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This study aims to incorporate a big dataset of composition profiles of fcc AlCoCrFeNi alloys, in addition to those of the related subsystem, to develop a self-consistent kinetic description for quinary high-entropy alloys. The latest feature of the HitDIC (High-throughput Determination of Interdiffusion Coefficients) code was adopted in a high-throughput and automatic manner for accommodating a dataset of composition profiles with up to 87 diffusion couples. A good convergence for the optimization process was achieved, while satisfactory results regarding the composition profiles and previously evaluated diffusion properties were obtained. Here, we present an investigation into the elemental effect of Al towards interdiffusion and tracer diffusion, and their potential effect on creep and precipitation processes. [ABSTRACT FROM AUTHOR]

The study on the temperature-dependent kinetic behavior of intermetallic compounds (IMCs) in Mg–Al–Zn (AZ) series alloy system is important since its close interrelation with the microstructure evolution under various alloying conditions as well as the T-dependent performance. However, there is a very lack of experimental study on the diffusion kinetics of the ternary IMCs in the AZ series alloy systems. The current work combines the diffusion couple technique and numerical inverse method to investigate the T-dependent kinetic coefficients, i.e., the parabolic growth constant (PGC) and interdiffusion coefficients, for ϕ-Mg5Al2Zn2 ternary IMC in the Mg–Al–Zn alloy system. The Arrhenius formula of both PGC and main interdiffusivities is obtained, i.e., ϕ k p = 5.48 × 10 - 5 exp 120010 RT m2/s, ϕ D ~ MgMg Al = 3.48 × 10 - 10 exp 50420 RT m2/s and ϕ D ~ ZnZn Al = 2.87 × 10 - 7 exp 91440 RT m2/s, based on which a numerical reproduction of the experimentally determined IMC growth is performed for verification. By comparing the current experimental and calculation results, the rate-controlling factor of the temperature-dependent diffusion growth of ϕ ternary IMC in the Mg–Al–Zn system is further discussed. [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]

Accurate interdiffusion coefficients of composition and temperature dependence are significantly important for understanding different materials processes. However, the high-throughput determination of high-quality interdiffusion coefficients, especially in multicomponent systems, has been sustaining as a challenge in materials community. This review dealt with a comprehensive summarization of the recent progress in this field, aiming at advancing a scientific routine for realizing the high-throughput determination of high-quality interdiffusion coefficients in metallic solids. First, an introduction of traditional Matano-based approaches and their recent development was given. Second, the numerical inverse methods were described, with a focus on the recently developed pragmatic numerical inverse method and related public toolkits. Potential strategies for resolving the problems about accuracy and uniqueness of the solutions to the numerical inverse methods were highlighted. The combination of numerical inverse method and diffusion multiple technique was highly proposed for high-throughput determination of interdiffusion coefficients in metallic solids with any number of components. After that, the case studies on the high-throughput determination of interdiffusivity matrices in the real Ni-based, high-entropy/high-entropy superalloys were demonstrated. Discussion on the substitution of Re in Ni-based single-crystal superalloys and the sluggish diffusion in high-entropy/high-entropy superalloys was also carried out. Fourth, the general idea for the uncertainty quantification was proposed in order to obtain high-quality interdiffusion coefficients, followed by the introduction of recent progress on the uncertainty quantification in both Matano-based methods and numerical inverse methods. Finally, the conclusions were drawn, and the future trends in diffusion community were also pointed out. [ABSTRACT FROM AUTHOR]

