Search

Classical MD simulations of metallic systems were performed to study the melting behavior of multiple types of Al-based solid phases. Considerations of the local chemical ordering are used to better understand and describe their melting behavior.

International audience

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

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 Al3Zr-based intermetallics. Nevertheless, current FactSage databases do not consider the potential substitution of Si within the Al3Zr-D023 solid solution. In this work, Si substitution within the (Al,Si)3Zr-D023 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)3Zr and a non-Si-doped (Al3Zr) simulation cells were analyzed. It is shown that (even in dilution), Si significantly impacts the electronic structure of the Al3Zr-D023 structure. Specifically, the presence of Si localizes electrons in the p orbital of Al, and increases the DOS of the dxy, dxz , and dyz sub-orbitals of Zr at low energies. Thus, yielding a coupled effect that stabilizes the D023 intermetallic. These findings are a benchmark for the future integration of a Si-based end-member within the Al3Zr-D023 solid solution of FactSage databases.

Contrary to the ionic conductivity, the electronic conductivity of cryolitic melts, which can be up to 30 pct of the total conductivity in industrial electrolysis cells, remains largely unknown as very few experimental data are reported in the literature. The aim of this work is to fill this gap by providing reliable estimations of the electronic conductivity as a function of both cryolitic ratio and temperature in the range of interest for the aluminum production industry.

In aluminium reduction cells, an electrochemical reaction occurs between the molten electrolyte film below the aluminium pad and the carbon cathode blocks, leading to the formation of an Al4C3 layer on the cathode blocks. The properties and role of this Al4C3 layer are therefore important for the aluminium production industry, as they could help increase the life expectancy of electrolysis cells and impact the resistive voltage losses. The purpose of this study is to gain a better understanding of the formation, growth and mechanical stability of the aluminium carbide layer formed on top of the cathode block. A reliable scenario describing both the mechanical and electrochemical behaviours of the Al4C3 layer is proposed. For different industrial graphitized cathode grades, a series of experiments were carried out in a bench-scale Hall-Heroult electrolysis cell and the Al4C3 layer formed on top of the cathode was characterized. Thereafter, the CALPHAD method was combined with density functional theory simulations to estimate the electrical and physical properties of Al4C3 together with the phase equilibria occurring at the interface between the carbide layer and the aluminium pad and the cathode blocks respectively. From these calculations, a scenario for carbide layer growth and mechanical stability was established.

Experimental surface tension data for many binary, ternary and higher order metallic systems is unfortunately currently unavailable in the literature. This could be detrimental in several practical and industrial applications. Consequently, having a theoretical model with a good predictive capability is highly desirable. In general, the surface tension of metallic alloys is predicted via the well-established Butler model. This model assumes a linear relationship between the excess Gibbs energy in the Bulk and on the surface. For many systems, this assumption is not valid, especially for systems based on elements with different bulk electronic structures, for which the Butler model fails to predict the composition dependence of the surface tension (As demonstrated in this work, the Butler model is accurate only for about 65% of metallic system for which experimental data is available). The aim of this paper is to propose an alternative to the Butler model to represent accurately the surface tension multi component liquid metals. The proposed model is an extension of the Guggenheim model of ideal solutions to take into account the difference of electronic structures between elements of a solution. The model is compared with the 36 binary and 7 ternary metallic alloys for which experimental data is available. It is shown that the accuracy of the model is higher than 95%. On that basis, the composition dependence of the surface tension of many other binary alloys for which experimental data is not available is predicted. The extension of the model to ternary and higher order systems is proposed without introducing any new parameters, i.e. by considering only the binary parameters. It is shown that the extended model provides also an accurate prediction of the surface tension for ternary metal.

