This study discusses the atomic interactions between Aland Si in the mixed sites of the tau(11)-Al4Fe1.7Si solid solution structure, with respect to chemical composition and temperature. We first investigated the crystal structure of the tau(11)-Al4Fe1.7Si solid solution using Density Functional Theory (DFT), confirming recent findings suggesting significant changes to the solution structure. Subsequently, we quantified the 0 K short-range ordering (SRO) in the structure by analysing the coordination polyhedra of the mixed sites and calculating the energies of structures with mixed Al/Si occupations. Our results indicate that the SRO contribution can be neglected. In addition, we generated all the end-members corresponding to the substitution of Al by Si on the mixed sites of the structure and considering site 2d as occupied by Fe or vacant. We calculated the formation enthalpies of these end-members by DFT and determined their isobaric heat capacities by using a Debye-Wang model together with the DFT calculations of their equation of state. Using these calculations, we determined Si site fractions over a temperature range from 0 K to the decomposition temperature of the solid solution, applying a model derived from the Bragg-Williams approximation. Our findings enable us to propose reliable sublattice model for the solid solution, which differ significantly from existing models in the literature.

This paper presents a study of the crystal structure and crystal chemistry of the tau-Mg 32 (Al,Zn) 49 phase. We first performed DFT calculations to resolve conflicting data concerning the occupancy of site 2 a of the solid solution crystal structure. Subsequently, 16 ordered configurations derived from the mixing of Al/Zn on sites 24 g 1 , 24 g 2 and 48 h of the solid solution structure, as well as the mixing of Mg/Zn on site 12 e 1 were generated. We then used DFT calculations to derive the formation enthalpies of all the end-members of the solid solution, their elastic constants by imposing 51 finite deformations for each end-member , and their energies as a function of volume. These calculations were used in a Debye-Wang model (in Slater form) to calculate the heat capacities of the 16 end-members and to obtain in fine their Gibbs energies. At last, these calculations were used to support a thermodynamic model based on the Bragg-Williams approximation, enabling all mixed sites occupancies to be calculated at any temperature and chemical composition. For instance, the predictions we carried out at 633 K and 800 K are in very good agreement with the available measurements. On the basis of these new results, we have determined the chemical ordering of the solid solution over a very wide range of chemical composition and temperature, which has enabled us to propose a new sublattice model for the tau-Mg 32 (Al,Zn) 49 solid solution. This sublattice model is both simpler and more accurate than all the other models used in the literature since it agrees with the crystal structure and the crystal chemistry of the tau-Mg 32 (Al,Zn) 49 phase in a large range of temperature and chemical composition.

This paper presents a comprehensive examination of the τ8-Al2Fe3Si4 solid solution, investigating its crystal chemistry and short-range order. To do so, Density functional theory (DFT) calculations were performed, simulating partial substitutions of Al and Si on the four mixed sites of the structure. Our results indicates a negligible contribution from the SRO, allowing the Bragg-Williams approximation to be used to describe its crystal chemistry. Subsequently, systematic substitutions of Al and Si on all mixed sites generated a complete set of ordered structures, called end-members. The formation enthalpies, equation of state and elastic constants for each end-member were calculated, allowing the Gibbs free energy of the solid solution to be derived using the Debye-Wang model. On the basis of this new theoretical insights, a thermodynamic model was developed, predicting the Si occupancy factors in all the mixed sites of the structure at different temperatures, allowing the quantification of its chemical ordering.

(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.

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.

This paper presents investigations on the thermodynamic stability of the Al13Fe4 solid solution in the Al-Fe-Mn ternary system as well as its crystal chemistry characterisation. In order to carry out this study, the isobaric heat capacity of the solution was measured at high temperature using a high precision three-dimensional probe. The heat capacity of the Al13Fe4 binary compound measured in this study between 600 K and 1223 K is CP(T) = 23.97 + 8.18.10−2T − 7.63.105T2. This value is significantly different from other measurements in the literature and we show in this paper that our measurements are not only more accurate than those in the literature but also more thermodynamically consistent with all other measurements and calculations of the enthalpy of formation of this phase. Measurements of the enthalpy of formation of the solid solution were also performed by in − situ synthesis in a DSC. These new measurements were complemented by DFT calculations of the enthalpy of formation at 0 K of the solid solution. Our calculations and measurements show that the substitution of Fe by Mn is responsible for a large increase in the solid solution enthalpy of formation. These new experimental and calculated data were used to develop a thermodynamic model of the solution. Finally, we utilized our model to calculate the Fe sof of the solid solution structure over its entire chemical composition range (simulating the complete substitution of all Fe atoms with Mn) as a function of temperature. The chemical ordering of the solid solution was thus quantified, revealing its ideal nature near its melting temperature. These results allowed the development of a new SL-model for the solution, both simpler and more reliable than those used in the literature.

