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Balancing the hardness and electrical conductivity of copper alloys within complex compositions and processes poses a formidable challenge. This study proposes a strategy combining machine learning with the Pareto front techniques to identify optimal combinations of composition and processing for Cu-xTi (1.5 ≤ x ≤ 5.4, in wt.%) alloys. Through thermodynamic calculations, precipitation simulations, and experimental characterizations, the microstructural evolution of β'-Cu4Ti precipitates in the designed alloys was explored. The interpretability and predictability of the machine learning model played a crucial role in understanding impact of complex alloy compositions and processing on the evolution of properties, thereby guiding the design of Cu-Ti alloys towards improved attributes. A novel strategy integrating machine learning with Pareto front is proposed for alloy design, facilitating the rapid screening of Cu-Ti alloys that exhibit superior hardness and electrical conductivity simultaneously. [ABSTRACT FROM AUTHOR]

In this paper, quantitative two-dimensional (2-D) phase-field simulations were performed to gain insight into the effects of B and Nb for Al-Ti-Nb balanced-ratio GH4742 alloys. The microstructure evolution during the precipitation process was simulated using the MICRESS (MICRostructure Evolution Simulation Software) package developed in the formalism of the multi-phase field model. The coupling to CALPHAD (CALculation of PHAse Diagram) thermodynamic databases was realized via the TQ interface. The morphological evolution, concentration distribution, and thermodynamic properties were extensively analyzed. It is indicated that a higher Nb content contributes to a faster precipitation rate and higher amounts and the smaller precipitate size of the γ′ phase, contributing to better mechanical properties. The segregation of the W element in γ′ precipitate due to its sluggish diffusion effect has also been observed. Higher temperatures and lower B contents accelerate the dissolution of boride and reduce the precipitation of borides. With the increased addition of B, the formation of borides may have a pinning effect on the grain boundary to hinder the kinetic process. In addition, borides are prone to precipitate around the interface rather than in the bulk phase. Once the M3B2 borides nucleate, they grow in the consumption of γ′ phases. [ABSTRACT FROM AUTHOR]

Scandium is the best alloying element to improve the mechanical properties of industrial Al-Si-Mg casting alloys. Most literature reports devote to exploring/designing optimal Sc additions in different commercial Al-Si-Mg casting alloys with well-defined compositions. However, no attempt to optimize the contents of Si, Mg, and Sc has been made due to the great challenge of simultaneous screening in high-dimensional composition space with limited experimental data. In this paper, a novel alloy design strategy was proposed and successfully applied to accelerate the discovery of hypoeutectic Al-Si-Mg-Sc casting alloys over high-dimensional composition space. Firstly, high-throughput CALculation of PHAse Diagrams (CALPHAD) solidification simulations of ocean of hypoeutectic Al-Si-Mg-Sc casting alloys over a wide composition range were performed to establish the quantitative relation 'composition-process-microstructure'. Secondly, the relation 'microstructure-mechanical properties' of Al-Si-Mg-Sc hypoeutectic casting alloys was acquired using the active learning technique supported by key experiments designed by CALPHAD and Bayesian optimization samplings. After a benchmark in A356-xSc alloys, such a strategy was utilized to design the high-performance hypoeutectic Al-xSi-yMg alloys with optimal Sc additions that were later experimentally validated. Finally, the present strategy was successfully extended to screen the optimal contents of Si, Mg, and Sc over high-dimensional hypoeutectic Al-xSi-yMg-zSc composition space. It is anticipated that the proposed strategy integrating active learning with high-throughput CALPHAD simulations and key experiments should be generally applicable to the efficient design of high-performance multi-component materials over high-dimensional composition space. [ABSTRACT FROM AUTHOR]

In this paper, an efficient design of a Ti-modified Al-Si-Mg-Sr casting alloy with simultaneously enhanced strength and ductility was achieved by integrating computational thermodynamics, machine learning, and key experiments within the Bayesian optimization framework. Firstly, a self-consistent Al-Si-Mg-Sr-Ti quinary thermodynamic database was established by the calculation of phase diagram method and verified by key experiments. Based on the established thermodynamic database, a high-throughput Scheil-Gulliver solidification simulation of the A356-0.005Sr alloy with different Ti contents was carried out to establish the "composition-microstructure" quantitative relationship of the alloy. Then, by combining the computational thermodynamic, machine learning, and experimental data within the Bayesian optimization framework, the relationship "composition/processing-microstructure-properties" of A356-0.005Sr with different Ti contents was constructed and validated by the key experiments. Furthermore, the optimum alloy composition of the Ti-modified A356-0.005Sr casting alloy was designed based on this integration method with the Bayesian optimization framework and verified by the experiments. It is anticipated that the present integration method may serve as a general one for the efficient design of casting alloys, especially in the high-dimensional composition space. [ABSTRACT FROM AUTHOR]