The effect of coherent strains which is involved during the fast charge/discharge processes and the influence of particle size reduction which improves the electrochemical performance of the cathode material are modelled in this study. An extension of the linear isotropic approximation for elastic energy stored in the coherent boundaries of an orthorhombic system is performed for the first time to calculate the coherent miscibility gaps of the LiFePO4-FePO4 cathode join. Noticeably, this approach is applicable for any thermodynamic models used for describing the equilibrium LiFePO4-FePO4 join. The coherent miscibility gaps corresponding to various crystallographic directions, which could explain the occurrence of a metastable phase, favorable phase boundaries during lithiation (delithiation), and the formation of dislocations or cracks via cycling, are presented. (100) is considered as the softest direction for coherence to form and the existence of (110) and (010) habit planes is also possible. Moreover, it is the first time that a model of particle size effect on both equilibrium and coherent olivine join is developed. Additionally, it is the first combined coherency-size type of calculation ever reported. The difference between the surface energies of the pure LiFePO4 and FePO4 and the excess surface energy of the olivine solid solution are the two important model parameters affecting the equilibrium and the coherent miscibility gaps. As the particle size decreases, the miscibility gaps shrink favoring the intermediate phase region between the two miscibility gaps. At nanoscale, coherent phase transformation seems to be more likely.

The surface tension of liquid metals depends strongly on atmosphere conditions, in particular on the partial pressure of oxygen, on top of temperature. Predicting the surface tension of metals in different atmosphere conditions is highly desirable for many fundamental and practical applications. Currently, none of the theoretical and semi-empirical approaches reported in the literature can predict accurately the non-metallic impurities (oxygen, sulphur, phosphorous, carbon…) effect upon the surface tension. These models are mainly descriptive, i.e. they must be adjusted to the experiential datasets. The aim of this work is to fill this gap. A semi-empirical model describing the oxygen effect upon the surface tension of liquid metals is proposed. The key parameter describing this model is the metal recovery rate saturated with oxygen, which can be predicted from crystallographic data of the monoxide. For liquid metals where sufficient reliable experimental data is available, the surface tension as a function of oxygen content is predicted using the present theoretical model and compared with experimental data. A very good agreement is found. It is also shown that the proposed model is valid for semiconductors and semimetals and as well.

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.

The short-range structures of LiF���ThF$_{4}$, NaF���AnF$_{4}$, KF���AnF$_{4}$, and Cs���AnF$_{4}$ (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 ThF$_{4}$ and UF$_{4}$ 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 [AnFx]$^{4-x}$ (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 AnF$_{4}$ 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.

© 2021 The Authors 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.

Thermodynamic models of solid solutions used in computational thermochemistry have not been modernized in recent years. With the advent of fast and cheap computers, it is nowadays possible to add, at a minimal computational cost, physical ingredients such as coordination numbers, inter-atomic distances and classical interatomic potentials to the function describing the energetics of ordered and disordered solid solutions. As we show here, the integration of these elements into a robust statistical thermodynamic model of solution establishes natural connections with other deterministic and stochastic atomistic methods such as Monte Carlo and molecular dynamics simulations. Ultimately, all these numerical approaches need to be self-consistent and generate complementary sets of numerical thermo-physical properties. The present work proposes a new formalism to define the Gibbs free energy of ordered and disordered solid solutions. It allows for a complete prediction of the thermal, volumetric and compositional dependence of the Gibbs free energy by solving a constrained minimization problem. As a proof of concept, we explore the energetic behavior of pure face-centered cubic gold as well as the AuCu L10 ordered solution as a function of both temperature and pressure. We finally compare these results with the average properties obtained from classical molecular dynamics simulations and explain the origin of the existing differences between the two approaches based on how the temperature is accounted for in each method.

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+, BeF4 2− and F− predominant species at low BeF2 content, and a polymeric liquid at high BeF2 content, with the formation of polymers (Be2F7 3−, Be3F10 4−, Be4F13 5−, 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.

The next generations of Concentrated Solar Thermal Power (CSTP) systems use anhydrous salts as the heat transfer fluid and thermal storage medium. Unfortunately, a severe lack of experimental data is observed for the thermal transport properties of molten salt mixtures, generating constraints in exploring new potential materials for CSTP systems. The present paper presents a reliable theoretical framework for the prediction of both the thermal conductivity and thermal diffusivity of multicomponent molten salts. As a case study, the thermal conductivity of the NaCl-KCl-MgCl 2 system is predicted as a function of temperature and composition. This system is considered as a one of the most promising thermal storage medium of the next generation of CSTP systems. The temperature dependent thermal conductivity of pure MgCl 2 is formulated based on atomistic simulations via classical and Ab initio equilibrium molecular dynamics. Thereafter, to assess the predictive capability of the proposed methodology, the thermal conductivity and thermal diffusivity of KCl-MgCl 2 and NaCl-KCl-MgCl 2 molten mixtures are predicted as a function of both temperature and composition and compared to the available experimental data and the present first principles simulations. A good agreement is achieved with both experimental and first principle data, indicating the robustness of the proposed methodology.

