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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.

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 Cr2Nb 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.

The thermodynamic description of the Ni-Mo-W system has been updated and thereafter the ternary fcc Ni-Mo-W diffusion couples annealed at 1473 K for 72 h have been scanned to measure the composition profiles by using electron probe microanalysis (EPMA). By analyzing the composition profiles using the Whittle-Green method, the interdiffusion coefficients were deduced at the intersections of every two diffusion paths. These data were then combined with the thermodynamic description to determine the diffusion mobilities of Ni, Mo and W by means of DICTRA software. The calculated composition profiles and diffusion paths were carefully compared with the experimentally measured data, and an excellent agreement has been achieved. A previous conclusion that Mo diffuses faster than W in the Ni-base alloys was confirmed in the present work. In addition, Co promotes the diffusion of Mo whereas both Cr and W retard its diffusion in the Ni-base alloys containing 5.0 at% Mo. Both Co and Mo retard the diffusion of W in the Ni-base alloys containing 5.0 at%W.

Based on 18 face centered cubic (fcc) single-phase diffusion couples in ternary Ni–Al–X (X = Rh and W) systems together with the recently developed numerical inverse method, high-throughput measurements of the composition-dependent interdiffusivity matrices in fcc Ni–Al–X (X = Rh and W) alloys at 1423, 1473 and 1523 K were performed in the present work. Their reliability was comprehensively validated through comparison between the model-predicted composition/interdiffusion flux profiles for each diffusion couple and the corresponding experimental data. Moreover, the direct comparison with the interdiffusivities evaluated from traditional Matano-Kirkaldy method as well as those from the literature and in the boundary binary systems was also made. The errors for the determined interdiffusivities were evaluated by a scientific method considering the error propagation. The three-dimensional main interdiffusivity planes for fcc Ni–Al–X (X = Rh and W) systems over the investigated concentration ranges at 1423, 1473 and 1523 K were subsequently constructed. It was then found that D ˜ A l A l N i is generally larger than D ˜ R h R h N i , while D ˜ W W N i is the smallest.

In this study, the phase equilibria of the Cu–Ni–Sn ternary system reported in the literature were critically reviewed and the discrepancies between the results from different sources were clarified. The thermodynamic parameters of the sub-binary Ni–Sn system were updated using the CALculation of PHAse Diagram (CALPHAD) approach yielding significant improvements in the description of Fcc phase boundary. Besides, the artificial miscibility gap in Ni–Sn liquid phase obtained in the previous assessment was successfully removed. Subsequently, a set of self-consistent thermodynamic parameters for the Cu–Ni–Sn ternary system over the whole composition range was systematically optimized by considering the reviewed experimental information together with the updated thermodynamic description for the Ni–Sn binary system. Comprehensive comparison of the calculated and reported thermodynamic properties as well as isothermal and vertical sections shows that the experimental information is satisfactorily reproduced by the present modeling, further validating the thermodynamic descriptions developed in this work.

On the basis of 13 groups of single-phase diffusion couples together with electron probe microanalysis technique, the composition profiles in γ and γ′ Ni–Al–Co systems at 1373–1523 K were measured. Atomic mobilities in γ Ni–Al–Co alloys were directly assessed from 9 groups of concentration profiles by means of HitDIC software. The established atomic mobilities contain only two interaction parameters, and their reliability was verified by comprehensively comparing the model-predicted concentration profiles with the experimental data in the literature and the present work. After that, the composition-dependent interdiffusion coefficients along the entire diffusion path in γ and γ′ Ni–Al–Co alloys were also evaluated at 1373–1523 K by using HitDIC. D ˜ A l A l N i and D ˜ C o C o N i in γ Ni-Al-Co alloys were validated by the results obtained by Matano-Kirkaldy method and the corresponding experimental values in Ni-Al and Ni-Co binary alloys. Comprehensive comparisons between the interdiffusion coefficients in the present work and those reported the literature validated the reliability of the presently evaluated interdiffusivities in γ’ Ni-Al-Cr alloys. The influences of Al and X contents on the D ˜ X X N i in γ Ni-Al-2 at% X (X= Co, Rh, Ta, W, Re, Os, and Ir) alloys and D ˜ A l A l N i in γ Ni-2 at% Al-X alloys were further discussed.