Abstract Diffusion behaviors of Rh, Ta, W, Re, Os, and Ir in ternary γ′-Ni 3 Al alloys were investigated at 1373–1473 K using solid-solid single-phase diffusion couples together with the recently developed HitDIC software. The temperature- and concentration-dependent ternary interdiffusivities in Ni 3 Al-X (X = Rh, Ta, W, Re, Os, and Ir) were determined from the experimental concentration profiles, and also fully validated. After that, a thorough comparison among the interdiffusivities in γ′ Ni–22.9 at% Al–0.1 at% X (X = Ti, V, Cr, Fe, Co, Ni, Nb, Mo, Ru, Rh, Ta, W, Re, Os, Ir and Pt) alloys at 1373–1473 K was then conducted, from which it can be concluded that W exhibits the lowest interdiffusivities in γ′-Ni 3 Al alloy, followed by Ta. It is finally suggested that addition of W and Ta in γ′ phase can retard the coarsening of γ′ phase and stabilize the microstructure of the nickel-based single crystal superalloys in terms of the diffusion coefficient. Highlights • Interdiffusivities in γ′ Ni–Al–X (X = Rh, Ta, W, Re, Os, Ir) alloys were determined. • Interdiffusivities in γ′ Ni–22.9 at% Al–0.1 at% X alloys at 1373–1473 K were compared. • W possesses the lowest diffusion rate in Ni 3 Al, followed by Ta. [ABSTRACT FROM AUTHOR]

A popular area of research in the field of high-temperature alloys concerns the search of substitutional elements for Re in order to manufacture single-crystal Ni-based superalloys with less or even no Re addition. To find the elements with similar or even lower diffusion coefficients than Re is an effective strategy. Based on 29 fcc diffusion couples in ternary Ni-Al-X (X = Re, Os, and Ir) systems, high-throughput measurement of composition- and temperature-dependent interdiffusivity matrices was performed using our recently developed numerical inverse method implemented in HitDIC software. The reliability of the determined interdiffusivities was validated by comprehensively comparing the model-predicted composition/interdiffusion flux profiles for each diffusion couple with the corresponding experimental data. Moreover, we also conducted a comparison with the interdiffusivities evaluated using the traditional Matano-Kirkaldy method as well as those from the literature and in boundary binary systems. After that, a comprehensive comparison of the interdiffusion coefficients in fcc Ni-2 wt pct Al-6 wt pct X (X = Ti, Co, Ni, Nb, Mo, Ru, Rh, Ta, W, Re, Os, Ir, and Pt) alloys at 1423 K to 1573 K was conducted. Results indicate that the diffusion rate of Re is lower than that of Os at 1473 K and 1523 K; but higher at 1573 K, while the diffusion rate of Ir is always slightly higher than those of Os and Re at 1473 K to 1573 K. Further analysis of the magnitude of the interdiffusion coefficient correlates with the alloying concentration, activation energy, atomic number, and atomic radius of different diffusing transition metal species (i.e., Ti, Co, Ni, Nb, Mo, Ru, Rh, Ta, W, Re, Os, Ir, and Pt) was conducted, which is expected to provide useful information regarding element choice in the development of new-generation Ni-based single-crystal superalloys. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Utilizing 8 bulk single–phase diffusion couples together with the electron probe microanalysis technique, the composition–distance profiles of fcc binary Co–Ti and Co–W systems as well as ternary Co–Ti–W system at 1373 K were first measured. The measured composition profiles for Co–rich Co–Ti, Co–W and Co–Ti–W systems at 1373 K were then adopted to evaluate the corresponding binary and ternary interdiffusivities by using the newly proposed pragmatic numerical inverse method. The comprehensive comparisons between various model–predicted diffusion properties based on the evaluated interdiffusivities due to the pragmatic numerical inverse method, including composition profiles, interdiffusion fluxes and diffusion paths, and the experimental data were conducted to validate their reliability. Moreover, the presently obtained binary and ternary interdiffusivities by the numerical inverse method were further validated by the literature data and the calculated results by using the traditional Sauer–Freise method and Matano–Kirkaldy method. [ABSTRACT FROM AUTHOR]

High-throughput measurement using the numerical inverse method combined with the diffusion multiple technique was employed to determine the composition-dependent interdiffusion coefficients in fcc Al--Co--Cr--Fe--Ni high-entropy alloys at 1273, 1323, and 1373 K. The reliability of the obtained interdiffusion coefficients was confirmed by comparing the model-predicted composition/interdiffusion flux profiles with the experimental data. The tracer diffusivities of the components were then predicted based on the obtained interdiffusion coefficients and the simplified thermodynamic description. The diagonal interdiffusion coefficients in the present high-entropy alloys were comprehensively compared with those in conventional fcc alloys. Therefore, the sluggish diffusion effect does not apply for all the elements in the present fcc Al--Co--Cr--Fe--Ni high-entropy alloys. A similar result was also observed for the evaluated tracer diffusivities. [ABSTRACT FROM AUTHOR]