In an attempt to identify new low-cost metallic materials with interesting thermo-physical properties from the Fe-Cr-Mn-Ni-V-Ti-Al- (Co-Mo) system, we present here an original tool for the design of first-generation High Entropy Alloys (HEAs). The composition of potential HEAs is calculated under a set of non-smooth and non-linear constraints and multi-objective functions linked to the single-phase start temperature, the room-temperature driving force for phase assemblage evolution and the solidification range. These are all new thermodynamic criteria for the design of HEAs. This tool links a constrained Gibbs energy minimization algorithm that uses accurate thermodynamic databases to an optimization algorithm implemented for solving “blackbox” objective functions and constraints. As a result of this work, we have identified entire sets of new FCC and BCC first-generation HEAs potentially suitable for future industrial applications. The proposed methodology is also successfully applied to identify two-phase heavily alloyed materials.

Molten cryolite mixed with some additives is used as solvent of alumina by aluminium producers. Cryolite represents the dominating compounds in the wall protecting side-ledge and at the bottom part of the frozen crust on the top of the cells. As the heat, generated in the cell, is lost mainly through the top and the lateral sides of the pot, the thermo-physical properties of the cryolite determine thermal equilibrium and its knowledge is crucial for any numerical thermal model of the cell. Unfortunately, there is a serious lack in experimental thermal diffusivity and conductivity data for pure cryolite. The goal of this paper was to determine experimentally the apparent thermal diffusivity of the purest available cryolite in a wide temperature range and compare it with an earlier published theoretical model, based on first principle calculations. Measurement was carried out using monotone heating technique between 200 and 850 °C on low porosity synthetic cryolite, containing 0.9 mass% of alumina. Experiment setup was improved at the level of protection of the thermocouples compared to earlier published article. This permitted to repeat the test more times with the same sample and reach higher temperatures. Results suggest that the thermal diffusivity of α-cryolite increases very slowly from 3 × 10−7 to 3.5 × 10−7 m2 s−1 between 200 and 560 °C where α–β transformation starts to take place. The transformation is completed around 600 °C. The thermal diffusivity of the β-cryolite is somewhat higher and rise significantly faster with temperature compared to the α-crystal. Namely, it increases from 4.1 × 10−7 to 7.3 × 10−7 m2 s−1 between 600 and 850 °C. DSC tests were carried out, to help to evaluate deviations on the monotone heating curves. Experimental results are in good agreement with the earlier published theoretical model.

The present paper develops a thermodynamic model for the calculation of the Gibbs energy of graphitizable carbons near the graphitization temperature threshold of 2550 K . The graphitization threshold is the minimal heat treatment temperature for the establishment of true graphitic ordering in a graphitizable carbon. The present model represents the structure of graphitizable carbons with a simplified cluster approach. In the model, two distinct clusters share the totality of the carbon atoms in the material: Oberlin's Local Molecular Orientation clusters (LMOs) and mesoscale grain boundary clusters (mGBs). The ability of a carbon material to graphitize is proportional to the size of the LMOs (larger LMOs = more graphitizable). Strongly graphitizing carbons have a large average size for their LMOs. Thus, for these carbons, the fraction of carbon atoms in mGBs can be neglected relative to the one in LMOs. In a LMO, two phases are present in pseudo-thermodynamic equilibrium: the intercrystalline matter phase (IMP) and the coke crystallite phase (CCP). If the average crystallite diameter ( L a ) of the CCP is sufficiently large, the model assumes that the number of carbon atoms in the IMP relative to the CCP is negligible. The paper presents an additive scheme to calculate the Gibbs energy of carbon atoms in a graphitizable carbon based on the present cluster description. The current Gibbs energy model accounts for the contribution of intercrystalline matter removal by the irreversible densification of LMOs up to the graphitization temperature threshold of 2550 K .

