The ion’s transference number holds significant importance in numerous practical and industrial electrochemical applications. However, due to limited, outdated, and often inaccurate experimental data, our understanding of it remains considerably unclear even today. Unlike integral properties such as viscosity or thermal and electrical conductivity, atomistic simulations only provide insight into the self-diffusion coefficients as a partial charge transport property. A clear framework for deriving partial conductivities, often defined by transference numbers, is lacking. This work aims to develop an original approach for deriving transference numbers in dissociated molten salt mixtures, aligning with the calculation of total ionic conductivity. We employ Green-Kubo theory and Onsager’s phenomenological coefficient to introduce our approach, which is rooted in perturbation theory. We expand the partial ionic conductivity through the Nernst-Einstein expression and Onsager’s coefficients, which describe the electrostatic ion-ion interactions. Phase trajectories, crucial for deriving partial conductivities, are calculated via equilibrium molecular dynamics simulations using a polarizable ion method as the force field. These simulations encompass all molten halide compounds and several molten binary and ternary systems, particularly those with reported experimental data. Our results demonstrate the proposed theoretical approach’s strong predictive capability.

This study investigates the interdependent influence of microstructural parameters and thermodynamic (temperature between 298 K and 473 K, pressure between 0.1 Pa and 3 107 Pa, various gas composition e.g., air, Ar, H2, He, N2) conditions of the atmosphere on thermal transport within granular media. To accurately describe the thermal conductivity behavior, we propose an extended analytical model based on the Rombouts’s model (Rombouts et al., 2005). This study investigates three types of microstructures: dense non-cohesive particles, dense and cohesive particles and porous non-cohesive particles. Analysis of the results provides a precise understanding of the influence of these typical microstructure parameters on thermal conductivity. We underscore the pivotal roles of intraparticle porosity in governing the heat transfer transition in the gas phase. A comparative analysis between our model and a percolation model approach reveals a robust correlation between the two formulations. Our findings indicate that an increase in conductance between particles leads to an enhanced thermal coordination within the system, consequently shifting the thermal percolation threshold to higher values (from 0.1 to 0.5).

This work introduces solar, a collection of ten optimization problem instances for benchmarking blackbox optimization solvers. The instances present different design aspects of a concentrated solar power plant simulated by blackbox numerical models. The type of variables (discrete or continuous), dimensionality, and number and types of constraints (including hidden constraints) differ across instances. Some are deterministic, others are stochastic with possibilities to execute several replications to control stochasticity. Most instances offer variable fidelity surrogates, two are biobjective and one is unconstrained. The solar plant model takes into account various subsystems: a heliostats field, a central cavity receiver (the receiver), a molten salt thermal energy storage, a steam generator and an idealized power block. Several numerical methods are implemented throughout the solar code and most of the executions are time-consuming. Great care was applied to guarantee reproducibility across platforms. The solar tool encompasses most of the characteristics that can be found in industrial and real-life blackbox optimization problems, all in an open-source and stand-alone code.

Molten salts are among the most promising materials for advanced energy systems in the renewable energy and nuclear fields, with thermal conductivity being a critical property that directly impacts the efficiency of heat transfer processes. However, reliable experimental data on the thermal conductivity for molten salt mixtures is scarce, requiring the use of atomistic simulations and robust theoretical frameworks to fill this gap. This study extends a previously developed kinetic theory-based model for common-anion molten salt mixtures to reciprocal molten salt mixtures (for example, LiF-KCl) as a function of temperature and composition. To account for the effects of first nearest neighbor short-range ordering between cations and anions, pair fractions in the Modified Quasi-chemical Model in the Quadruplet Approximation were employed. The current model fills an important gap in the modeling of thermal conductivity for reciprocal molten salt mixtures, since no existing model has accurately characterized their thermal conductivity. Predicted results were compared with various equilibrium molecular dynamics simulations performed in this work for solutions involving Li+, Na+, K+/F-, Cl-, as well as with existing experimental measurements. The model also predicted the thermal conductivity of reciprocal molten salt mixtures proposed in the literature as potential phase change materials. The current model demonstrated excellent predictive capability and accuracy of thermal conductivity for both monoatomic and polyatomic anion reciprocal molten salt mixtures, with an estimated error margin up to 20%. This advancement will significantly contribute to improving the statement of knowledge of reciprocal molten salt thermal conductivity and provide valuable tools for evaluating the thermal conductivity of molten salt mixtures in engineering applications.