16 Mg–Al–Zn–Bi quaternary alloys were utilized to measure the phase equilibria and transformation temperatures in the Mg-rich Mg–Al–Zn–Bi quaternary system by means of the X-ray diffraction, electron probe micro-analysis and differential scanning calorimetry techniques. The isothermal section at 400 °C and three vertical sections along Mg–8 wt%Al–0.75 wt%Zn– x Bi, Mg–3.4 wt%Al–0.5 wt%Zn– x Bi and Mg–6.9 wt%Al–2.3 wt%Zn– x Bi in the Mg–Al–Zn–Bi quaternary system were constructed. Based on the literature data, the ternary Mg–Al–Bi and Mg–Bi–Zn systems were re-assessed using the CALculaiton of PHAse Diagram (CALPHAD) approach. The calculated phase equilibria agree well with the measured data. By directly extrapolating the constituent sub-ternary systems, the thermodynamic database for the Mg–Al–Zn–Bi quaternary system was developed. The remarkable consistency between the predicted phase equilibria and the presently measured data in Mg–Al–Zn–Bi quaternary system further demonstrated the accuracy and reliability of the established thermodynamic database. After that, by using the newly developed thermodynamic database, the growth restrict factors and the solidification curves in Bi-containing AZ series magnesium alloys were calculated and analyzed. It was confirmed that the grain size of AZ alloys can be refined with the addition of Bi, and the component Al had larger grain refinement effect than Bi. Besides, the amount of Bi had also noticeable effect on the solidification sequence of the AZ alloys. [ABSTRACT FROM AUTHOR]

A variety of experimental tracer diffusivities of Mg and O in magnesium oxide available in the literature were first assessed. Atomic mobilities including bulk and short-circuit diffusion of Mg and O were then obtained by means of the CALPHAD (Calculation of Phase Diagram) approach. Afterwards, the diffusion-controlled kinetic model of oxidation in a gas-MgO-Mg environment was developed based on the moving boundary model and Fick's law, coupling with the modified thermodynamic description of MgO. A mathematical expression for parabolic rate constant k p of the oxide scale was derived for magnesia and correlated with the thermodynamic and diffusion kinetic information. The evaluated k p results were in line with the experimental data. Finally, the oxidation process of pure magnesium at 673 K was model-predicted, and the predicted evolution of the oxide thicknesses agreed very well with the experimental data. It was indicated that the grain boundaries diffusion of magnesium cations predominated the high temperature oxidation process. [ABSTRACT FROM AUTHOR]

The solidification diagrams of A357-Sc, A360-Sc and A380-Sc were constructed on the basis of the Scheil-Gulliver solidification simulations and previously well-established thermodynamic database, from which the optimal additional amounts of Sc in Al-Si-(Mg) series hypoeutectic alloys were designed for the best mechanical properties, and then validated by the microstructure observation and mechanical property test. With the designed levels of Sc addition, the eutectic (Si) particles were well refined and the primary (Al) grains evolved from the elongated ones to the equiaxial ones. The primary/eutectic (Al)/AlSc 2 Si 2 interfaces were determined using the high resolution transmission electron microscope technique to be partially coherent in three dimensions. Furthermore, it was finally understood that the grain refinement of eutectic (Si) and the occurrence of partially coherent AlSc 2 Si 2 phase with (Al) matrix due to the addition of Sc allow the high density of dislocations to accommodate at grain boundary, and thus improve the mechanical strengths and ductility of Al-Si-(Mg) cast alloys. Image 1 • The optional composition of A357-Sc, A360-Sc and A380-Sc alloys were designed. • The (Al)/AlSc 2 Si 2 interfaces were determined to be partially coherent. • Dislocations accommodate at grain boundary of refined (Si) and AlSc 2 Si 2. • Mechanisms of improvement in strengths and ductility of the alloys were proposed. [ABSTRACT FROM AUTHOR]

In this paper, a comprehensive understanding of stable and metastable phase equilibria in binary Mg-Gd system was conducted with an aid of the CALculation of PHAse Diagram (CALPHAD) modeling. Firstly, thermodynamic descriptions of all the stable phases in the Mg-Gd system were re-assessed by considering all the experimental data in the literature. The discrepancy between the phase equilibria and thermochemical properties existing in the previous assessments was eliminated, and the better agreement with the experimental data was achieved in the present assessment. Secondly, the Gibbs energies for metastable β''-Mg 3 Gd and β'-Mg 7 Gd were constructed based on the first-principles and CALPHAD computed results as well as their correlation, and then incorporated into the CALPHAD descriptions. The model-predicted solvuses of (Mg) in equilibrium with the metastable β''-Mg 3 Gd and β'-Mg 7 Gd compounds showed very good agreement with the limited experimental data. Finally, the presently obtained thermodynamic descriptions of both stable and metastable phases in the binary Mg-Gd system were further validated by realizing the quantitative Scheil-Gulliver solidification simulations of 5 as-cast Mg-Gd alloys, and the successful prediction of the precipitation sequences in Mg-15Gd and Mg-12Gd alloys during the aging process. [ABSTRACT FROM AUTHOR]

