On the exploration of the melting behavior of metallic compounds and solid solutions via multiple classical molecular dynamics approaches: application to Al-based systems.

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.

On the transferability of classical pairwise additive atomistic force field to the description of unary and multi-component systems: applications to the solidification of Al-based alloys.

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.

On the elaboration of the next generation of thermodynamic models of solid solutions.

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.

In situ high-temperature EXAFS measurements on radioactive and air-sensitive molten salt materials.

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.

Coherent phase equilibria of systems with large lattice mismatch.

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.

Thermal conductivity of the sideledge in aluminium electrolysis cells: Experiments and numerical modelling.

During aluminium electrolysis, a ledge of frozen electrolytes is generally formed, attached to the sides of the cells. This ledge acts as a protective layer, preventing erosion and chemical attacks of both the electrolyte melt and the liquid aluminium on the side wall materials. The control of the sideledge thickness is thus essential in ensuring a reasonable lifetime for the cells. The key property for modelling and predicting the sideledge thickness as a function of temperature and electrolyte composition is the thermal conductivity. Unfortunately, almost no data is available on the thermal conductivity of the sideledge. The aim of this work is to alleviate this lack of data. For seven different samples of sideledge microstructures, recovered from post-mortem industrial electrolysis cells, the thermal diffusivity, the density, and the phase compositions were measured in the temperature range of 423 K to 873 K. The thermal diffusivity was measured with a laser flash technique and the average phase compositions by X-ray diffraction analysis. The thermal conductivity of the sideledge is deduced from the present experimental thermal diffusivity and density, and the thermodynamically assessed heat capacity. In addition to the present experimental work, a theoretical model for the prediction of the effective thermal transport properties of the sideledge microstructure is also proposed. The proposed model considers an equivalent microstructure and depends on phase fractions, porosity, and temperature. The strength of the model lies in the fact that only a few key physical properties are required for its parametrization and they can be predicted with a good accuracy via first principles calculations. It is shown that the theoretical predictions are in a good agreement with the present experimental measurements.

Thermal conductivity of molten salt mixtures: Theoretical model supported by equilibrium molecular dynamics simulations.

A theoretical model for the description of thermal conductivity of molten salt mixtures as a function of composition and temperature is presented. The model is derived by considering the classical kinetic theory and requires, for its parametrization, only information on thermal conductivity of pure compounds. In this sense, the model is predictive. For most molten salt mixtures, no experimental data on thermal conductivity are available in the literature. This is a hindrance for many industrial applications (in particular for thermal energy storage technologies) as well as an obvious barrier for the validation of the theoretical model. To alleviate this lack of data, a series of equilibrium molecular dynamics (EMD) simulations has been performed on several molten chloride systems in order to determine their thermal conductivity in the entire range of composition at two different temperatures: 1200 K and 1300 K. The EMD simulations are first principles type, as the potentials used to describe the interactions have been parametrized on the basis of first principle electronic structure calculations. In addition to the molten chlorides system, the model predictions are also compared to a recent similar EMD study on molten fluorides and with the few reliable experimental data available in the literature. The accuracy of the proposed model is within the reported numerical and/or experimental errors.

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.

Thermal conductivity of halide solid solutions: measurement and prediction.

The composition dependence of the lattice thermal conductivity in NaCl-KCl solid solutions has been measured as a function of composition and temperature. Samples with systematically varied compositions were prepared and the laser flash technique was used to determine the thermal diffusivity from 373 K to 823 K. A theoretical model, based on the Debye approximation of phonon density of state (which contains no adjustable parameters) was used to predict the thermal conductivity of both stoichiometric compounds and fully disordered solid solutions. The predictions obtained with the model agree very well with our measurement. A general method for predicting the thermal conductivity of different halide systems is discussed.

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 ß-Na2ThF6 and NaTh2F9 compounds were synthesized and subsequently analyzed with the use of X-ray diffraction. The heat capacities of both compounds were measured in the temperature ranges (2-271 K) and (2-294 K), respectively, by thermal relaxation calorimetry. Finally, a CALPHAD model coupling the structural and thermodynamic data was developed using both EMD and experimental data as input and a quasichemical formalism in the quadruplet approximation. Here, 7- and 8-coordinated Th4+ cations were introduced on the cationic sublattice alongside a 13-coordinated dimeric species to reproduce the chemical speciation, as calculated by EMD simulations and to provide a physical description of the melt.

Temperature and oxygen adsorption coupling effects upon the surface tension of liquid metals.

An accurate knowledge of the surface tension of liquid metals is critical for many theoretical and practical applications, especially in the current context of emerging growth of nanotechnology. The surface tension and its temperature dependence are drastically influenced by the level of impurities in the metal such as oxygen, sulphur or carbon. For this reason, experimental surface tension data of metals reported in literature are scattered. Strictly speaking, when referring to the surface tension of liquid metals, both variables temperature and oxygen content must be specified. There exists no clear formalism describing the coupling effect temperature and the oxygen content upon the surface tension of liquid metals. The aim of this work is to fill this gap. A thermodynamically self-consistent formulation for the surface tension of liquid metals and semiconductors as a function of temperature and oxygen content is established. According to the proposed formalism, a reliable expression for the surface tension of pure and oxygen saturated metals is then derived. The proposed model is found to be in good agreement with available experimental data, showing a good predictive capability. Aluminium is chosen and thoroughly evaluated as a case study, due to its very high sensitivity to oxygen level. Its surface tension is explicitly formulated as a function of temperature and oxygen content.

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.

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.

Important Variation in Vibrational Properties of LiFePO4 and FePO4 Induced by Magnetism.

A new thermodynamically self-consistent (TSC) method, based on the quasi-harmonic approximation (QHA), is used to obtain the Debye temperatures of LiFePO4 (LFP) and FePO4 (FP) from available experimental specific heat capacities for a wide temperature range. The calculated Debye temperatures show an interesting critical and peculiar behavior so that a steep increase in the Debye temperatures is observed by increasing the temperature. This critical behavior is fitted by the critical function and the adjusted critical temperatures are very close to the magnetic phase transition temperatures in LFP and FP. Hence, the critical behavior of the Debye temperatures is correlated with the magnetic phase transitions in these compounds. Our first-principle calculations support our conjecture that the change in electronic structures, i.e. electron density of state and electron localization function, and consequently the change in thermophysical properties due to the magnetic transition may be the reason for the observation of this peculiar behavior of the Debye temperatures.