In recent years, there has been a renewed interest in accurately quantifying the ion's transference number within molten salts. Surprisingly, despite efforts to address the severe lack of experimental data, there is still no reliable theoretical framework that establishes a clear link between the transference number and simulated phase trajectories through atomistic simulations or a dependable theoretical relationship for precise estimation. In general, overcoming limitations in both experimental and fundamental aspects, transference numbers are typically estimated by either considering the Nernst-Einstein (NE) approximation or employing the so-called "golden rules". However, it is worth noting that neither the Nernst-Einstein approximation nor the "golden rules" provide a truly accurate prediction. This work concentrates on establishing a robust theoretical framework to accurately define transference number boundaries and averages within molten salt systems. This is achieved by integrating principles from kinetic theory with an in-depth exploration of the electronic structure and local ordering of molten salts. Unlike prevailing theoretical approaches that are heavily reliant on Einstein's concept of ion mobility, which correlate with self-diffusion, the proposed theoretical framework is fundamentally grounded in the inherent mobility of ions. In summary, the introduction of this original "golden rule" showcases robust predictive capabilities, effectively addressing the scarcity of diverse observations gleaned from various experimental sources in the literature. Finally, the proposed formalism is extended to complex molten salts through a microscopic consideration of the impact of the cation associated with the anion upon its diffusional cross-section. Based on this, the cationic transference number of all divalent metal halide molten salts is predicted to be very close to that reported in the literature.

Contrary to the solid state, the understanding of thermal transport within molten salts remains limited. This study aims at establishing a robust theoretical framework for describing and predicting thermal transport in complex and dissociated multicomponent molten salt mixtures, considering both the composition and temperature variables. The proposed approach, based on kinetic theory, considers the local perturbation of kinetic energy through mass fluctuation, weighted by a function dependant on the thermal conductivity of the uncorrelated system and the local structure. The local structure is described in terms of the concentration of free and complex ions, determined either experimentally (using NMR) or through equilibrium atomistic simulations. The thermal transport within several molten salt systems, including KCl, Al2O3, LiF-KF, LiF-NaF-KF (FLiNaK), KCl-MgCl2, NaCl-KCl-MgCl2, and the NaF-AlF3 system, are presented as case studies using the proposed approach. Furthermore, a molecular-level perspective of thermal conduction within molten salts is discussed.

(Al,Si)(3)(Zr,Ti)-D0(22)/D0(23) are phases that may form in aerospace and automotive aluminium alloys. The substitution of Zr/Ti in these solid solutions is widely reported in the literature; however, it remains relatively unexplored for Si. In this work, in situ precipitation of (Al,Si)(3)(Zr,Ti)-D0(22)/D0(23) intermetallics was performed using Al-Si-Zr-Ti alloys. The precipitation, sedimentation and concentration of numerous intermetallic particles were accomplished by filtrating the residual molten aluminium using a temperature/pressure-controlled vessel adapted with a PoDFA filter. A combination of SEM, TEM, XRD and EMP analysis allowed the identification of (Al,Si)(3)(Zr,Ti)-D0(22)/D0(23) intermetallics concentrated within..-FCC matrices of non-Si-doped (sample S2) and Si-doped (samples S4 and S6) alloys. EDS analysis confirmed that Zr and Ti substitute each other in the D0(22) and D0(23) phases, whereas Si substitutes in Al sites. Acceptance of Si inside the D0(23) phase was not expected according to FTlite (FactSage) and TCAL7 (Thermo-Calc) databases. Additionally, Si was found to enhance the formation of (Al,Si)(3)(Zr,Ti)-D0(22) intermetallics with high Zr-content, contrary to FactSage 7.3 predictions. TEM results showed intermetallic/FCC crystal coherency for samples S2 and S6, implying that these intermetallics acted as nucleation sites for the Al-phase due to their small lattice mismatch. Furthermore, Si site occupancy was calculated for both (Al,Si)(3)Ti-D0(22) and (Al,Si)(3)Zr-D0(23) phases via DFT, showing that sites 2b and 4e are the most favorable for Si occupation, respectively. Finally, a thermodynamic model is derived to describe Si substitution upon solidification. Experimental and numerical examinations indicate that Si substitution preferentially occurs in the D0(22) intermetallics compared to the D0(23) phase.