This work investigates the mixed site occupancy of aluminium and silicon atoms in the β-AlFeSi phase. For this purpose, the six mixed Al/Si sites of the β-AlFeSi structure were considered independent and alternatively substituted by Al or Si, thus generating 64 ordered structures or end-members. The enthalpy of formation of each end-member was calculated by DFT. These calculations allowed us to derive the enthalpy of mixing of the solid solution at 0 K, over a wide range of chemical compositions, from the Al-Fe binary system to the Si-Fe binary system. In addition, the heat capacities of the solid solution were determined using a Debye model based on the calculation of the elastic constants and the equation of state of each end-member. These heat capacity values were used along with the enthalpy of formation we calculated to determine the Gibbs free energies of all the end-members of the β-AlFeSi structure. Finally, the configurational entropy of mixing from the Compound Energy Formalism (CEF) for the configurational entropy of mixing was subsequently used to calculate the occupation fractions of the Si sites on the Al sites of the β-AlFeSi structure, at 300 K and 938 K, the latter being the thermal decomposition temperature of this compound. These original site occupancy data were used to quantify the chemical ordering of the solid solution and to compare different sublattice (SL) models. We thus highlight that the SL model of the β-AlFeSi solution most commonly accepted in the literature generates considerable errors in its thermodynamic description, contrary to the model proposed in this paper, which is both simple and particularly accurate, consisting in merging the sites Al(1)-Al(6), the sites Al(2)-Al(3) as well as the sites Al(4)-Al(5).

The crystal chemistry of the Al-13(Fe,TM)(4 )(TM = Co, Cr, Ni, Pt) solid solutions has been investigated by combining formation enthalpy measurements by differential scanning calorimetry (DSC), density functional theory (DFT) calculations and thermodynamic modelling. The formation enthalpies of seven alloys of the Al-13(Fe,Co)(4) solid solution were measured by DSC at 920 K, allowing the determination of the mixing enthalpy of the solution. These measurements are presented here for the first time and highlight the ideal nature of this solid solution. In addition, the mixing enthalpy of the Al-13(Fe,TM)(4) solid solutions (TM = Co, Cr, Ni, Pt) was determined by DFT at 0 K. These calculated and measured data (in the case of the Al-13(Fe,Co)(4) solid solution) were used to perform thermodynamic modelling of the solid solutions and better understand their thermodynamic stability. In addition, our modelling was used to calculate the TM occupancy on the Fe sites of the Al-13(Fe,TM)(4) solid solution structure at different temperatures. These data were used to quantify the chemical ordering of the solid solutions as a function of temperature. While these solid solutions show significant chemical ordering at low temperatures, only the Al-13(Fe,Pt)(4) solution remains highly ordered at high temperatures. These data are presented for the first time in this paper and have allowed us to design an optimal sublattice (SL) model for the Al13Fe4 solid solutions. (C) 2022 Elsevier B.V. All rights reserved.

This paper is dedicated to the Calphad modelling of the Cr–Fe–Nb–Sn–Zr quinary system. In previous papers, the thermodynamic modelling of the Cr–Nb–Sn–Zr quaternary system, the Fe–Sn–Zr and Fe–Nb–Zr ternary systems as well as the Fe–Nb binary system were carried out. Since no experimental data were available for the Cr–Fe–Sn and Fe–Nb–Sn ternary systems, new partial isothermal sections have been measured at 1073K and 973K, respectively. In addition to these experimental data, Density Functional Theory (DFT) calculations are performed in order to determine formation enthalpies of the stable and metastable ordered compounds. At last, the Special Quasirandom Structures (SQS) method is used together with DFT calculations in order to calculate the mixing enthalpy of the A2 (bcc) binary solid solution. Finally, these experimental and calculated data are jointly used with those from the literature as input data for the Calphad modelling of the Cr–Fe binary system as well as the Cr–Fe–Nb, Cr–Fe–Sn, Cr–Fe–Zr and Fe–Nb–Sn ternary systems. The ternary systems are then combined into a quinary database for which application examples are provided.