In this report, a combination of the diffusion multiple technique and the recently developed pragmatic numerical inverse method was employed for a high-throughput determination of interdiffusivity matrices in Co-Cr-FeMn-Ni high-entropy alloys (HEAs). Firstly, one face-centered cubic (fcc) quinary Co-Cr-Fe-Mn-Ni diffusion multiple at 1373 K was carefully prepared by means of the hot-pressing technique. Based on the composition profiles measured by the field emission electron probe micro analysis (FE-EPMA), the composition-dependent interdiffusivity matrices in quinary Co-Cr-Fe-Mn-Ni system at 1373 K were then efficiently determined using the pragmatic numerical inverse method. The determined interdiffusivities show good agreement with the limited results available in the literature. Moreover, the further comparison with the interdiffusivities in the lower-order systems indicates the sluggish diffusion effect in Co-Cr-Fe-Mn-Ni HEAs, which is however not observed in tracer diffusivities. In order for the convenience in further analysis, a generalized transformation relation among interdiffusivities with different dependent components in multicomponent systems was finally derived. [ABSTRACT FROM AUTHOR]

Based on 15 diffusion couples located in face centered cubic single-phase region of ternary Ni–Al–Mo system, high-throughput determination of composition-dependent interdiffusivity matrices at 1273, 1373, and 1473 K was performed by using the recently developed numerical inverse method. The determined main interdiffusivities over the investigated composition and temperature ranges are all positive, and $\tilde D_{{\rm{AlAl}}}^{{\rm{Ni}}}$ is generally larger than $\tilde D_{{\rm{MoMo}}}^{{\rm{Ni}}}$. Moreover, $\tilde D_{{\rm{AlAl}}}^{{\rm{Ni}}}$ generally increases with concentration of Al, while $\tilde D_{{\rm{MoMo}}}^{{\rm{Ni}}}$ increases with concentrations of both Al and Mo. In contrast, the cross interdiffusivities can be either positive or negative. Average relative errors of $\tilde D_{{\rm{AlAl}}}^{{\rm{Ni}}}$, $\tilde D_{{\rm{AlMo}}}^{{\rm{Ni}}}$, $\tilde D_{{\rm{MoAl}}}^{{\rm{Ni}}}$, and $\tilde D_{{\rm{MoMo}}}^{{\rm{Ni}}}$ were evaluated to be 2.4, 5.1, 16.1, and 1.7% using error propagation. Furthermore, our prediction of composition profiles and interdiffusion fluxes based on evaluated interdiffusivity matrices agrees quite well with measured data. Traditional Matano–Kirkaldy method was also applied to further verify the reliability of obtained interdiffusivities. Besides, three-dimensional planes of activation energies of main interdiffusivities were also evaluated using the Arrhenius equation. [ABSTRACT FROM AUTHOR]