An accurate knowledge of the interfacial tension between liquid aluminium and cryolitic melts is critical to better understand the process parameters influencing the current efficiency in electrolysis cells. In principle, the interfacial tension can be predicted from the surface tension of liquid aluminium, cryolitic melts and their adhesion energy. In industrial electrolysis cells, liquid aluminium contains several impu-rities (Na, Si, Fe, V, O, ...) for which the concentration is modulated by the current density and the ther-mochemical and electrochemical reactions between aluminium and cryolitic melts, strongly impacting the surface tension of the liquid metal and therefore the interfacial tension. The aim of this paper is to present a predictive model describing the interfacial tension between the liquid aluminium pad and cry-olitic melts taking into account the thermochemical and electrochemical reactions within industrial elec-trolysis cells, depending on the current density. The impurity concentrations within the metal pad are calculated from the cryolitic melt compositions and the current density. The presence of Na and O, even if just a few ppm, may drastically decrease the surface tension of the liquid pad. As no experimental data is available for Al-Na-O system, it has been predicted based on a theoretical approach. Overall, the pre-dicted interfacial tension with the proposed model is in good agreement with the different experimental datasets reported in the literature. A mapping of interfacial tension as a function of electrolyte composi-tion, temperature and current density is proposed. Lastly, based on the proposed interfacial tension model, the probability of precipitation of undissolved alumina particles at the bottom of the cells and its impact upon the current efficiency is discussed.(c) 2022 Elsevier B.V. All rights reserved.

This study deals with the effective thermal conductivity of porous and ultra-porous unconnected solid phase media composed of alpha-alumina in air at low temperature ( < 50 0K), and at ambient pressure. A multi-scale model is developed, starting from the quantum scale, to describe the conductivity of the sin-gle crystal, passing through a microscopic scale to describe the particles (grain size), a mesoscopic scale to take into account the intraparticle porosity and a macroscopic scale with the interparticle porosity. The model is based on percolation theory to describe the strong decrease in conductivity with porosity in this type of medium. This translates into the breaking of contacts between particles past a certain porosity, the critical porosity pc. This original approach makes it possible to consider this microstructural factor, which accounts for the thermal contacts between particles. These parameters are theoretically deduced or measured for certain samples using an X-ray micro-tomograph (mu CT). Combining all these parameters, our model is able to predict 99.7% of the thermal conductivity decay from the pure crystal to the parti-cle bed. Our model proves to be more consistent than current existing models on the same subject. Its validation range extends over the entire porosity range from 0 to 1. (c) 2023 Elsevier Ltd. All rights reserved.