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–Ti1−xAlxN 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.

Based on the recently developed numerical inverse method, high-throughput measurement of the composition-dependent interdiffusivity matrices in the bcc_A2 Fe-Mn-Si alloys at 1173, 1273 and 1373 K was performed in the present work. To verify the reliability of the presently determined interdiffusivities, the ternary interdiffusivities evaluated by the traditional Matano-Kirkaldy method at the intersection points of the diffusion paths were employed to make a direct comparison. Subsequently, on the basis of the presently obtained interdiffusivities together with the thermodynamic descriptions for bcc_A2 phase in the Fe-Mn-Si system, atomic mobilities of Fe, Mn and Si in bcc_A2 Fe-Mn-Si alloys were assessed by means of DICTRA (DIffusion Controlled TRAnsformatim) software package. The comprehensive comparison between various calculated/model-predicted diffusion properties, including interdiffusivities, concentration profiles, interdiffusion fluxes and diffusion paths, and the experimental data indicates that most of the experimental data can be well produced by the presently obtained atomic mobilities. Moreover, the reliability of the present atomic mobilities was further validated by reproducing the experimental composition profiles which were not utilized in the assessment procedure.

A novel thermodynamic modeling strategy of stable solid alloy phases is proposed based on segmented regression approach. The model considers several physical effects (e.g. electronic, vibrational, etc.) and is valid from 0 K up to the melting temperature. The preceding approach has been applied for several pure elements. Results show good agreement with experimental data at low and high temperatures. Since it is not a first attempt to propose a “universal” physical-based model down to 0 K for the pure elements as an alternative to current SGTE description, we also compare the results to existing models. Analysis of the obtained results shows that the newly proposed model delivers more accurate description down to 0 K for all studied pure elements according to several statistical tests.

In the present work, the liquidus and solidus for a series of NixCo1-2xCrx alloys were measured by means of differential scanning calorimetry, and the first-principles calculations were performed to obtain total energies for all solid solutions and end-members of the intermediate phases in the Ni–Co–Cr ternary system. Various types of data from the present work and the literature were used in the assessments of the Ni–Co–Cr ternary system and sub-binary systems by the CALPHAD method, and were well reproduced by the present thermodynamic database. In addition, diffusion couples of fcc Co–Cr and Ni–Co–Cr alloys were assembled and annealed at different temperatures to extract interdiffusion coefficients. Experimental diffusion data from the present work and the literature, in conjunction with thermodynamic parameters, were adopted to assess the atomic mobilities of the fcc phase in the Ni–Co–Cr system. The calculated and experimental diffusion coefficients reach a satisfactory agreement. The diffusional kinetic database developed was further validated by appropriate predictions of composition profiles and diffusion paths.

The recently developed Arrhenius formula of a modified Sutherland equation was employed to calculate the self– and impurity diffusivities in liquid Sn, Ag, In and Sb. The reliability of the calculated self– and impurity diffusivities was validated by comparing the presently calculated results with the critically reviewed literature data. Based on the reliable tracer and chemical diffusivities available in the literature, the atomic mobility parameters in Sn–Ag–In and Sn–Ag–Sb melts were then evaluated with the aid of the available thermodynamic descriptions for the liquid phase. Comprehensive comparisons show that most of the measured and theoretical diffusivities in Sn–Ag–In and Sn–Ag–Sb melts can be reasonably reproduced by the currently obtained atomic mobilities. Moreover, the atomic mobilities were further verified by comparing the model–predicted concentration profiles with the measured ones in various liquid Sn–Ag–Sb diffusion couples.

