Prediction of the thermophysical properties of molten salt fast reactor fuel from first-principles

In Situ Determination of Speciation and Local Structure of NaCl-SrCl2 and LiF-ZrF4 Molten Salts

Understanding the local environment of the metal atoms in salt melts is important for modeling the properties of melts and predicting their behavior and thus helping enable the development of technologies such as molten salt reactors and solar-thermal power systems and new approaches to recycling rare-earth metals. Toward that end, we have developed an in situ approach for measuring the coordination of metals in molten salt coupling X-ray absorption spectroscopy (XAS) and Raman spectroscopy. Our approach was demonstrated for two salt mixtures (1.9 and 5 mol % SrCl₂ in NaCl, 0.8 and 5 mol % ZrF₄ in LiF) at up to 1100 °C. Near-edge (X-ray absorption near-edge structure, XANES) and extended X-ray absorption fine structure (EXAFS) spectra were measured. The EXAFS response was modeled using ab initio FEFF calculations. Strontium's first shell is observed to be coordinated with chlorine (Sr²⁺-Cl^-) and zirconium's first shell is coordinated by fluorine (Zr⁴⁺-F^-), both having coordination numbers that decrease with increasing temperature. Multiple zirconium complexes are believed to be present in the melt, which may interfere and distort the EXAFS spectra and result in an anomalously low zirconium first shell coordination number. The use of boron nitride (BN) powder as a salt diluent for XAFS measurements was found to not interfere with measurements and thus can be used for investigations of such systems.

Thermodynamic and Transport Properties of LiF and FLiBe Molten Salts with Deep Learning Potentials

Molten salts have attracted interest as potential heat carriers and/or fuel solvents in the development of new Gen IV nuclear reactor designs, high-temperature batteries, and thermal energy storage. In nuclear engineering, salts containing lithium fluoride-based compounds are of particular interest due to their ability to lower the melting points of mixtures and their compatibility with alloys. A machine learning potential (MLP) combined with a molecular dynamics study is performed on two popular molten salts, namely, LiF (50% Li) and FLiBe (66% LiF and 33% BeF₂), to predict the thermodynamic and transport properties, such as density, diffusion coefficients, thermal conductivity, electrical conductivity, and shear viscosity. Due to the large possibilities of atomic environments, we employ training using Deep Potential Smooth Edition (DPSE) neural networks to learn from large datasets of 141,278 structures with 70 atoms for LiF and 238,610 structures with 91 atoms for FLiBe molten salts. These networks are then deployed in fast molecular dynamics to predict the thermodynamic and transport properties that are only accessible at longer time scales and are otherwise difficult to calculate with classical potentials, ab initio molecular dynamics, or experiments. The prospect of this work is to provide guidance for future works to develop general MLPs for high-throughput thermophysical database generation for a wide spectrum of molten salts.

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.

Study of the Partial Charge Transport Properties in the Molten Alumina via Molecular Dynamics

Knowing the charge-transport properties of molten oxides is essential for industrial applications, particularly when attempting to control the energy required to separate a metal from its ore concentrate. Nowadays, in the context of a drastic increase of computational resources, research in industrial process simulation and their optimization is gaining popularity. Such simulations require accurate data as input for properties in a wide range of compositions, temperatures, and mechanical stresses. Unfortunately, due to their high melting points, we observe a severe lack of (reproducible) experimental data for many of the molten oxides. An alternative consists in using molecular dynamic simulations employing nonempirical force fields to predict the charge-transport properties of molten oxides and thus alleviate the lack of experimental data. Here, we study molten alumina using two polarizable force fields, with different levels of sophistication, parameterized on electronic structure calculations only. After validating the models against the experimental sets of density and electrical conductivity, we are able to determine the various ionic contributions to the overall charge transport in a wide range of temperatures.

Influence of molten salt-(FLiNaK) thermophysical properties on a heated tube using CFD RANS turbulence modeling of an experimental testbed

In a liquid fuel molten salt reactor (MSR) a key factor to consider upon its design is the strong coupling between different physics present such as neutronics, thermo-mechanics and thermal-hydraulics. Focusing in the thermal-hydraulics aspect, it is required that the heat transfer is well characterized. For this purpose, turbulent models used for FLiNaK flow must be valid, and its thermophysical properties must be accurately described. In the literature, there are several expressions for each material property, with differences that can be significant. The goal of this study is to demonstrate and quantify the impact that the uncertainty in thermophysical properties has on key metrics of thermal hydraulic importance for MSRs, in particular on the heat transfer coefficient. In order to achieve this, computational fluid dynamics (CFD) simulations using the RANS k-ω SST model were compared to published experiment data on molten salt. Various correlations for FLiNaK’s material properties were used. It was observed that the uncertainty in FLiNaK’s thermophysical properties lead to a significant variance in the heat coefficient. Motivated by this, additional CFD simulations were done to obtain sensitivity coefficients for each thermophysical property. With this information, the effect of the variation of each one of the material properties on the heat transfer coefficient was quantified performing a one factor at a time approach (OAT). The results of this sensitivity analysis showed that the most critical thermophysical properties of FLiNaK towards the determination of the heat transfer coefficient are the viscosity and the thermal conductivity. More specifically the dimensionless sensitivity coefficient, which is defined as the percent variation of the heat transfer with respect to the percent variation of the respective property, was −0.51 and 0.67 respectively. According to the different correlations, the maximum percent variations for these properties is 18% and 26% respectively, which yields a variation in the predicted heat transfer coefficient as high as 9% and 17% for the viscosity and thermal conductivity, respectively. It was also demonstrated that the Nusselt number trends found from the simulations were captured much better using the Sieder Tate correlation than the Dittus Boelter correlation. Future work accommodating additional turbulence models and higher fidelity physics will help to determine whether the Sieder Tate expression truly captures the physics of interest or whether the agreement seen in the current work is simply reflective of the single turbulence model employed.

