A First-Principles Description of Liquid BeF2and Its Mixtures with LiF: 1. Potential Development and Pure BeF2

Compositional transferability of deep potential in molten LiF-BeF2 and LaF3 mixtures: prediction of density, viscosity, and local structure

The accumulation of lanthanide fission products carries the risk of altering the structure and properties of the nuclear fuel carrier salt LiF-BeF2 (Flibe), thereby downgrading the operating efficiency and safety of the molten salt reactor. However, the condition-limited experimental measurements, spatiotemporal-limited first-principles calculations, and accuracy-limited classical dynamic simulations are unable to capture the precise local structure and reliable thermophysical properties of heterogeneous molten salts. Therefore, the deep potential (DP) of LaF3 and Flibe molten mixtures is developed here, and DP molecular dynamics simulations are performed to systemically study the densities, diffusion coefficients, viscosities, radial distribution functions and coordination numbers of multiple molten Flibe + xLaF3, the quantitative relationships between these properties and LaF3 concentration are investigated, and the potential structure-property relationships are analyzed. Eventually, the transferability of DP on molten Flibe + LaF3 with different formulations as well as the predictability of structures and properties are achieved at the nanometer spatial scale and the nanosecond timescale.

Probing the local structure of FLiBe melts and solidified salts by in situ high-temperature NMR

The 2LiF-BeF2 (FLiBe) salt melt is considered the primary choice for a coolant and fuel carrier for the generation IV molten salt reactor (MSR). However, the basics of ionic coordination and short-range ordered structures have been rarely reported due to the toxicity and volatility of beryllium fluorides, as well as the lack of suitable high-temperature in situ probe methods. In this work, the local structure of FLiBe melts was investigated in detail using the newly designed HT-NMR method. It was found that the local structure was comprised of a series of tetrahedral coordinated ionic clusters (e.g., BeF42-, Be2F73-, Be3F104-, and polymeric intermediate-range units). Li+ ions were coordinated by BeF42- ions and the polymeric Be-F network through the analysis of the NMR chemical shifts. Using solid-state NMR, the structure of solid FLiBe solidified mixed salts was confirmed to form a 3D network structure, significantly similar to those of silicates. The above results provide new insights into the local structure of FLiBe salts, which verifies the strong covalent interactions of Be-F coordination and the specific structural transformation to the polymeric ions above 25% BeF2 concentration.

Constant-Potential Molecular Dynamics Simulations of Molten-Salt Double Layers for FLiBe and FLiNaK

We report the results of constant-potential molecular dynamics simulations of the double- layer interface between molten FLiBe and FLiNaK fluoride mixtures and idealized solid electrodes. Employing methods similar to those used in studies of chloride double layers, we compute the structure and differential capacitance of molten fluoride electric double layers as a function of applied voltage. The role of molten salt structure is probed through comparisons between FLiBe and FLiNaK, which serve as models for strong and weak associate- forming salts, respectively. In FLiBe, screening involves changes in Be-F-Be angles and alignment of the oligomers parallel to the electrode, while in FLiNaK the electric field is screened mainly by rearrangement of individual ions, predominantly the polarizable potassium cation.

Computational methods to simulate molten salt thermophysical properties

Molten salts are important thermal conductors used in molten salt reactors and solar applications. To use molten salts safely, accurate knowledge of their thermophysical properties is necessary. However, it is experimentally challenging to measure these properties and a comprehensive evaluation of the full chemical space is unfeasible. Computational methods provide an alternative route to access these properties. Here, we summarize the developments in methods over the last 70 years and cluster them into three relevant eras. We review the main advances and limitations of each era and conclude with an optimistic perspective for the next decade, which will likely be dominated by emerging machine learning techniques. This article is aimed to help researchers in peripheral scientific domains understand the current challenges of molten salt simulation and identify opportunities to contribute.

Solvation of anthraquinone and TEMPO redox-active species in acetonitrile using a polarizable force field

Redox-active molecules are of interest in many fields, such as medicine, catalysis, or energy storage. In particular, in supercapacitor applications, they can be grafted to ionic liquids to form so-called biredox ionic liquids. To completely understand the structural and transport properties of such systems, an insight at the molecular scale is often required, but few force fields are developed ad hoc for these molecules. Moreover, they do not include polarization effects, which can lead to inaccurate solvation and dynamical properties. In this work, we developed polarizable force fields for redox-active species anthraquinone (AQ) and 2,2,6,6-tetra-methylpiperidinyl-1-oxyl (TEMPO) in their oxidized and reduced states as well as for acetonitrile. We validate the structural properties of AQ, AQ^•-, AQ^2-, TEMPO^•, and TEMPO⁺ in acetonitrile against density functional theory-based molecular dynamics simulations and we study the solvation of these redox molecules in acetonitrile. This work is a first step toward the characterization of the role played by AQ and TEMPO in electrochemical and catalytic devices.