Thermodynamic assessments have been performed for the Ni-Ti binary and Ni-Cr-Ti ternary system by the CALPHAD method. Combining the experimental and ab initio calculated data on the enthalpies of formation of Ni-Ti compounds, a better description for Ni-Ti phases has been obtained. Based on the new assessments of the binary sub-systems and the recent experimental data on phase equilibria, a reassessment of the Ni-Cr-Ti system was carried out. Apart from the thermodynamic assessments, the interdiffusion coefficients for the fcc phase of the binary Ni-Ti were re-optimized and the ternary Ni-Cr-Ti system were determined experimentally over a temperature range from 1123 to 1273 K employing the diffusion-couple technique. Subsequently, atomic mobility data for the fcc phase of the Ni-Cr-Ti system were assessed and most diffusivity data were satisfactorily described. [ABSTRACT FROM AUTHOR]

Based on the recently proposed physically-based segmented model, the descriptions for Gibbs energy of pure Cr and Nb down to 0 K were first established. After that, a thermodynamic re-assessment of binary Cr-Nb system down to 0 K was then performed by taking into account all the experimental phase equilibria and thermodynamic properties. Especially, the experimental heat capacities of Cr 2 Nb at low temperatures ignored in previous assessments were utilized in the present assessment. The calculated phase equilibria and thermodynamic properties according to the presently obtained thermodynamic descriptions of binary Cr-Nb system agree well with most of the experimental data, and show better agreement than the previous assessments. [ABSTRACT FROM AUTHOR]

In order to establish a self-consistent thermodynamic database for Al-Si-Mg-Ce quaternary system, all the thermodynamic descriptions of 6 boundary binaries, i.e., Al-Mg, Al-Si, Al-Ce, Mg-Si, Mg-Ce, and Si-Ce were first unified. Then, the thermodynamic descriptions for ternary Al-Mg-Ce system were re-assessed using the CALculation of PHAse Diagrams (CALPHAD) method based on all the critically reviewed experimental phase equilibria. Moreover, the consistency between thermodynamic descriptions for Al-Si-Ce ternary system and those for the unified binaries was checked and confirmed. Subsequently, the thermodynamic database for the Al-Si-Mg-Ce quaternary system was established by combining the four ternary subsystems, and the phase equilibria/thermodynamic properties of the quaternary system were predicted via direct extrapolation from the ternary systems. The reliability of the established database was finally validated in one Al-7Si-0.6Mg-0.4Ce quaternary model alloy by comprehensively comparing its experimentally measured phase transition temperatures and solidified microstructure characteristics with the Gulliver-Scheil simulation ones. Good agreement between the thermodynamic predictions and experimental results indicates the present thermodynamic database is reliable. [ABSTRACT FROM AUTHOR]

Using published experimental phase equilibria, a self-consistent thermodynamic database of the Al-Si-Mg-Sc quaternary system in Al-rich corner was established by application of the CALPHAD (CALculation of PHAse Diagram) technique. The reliability of the thermodynamic database was tested in two quaternary model cast alloys by comprehensive comparison of their experimentally measured solidified microstructure characteristics and phase transition temperatures with the calculated ones. Scheil-Gulliver simulations were performed, allowing construction of a solidification diagram for Sc-added A356 alloys to examine the influence of Sc levels on the solidification behavior of cast A356 alloys. With the aid of theoretical solidified microstructure analysis and its qualitative relationship with mechanical properties, the optimal amount of added Sc in A356 alloys was determined to be 0.54 wt.%. The experimental mechanical property measurements and microstructural characterizations confirmed that the A356-0.54 wt.% Sc alloy exhibits the best comprehensive mechanical performance. Additionally, the grain refining mechanisms in Sc-supplemented A356 alloys were described, suggesting a path for further improvement of the overall mechanical performance. [ABSTRACT FROM AUTHOR]

Metastable c-TiAlCrN is a new generation quaternary hard protective coating that is of interest due to its excellent performance. Based on limited experimental phase stability data together with the first-principles computed free energies, a thermodynamic evaluation of the pseudo-ternary c-TiN/c-AlN/c-CrN system was first performed using the CALculation of PHAse Diagram (CALPHAD) technique, allowing the construction of the metastable phase equilibria. This thermodynamic description was used in combination with the Cahn-Hilliard model to perform numerical simulation of the microstructure evolution in c-Ti 0.45 Al 0.47 Cr 0.08 N coating during spinodal decomposition. The simulated results showed that Cr atoms were distributed in both c-TiN- and c-AlN-rich domains with preferential location at the interface regions. This enrichment at the interface can decrease the lattice mismatch and lead to a smaller driving force for spinodal decomposition compared with Cr-free coatings. Overall, the simulated composition wavelengths after 7200 s agree well with the experimental results. [ABSTRACT FROM AUTHOR]