This study presents a theoretical model, based on kinetic theory, for accurately predicting thermal conductivity in molten salt mixtures, a vital factor in designing advanced energy systems such as concentrating solar power, thermal energy storage, and advanced nuclear reactors. Applicable to non-complex, non-reciprocal systems, the model represents thermal conductivity with respect to composition and temperature. We evaluated the model using molecular dynamics simulations on binary systems from fluoride, chloride, bromide, iodide salt families. The model predictions were also compared against existing experimental datasets for those families as well as binary nitrates and carbonates. The model demonstrated an improvement in predictive accuracy over the ideal linear estimation and showed reasonable agreement with the reliable experimental data. Deviations from ideal conductivity, analyzed using the Redlich-Kister method, pointed to the molecular weight and thermal conductivity of individual compounds as primary influencing factors. When applied to predict the thermal conductivity of higher order eutectic salt mixtures relevant to energy applications, the model showed predictive accuracy comparable to empirical methods. The model was further applied to generate compositional mapping to quantify deviations from ideality over the compositional space. This advance enhances new molten salt mixtures evaluation efficiency and extends the model to complex mixtures.

The present work describes the application of a recently developed Calculation of Phase Diagrams (CALPHAD) method to perform condensed-phase thermochemical equilibrium calculations of Chapman-Jouguet (CJ) detonation properties for a number of new mixtures speculated to support gasless detonation. Mixtures in question are titanium-silicon (Ti-Si), the common thermite mixture of aluminum-iron oxide (Al-Fe2O3), and zinc-sulfur (Zn-S). The high-pressure products of these reactive mixtures were found to be stable, and thus suitable for gasless CJ detonation calculations. The CJ calculation method was found to be successful for these mixtures, and the results showed CJ detonation properties with high temperatures, but only marginal volume increase. While this is expected for condensed-phase products, the calculations nevertheless show that gasless detonation may be possible under a very narrow range of conditions.

We present in this work a new formalism for the rapid and accurate evaluation of the thermodynamic properties of compounds and solid solution end-members which are required in the high-throughput computational thermochemistry discovery of new materials. The method is based on the Debye approximation and is fully thermodynamically self-consistent. It considers several energetic contributions, such as the vibrational free energy (including both implicit and explicit anharmonicity), the defect-free energy (via the introduction of thermal vacancies), the energetic effect of thermal excitation of electrons (for metallic solids) as well as other excess terms to precisely reproduce experimental data. Sets of fully self-consistent pressure- and temperature-dependent thermodynamic properties are evaluated from the exact differentiation of this complete free energy formalism. This strategy allows the formalism to be fully integrated in the CALPHAD framework for the development of large thermodynamic databases of both stable and metastable compounds which may form in multicomponent/high-order systems. An emphasis is put in this work on the analysis and precise description of anharmonic vibrational contributions. Finally, sets of self-consistent thermodynamic and thermo-physical properties have been predicted as a function of temperature and compared with both experiments and classical QHA for pure elements (i.e. Ag, Li, V, Al, and C) and stoichiometric compounds of different chemical nature (i.e. MgO, CaO, Al2O3, NaCl, LiFePO4 and InP). The impact of various input parameters of the formalism on the free energy and the derived thermodynamic properties for these solids is analyzed. A better predictive capability and the enhanced flexibility of the proposed formalism are demonstrated.

A theoretical model for predicting the temperature-dependent thermal conductivity of pure molten salts, both simple and complex, is presented. The model is based on kinetic theory and incorporates Einstein’s concept of minimum thermal conductivity. The proposed formulation can consider the magnitude of thermal conductivity for separate salts, including complex and polymerizing salts. The model’s thermal conductivity predictions were compared to reliable experimental data in the literature and a previously recommended thermal conductivity model using the Bland–Altman method. The comparison showed accurate thermal conductivity predictions relative to the reliable experimental data, with an average deviation of 10% or less. The model’s predictions were also compared to the experimental data on an individual basis for halide, divalent halide, carbonate, nitrate, nitrite, sulfate, and hydroxide molten salts, demonstrating reliable predictions for the molten salts studied and improved accuracy over the previous model. Lastly, a database of simple and complex molten salts, with the necessary parameters for modeling their thermal conductivity, is recommended.