The aim of this work is a formulation of a thermodynamic model for the development of new aluminum machining alloys. The three additives Bi, Pb and Sn have proven to help machining. Hence, a review of the literature showed that the liquid phase equilibria and thermodynamic data for the three binary systems Al-Bi, Al-Pb and Al-Sn is very thorough but the limited information for the FCC solution required the use of Density Functional Theory (DFT) to predict thermodynamic data. The partial heat of mixing of these three machining additives in Al(FCC) are obtained and the results helped to improve the thermodynamic model using the CALPHAD method. It was shown that for all three binary systems, the thermodynamic data obtained at three fixed compositions and that obtained for a very dilute solution gave different enthalpy curves. The thermodynamic model was used to compute the ternary systems Al-Bi-Pb, Al-Bi-Sn and Al-Pb-Sn and small adjustable parameters were added to reproduce the literature data.

An electrothermodynamic model is proposed for the carbon anode consumption of the aluminium electrolysis process. Anode consumption produces a primary anode gas composed of CO and C O 2 . Experimentally, higher electrolysis potentials at the bath/anode interface promotes the formation of C O 2 over CO, reducing the carbon consumption at the cost of greater power requirement. Based on the graphenic character of the anode nanostructure, the model successfully predicts this phenomena. The model predicts the charge capture phenomena occurring at the bath/anode interface during electrolysis as a function of the extent of the graphenic crystallites of the carbon anode. Calculated electrolysis C O 2 /CO ratios are also in good agreement with experimental values. The electrothermodynamic model for the interdependence between the structural, chemical and electrical properties of the anode graphenic crystallites and the primary anode gas C O 2 /CO ratio could improve industrial optimization of the anode consumption for various nanostructures and interface potentials. For example, it is predicted that increasing the maximal heat treatment temperature of the anode by 100 K (which improves the extent of the graphenic nanostructure) could lower the anode consumption by ∼ 6 % , similar to experimentally reported values ( ∼ 9 % ).

This paper presents a database for the temperature-dependent thermal conductivity of compounds potentially present in the side ledge formed in aluminium electrolysis cells, between the molten electrolyte used to dissolve the alumina and the side wall. The database is given in the form of an analytical model with sets of parameters for each compound. To determine the model parameters, we considered a robust optimisation approach based on reliable models derived from fundamental physics. Where data are missing, first-principles calculations are utilized to estimate the parameters directly. For all compounds for which data are available, the model’s predictions are found to be in very good agreement with reported experimental data.

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.

Not all carbons graphitize in equal measure. Some will develop a structure which approaches the one of perfect graphite (graphitizable carbons) upon heat treatment, while others will not (non-graphitizable carbons). The present work develops a phenomenological model for the conceptual understanding of graphitizability (capacity to graphitize). To support this model, a mathematical formalism, inspired from thermodynamics, is proposed to calculate the Ultimate Graphitizability ( η g ) of some graphitizable and non-graphitizable carbon materials. η g is the average interlayer spacing ( d 002 ) of a graphenic carbon following graphitization at ∼ 3400 K . η g can be estimated assuming a topological graphitization mechanism operating between 1700 K and 3400 K . Two independent variables define η g : d 002 ( T α ) and d 002 ( T β ) . T α and T β are arbitrarily selected temperatures between 1700 K and 2550 K (the graphitization threshold). In order to better understand the parameters affecting d 002 ( T α ) and d 002 ( T β ) , new carbonization/graphitization experimental results are presented. These suggest that d 002 ( T α ) and d 002 ( T β ) are correlated to the oxygen/hydrogen composition ratio and the relative mesoscale crystallite orientation of some graphitizable carbons following the end of primary carbonization.