Two-dimensional (2-D) phase-field simulations were employed in the present work to investigate the effect of temperature gradient on the microstructure evolution in various Ni–Al–Cr bond coat/substrate systems (i.e., β/γ + γ′, γ + β/γ + γ′, γ′ + β/γ + γ′ and γ + γ′/γ + γ′) with the aid of MICRESS (MICRostructure Evolution Simulation Software). Reliable CALPHAD (CALculation of PHAse Diagram) thermodynamic and atomic mobility databases were coupled via TQ interface. The γ/γ′ interfacial energy was estimated by using the Kaptay's method. The present phase-field simulations indicate that component Al migrates towards substrate, while component Cr towards bond coat during the interdiffusion process. The temperature gradient promotes diffusion of both Al and Cr, which greatly accelerates the failure of various bond coat/substrate systems caused by the rapid depletion of Al concentration in bond coat. Furthermore, the formation of γ′ polycrystalline structure around bond coat/substrate interface as well as in the substrate is also observed, which may result in the generation of intergranular fracture and crack propagation. [ABSTRACT FROM AUTHOR]

In this paper, a general and effective strategy was first developed to maintain the CALPHAD atomic mobility database of multicomponent systems, based on the pragmatic numerical method and freely accessible HitDIC software, and then applied to update the atomic mobility descriptions of the hcp Mg–Al–Zn, Mg–Al–Sn, and Mg–Al–Zn–Sn systems. A set of the self-consistent atomic mobility database of the hcp Mg–Al–Zn–Sn system was established following the new strategy presented. A comprehensive comparison between the model-predicted composition–distance profiles/inter-diffusivities in the hcp Mg–Al–Zn, Mg–Al–Sn, and Mg–Al–Zn–Sn systems from the presently updated atomic mobilities and those from the previous ones that used the traditional method indicated that significant improvement can be achieved utilizing the new strategy, especially in the cases with sufficient experimental composition–distance profiles and/or in higher-order systems. Furthermore, it is anticipated that the proposed strategy can serve as a standard for maintaining the CALPHAD atomic mobility database in different multicomponent systems. [ABSTRACT FROM AUTHOR]

Abstract: Based on the thermodynamic description, the atomic mobilities of Cu, Fe and Ni are inversely parameterized from the experimental data on tracer diffusion and interdiffusion. The quality of atomic mobilities obtained in the present work has been verified through extensive comparisons between the calculated and measured tracer diffusion coefficients, interdiffusion coefficients, concentration profiles and diffusion paths in ternary Cu–Fe–Ni alloys. With such thermodynamic and kinetic descriptions of fcc Cu–Fe–Ni alloys, it is convenient to computationally study the presence and evolution of zero-flux planes (ZPFs) with respect to the lattice-fixed frame of reference as well as the number-fixed frame of reference, the results of which shed light on novel Cu-based and Fe-based alloy design for industry. [Copyright &y& Elsevier]

Abstract: In order to assist the design of bcc Ti–Ta and Ta–W alloys, the atomic mobilities of Ti, Ta and W are studied critically with the DICTRA software (DIffusion Controlled TRAnsformation), based on the published thermodynamic description, self-diffusion coefficients, impurity diffusion coefficients, intrinsic diffusion coefficients and interdiffusion coefficients. Good agreement is obtained from the comprehensive comparisons between the calculated and measured diffusion coefficients. To further verify the obtained atomic mobilities, the concentration profiles and Kirkendall marker shift in bcc Ti–Ta and Ta–W diffusion couples are explored computationally, the results of which can reproduce satisfactorily the experimental measurements. [Copyright &y& Elsevier]

Abstract: Based on the experimental data available in the literature, the mobility end-members for impurity diffusion of twelve elements, i.e. Ag, Al, As, Au, Cu, Mo, Nb, Sb, Sn, Ti, W and Zn, in bcc Fe have been critically studied. The effect of ferromagnetic ordering is taken into consideration, which allows the dramatic change of kinetic behaviors around the Curie temperature to be considered. Comprehensive comparisons between the calculated and experimentally measured impurity diffusion coefficients are made, where the good agreement confirms not only the parameters obtained in this work but also the model developed by Jönsson. This work contributes to the establishment of a general mobility database to computationally study microstructure evolution upon heat treatment and performance prediction during service. [Copyright &y& Elsevier]

Abstract: A reaction calorimeter coupled with first-principles calculations was employed to obtain enthalpies of formation for τ1 (Al9FeNi) and τ2 (Al10Fe3Ni) compounds. The previous thermodynamic model for describing the disorder/order transition (fcc_A1/L12) in the Al–Fe–Ni system was modified to extrapolate this model to quaternary and higher-order systems. The first-principles energy calculations for the end-members of sub-lattice models in ternary compounds and L12 phase were performed to facilitate subsequent modeling. The existence of the experimentally observed miscibility gap for ternary B2-ordered phase is detected by the present calculation. Such a feature cannot be identified with available thermodynamic software due to the tiny difference between the Gibbs energies associated with different phase assemblages. A set of thermodynamic parameters for the Al–Fe–Ni system was obtained via thermodynamic modeling. Numerous experimental data including phase diagram, thermodynamic properties and site occupation of Fe in B2 phase are well accounted for by the present modeling. [Copyright &y& Elsevier]