Aluminum alloys commonly contain Si as an impurity or alloying element. The energetic behavior of Si within multiple compounds and solutions is incorporated inside thermochemical packages, such as FactSage. This tool allows determining the Si partitioning within complex multiphasic systems. Recent experimental research suggests that Si can be found within Al 3 Zr-based intermetallics. Nevertheless, current FactSage databases do not consider the potential substitution of Si within the Al 3 Zr-D0 23 solid solution. In this work, Si substitution within the (Al,Si) 3 Zr-D0 23 phase was investigated by means of first-principles calculations. Replacement of Al atoms by Si resulted in a negative enthalpy of mixing, indicating that Si substitution is energetically enabled. The density of states (DOS) for both a Si-diluted (Al,Si) 3 Zr and a non-Si-doped (Al 3 Zr) simulation cells were analyzed. It is shown that (even in dilution), Si significantly impacts the electronic structure of the Al 3 Zr-D0 23 structure. Specifically, the presence of Si localizes electrons in the p orbital of Al, and increases the DOS of the d xy , d xz , and d yz sub-orbitals of Zr at low energies. Thus, yielding a coupled effect that stabilizes the D0 23 intermetallic. These findings are a benchmark for the future integration of a Si-based end-member within the Al 3 Zr-D0 23 solid solution of FactSage databases.

Classical molecular dynamics simulations of metallic systems have been extensively applied in recent years for the exploration of the energetic behavior of mesoscale structures and for the generation of thermodynamic and physical properties. The evaluation of the conditions leading to the melting of pure metals and alloys is particularly challenging as it involves at one point the simultaneous presence of both a solid and a liquid phase. Defects such as vacancies, dislocation, grain boundaries and pores typically promote the melting of a solid by locally increasing its free energy which favors the destruction of long-range ordering at the origin of this phase transition. In real materials, many of these defects are microscopic and cannot yet be modelled via conventional atomistic simulations. Still, molecular dynamics-based methodologies are commonly used to estimate the melting temperature of solids. These methods involve the use of mesoscale supercells with various nanoscale defects. Moreover, the deterministic nature of classical MD simulations requires the adequate selection of the initial configuration to be melted. In this context, the main objective of this paper is to quantify the precision of the existing classical molecular dynamics computational methods used to evaluate the melting point of pure compounds as well as the solidus/liquidus lines of Al-based binary metallic systems. We also aim to improve the methodology of different approaches such as the void method, the interface method as well as the grain method to obtain a precise evaluation of the melting behavior of pure metals and alloys. We carefully analyzed the importance of the local chemical ordering on the melting behavior. The ins and outs of different numerical methods in predicting the melting temperature via MD are discussed through several examples related to pure metallic elements, congruently and non-congruently melting compounds as well as binary solid solutions. It is shown that the defect distribution of the initial supercell configuration plays an important role upon the description of the melting mechanism of solids leading to a poor predictive capability of melting temperature if not properly controlled. A new methodology based on defect distribution within the initial configuration is proposed to overcome these limitations.

In Hall-He ' roult cells the uninvolved alumina precipitates on the top of the cathode to form resistive deposits which could significantly impact the energy consumption. A dynamic energy conservation (DEC) approach has been developed to quantify the flux of undissolved alumina piercing the interface between the electrolyte and the liquid metal in Hall-He ' roult cells. The proposed DEC model considers both electrochemical and interfacial phenomenon between the electrolyte and the liquid metal. A critical radius at or below which a particle of undissolved alumina is retained at the electrolyte/liquid metal pad interface is defined and quantified considering the heat transfer and electrolysis cell operating parameters: temperature, electrolyte composition, alumina porosity, and current density. The proposed approach appears reliable to quantify the amount of undissolved alumina which pierces the electrolyte/liquid metal pad interface and precipitates to the bottom of the cell to form a deposit on the cathode.