Chromium is considered an essential addition element in multiple industrial applications. Therefore, obtaining an accurate and robust description of its properties is important. Recently, several attempts were made to improve the thermodynamic description of pure elements and binary systems in the frame of the third generation CALPHAD databases. Moreover, it became increasingly important to develop mathematical tools that can allow researchers more access to each phase of the material over the entire temperature range. Thus, the recently proposed segmented regression model was modified using the so-called sigmoid function for the case of pure Cr. A comprehensive analysis of phase equilibria and thermodynamic properties of pure Cr was used to develop an updated unary description from 0 K to 6000 K using the proposed modified segmented regression (MSR) model. In addition, two newly developed machine learning tools were utilized to analyze the datasets used in this assessment to determine any possible outliers.

s All the experimental phase equilibria and thermodynamic properties in the Si–Sr and Al–Si–Sr systems were critically reviewed. Based on the reviewed experimental data, the thermodynamic descriptions of the Si–Sr binary system were updated by using the CALculation of PHAse Diagram (CALPHAD) technique, resulting in better agreement with the experimental data, especially for the standard enthalpies of formation, than those in the previous assessment. After that, the thermodynamic assessment of the Al–Si–Sr ternary system was carried out using the CALPHAD approach. Comprehensive comparisons indicate a good agreement between the calculated phase equilibria/thermodynamic properties and the experimental/first-principles data in Al–Si–Sr ternary system. Moreover, the as-cast microstructures of 4 Sr-additional Al–Si alloys were experimentally investigated by using the scanning electron microscope and electron probe microanalysis techniques. The solidification sequence and volume fractions of precipitated phases in the 4 alloys predicated from Scheil-Gulliver solidification simulations agree reasonably with the presently measured data, which further validates the reliability of the present thermodynamic descriptions.

A systematical study of thermodynamics and diffusion kinetics in the binary Ni–Os system was performed in the present work by means of CALculation of PHAse Diagram (CALPHAD) method supported by key experiments. Based on all the available experimental phase equilibria, a full thermodynamic assessment of binary Ni−Os system was conducted. A reasonable set of thermodynamic description for the binary Ni−Os system was obtained. Comparisons between the calculated and the measured phase equilibria showed that most of the experimental information can be satisfactorily accounted for by the present thermodynamic description. Moreover, the interdiffusion coefficients in face-centered cubic (fcc) Ni−Os alloys at 1373, 1473, 1523, 1573 and 1623 K were measured by using five groups of Ni−Os semi-infinite diffusion couples together with the Sauer–Freise method. On the basis of the interdiffusion coefficients from the present work and the literature as well as the presently obtained thermodynamic description, atomic mobilities in fcc Ni−Os alloys were then assessed by means of DIffusion-Controlled TRAnsformation (DICTRA) software package. Comprehensive comparisons between the calculated and the measured diffusivities show that most of the experimental data can be well reproduced by the presently obtained atomic mobilities. In addition, the reliability of the atomic mobilities obtained in the present work were further validated by comparing the model-predicted concentration profiles of fcc Ni−Os diffusion couples with the experimental data.

The experimental viscosities and diffusivities in Al–Mg–Si melts as well as the experimental diffusivities in fcc Al–Mg–Si alloys available in the literature were first critically reviewed. The Sutherland equation was then employed to convert the experimental viscosity data into self-/tracer diffusivity data in Al–Mg–Si melts. Based on the experimental diffusivities together with the converted ones, the atomic mobilities in liquid and fcc phases of the Al–Mg–Si system were assessed by means of DIffusion-Controlled TRAnsformation (DICTRA) software package. Comprehensive comparisons showed that most of the measured and converted diffusivities in liquid and fcc Al–Mg–Si system can be reasonably reproduced by the currently obtained atomic mobilities. Moreover, the reliability of the established atomic mobilities of liquid and solid phases were further verified by two typical cases in Al–Mg–Si alloys during solidification and dissolution processes. The simulation results agree well with the experimental information, not only validating the reliability of the atomic mobilities, but also demonstrating the importance of the accurate atomic mobility database in quantitative simulation of microstructure during various preparation processes.