Abstract: Following the treatment in CALPHAD, experimental data on diffusivities in Fe–Mn and Fe–C binary systems are critically evaluated with the DICTRA software to derive atomic mobilities. The effect of magnetic ordering on diffusion in bcc phase is taken into account, and the obtained atomic mobilities are expressed as functions of temperature and compositions with the Redlick–Kister polynomials. Based on the mobility parameters obtained in this work for the end-members and the interaction terms, comprehensive comparisons between the calculated and experimentally measured quantities are made. Due to the lack of experimental diffusivities for the ternary system, extrapolation based on binary information is performed, the results of which are used to study uphill diffusion of C in fcc Fe–Mn–C alloys. Such C diffusion against its own concentration gradient is a common occurrence for ternary systems containing one interstitial element, provided that the initial alloy compositions of diffusion couples are well chosen. In addition, the operating tie line evolution for proeutectic ferrite growth is also investigated, where C diffusion-controlled fast and Mn diffusion-controlled slow growths are discussed. [Copyright &y& Elsevier]

Abstract: On the basis of the available thermodynamic parameters, the atomic mobilities of Nb and Zr in bcc Nb–Zr alloys are critically assessed as functions of temperatures and compositions by the CALPHAD method, where self-diffusion coefficients, impurity diffusion coefficients, tracer diffusion coefficients, interdiffusion coefficients and concentration curves are simultaneously optimized. Comparisons between the calculated and experimentally measured diffusion coefficients are made, where good agreement is evident. In addition, the obtained mobility parameters can reproduce a reasonable concentration profile for the Nb/Zr diffusion couple annealed at 1868 K for 5400 s. [Copyright &y& Elsevier]

Phase-field modeling coupled with calculation of phase diagram (CALPHAD) database was utilized to perform a series of two-dimensional phase-field simulations of microstructure evolution in the γ + γ′/γ + γ′ Ni–Al–Cr mode bond coat/substrate systems. With the aid of phase-field simulated microstructure evolution, the relationship between the interdiffusion microstructure and the cohesiveness/aluminum protective property with different alloy compositions and bond coat thicknesses was fully discussed. A semi-quantitative tie-line selection criteria for alloy composition of the bond coat/substrate system with the identical elements, i.e., that the equilibrium Al concentrations of γ′ and γ phases in the bond coat should be similar to those in substrate, while the phase fraction of γ′ in the bond coat tends to be higher than that in the substrate, was then proposed to reduce the formation of polycrystalline structure and thermal shock from the temperature gradient. [ABSTRACT FROM AUTHOR]

In this paper, a critical review of all the experimental diffusivities in fcc Ni−X (X = Rh, Ta, W, Re, and Ir) systems available in the literature was first performed. The four end-member parameters corresponding to self- and impurity diffusivities in fcc Rh, Ta, W, Re and Ir in Ni−X (X = Rh, Ta, W, Re, and Ir) systems were then evaluated based on the literature data, first-principles results and semi-empirical equations. After that, the atomic mobilities for fcc Ni−X (X = Rh, Ta, W, Re, and Ir) systems were assessed by using DICTRA (DIffusion-Controlled TRAnsformations) software package on the basis of the critically reviewed diffusivities and the corresponding thermodynamic descriptions. The excellent agreement between various calculated diffusion properties, including impurity/tracer diffusivities and interdiffusivities, and the experimental data was obtained. Finally, the reliability of the currently obtained atomic mobilities in fcc Ni−X (X = Rh, Ta, W, Re, and Ir) alloys were validated by comparing the model-predicted concentration profiles of 24 groups of fcc Ni/Ni−X (X = Rh, Ta, W, Re, and Ir) diffusion couples with the experimental data. The presently obtained atomic mobility descriptions for fcc Ni−X (X = Rh, Ta, W, Re, and Ir) systems are to be merged into the atomic mobility database for nickel-based superalloys. • Self- and impurity diffusivities were evaluated based on first-principles results and semi-empirical equations. • The atomic mobilities of fcc Ni-rich Ni–X (X = Rh, Ta, W, Re, and Ir) alloys were constructed. • Comparisons between the calculated and experimental data show the mobility parameters lead to a better agreement. • To further verify the accuracy of the obtained mobility parameters in this work, the concentration curves are reproduced. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the thermodynamic descriptions of the binary Al-Sn and ternary Mg-Al-Sn systems were updated by using the CALculation of PHAse Diagram (CALPHAD) approach. For the Al-Sn sub-binary system, the solubility of Sn in (Al) fcc , which was ignored in the previous assessment, together with the recently experimental enthalpies of mixing in the liquid phase were taken into account. The calculated phase equilibria and thermodynamic properties in the binary Al-Sn system showed better agreement with more experimental information than those in the previous assessment. As for the Mg-Al-Sn ternary system, the newly updated thermodynamic descriptions of the Al-Sn system as well as those of the Mg-Al and Mg-Sn binary systems from the literature were adopted. A set of reliable and self-consistent thermodynamic parameters for the Mg-Al-Sn ternary system were obtained by reassessing the thermodynaic parameters of the liquid and solid solutions. Better agreement between the calculated results and the experimental data was achieved in the present assessent in comparison with the previous one. Furthermore, the Scheil-Gulliver solidification simulations were performed to predict the volume fractions of Mg 2 Sn, (Mg) hcp and γ (Mg 17 Al 12) phases in the 9 as-cast Mg-Al-Sn alloys. The simulation results were compared with the experiental as-cast microstructures in the literature, which further validated the presently obtained thermodynamic descriptions. Highlights • Solubility of Sn in (Al) fcc was considered. • New enthalpies of mixing in Al-Sn liquid phase were considered. • Thermodynamic descriptions for Al-Sn and Mg-Al-Sn systems were updated. • Better agreement with the experimental data were achieved. • Scheil solidification simulations were performed. [ABSTRACT FROM AUTHOR]