Thermodynamic and kinetic calculations are commonly used for forecasting phase transformations in multicomponent alloys as a function of composition, temperature, and time. They also turn to be very useful for new alloy design. Thus, in the framework of the qualification of existing industrial alloys and the development of new ones (chromium [Cr]-coated zirconium [Zr] alloys, for instance), a new generation of thermodynamic databases has been developed thanks to the systematic use of ab initio calculations. Indeed, density functional theory calculations are significant for the determination of formation enthalpies of stable and metastable phases. Moreover, the special quasirandom structure method is used for the prediction of face-centered cubic, body-centered cubic, and hexagonal closest packed mixing enthalpies in binary solid solutions. The resulting thermodynamic database is a very powerful tool for correctly predicting second-phase precipitate occurrence in industrial alloys and precisely calculate their volume fraction, chemical composition, and existence domain as a function of temperature. The second part of the paper deals with the development of the Ekinox-Zr numerical tool that has been linked to the Zr thermodynamic database using the OpenCalphad Application Software Interface (OCASI) interface of the OpenCalphad software (a free software for multicomponent equilibrium calculations). This tool has been developed to accurately simulate oxide growth and oxygen diffusion into the alloy during high-temperature isothermal oxidation of Zr alloys. The recent developments have been dedicated to the simulation of high-temperature transients showing a good agreement with experimental data.

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 AuCuL1(0)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 Fe-Sn-Zr system has been studied by first principles calculation and modelled with the Calphad method using the literature and new experimental data. The work includes a revision of Fe-Sn and Fe -Zr systems. Our experimental study has confirmed that the W5Si3 phase (stoichiometry Zr5Sn2,3Fe0,7) is stable at 1350 degrees C but also down to 1000 degrees C. Moreover, the crystal structure of the X '' phase has been determined. The formation enthalpies of all the ordered configurations of the C15, C16, C36, E1a phases and the stoichiometric Fe5Sn3, Fe3Sn2, FeSn, FeSn2, Fe23Zr6, FeSn2Zr6 (theta), Fe36.36Sn36.36Zr27.27 (N) et Fe14.39Sn43.47Zr39.13 (X '') compounds have been calculated using the Density Functional Theory (DFT). The mixing enthalpies of the A1, A2 and A3 binary solid solutions have been calculated using the Special Quasirandom Structures (SQS) and DFT calculation. From these new experimental and calculated data, new thermodynamic assessments are proposed for Fe-Sn, Fe-Zr and Fe-Sn-Zr systems. (C) 2019 Elsevier B.V. All rights reserved.

This work reports the Calphad modelling of the Cr-Nb-Sn-Zr quaternary system. In a previous paper, the thermodynamic modelling of the Cr-Nb-Sn system was presented. Since no experimental data were available for the Cr-Sn-Zr ternary system, new experimental data are provided, within this study, on the isothermal section at 900 degrees C. A ternary C14 phase has been identified on the Sn-poor side of the phase diagram. In addition to these experimental data, Density Functional Theory (DFT) calculations are carried out in order to determine formation enthalpies of the stable and metastable compounds. At last, the Special Quasirandom Structures (SQS) method is jointly used with DFT calculations in order to estimate the mixing enthalpies of the A2 and A3 binary solid solutions. Finally, these experimental and calculated data in addition to those from the literature, are used as input data for the Calphad modelling of the Cr-Zr, Nb-Zr and Sn-Zr binary systems and the Cr-Nb-Zr, Cr-Sn-Zr and Nb-Sn-Zr ternary systems. A complete database for the Cr-Nb-Sn-Zr quaternary system is provided.

The Cr-Nb-Sn system has been studied experimentally, by first principles calculation and finally modeled with the Calphad method. The experimental study has been carried out on the Cr-Sn binary system to determine the solubility of Sn in the A2 (Cr) solid solution, but also in the Cr-Nb-Sn ternary system in order to determine phase equilibria of the isothermal section at 800°C and 1100°C. Besides, the formation enthalpies of all the ordered configurations of the C15 and A15 phases and the stoichiometric Nb6Sn5 and NbSn2 phases have been calculated using the Density Functional Theory (DFT). The mixing enthalpies of the A2 binary solid solutions have been estimated using the Special Quasirandom Structures (SQS). All these new experimental and calculated data have been taken into account for a new thermodynamic assessment of the three binary and the ternary systems.