Based on the first-principles computed activation energy, the frequency prefactor for impurity diffusivity of Pt in fcc Al was calculated by means of the Swalin correlation. The Vignes–Birchenall correlation originally developed for binary solutions with unlimited solubility was simplified to evaluate the interdiffusivities in binary terminal solutions with limited solubility. The simplified correlation was validated in fcc Ni–Al alloys, and then applied to evaluate interdiffusivities in fcc Pt–Al alloys, showing a reasonable agreement with the limited experimental data. On the basis of the limited experimental diffusivities in the literature and the presently evaluated interdiffusivities, a set of reasonable atomic mobilities in fcc Pt–Al alloys was established. This combinational approach by utilizing the limited experimental data, first-principles results, semi-empirical/empirical correlations and DIffusion Controlled TRAnsformation (DICTRA) software package is of general validity and applicable in other binary alloys with limited diffusivity information.

The interdiffusion coefficients in fcc Co–Cr–W alloys at 1373 K have been determined from the concentration profiles across the solid–solid diffusion couples using the Whittle and Green method. On the basis of the experimental interdiffusion coefficients in this work, together with the critically reviewed experimental diffusivities available in the literature, atomic mobilities of Co, Cr and W in fcc Co–Cr–W alloys were assessed as a function of temperature and composition by means of DICTRA (DIffusion Controlled TRAnsformation) software. Comprehensive comparisons between the calculated results and the experimental data indicate that the presently obtained atomic mobilities can reasonably reproduce most of the diffusivities, concentration profiles and diffusion paths in binary and ternary systems.

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.

In this paper, a series of Ni-Al-Os alloys and Ni-Al-Cr-Os alloys were prepared, and employed to investigate their phase equilibria at 1200 °C in Ni-rich corner together with the electron probe microanalysis and X-ray diffraction techniques. For the ternary Ni-Al-Os system, the isothermal section at 1200 °C in Ni-rich corner, consisting of 1 single-phase (γ), 2 two-phase (γ'+δ and γ+γ′), and 1 three-phase (γ'+γ+δ) regions, was determined. While for the quaternary Ni-Al-Cr-Os system, the isothermal tetrahedron in Ni-rich region at 1200 °C was determined. 1 single-phase (γ), 2 two-phase (γ+β and γ+γ′), and 2 three-phase (γ'+γ+β and γ'+γ+δ) regions were constructed in 3-D space. Moreover, the solubilities of Os in both γ and γ′ phases of Ni-Al-Os and Ni-Al-Cr-Os systems were also measured. In order for a clear demonstration of the evolution of phase regions with Os addition, the isothermal projection of Ni-Al-Cr-Os at 1200 °C was utilized. After that, the possibility of replacing Re with Os during the development of new-generation single crystal Ni-base superalloys was analyzed. The results indicated that Os might be an alternative element of Re in the new-generation single crystal Ni-base superalloys.

Based on three groups of Ni/Ni–9 at% Ge diffusion couples, interdiffusion coefficients were determined in the face-centered (fcc_A1) Ni–Ge alloys at 1173, 1273 and 1373 K by means of the Boltzmann–Matano method coupled with electronic probe microanalysis (EPMA) technique. On the basis of various critically-reviewed experimental diffusivities as well as the available thermodynamic descriptions, atomic mobilities in fcc_A1 Ni–X (X=Ge, Ti and V) alloys were assessed by means of DIffusion Controlled TRAnsformation (DICTRA) software package. For the self-diffusivities in dynamically unstable fcc_A1 Ge, Ti and V, a semi-empirical correlation was employed. Moreover, the first-principles calculations were also used to calculate the activation energy for self-diffusion in fcc_A1 Ge. Comprehensive comparison between the calculated and the measured diffusivities shows that most of the experimental data can be reproduced by the atomic mobilities obtained in the present work. In addition, the reliability of the currently obtained atomic mobilities in fcc_A1 Ni–X (X=Ge, Ti and V) alloys were further validated by comparing the model-predicted concentration–distance profiles and the experimental ones.

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.

Based on critically reviewed experimental diffusion data available in the literature, atomic mobilities of Fe, Si, Cu and Zn in bcc_A2 Fe–Cu, Fe–Si and Fe–Zn alloys were assessed as a function of temperature and composition by means of DICTRA simulation package. Semi-empirical correlations were used to obtain the self-diffusivities of Cu, Si and Zn in the metastable bcc_A2 phase. Comprehensive comparisons between calculated and measured diffusivities indicate that most experimental data can be well reproduced by the presently obtained atomic mobility parameters.