In this paper, a series of terminal alloys were first prepared, undergoing microstructure and composition characterizations through a combination of X-ray diffraction (XRD), scanning electron microscopy (SEM), and electron probe microanalysis (EPMA) techniques. Subsequent diffusion couple experiments were conducted to acquire initial concentration profiles in fcc Co-Mn-Fe and Co-Mn-Ni alloys. By leveraging experimental composition profiles from 12 groups of diffusion couples measured using EPMA, alongside the reported thermodynamic data, atomic mobility parameters within the fcc phase of the two ternary systems were accurately determined using HitDIC software. Employing the resulting kinetic databases, a comprehensive set of simulated data, including composition profiles and diffusion paths, was generated for all diffusion couples, demonstrating strong alignment with corresponding experimental results. Moreover, interdiffusivities spanning a wider composition range within the fcc phase of Co-Mn-Fe and Co-Mn-Ni systems were computed at different temperatures, shedding light on the diffusion behavior of alloy components in response to temperature and concentration fluctuations. Finally, drawing from the reported thermodynamic data and the currently matched atomic mobility parameters, overviews of the intricate relationships among diffusion-related properties and configurational entropy indicate that the endeavor to develop comprehensive thermodynamic and kinetic databases is essential for tailoring High-Entropy Alloys. • 12 groups of fcc single-phase Co-Mn-X (X = Fe, Ni) diffusion couples were prepared. • Self-consistent kinetic descriptions for target alloys were accurately determined. • High-throughput determination is achieved using the numerical inverse method. • Accuracy of the evaluated kinetic descriptions was comprehensively proved. [ABSTRACT FROM AUTHOR]

Abstract: A hybrid approach of CALPHAD and first-principles calculations was employed to perform a thermodynamic modeling of the Sn–Sr system. The experimental phase diagram and thermodynamic data available in the literature were critically reviewed. The enthalpies of formation for the 6 stoichiometric compounds (i.e. Sr2Sn, Sr5Sn3, SrSn, Sr3Sn5, SrSn3 and SrSn4) at 0K were computed by means of first-principles calculations. These data were used as the experimental values in the optimization module PARROT in the subsequent CALPHAD assessment to provide thermodynamic parameters with sound physical meaning. A set of self-consistent thermodynamic parameters was finally obtained by considering reliable literature data and the first-principles computed results. Comprehensive comparisons between the calculated and measured quantities indicate that all the reliable experimental information can be satisfactorily accounted for by the present thermodynamic description. [Copyright &y& Elsevier]

Abstract: An exponential formulation was proposed to replace the linear interaction parameter in the Redlich–Kister (R–K) polynomial for the excess Gibbs energy of ternary solution phase. The theoretical analysis indicates that the proposed new exponential formulation can not only avoid the artificial miscibility gap at high temperatures but also describe the ternary system well. A thermodynamic description for the Al–Mg–Si system and its boundary binaries was then performed by using both R–K linear and exponential formulations. The inverted miscibility gaps occurring in the Mg–Si and the Al–Mg–Si systems at high temperatures due to the use of R–K linear polynomials are avoided by using the new formulation. Besides, the thermodynamic properties predicted with the new formulation confirm the general thermodynamic belief that the solution phase approaches to the ideal solution at infinite temperatures, which cannot be described with the traditional R–K linear polynomials. [Copyright &y& Elsevier]