In many metallurgical applications, an accurate knowledge of miscibility gaps and spinodal decompositions is highly desirable. Some binary systems where the main constituents of the same crystal structures have similar lattice parameters (less than 15% difference) reveal a composition, temperature shift of the miscibility gap due to lattice coherency. So far, the well-known Cahn's approach is the only available calculation method to estimate the coherent solid state phase equilibria. Nevertheless, this approach shows some limitations, in particular it fails to predict accurately the evolution of phase equilibria for large deformation, i.e. the large lattice parameter difference (more than 5%). The aim of this study is to propose an alternative approach to overcome the limits of Cahn's method. The elastic contribution to the Gibbs energy, representing the elastic energy stored in the coherent boundary, is formulated based on the linear elasticity theory. The expression of the molar elastic energy corresponding to the coherency along both directions [100] and [111] has been formulated in the small and large deformation regimes. Several case studies have been examined in cubic systems, and the proposed formalism is showing an appropriate predictive capability, making it a serious alternative to the Cahn's method. The present formulation is applied to predict phase equilibria evolution of systems under other stresses rather than only those induced by the lattice mismatch.

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.

It has been already shown that the density functional theory (DFT) combined with the quasi-harmonic approximation (QHA) overestimates the specific heat capacity (and in general the thermal properties) of fcc metals. DFT + QHA seemingly shows a large anharmonic contribution to the heat capacity. However, in this article we show that this anharmonicity has no physical origin and it is a consequence of the deviation of the QHA from the Maxwell relations. We show that one can simply avoid this overestimation by enforcing the QHA method to obey the Maxwell relations throughout the thermodynamically self-consistent (TSC) method, instead of considering non-real local anharmonic effects.

The FactSage computer package consists of a series of information, calculation and manipulation modules that enable one to access and manipulate compound and solution databases. With the various modules running under Microsoft Windows® one can perform a wide variety of thermochemical calculations and generate tables, graphs and figures of interest to chemical and physical metallurgists, chemical engineers, corrosion engineers, inorganic chemists, geochemists, ceramists, electrochemists, environmentalists, etc. This paper presents a summary of the developments in the FactSage thermochemical software and databases during the last six years. Particular emphasis is placed on the new databases and developments in calculating and manipulating phase diagrams.

How graphitic structures evolve from non-graphitic carbons, during heat treatment, is conceptually understood through the graphitization mechanisms of the turbostratic model. However, inadequacies exist, most notably concerning the temperature behaviour of the intercrystalline carbon material located between turbostratic crystallites. Previous thermodynamic calculations for idealized crystallites predicted a null surface energy near 2500–2600 K; the experimental temperature range where sudden stiffness of graphenic layers occurs during graphitization. Interpreting this thermodynamic temperature as a critical parameter for intercrystalline carbon removal can accurately model the irreversible second-order structural transformation to long-range graphitic order. The present model is validated by the prediction of relevant experimental data such as strict graphitization degree (P1), average interlayer spacing (d002), electrical resistivity (ρ) and thermal diffusivity (α) for 51 graphitizable and semi-graphitizable carbons. For the calculation of d002, a Nash-Sutcliffe coefficient of 0.99 was computed; this is associated with near-ideal accuracy. A Bland-Altman analysis reveals that the predictive error for d002 calculations could be within an expected experimental uncertainty (0.5 pm) for more than 90% of the data. The model is applicable to increasing heat treatment temperatures from 2000 to 3300 K.

Numerical modeling of heat transport in the side ledge of a cryolite bath as a function of its thickness requires an accurate knowledge of the thermal transport properties of the cryolite bath as well as the solid phases constituting the side ledge. Unfortunately, due to experimental limitations, there is a lack of experimental data on this subject. The aim of this work is to predict these otherwise unknown properties. The thermal conductivity of major constituents of the side ledge in their solid state, namely: NaF, β– Na3AlF6 and Na5Al3F14 as well as molten Na3AlF6 are formulated as a function of temperature. To achieve this, we have performed a series of equilibrium molecular dynamics simulations (EMD) in both the NPT (isobar-isotherm) and NVT (canonical) statistical ensembles. The proposed approach is purely predictive as the ionic interaction potentials were parametrized on the basis of Density Functional Theory (DFT). The results are then compared to a theoretical model which has been shown to be a ...