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.

Temperature-Dependent Properties of Molten Li2BeF4 Salt Using Ab Initio Molecular Dynamics

Molten lithium tetrafluoroberyllate (Li₂BeF₄) salt, also known as FLiBe, with a 2:1 mixture of LiF and BeF₂ is being proposed as a coolant and solvent in advanced nuclear reactor designs, such as the molten salt reactor or the fluoride salt cooled high-temperature reactor. We present the results on the structure and properties of FLiBe over a wide range of temperatures, 0-2000 K, from high-throughput ab initio molecular dynamics simulation using a supercell model of 504 atoms. The variations in the local structures of solid and liquid FLiBe with temperature are discussed in terms of a pair distribution function, coordination number, and bond angle distribution. The temperature-dependent electronic structure and optical and mechanical properties of FLiBe are calculated. The optical and mechanical property results are reported for the first time. The results above and below the melting temperature (∼732 K) are compared with the experimental data and with data for crystalline FLiBe. The electronic structure and interatomic bonding results are discussed in correlation with the mechanical strength. A novel concept of total bond order density (TBOD), an important quantum mechanical parameter, is used to characterize the internal cohesion and strength in the simulated models. The results show a variation in the rate of change in properties in solid and liquid phases with anomalous behavior across the melting region. The observed trend is the decrease in mechanical strength, band gap, and TBOD in a nonlinear fashion as a function of temperature. The refractive index shows a surprising minimum at 850 K, among the tested temperatures, which lies above the melting point. These findings provide a new platform to understand the interplay between the temperature-dependent structures and properties of FLiBe salt.

Modeling LiF and FLiBe Molten Salts with Robust Neural Network Interatomic Potential

Lithium-based molten salts have attracted significant attention due to their applications in energy storage, advanced fission reactors, and fusion devices. Lithium fluorides and particularly 66.6%LiF-33.3%BeF₂ (Flibe) are of considerable interest in nuclear systems, as they show an excellent combination of favorable heat transfer, neutron moderation, and transmutation characteristics. For nuclear salts, the range of possible local structures, compositions, and thermodynamic conditions presents significant challenges in atomistic modeling. In this work, we demonstrate that atom-centered neural network interatomic potentials (NNIPs) provide a fast method for performing molecular dynamics of molten salts that is as accurate as ab initio molecular dynamics. For LiF, these potentials are able to accurately reproduce ab initio interactions of dimers, crystalline solids under deformation, crystalline LiF near the melting point, and liquid LiF at high temperatures. For Flibe, NNIPs accurately predict the structures and dynamics at normal operating conditions, high-temperature-pressure conditions, and in the crystalline solid phase. Furthermore, we show that NNIP-based molecular dynamics of molten salts are scalable to reach long time scales (e.g., nanosecond) and large system sizes (e.g., 10⁵ atoms) while maintaining ab initio density functional theory accuracy and providing more than 3 orders of magnitude of computational speedup for calculating structure and transport properties.

Examination of the short-range structure of molten salts: ThF4, UF4, and related alkali actinide fluoride systems

The short-range structures of LiF-ThF₄, NaF-AnF₄, KF-AnF₄, and Cs-AnF₄ (An = Th, U), were probed using in situ high temperature Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy. Signally, the EXAFS spectra of pure molten ThF₄ and UF₄ were measured for the first time. The data were interpreted with the aid of Molecular Dynamics (MD) and standard fitting of the EXAFS equation. As in related studies, a speciation distribution dominated by [AnF_x]^4-x (x = 7, 8, 9) coordination complexes was observed. The average coordination number was found to decrease with the increasing size of the alkali cation, and increase with AnF₄ content. An average coordination number close to 6, which had not been detected before in melts of alkali actinide fluorides, was seen when CsF was used as solvent.