Abstract: Knowledge of thermodynamics and phase diagram is a prerequisite for understanding many scientific and technological disciplines. To establish a reliable thermodynamic database, an integrated approach of key experiments and thermodynamic modeling, supplemented with first-principles calculations, can be utilized. In this paper, first investigations of phase diagram and thermodynamics of technologically important Al alloys (focusing on the Al–Cu–Fe–Mg–Mn–Ni–Si–Zn system, which covers the major elements in most commercial Al alloys) is reviewed with an emphasis on the need of the integrated approach. Second, the major experimental methods (X-ray diffraction, metallography, electron probe microanalysis, differential thermal analysis, diffusion couple method, and calorimetry), which are widely employed to provide phase diagram and thermodynamic data, are briefly described. Third, the basics of the first-principles calculations and CALPHAD are presented focusing on the integration of these two computational approaches. Case study for the representative Al–Fe–Ni ternary system is then demonstrated, followed by a thermodynamic modeling of the quinary Al–Fe–Mg–Mn–Si system and a brief summary to our recent activities on investigations of phase equilibria in multicomponent Al alloys. [Copyright &y& Elsevier]

Abstract: In conjunction with the thermodynamic parameters in the literature, the atomic mobilities of the V–Nb and V–Zr bcc alloys were assessed from experimental diffusion coefficients. The assessed atomic mobilities are given as functions of temperatures and composition in the CALPHAD format. Comparisons between the calculated and experimental quantities show that the obtained mobility parameters enable most of the experimental diffusion data to be well reproduced. Based on the velocity constructions for lattice planes in V/Nb diffusion couples, the displacements of Kirkendall makers were investigated under various annealing conditions, and the results are in general agreement with experimental values. In addition, computational studies of V/Zr diffusion couples were carried out for the kinetic behaviors of V 2Zr at various annealing temperatures, from which the temperature dependence of the interdiffusion coefficients for V 2Zr was evaluated. [Copyright &y& Elsevier]

Abstract: Based on the thermodynamic parameters and various experimental diffusion data available in the literature, the atomic mobilities of Ti and Nb in bcc Ti–Nb alloys are critically evaluated with respect to temperatures and compositions in terms of the CALPHAD method. The finally obtained mobility parameters are presented, and extensive comparisons between the calculated and experimentally measured quantities are made. The results show that the obtained mobility parameters can satisfactorily reproduce most of the experimental results, and therefore they can be safely used in diffusion-related simulations to deal with practical problems of interest. In addition, the obtained mobilities, together with the published thermodynamic information, are successfully applied to model the movement of Kirkendall markers in the Ti/Nb diffusion couples. [Copyright &y& Elsevier]

Valence electron concentration (VEC) was treated as a useful parameter to predict solid solution phases, and the VEC rule was proposed for high entropy alloys (HEAs). However, this empirical rule has its limitations, which restricts its applications for phase predictions in HEAs. In this paper, we revisited the empirical VEC rule with the HT-CALPHAD approach in the Al–Co–Cr–Fe–Ni system. Our investigation showed that more than 90% compositions are observed to have BCC structures when 5.7≤VEC≤7.2 and we got 100% FCC structures when VEC≥8.4. Meanwhile, we proposed a data screening procedure to classify and discover the new HEAs. The concepts of average density (ρ HEA), highest BCC/FCC temperatures (T B C C / F C C m a x), and temperature ranges (Δ T BCC / FCC) were introduced as useful data screening criteria to down-screen the candidate alloy compositions for specific engineering applications. In the current work, we have identified three HEA categories (refractory BCC HEAs, light-weight BCC HEA and refractory FCC HEAs) in the Al–Co–Cr–Fe–Ni system and proposed the best candidate in each group. More importantly, our investigation showed the HEA non-equiatomic composition space provides ample opportunities for the discovery of the next-generation HEAs. Image, graphical abstract [ABSTRACT FROM AUTHOR]

In this paper, thermodynamic descriptions of binary Si–Yb and ternary Al–Si-Yb system were assessed using the CALculation of PHAse Diagram (CALPHAD) technique, from which insights to the solidification behaviors of Yb-modified Al–Si alloys were attained. Firstly, all the experimental phase equilibria and thermodynamic properties in binary Si–Yb and ternary Al–Si-Yb systems were critically evaluated. Based on evaluated experimental data in the literature, the thermodynamic parameters of binary Si–Yb system were then updated, resulting in a better agreement with the experimental phase equilibrium data in Si-rich part than the previous assessment in the literature. Afterward, the thermodynamic descriptions of ternary Al–Si-Yb system were established on the basis of thermodynamic parameters of three boundary binaries, and their reliability was verified by comprehensively comparing the predicted thermodynamic properties/solidified behaviors with the literature data. Finally, the Scheil-Gulliver solidification simulations of different Yb-modified Al–Si alloys were conducted, from which the effect of Yb additions on the solidification sequences, phase transition temperatures, and phases/structures fractions in Al–Si-Yb alloys was analyzed. • All the literature data in Si–Yb and Al–Si-Yb systems were critically reviewed. • Thermodynamic descriptions of binary Si–Yb system were updated. • Thermodynamic assessment of ternary Al–Si-Yb system was conducted. • Solidification behaviors of Yb-modified Al–Si alloys were analyzed. [ABSTRACT FROM AUTHOR]