Multi-component and multiphasic materials are continually being developed for electronics, aircraft, automotive, and general applications. Integrated Computational Materials Engineering (ICME) is a multiple-length scale approach that greatly benefits from atomistic scale simulations to explore new alloys. Molecular Dynamics (MD) allows to perform large-scale simulations by using classical interatomic potentials. The main challenge of using such a classical approach is the transferability of the interatomic potentials from one structure to another when one aims to study multi-component systems. In this work, the reliability of Zr, Al-Cu, Al-Cr and Al-Zr-Ti force field potentials is examined. It has been found that current interatomic potentials are not completely transferable due to the structure dependence from their parameterization. Besides that, they provide an appropriate description of unary and binary systems, notably for liquids, isotropic solids, and partially isotropic compounds. For solidification purposes, it has been found that coherent primary solidification of the FCC-phase in pure Al is highly dependent on the formalism to tune interatomic interactions. For Al-Cr alloys, the icosahedral short-range ordering (ISRO) increased by adding Cr to the melts. The different steps of solidification (formation of nuclei, effective germination of the α-Al phase and end of solidification) have been related to the evolution of the ISRO. The addition of Cr in melts prevented undercooling via icosahedral-enhanced nucleation of the α-Al phase. Precipitation of primary intermetallics in hyper-peritectic Al-Cr alloys was also tested. Contrary to classical thermodynamics predictions, α-Al phase was the primary precipitate for these alloys. This implies that Cr supersaturated the α-Al phase rather than forming intermetallic phases due to the high cooling rates.

Among all the properties required for the design of the next generation of phase change materials (PCMs) (density, heat capacity, thermal expansion, latent energy, volume change upon melting, corrosion rate, etc.) the thermal transport properties are by far the least known, especially for molten salt mixtures and solid solutions. We present in this paper a theoretical framework for accurate predictions of thermal conductivity of multi-component salt-based PCMs, from 273.15 K up to above melting temperature. The solid phase is considered as a microstructure with its proper temperature dependent parameters: phase volume fraction, grain size distribution, porosity, etc. As case studies, five new potential PCMs for concentrated solar power (CSP) applications are considered. Their thermal conductivity is estimated as a function of temperature, from room temperature to 200 K above their melting point. The predictive capability of the proposed framework is discussed based on a comparison with available experimental data. The effect of equilibrium and non-equilibrium microstructural parameters (i.e. phase fraction, phase composition, average grain size, inter-grain, and intra-grain porosity) on the effective thermal conductivity of the solid states of the promising chloride PCMs is discussed. Lastly, rec-ommendations for the design of next generations of PCM materials are suggested in order to improve their thermal transport properties.

Molten salts are being proposed for numerous advanced energy applications, including advanced nuclear reactors, concentrating solar power plants, thermal energy storage, and fusion reactors. Accurate knowledge of the thermophysical properties of molten salts directly impact the performance of these energy systems and are essential for design and safety analyses. Thermal conductivity data for fluoride molten salts and mixtures are especially lacking. In this work, experimental measurements of thermal conductivity using the steady-state variable gap technique were performed on eutectic LiF-NaF-KF from 834 to 1195 K. The experiment accounts for radiative, convective, and conductive heat losses. In addition, theoretical and molecular dynamics models are used, from 750 K up to 1300 K, to estimate the thermal conductivity for comparison with the experimental results. The results of experiments show a weak negative deviation of thermal conductivity with temperature, unlike previous experimental results in the literature. The measured thermal conductivity magnitudes agree with the theoretical and molecular dynamics predictions, aside from the data above 1100 K, where heat losses and radiative errors are the most significant, having a 16% maximum deviation from theory. These experimental results provide new thermal conductivity data for the LiF-NaF-KF system and further validation of the predictive models. The theoretical model was used to map the composition and temperature dependent thermal conductivity of LiF-NaF-KF and the mapping's deviation from a linear additivity estimation of thermal conductivity. This mapping showed the highest deviations from linearity for KF-LiF rich mixtures and increasing deviation with temperature. Notably, the deviation from linearity near the LiF-NaF-KF eutectic composition was around 25%. (C) 2022 Published by Elsevier B.V.