The CALPHAD technique has been utilized to study the diffusion characteristics and atomic mobilities in fcc Au–Pt alloys, where the thermodynamics and kinetics descriptions are concurrently taken into consideration. For the investigated atomic mobilities, the end-members and interaction parameters are explored with the impurity diffusion coefficients, intrinsic diffusion coefficients and interdiffusion coefficients. Concentration curves in diffusion couples are computationally studied, the results of which are compared with the experimental values. In addition, the shift and distribution of Kirkendall markers are brought into discussion, based on the intrinsic diffusivities described in the lattice-fixed frame of reference.

CALPHAD kinetics has gained rapid development in recent years, due to its wide applications in engineering novel alloys. In order to simulate the diffusion problems of interest, high-quality atomic mobilities are indispensable. Based on the thermodynamic descriptions for the Mo–Ta, Mo–W, and Mo–Nb binary systems, the atomic mobilities for such alloys are inversely parameterized in this work, including the mobility end-members as well as the interaction parameters. Due to the large experimental errors for diffusion characteristics of refractory alloys at high temperatures, the experimental data are quite scattered. However, this work allows such data to be carefully selected and a set of self-consistent atomic mobilities to be well established, which can be used to study diffusion-related characteristics for Mo-based refractory alloys.

The phase diagrams and thermodynamic properties of the C–RE (RE=La, Ce and Pr) binary systems were assessed by using the CALPHAD method applied to the experimental data in the literature. In the C–RE (RE=La, Pr) systems, RE2C3 and β REC 2 (high-temperature form of REC2 phase) were modeled as non-stoichiometric phases while α REC 2 (low-temperature form of REC2 phase) was considered to be stoichiometric phase. For La2C3 phase, enthalpy increment ( H T – H 298 K ) information was also considered in the optimization. Due to their negligible homogeneities, intermediate compounds Ce2C3 and CeC2 in the C–Ce system, were treated as stoichiometric phases. One set of self-consistent thermodynamic parameters was finally obtained for each of these binary systems. Comparisons between calculated and measured phase diagrams as well as thermodynamic properties showed that most of the experimental information can be satisfactorily accounted for by the present thermodynamic descriptions.

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.

On the basis of the critically reviewed experimental diffusivities available in the literature, the atomic mobilities of Cu, Mn and Ni in fcc Cu–Mn–Ni alloys were assessed as a function of temperature and composition by means of DICTRA (DIffusion Controlled TRAnsformation) software. Comprehensive comparisons between the calculated results and the experimental data show that a good agreement is obtained for various diffusivities in binary and ternary systems, including impurity diffusion coefficients, tracer diffusion coefficients and interdiffusion coefficients. The atomic mobilities obtained can also be used to describe various diffusion phenomena for a series of binary and ternary diffusion couples, such as concentration profiles, the Kirkendall shift, the interdiffusion flux and diffusion paths.

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.

CALPHAD kinetics has evolved to be a well-established discipline, which allows complex non-equilibrium processes to be fully explored. Such a success relies on the use of Redlich–Kister polynomials to describe atomic mobilities, with the effect of temperature, composition, magnetic ordering and chemical ordering sufficiently taken into consideration. There is thus an increasing demand to construct high-quality atomic mobility databases for alloys of interest. Based on the CALPHAD framework, the atomic mobilities in fcc Cu–Ag–Au alloys are reported in this work, the results of which can provide fruitful information on alloy design.

The isothermal section of the Cu–Si–Zn ternary system at 600 °C was experimentally determined with fifteen alloys by means of optical microscopy, X-ray diffraction, and the scanning electron microscopy with energy dispersive X-ray spectroscopy. At 600 °C, no ternary compounds were observed, and five three-phase equilibria were well determined. In particular, the longstanding controversy regarding the four three-phase equilibria in the Cu-rich corner involving the phases α , β , γ - Cu5Zn8, and κ - Cu7Si was resolved experimentally in the present work. In an effort to provide a compatible thermodynamic description of the Cu–Si–Zn system for the multi-component Al-based thermodynamic database, the Cu–Zn system was remodeled using the CALPHAD approach with a new sublattice model Zn4(Cu,Zn)1(Cu,Zn)8 for the γ - Cu5Zn8 phase. Besides, the temperature dependence of enthalpy of mixing was also taken into account for the liquid phase. Subsequently, a thermodynamic description of the Cu–Si–Zn system was obtained over the entire composition range based on the presently modeled Cu–Zn system and the experimental data from the literature and the present measurements. It is found that most reliable experimental data in this ternary system are satisfactorily reproduced by the present thermodynamic modeling.