A model is presented for the development of the thermodynamic functions of enthalpy, entropy, and Gibbs energy for the elements carbon and sulfur in coke crystallites. The crystallites of various degrees of graphitization may be described by crystallite length L a and crystallite height L c. This carbon/sulfur model has been developed using concepts similar to those in the carbon/hydrogen model for coke crystallites. The major model parameters are derived from reported thermodynamic properties. Approximately 75 pct of the model parameters for the carbon/hydrogen and carbon/sulfur system are parameters common to both systems. The resulting crystallite size (L a) constrained in the carbon/sulfur phase diagram, computed by a Gibbs energy minimization technique, is presented for 1 atm and temperatures between 1500 K and 2500 K (1227 °C and 2227 °C). A very good agreement is obtained between the predicted thermal desulfurization of petroleum cokes and critically assessed experimental data. The removal of sulfur from coke crystallites is predicted to occur mostly between 1600 K and 1850 K (1327 °C and 1577 °C) at 1 atm, depending on the L a value. The precision in the predictive calculations and the transferability of the model parameters are two aspects that tend to support the usefulness and the theoretical basis of the entire approach.

In this study, density functional theory (DFT) with a thermodynamically self-consistent (TSC) method are used to predict the thermophysical properties of metallic compounds. The TSC method used in this work is, in summary, an extension of the classical quasi-harmonic approximation satisfying the Maxwell relations and thus ensuring thermodynamic consistency. Electronic band structure and density of state (DOS) of titanium nitride (TiN) and vanadium nitride (VN) are calculated by generalized gradient approximation (GGA) and local density approximation (LDA) to reveal their metallic character. The electron contribution to the heat capacity and thermal expansion is deduced from the DOS and Fermi-Dirac distribution at temperatures above the ground state. The vibrational contribution to thermophysical properties at high temperatures is calculated using the TSC method as an alternative for the existing quasi-harmonic approximations. In addition, elastic and mechanical properties of TiN and VN are calculated. These results show that VN is more anisotropic than TiN, which is manifested in the calculated results. It has been shown that this anisotropic character is rooted in the electronic structure and charge distribution in VN. Thus, the electron localization function (ELF) is calculated to highlight the way in which electrons are localized and the nature of the chemical bonding between the atoms. The significance of the anharmonicity contribution, due to phonon–phonon interaction, for the thermal properties is discussed. Predicted heat capacities and thermal expansions by the TSC method accord well with experimental data. Overall, it has been shown that the TSC method, together with consideration of the electronic structure, is a powerful tool to predict the thermophysical properties of non-magnetic metallic systems, with a high accuracy.

Due to the important similarities between olivine-LiFePO4 and olivine-LiMnPO4, manganese doping has drawn a lot of attention since it can improve the electronic and ionic conductivity of LiFePO4, hence enhance the electrochemical properties. The thermodynamic behavior of Mn-doped-LiFePO4 cathodes has been examined through the thermodynamic investigation of Li(MnyFe1-y)PO4-(MnyFe1-y)PO4 olivine joins. New sublattice thermodynamic models are proposed to describe the para-equilibrium in Li(MnyFe1-y)PO4-(MnyFe1-y)PO4 joins. Moreover, the elastic Gibbs energy approach extended in the large deformation regime is used to calculate the coherent miscibility gaps corresponding to (100) habit plane. The para-equilibrium and coherent miscibility gaps are calculated providing our prior estimated enthalpy of formation and the elastic constants of olivine compounds and enthalpy of mixing of binary sub-systems from first principles simulations based on Density Functional Theory (DFT). The experimental data on the para-equilibrium join is successfully reproduced, and the system is likely to experience the (100) coherent phase transformation. Our thermodynamic models of the Li(MnyFe1-y)PO4-(MnyFe1-y)PO4 join are able to describe most of the features of the electrochemical behavior of Li(MnyFe1-y)PO4 cathodes including the electrochemically driven phase diagram, open circuit voltage (OCV), asymmetry of charging/discharging processes, potential shift and favorable coherent phase transformation.