Molecular dynamics determination of liquid-vapor coexistence in molten alkali halides

We show by extensive molecular dynamics simulations that accurate predictions of liquid-vapor coexistence in molten alkali halides can be achieved in terms of a rigid ion potential description in which temperature-dependent ionic diameters are employed. The new ionic sizes result from the fitting of the experimental isothermal compressibilities, a condition whose physical implications and consequences are illustrated. The same diameters also allow us to formulate confident predictions for the compressibilities of salts in cases where the experimental data are lacking. The extension of the present approach to molten alkali-halide mixtures and to other classes of molten salts is discussed.

Experimental Determination of the Thermal Diffusivity of α-Cryolite up to 810 K and Comparison with First Principles Predictions

In aluminum electrolysis cells, a ledge of frozen electrolyte is formed on the sides. Controlling the side ledge thickness (a few centimeters) is essential to maintain a reasonable life span of the electrolysis cell, as the ledge acts as a protective layer against chemical attacks from the electrolyte bath used to dissolve alumina. The numerical modeling of the side ledge thickness, by using, for example, finite element analysis, requires some input data on the thermal transport properties of the side ledge. Unfortunately, there is a severe lack of experimental data, in particular, for the main constituent of the side ledge, the cryolite (Na₃AlF₆). The aim of this study is twofold. First, the thermal transport properties of cryolite, not available in the literature, were measured experimentally. Second, the experimental data were compared with previous theoretical predictions based on first principle calculations. This was carried out to evaluate the capability of first principle methods in predicting the thermal transport properties of complex insulating materials. The thermal diffusivity of a porous synthetic cryolite sample containing 0.9 wt % of alumina was measured over a wide range of temperature (473-810 K), using the monotone heating method. Because of limited computational resources, the first principle method can be used only to determine the thermal properties of single crystals. The dependence of thermal diffusivity of the Na₃AlF₆ + 0.9 wt % Al₂O₃ mixture on the microstructural parameters is discussed. A simple analytical function describing both thermal diffusivity and thermal conductivity of cryolite as a function of temperature is proposed.

Trapping of Li(+) Ions by [ThFn](4-n) Clusters Leading to Oscillating Maxwell-Stefan Diffusivity in the Molten Salt LiF-ThF4

A molten salt mixture of lithium fluoride and thorium fluoride (LiF-ThF4) serves as a fuel as well as a coolant in the most sophisticated molten salt reactor (MSR). Here, we report for the first time dynamic correlations, Onsager coefficients, Maxwell-Stefan (MS) diffusivities, and the concentration dependence of density and enthalpy of the molten salt mixture LiF-ThF4 at 1200 K in the composition range of 2-45% ThF4 and also at eutectic composition in the temperature range of 1123-1600 K using Green-Kubo formalism and equilibrium molecular dynamics simulations. We have observed an interesting oscillating pattern for the MS diffusivity for the cation-cation pair, in which ĐLi-Th oscillates between positive and negative values with the amplitude of the oscillation reducing as the system becomes rich in ThF4. Through the velocity autocorrelation function, vibrational density of states, radial distribution function analysis, and structural snapshots, we establish an interplay between the local structure and multicomponent dynamics and predict that formation of negatively charged [ThFn](4-n) clusters at a higher ThF4 mole % makes positively charged Li(+) ions oscillate between different clusters, with their range of motion reducing as the number of [ThFn](4-n) clusters increases, and finally Li(+) ions almost get trapped at a higher ThF4% when the electrostatic force on Li(+) exerted by various surrounding clusters gets balanced. Although reports on variations of density and enthalpy with temperature exist in the literature, for the first time we report variations of the density and enthalpy of LiF-ThF4 with the concentration of ThF4 (mole %) and fit them with the square root function of ThF4 concentration, which will be very useful for experimentalists to obtain data over a range of concentrations from fitting the formula for design purposes. The formation of [ThFn](4-n) clusters and the reduction in the diffusivity of the ions at a higher ThF4% may limit the percentage of ThF4 that can be used in the MSR to optimize the neutron economy.

Thermal transport properties of halide solid solutions: Experiments vs equilibrium molecular dynamics

The composition dependence of thermal transport properties of the (Na,K)Cl rocksalt solid solution is investigated through equilibrium molecular dynamics (EMD) simulations in the entire range of composition and the results are compared with experiments published in recent work [Gheribi et al., J. Chem. phys. 141, 104508 (2014)]. The thermal diffusivity of the (Na,K)Cl solid solution has been measured from 473 K to 823 K using the laser flash technique, and the thermal conductivity was deduced from critically assessed data of heat capacity and density. The thermal conductivity was also predicted at 900 K in the entire range of composition by a series of EMD simulations in both NPT and NVT statistical ensembles using the Green-Kubo theory. The aim of the present paper is to provide an objective analysis of the capability of EMD simulations in predicting the composition dependence of the thermal transport properties of halide solid solutions. According to the Klemens-Callaway [P. G. Klemens, Phys. Rev. 119, 507 (1960) and J. Callaway and H. C. von Bayer, Phys. Rev. 120, 1149 (1960)] theory, the thermal conductivity degradation of the solid solution is explained by mass and strain field fluctuations upon the phonon scattering cross section. A rigorous analysis of the consistency between the theoretical approach and the EMD simulations is discussed in detail.