The progression of thermodynamic anomalies in MX2 networks with local tetrahedral geometries

Key thermodynamic anomalies in density and compressibility, as well as the related stability limits, are determined using an ionic model for BeF₂ which includes many-body polarization terms. BeF₂ is chosen as an example of an archetypal network-forming system whose structure can be rationalised in terms of connected local tetrahedral coordination polyhedra. The anion dipole polarizability (which effectively controls the bond angles linking neighbouring tetrahedra) is used as a single free parameter in order to help rationalise the changes in the anomaly locations in phase space, whilst all other potential parameters remain fixed. The anomalies and stability limits systematically shift to lower temperature and higher pressure as the anion polarizability is increased. At high dipole polarizabilities the temperature of maximum density anomaly locus becomes suppressed into the supercooled regime of the phase space. The movements of the anomaly loci are analysed in terms of the network structure and the correlation with the inter-tetrahedral bond angles is considered. The high sensitivity of the anomalies to the details of the potential models applied is discussed with reference to previous works on related systems. The relationship to analogous studies on Stillinger-Weber liquids is discussed.

Structure and dynamics in network-forming materials

The study of the structure and dynamics of network-forming materials is reviewed. Experimental techniques used to extract key structural information are briefly considered. Strategies for building simulation models, based on both targeting key (experimentally-accessible) materials and on systematically controlling key model parameters, are discussed. As an example of the first class of materials, a key target system, SiO₂, is used to highlight how the changing structure with applied pressure can be effectively modelled (in three dimensions) and used to link to both experimental results and simple structural models. As an example of the second class the topology of networks of tetrahedra in the MX₂ stoichiometry are controlled using a single model parameter linked to the M-X-M bond angles. The evolution of ordering on multiple length-scales is observed as are the links between the static structure and key dynamical properties. The isomorphous relationship between the structures of amorphous Si and SiO₂ is discussed as are the similarities and differences in the phase diagrams, the latter linked to potential polyamorphic and 'anomalous' (e.g. density maxima) behaviour. Links to both two-dimensional structures for C, Si and Ge and near-two-dimensional bilayers of SiO₂ are discussed. Emerging low-dimensional structures in low temperature molten carbonates are also uncovered.

Insight into structural phase transitions from the decoupled anharmonic mode approximation

We develop a formalism (decoupled anharmonic mode approximation, DAMA) that allows calculation of the vibrational free energy using density functional theory even for materials which exhibit negative curvature of the potential energy surface with respect to atomic displacements. We investigate vibrational modes beyond the harmonic approximation and approximate the potential energy surface with the superposition of the accurate potential along each normal mode. We show that the free energy can stabilize crystal structures at finite temperatures which appear dynamically unstable at T  =  0. The DAMA formalism is computationally fast because it avoids statistical sampling through molecular dynamics calculations, and is in principle completely ab initio. It is free of statistical uncertainties and independent of model parameters, but can give insight into the mechanism of a structural phase transition. We apply the formalism to the perovskite cryolite, and investigate the temperature-driven phase transition from the P21/n to the Immm space group. We calculate a phase transition temperature between 710 and 950 K, in fair agreement with the experimental value of 885 K. This can be related to the underestimation of the interaction of the vibrational states. We also calculate the main axes of the thermal ellipsoid and can explain the experimentally observed increase of its volume for the fluorine by 200-300% throughout the phase transition. Our calculations suggest the appearance of tunneling states in the high temperature phase. The convergence of the vibrational DOS and of the critical temperature with respect of reciprocal space sampling is investigated using the polarizable-ion model.

Sparse Cyclic Excitations Explain the Low Ionic Conductivity of Stoichiometric Li_{7}La_{3}Zr_{2}O_{12}

We have performed long time scale molecular dynamics simulations of the cubic and tetragonal phases of the solid lithium-ion electrolyte Li_{7}La_{3}Zr_{2}O_{12} (LLZO), using a first-principles parametrized interatomic potential. Collective lithium transport was analyzed by identifying dynamical excitations: persistent ion displacements over distances comparable to the separation between lithium sites, and stringlike clusters of ions that undergo cooperative motion. We find that dynamical excitations in c-LLZO (cubic) are frequent, with participating lithium numbers following an exponential distribution, mirroring the dynamics of fragile glasses. In contrast, excitations in t-LLZO (tetragonal) are both temporally and spatially sparse, consisting preferentially of highly concerted lithium motion around closed loops. This qualitative difference is explained as a consequence of lithium ordering in t-LLZO and provides a mechanistic basis for the much lower ionic conductivity of t-LLZO compared to c-LLZO.

Coordination numbers and physical properties in molten salts and their mixtures

Mixtures of trivalent metal halides with alkali halides are involved in many technologies but, from a more fundamental and general perspective, are worthy of study as interesting systems in which to examine the relationship between atomic-scale structure and physical properties. Here we examine the relationship between the viscosity and local and longer range structural measures in such mixtures where the trivalent metal cations span a significant size range and exhibit different behaviours in the dependence of their viscosity on the mixture composition. We characterise the structure and dynamics of the first coordination shell and the relationship between its structural relaxation time and the shear relaxation time of the mixture (the Maxwell relaxation time). We are then led to an examination of the structure of the networks which progressively form between the trivalent metal cations as their concentration increases in the mixtures. Here we find significant differences between small and larger cations, sufficient to explain the different behaviour of their viscosities. We draw attention to the similarities and differences of these networks with those which form in highly viscous, glass-forming materials like BeF₂:LiF.