The discovery of new metallic materials is of prime importance for the development of new technologies in many fields such as electronics, aerial and ground transportation as well as construction. These materials require metals which are obtained from various pyrometallurgical processes. Moreover, these materials need to be synthesized under extreme conditions of temperature where liquid solutions are produced and need to be contained. The design and optimization of all these pyrometallurgical processes is a key factor in this development. We present several examples in which computational thermochemistry is used to simulate complex pyrometallurgical processes including the Hall&ndash, Heroult process (Al production), the PTVI process (Ni production), and the steel deoxidation from an overall mass balance and energy balance perspective. We also show how computational thermochemistry can assist in the material selection in these extreme operation conditions to select refractory materials in contact with metallic melts. The FactSage thermochemical software and its specialized databases are used to perform these simulations which are proven here to match available data found in the literature.

Phosphorus is known to be a strongly segregating element in steel; even small amounts influence the solidification phenomena and product quality during casting processes. In order to provide an accurate prediction tool for process control in steelmaking, a CALPHAD-type thermodynamic optimization of the Fe–C–P system was performed including modeling of the binary Fe–P subsystem. The liquid phase was modeled using the Modified Quasichemical Model (MQM) in the pair approximation, which generally yields better results for strong short-range ordering (SRO) tendency in the solution. The solid bcc and fcc solutions were described using the Compound Energy Formalism (CEF). In addition, ab-initio calculations were performed to estimate the enthalpies of formation of the corresponding end-member for fcc and bcc, respectively. The phosphides Fe3P, Fe2P and FeP were treated as stoichiometric compounds. Higher order phosphides were not considered, since there is no reliable experimental information available in literature. The present model successfully reproduces most of the literature data within the experimental uncertainty in the Fe–C–P system without introducing a ternary parameter for the liquid phase. Compared with previous thermodynamic assessments, the agreement with recently published thermal analysis measurements of Fe–P and Fe–C–P alloys is significantly improved.

An accurate knowledge of the electrical properties of molten salts and slags is important for the design, optimization and control of several electrochemical processes. The electrical conductivity of molten salts and slags is in principle of ionic nature, however when metals are dissolved in electrolyte electrons may also contribute to the electrical conductivity. Only a few studies reporting an electronic conductivity of simple molten salts can be found in the literature and the microscopic aspect of the electron transport within ionically bonded systems remains vague. The aim of this work is to fill-up this gap. To do so, a new theoretical model, based on the Boltzmann transport equation, is developed to represent the electronic conductivity of metals diluted in molten salt systems at up to about 10 mol % of metal. It is shown that the proposed model has a good predictive capability for most molten salts-metal systems for which experimental data is available. Then, based on this approach, the electronic conductivity of different cryolitic melts of interest for the aluminum production industry are predicted. Particular attention is drawn to the melts containing both lithium and potassium fluorides as they are considered as potential additives for the next reduction cells generation. A good agreement is obtained with the only available set of experimental data for standard electrolytes reported by Haarberg et al. (1996), indicating on one hand the predictive capability of the model for more complex systems (i.e. those with a significant short range ordering) and on the other hand the reliability of our predictions for all cryolitic melts as a function of the cryolitic ratio, temperature and additive amount.

Thermal Energy Storage (TES) systems coupled to thermodynamic power cycles capable of generating electrical work are becoming strategic technologies of the future. The efficiency of TES fluids is a function of several thermodynamic and physical properties such as their heat capacity, latent enthalpy of melting and thermal conductivity. The stored thermal energy in these materials can be delivered to heat transfer fluids either by sensible heat or latent heat interactions. Challenges in the design of TES-based technologies are linked to the thermal stability and corrosivity of the selected heat storage fluid that needs to be encapsulated in metallic tubes/containers as well as the heat transfer efficiency. Latent heat storage materials, also known as Phase Change Materials (PCMs) offer high specific heat storage capacity and can operate at a constant temperature if their chemistry is adjusted so that they represent minima on liquidus surfaces. Working at a constant and minimal temperature is highly desirable from an engineering perspective as it limits corrosion degradation and temperature cycling stresses experienced by the container materials. Up to now, the identification of optimal PCMs has been mostly done via experimental trial-and-error based on limited amounts of thermodynamic data. Being able to theoretically identify PCM candidates and fine-tune their thermo-physical behavior would drastically improve their design. We present here an efficient tool specifically developed for the design of PCMs. This tool was used to identify 30 PCM candidates found in high-order anhydrous chloride-based salt systems that can operate at a temperature of 390 ± 10 ∘ C.