Diffusion in Ag-based solders is a practical topic that has attracted world-wide attention. With the available experimental data in the literature, the atomic mobilities of Ag, Cd and Sn in fcc Ag–Cd and Ag–Sn alloys are critically explored in this work. The proposed atomic mobility parameters can reproduce a great majority of experimental data, including impurity diffusion coefficients, tracer diffusion coefficients, intrinsic diffusion coefficients and interdiffusion coefficients. The evolutions of composition profiles and Kirkendall marker shifts in Ag–Cd binary diffusion couples are also computationally studied. The atomic mobilities obtained in this work are essential to guide the design of candidate Ag-based alloys.

On the basis of critically reviewed experimental diffusivities available in the literature, a through assessment of the atomic mobilities of Cu, Ni, and Zn in fcc Cu–Ni–Zn alloys was conducted using the DICTRA software. Comprehensive comparisons show that good agreements between the presently calculated diffusion coefficients and the experimental data were obtained. The reliability of the atomic mobilities obtained was further verified by comparing various model-predicted diffusion phenomena with the experimental information, such as concentration profiles, Kirkendall shift and diffusion paths in a series of binary and ternary diffusion couples.

Based on a critical evaluation of experimental data available in the literature, the isothermal section at 1023 K of the Cu-Fe-Si system was measured using a combination of X-ray analysis, scanning electron microscopy (SEM) with energy-dispersive X-ray (EDX) analysis, and electroprobe microanalysis (EPMA). In addition, fifteen alloys along two vertical sections at 30 and 70 at. pct Cu were subjected to differential thermal analysis (DTA), in order to provide new phase-transition temperatures. A thermodynamic modeling for the Cu-Fe-Si system was then conducted by considering reliable experimental data from the literature and the present work. All the calculated phase equilibria and thermodynamic properties agree well with the experimental ones. It is noteworthy that a stable liquid miscibility gap appears in the computed ternary phase diagrams, even though it is metastable in the three-boundary binaries. Significant improvements have been made compared with the previous assessments. The presently obtained parameters were also successfully applied to two technical cases in material design.

Various experimentally measured diffusivities of fcc Al–Mg, Cu–Mg and Al–Cu–Mg alloys available in the literature are critically reviewed in the present work. The first-principles calculations coupled with a semi-empirical correlation is employed to derive the temperature dependence of impurity diffusivity for Mg in fcc Cu. Atomic mobilities for the above fcc alloys are then evaluated as a function of temperature and composition by means of DICTRA (DIffusion Controlled TRAnsformation) software. Comprehensive comparisons between calculated and measured diffusivities show that most of the experimental data can be well reproduced by the presently obtained atomic mobilities. The concentration profiles and diffusion paths are predicted with the mobility parameters in a series of binary and ternary diffusion couples. A good agreement is obtained between experiment and simulation.

Based on various kinds of experimental diffusivities and thermodynamic parameters available in the literature, the atomic mobilities of Al and Cu in face-centered cubic (fcc) Al–Cu alloys have been assessed as a function of temperature and composition by means of DIffusion Controlled TRAnsformation (DICTRA) software package. Comprehensive comparisons between the calculated and measured diffusivities show that most of the experimental data can be well reproduced by the presently obtained atomic mobilities. In addition, the atomic mobilities obtained in the present work can also reasonably predict the concentration profiles for a variety of diffusion couples in fcc Al–Cu alloys including the one prepared in the present work.

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 Jonsson. This work contributes to the establishment of a general mobility database to computationally study microstructure evolution upon heat treatment and performance prediction during service.