Ceria co-doping: synergistic or average effect?

Ceria (CeO2) co-doping has been suggested as a means to achieve ionic conductivities that are significantly higher than those in singly doped systems. Rekindled interest in this topic over the last decade has given rise to claims of much improved performance. The present study makes use of computer simulations to investigate the bulk ionic conductivity of rare earth (RE) doped ceria, where RE = Sc, Gd, Sm, Nd and La. The results from the singly doped systems are compared to those from ceria co-doped with Nd/Sm and Sc/La. The pattern that emerges from the conductivity data is consistent with the dominance of local lattice strains from individual defects, rather than the synergistic co-doping effect reported recently, and as a result, no enhancement in the conductivity of co-doped samples is observed.

Water and water-like liquids: relationships between structure, entropy and mobility

Liquids with very diverse underlying interactions share the thermodynamic and transport anomalies of water, including metalloids, ionic melts and mesoscopic fluids. The generic feature that characterises such water-like liquids is a density-driven shift in the nature of local order in the condensed phases. The key semiquantitative relationships between structural order, thermodynamics and transport that are necessary in order to map out the consequences of this common qualitative feature for liquid-state properties and phase transformations of such systems are reviewed here. The application of these ideas to understand and model tetrahedral liquids, especially water, is discussed and possible extensions to other complex fluids are considered.

A transferable ab initio based force field for aqueous ions

We present a new polarizable force field for aqueous ions (Li(+), Na(+), K(+), Rb(+), Cs(+), Mg(2 +), Ca(2 +), Sr(2 +), and Cl(-)) derived from condensed phase ab initio calculations. We use maximally localized Wannier functions together with a generalized force and dipole-matching procedure to determine the whole set of parameters. Experimental data are then used only for validation purposes and a good agreement is obtained for structural, dynamic, and thermodynamic properties. The same procedure applied to crystalline phases allows to parametrize the interaction between cations and the chloride anion. Finally, we illustrate the good transferability of the force field to other thermodynamic conditions by investigating concentrated solutions.

A new model of chemical bonding in ionic melts

We developed a new physical model to predict macroscopic properties of inorganic molten systems using a realistic description of inter-atomic interactions. Unlike the conventional approach, which tends to overestimate viscosity by several times, our systems consist of a set of ions with an admixture of neutral atoms. The neutral atom subsystem is a consequence of the covalent/ionic state reduction, occurring in the liquid phase. Comparison of the calculated macroscopic properties (shear viscosity and self-diffusion constants) with the experiment demonstrates good performance of our model. The presented approach is inspired by a significant degree of covalent interaction between the alkali and chlorine atoms, predicted by the coupled cluster theory.

The effects of topology on the structural, dynamic and mechanical properties of network-forming materials

The effects of network topology on the static structural, mechanical and dynamic properties of MX(2) network-forming liquids (with tetrahedral short-range order) are discussed. The network topology is controlled via a single model parameter (the anion polarizability) which effectively constrains the inter-tetrahedral linkages in a physically transparent manner. Critically, it is found to control the balance between the stability of corner- and edge-sharing tetrahedra. A potential rigidity transformation is investigated. The vibrational density of states is investigated, using an instantaneous normal model analysis, as a function of both anion polarizability and temperature. A low frequency peak is seen to appear and is shown to be correlated with the fraction of cations which are linked through solely edge-sharing structural motifs. A modified effective mean atom coordination number is proposed which allows the appearance of the low frequency feature to be understood in terms of a mean field rigidity percolation threshold.

Thermal conductivity of ionic systems from equilibrium molecular dynamics

Thermal conductivities of ionic compounds (NaCl, MgO, Mg(2)SiO(4)) are calculated from equilibrium molecular dynamics simulations using the Green-Kubo method. Transferable interaction potentials including many-body polarization effects are employed. Various physical conditions (solid and liquid states, high temperatures, high pressures) relevant to the study of the heat transport in the Earth's mantle are investigated, for which experimental measures are very challenging. By introducing a frequency-dependent thermal conductivity, we show that important coupled thermoelectric effects occur in the energy conduction mechanism in the case of liquid systems.