Individual transport numbers provide a measure of the charge ratio which is carried by each ionic species of an electrolyte. However, unlike the electrical conductivity or diffusion coefficients, this quantity lacks a clear definition from the statistical mechanics point of view. In practice, it is measured via complex experimental setups, and most of the interpretation of the available data is made by using the Nernst–Einstein approximation. Here we show that this approach is not suitable in molten salts due to the large contributions of the cross-terms due to the ionic interactions in the total ionic conductivity. We propose a partition scheme that allows to attribute these cross-terms to the various ions, allowing for an estimate of the transport numbers in a series of molten salt formed by mixing NaF and AlF3 at various compositions. The results are interpreted using the speciation of the melt, which is characterized by the formation of various AlFx clusters. At large AlF3, the Na+ ions are shown to contribute almost totally to the ionic conductivity.

An experimental set-up and specific sample containment allowing high-temperature in situ EXAFS measurements of radioactive, air-sensitive and corrosive fluoride salts is described. First results are reported and compared with molecular dynamics simulations of the highly disordered liquid salts., The development at the Delft University of Technology (TU Delft, The Netherlands) of an experimental set-up dedicated to high-temperature in situ EXAFS measurements of radioactive, air-sensitive and corrosive fluoride salts is reported. A detailed description of the sample containment cell, of the furnace design, and of the measurement geometry allowing simultaneous transmission and fluorescence measurements is given herein. The performance of the equipment is tested with the room-temperature measurement of thorium tetrafluoride, and the Th—F and Th—Th bond distances obtained by fitting of the EXAFS data are compared with the ones extracted from a refinement of neutron diffraction data collected at the PEARL beamline at TU Delft. The adequacy of the sample confinement is checked with a mapping of the thorium concentration profile of molten salt material. Finally, a few selected salt mixtures (LiF:ThF4) = (0.9:0.1), (0.75:0.25), (0.5:0.5) and (NaF:ThF4) = (0.67:0.33), (0.5:0.5) are measured in the molten state. Qualitative trends along the series are discussed, and the experimental data for the (LiF:ThF4) = (0.5:0.5) composition are compared with the EXAFS spectrum generated from molecular dynamics simulations.

As part III of this series, the model is extended to iron oxide-containing melts. All available experimental data in the FeO-Fe2O3-Na2O-K2O-MgO-CaO-MnO-Al2O3-SiO2 system were critically evaluated based on the experimental condition. The variations of FeO and Fe2O3 in the melts were taken into account by using FactSage to calculate the Fe2+/Fe3+ distribution. The molar volume model with unary and binary model parameters can be used to predict the molar volume of the molten oxide of the Li2O-Na2O-K2O-MgO-CaO-MnO-PbO-FeO-Fe2O3-Al2O3-SiO2 system in the entire range of compositions, temperatures, and oxygen partial pressures from Fe saturation to 1 atm pressure.

A structural molar volume model was developed to accurately reproduce the molar volume of molten oxides. As the non-linearity of molar volume is related to the change in structure of molten oxides, the silicate tetrahedral Q-species, calculated from the modified quasichemical model with an optimized thermodynamic database, were used as basic structural units in the present model. Experimental molar volume data for unary and binary melts in the Li2O-Na2O-K2O-MgO-CaO-MnO-PbO-Al2O3-SiO2 system were critically evaluated. The molar volumes of unary oxide components and binary Q-species, which are model parameters of the present structural model, were determined to accurately reproduce the experimental data across the entire binary composition in a wide range of temperatures. The non-linear behavior of molar volume and thermal expansivity of binary melt depending on SiO2 content are well reproduced by the present model.

This work describes the application of a direct search method to the optimization of problems of real industrial interest, namely three new material science applications designed with the FactSage software. The search method is BiMADS, the biobjective version of the mesh adaptive direct search (MADS) algorithm, designed for blackbox optimization. We give a general description of the algorithm, and, for each of the three test cases, we describe the optimization problem, discuss the algorithmic choices, and give numerical results to demonstrate the efficiency of BiMADS.