Reliable diffusivities and atomic mobilities of fcc Co–Mn–Cr alloys are the important keystones for establishing the accurate diffusion database for CoCrFeMnNi high-entropy alloys and other relevant alloys, but they are still missing in the literature. In this paper, diffusion couple experiments together with Hi gh- t hroughput D etermination of I nterdiffusion C oefficients (HitDIC) software were employed to efficiently obtain diffusion descriptions of fcc Co–Mn–Cr alloys. Six diffusion couples were prepared and examined to provide the prerequisite composition profiles. Feature selection and regularization techniques in HitDIC software were adopted to extract the corresponding interdiffusion coefficients and atomic mobilities. A reliable set of diffusion descriptions of the fcc Co–Mn–Cr alloys were therefore obtained and verified. Investigations of the underlying composition- and temperature-dependent diffusion behaviors were enabled and demonstrated. [ABSTRACT FROM AUTHOR]

This paper starts from the critical review of all the phase equilibria of the Ni-Si-Zn ternary system reported in the literature. The discrepancies in the phase equilibria from different sources were comprehensively clarified. After that, the first-principles method was utilized to compute the enthalpies of formation for four Ni-Si-Zn ternary compounds at 0 K. The thermodynamic description for Ni-Si binary system was then updated by means of CALPHAD (CALculation of PHAse Diagram) approach using the 2-sublattice order/disorder transition model. The artificial miscibility gap in the liquid phase existing in all the previous assessments was successfully removed. Subsequently, a thermodynamic assessment of the Ni-Si-Zn system was performed by means of CALPHAD approach based on the critically reviewed literature data and first-principles results together with the updated thermodynamic descriptions for Ni-Si binary system. An optimal set of thermodynamic parameters in ternary Ni-Si-Zn system were obtained, yielding a good agreement with most of the experimental data. Based on the presently obtained thermodynamic parameters, the complete liquidus projection and reaction scheme were finally predicted and presented. • Discrepancies of experimental phase equilibria in Ni-Si-Zn system were clarified. • Enthalpies of formation for four ternary compounds were computed via FP method. • Ni-Si system was re-assessed by using 2-sublattice order/disorder transition model. • A set of reliable thermodynamic parameters of the Ni-Si-Zn system was obtained. [ABSTRACT FROM AUTHOR]

Based on the experimental equilibrium data on spinodal decomposition in the literature together with the newly measured data in the present work, a complete metastable phase diagram for the pseudo-binary c–TiN/c-AlN system was constructed for the first time, from which a self-consistent thermodynamic description was then established by means of CALculation of PHAse Diagram (CALPHAD) method with the aid of first-principles computed free energies. By coupling with the CALPHAD thermodynamic database, two- and three-dimensional quantitative numerical simulations of microstructure evolution in metastable c–Ti 1−x Al x N coatings during spinodal decomposition were performed using Cahn-Hilliard model. Three sets of diffusivity data available in the literature were carefully screened by comparing the simulated microstructures with the experimental ones, and one of them was chosen for the final simulations. The simulated composition wavelengths during spinodal decomposition at different temperatures agree with the experimental data. Moreover, the effect of the composition fluctuation on the microstructure evolution during spinodal decomposition was also comprehensively investigated. [ABSTRACT FROM AUTHOR]

Highlights: [•] Impurity diffusion coefficients in meta-stable fcc Mg are predicted. [•] Reliable diffusivities of the Al–Cu–Mg system are predicted systematically. [•] Combination of first-principles and CALPHAD is feasible to study diffusivity. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the experimental investigation of the liquid phase migration and its numerical simulation by applying the CALPHAD approach. The liquid phase migration during sintering is studied through the diffusion couple technique along with electron probe micro-analysis (EPMA) measurements. Based on the CALPHAD approach, the relation between the volume fraction of liquid phase and the mass fraction of Co is calculated for the WC–Co cemented carbide system. The information on the volume fraction of liquid phase could serve as the input in a numerical model. The simulation of liquid Co migration in WC–Co cemented carbide is performed and compared with the previous and present experimental results. These simulations could be used in choosing the suitable initial composition for raw materials of liquid phase sintered cemented carbide. [Copyright &y& Elsevier]

Abstract: Based on various kinds of diffusivities as well as the thermodynamic descriptions within the CALPHAD framework, the atomic mobilities of U, Ti, Nb and Mo are explored in this work with the DICTRA software. The mobility end-members are evaluated from the impurity diffusivities as well as the extrapolated interdiffusivities, while the interaction parameters for atomic mobilities are determined from the tracer diffusivities, the intrinsic diffusivities and the interdiffusivities. The reliability of such purely kinetic quantities is carefully verified by the comparison between the calculated and experimentally measured quantities, including the concentration profiles in Ti/U diffusion couples. This work is established to provide fundamental information for U-based alloy design when the kinetics of microstructure evolution is of prime concern. [Copyright &y& Elsevier]