and thermo-physical properties of molten salts. Case of a polymeric liquid LiF-BeF2

The (Li,Be)Fx fluoride salt is an ionic liquid with complex non-ideal thermodynamic behaviour due to the formation of short-range order. In this work, we explore the relationship between local structure, thermo-physical and thermodynamic properties in this system using a multidisciplinary approach that couples molecular dynamics simulations using the Polarizable Ion Model (PIM) and thermodynamic modelling assessment using the CALPHAD method. The density, thermal expansion, viscosity, thermal conductivity, molar and mixing enthalpies and heat capacity of the (Li,Be)Fx melt are extracted from the polarizable ionic interaction potentials and investigated across a wide range of compositions and temperatures. The agreement with the available experimental data is generally very good. The local structure is also examined in detail, in particular the transition between a molecular liquid with Li+, BeF42− and F− predominant species at low BeF2 content, and a polymeric liquid at high BeF2 content, with the formation of polymers (Be2F73−, Be3F104−, Be4F135−, etc.), and finally of a three-dimensional network of corner-sharing tetrahedrally coordinated Be2+ cations for pure BeF2. Based on the available experimental information and the output of the MD simulations, we moreover develop for the first time a coupled structural-thermodynamic model for the LiF-BeF2 system based on the quasi-chemical formalism in the quadruplet approximation, that provides a physical description of the melt and reproduces (in addition to the thermodynamic data) the chemical speciation of beryllium polymeric species predicted from the simulations.

Study of the NaF-ScF3 system as a molten bath for production of Sc alloys: A combination of NMR and molecular dynamics simulations

In situ high temperature NMR spectroscopy was used to characterize the NaF-ScF3 melt over a wide range of compositions. 19F, 23Na, and 45Sc NMR spectra were acquired in NaF-ScF3 melts of up to 70 mol% of ScF3. The interpretation of all experimental results obtained in situ in the melt is significantly enhanced by the contribution of Molecular Dynamics (MD) calculations. A new interatomic potential for the molten NaF-ScF3 system was developed by using a Polarizable Ion Model (PIM). The potential parameters were obtained by force-fitting to density functional theory (DFT) reference data. MD simulations were combined with further DFT calculations to determine NMR chemical shifts for 19F, 23Na, and 45Sc. The agreement between the experimental NMR data and the corresponding calculated data from our applied computational protocol indicated the polymerization and network formation in the melt. Additionally, the density and the electrical conductivity in the molten state were calculated from the statistical analysis of ionic trajectories obtained through MD simulations.

Classical Polarizable Force Field To Study Hydrated Charged Clays and Zeolites

Following our previous works on dry clays, we extend the classical polarizable ion model (PIM) to hydrated dioctahedral clays by considering Na-, Cs-, Ca-, and Sr-montmorillonites in the mono- and bihydrated states. The parameters of the force field are determined by optimizing the atomic forces and dipoles on density functional theory calculations. The simulation results are compared with results obtained with CLAYFF force field and validated in comparison with the experiment. The X-ray diffraction patterns calculated from classical molecular dynamics simulations performed with the PIM force field are in very good agreement with experiments. We also demonstrate the transferability of PIM force field to other aluminosilicates: here, a faujasite-type zeolite compensated with Na⁺ with a significant improvement in cation locations compared to nonpolarizable force fields.