Based on special quasirandom structures (SQS’s) and first-principles calculations, enthalpies of mixing have been predicted for four binary fcc solid solutions in the Al–Cu, Al–Si, Cu–Si, and Mg–Si systems at nine compositions ( x = 0.0625 , 0.125, 0.1875, 0.25, 0.5, 0.75, 0.8125, 0.875, 0.9375, where x is the mole fraction of A atoms in the A–B binary system). The present results are compared with previous first-principles calculations and thermodynamic modeling results available in the literature. In order to provide insight into the understanding of mixing behavior for these solid solutions, the spatial charge density distributions in these binary solid solutions are also analyzed. The results obtained herein indicate that the SQS model can be used to estimate the thermodynamic properties of solid solutions, especially for metastable phases, the thermodynamic qualities of which are rarely measured.

The phase equilibria of the ternary Cu–Mn–Ni system in the region above 40 at.% Mn at 600 ∘C were investigated by means of optical microscopy, X-ray diffraction, scanning electron microscopy with energy dispersive X-ray spectroscopy and electron probe microanalysis. The isothermal section of the Cu–Mn–Ni system at 600 ∘C consists of 4 two-phase regions (cbcc_A12 +fcc_A1, cub_A13 +fcc_A1, cbcc_A12 + cub_A13, L 1 0 +fcc_A1) and 1 three-phase region (cbcc_A12 +cub_A13 +fcc_A1). The disordered fcc_A1 phase exhibits a large continuous solution between γ (Cu,Ni) and γ (Mn). The L 1 0 phase only equilibrates with fcc_A1 phase, and the solubility of Cu in L 1 0 phase is up to 16 at.%. A thermodynamic modeling for this system was performed by considering reliable literature data and incorporating the current experimental results. A self-consistent set of thermodynamic parameters was obtained, and the calculated results show a general agreement with the experimental data.

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.

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.

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.

The temperature of the degenerated invariant reaction in the Cu–V system was accurately determined by means of Differential Scanning Calorimetry (DSC) measurements. On the basis of the experimental data from the present work and those critically assessed from the literature, an optimal thermodynamic data set for the Cu–V system was obtained. Significant improvements have been made, compared with the previous assessments.

This paper performs an extensive investigation for the complex Al–Fe–Ni system via key experiments and thermodynamic modeling. 12 decisive alloys are prepared with a desire to provide accurate phase relationships needed for the refinement of this ternary phase diagram. The order/disorder transitions between disordered BCC _ A 2 and ordered BCC _ B 2 phases as well as between disordered FCC _ A 1 and ordered L 1 2 phases are described as a two-sublattice model. The calculations indicate that the disordered and ordered phases can be described with a single equation. A self-consistent thermodynamic description of the Al–Fe–Ni system is obtained by considering the huge amount of experimental data from the literature and the present work. Most of the experimental data can be satisfactorily reproduced by the present modeling. The complete liquidus projection and reaction scheme are also presented.

The Co–Si system is investigated via experiment and modeling. Based on the critical evaluation of the phase diagram data available in the literature, one key Co/Si diffusion couple and eight decisive alloys are prepared. The diffusion couple, which is annealed at 1323.15 K for 8 days, is first examined by scanning electron microscopy (SEM) with energy dispersive X-ray analysis (EDX), and then by electron probe microanalysis (EPMA) to determine homogeneity ranges of the phases. The alloys, which are annealed at 1373.15 K for 3 days and then water-quenched, are analyzed using X-ray diffraction (XRD), optical microscopy, differential thermal analysis (DTA), and EPMA. The thermodynamic optimization for the Co–Si system is then conducted by using the assessed literature data and the present experimental data. For ( α Co ) and ( e Co ) , the magnetic contribution to the Gibbs energy is taken into account. The sublattice model is employed to describe β Co 2 Si (the high-temperature form of the Co 2 Si phase), α Co 2 Si (the low-temperature form of the Co 2 Si phase) and CoSi. A set of self-consistent thermodynamic parameters is finally obtained. Comprehensive comparisons show that the calculated phase diagram and thermodynamic properties agree well with the experimental ones. Significant improvements have been made, compared with the previous assessments.