Based on 9 groups of ternary Ni-Al-Ta diffusion couples, high-throughput measurement of the composition-dependent interdiffusivity matrices in Ni-rich fcc Ni-Al-Ta alloys at 1473, 1523 and 1573 K was performed in the present work by using the recently developed pragmatic numerical inverse method. The errors for the determined interdiffusivities were evaluated by a scientific method considering the error propagation. Since one set of adjustable parameters was utilized for all the diffusion couples at one temperature, the main interdiffusivity planes over the investigated composition range at three temperatures were then constructed. The reliability of the determined interdiffusivities was first validated by reproducing the experimental composition profiles and interdiffusion fluxes for each diffusion couple, then by directly comparing with the limit interdiffusivities calculated by the traditional Matano–Kirkaldy method, and finally by extrapolating ternary interdiffusivities into boundary Ni-Al and Ni-Ta binaries and comparing with the binary experimental data. The simulated/calculated diffusion properties can reproduce most of the experimental data, indicating that the interdiffusivities obtained via the pragmatic numerical inverse method are reliable. On the basis of the constructed main interdiffusivity planes at different temperatures, the composition-dependent activation energies for the main interdiffusivities were evaluated, from which the activation energy planes over the investigated composition range were then constructed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The recently developed phenomenological model (Helander T, Å gren J. 1999.) in two-sublattice (2SL) formalism for describing the effect of chemical ordering on diffusion in bcc-B2 ordered alloys was carefully re-analyzed and validated to be applicable in ordered bcc-B2, fcc-L1 0 and fcc-L1 2 phases. The model was then extended into one in four-sublattice (4SL) formalism in a thermodynamically consistent way. With the more physically based 4SL model, different ordered structures (e.g., fcc-L1 0 and fcc-L1 2 ) with respect to the same disordered phase (e.g., fcc-A1) can be simultaneously described. In order to evaluate the reasonable “endmembers” in 4SL model when the first-principles calculations and/or sufficient experimental diffusivities are not available, the “pair activation energy” was proposed in the present work to a first approximation. The suggested phenomenological model in 4SL formalism together with the concept of “pair activation energy” was finally applied to describe diffusion in the ordered fcc-L1 2 phase of the binary Ni–Al system. Several advantages of using the 4SL model over the 2SL model were also demonstrated. [ABSTRACT FROM AUTHOR]

The influence of composition and temperature on the atomic mobilities of Al, Ni and Fe in the bcc_A2 and bcc_B2 Al–Ni–Fe phases was investigated based on a recently developed phenomenological model, together with the newly published thermodynamic description. The experimental interdiffusivities and tracer diffusivities of Ni and Fe in various Al–Ni–Fe alloys available in the literature were critically evaluated. The calculated diffusivities can reasonably reproduce the experimental ones. The calculated iso-diffusivity lines in the B2 phase show a minimum around the quasi-binary section at 50 at.% Al for the main diffusivities of both Al and Ni, while for the cross diffusivities of Al and Ni, they show significantly different characteristics when changing from negative to positive values. The obtained atomic mobilities were further used to predict the concentration profiles and diffusion paths in a variety of B2 Al–Ni–Fe diffusion couples. The comparison reveals the importance of full diffusion-distance measurement for the accurate determination of diffusion coefficients. [ABSTRACT FROM AUTHOR]

Viscosity and diffusivity, two important transport coefficients, are systematically investigated from unary melt to binary to multicomponent melts in the present work. By coupling with Kaptay’s viscosity equation of pure liquid metals and effective radii of diffusion species, the Sutherland equation is modified by taking the size effect into account, and further derived into an Arrhenius formula for the convenient usage. Its reliability for predicting self-diffusivity and impurity diffusivity in unary liquids is then validated by comparing the calculated self-diffusivities and impurity diffusivities in liquid Al- and Fe-based alloys with the experimental and the assessed data. Moreover, the Kozlov model was chosen among various viscosity models as the most reliable one to reproduce the experimental viscosities in binary and multicomponent melts. Based on the reliable viscosities calculated from the Kozlov model, the modified Sutherland equation is utilized to predict the tracer diffusivities in binary and multicomponent melts, and validated in Al–Cu, Al–Ni and Al–Ce–Ni melts. Comprehensive comparisons between the calculated results and the literature data indicate that the experimental tracer diffusivities and the theoretical ones can be well reproduced by the present calculations. In addition, the vacancy-wind factor in binary liquid Al–Ni alloys with the increasing temperature is also discussed. What’s more, the calculated inter-diffusivities in liquid Al–Cu, Al–Ni and Al–Ag–Cu alloys are also in excellent agreement with the measured and theoretical data. Comparisons between the simulated concentration profiles and the measured ones in Al–Cu, Al–Ce–Ni and Al–Ag–Cu melts are further used to validate the present calculation method. [ABSTRACT FROM AUTHOR]

Nb3Sn plays an irreplaceable role in superconducting parts due to its stable performance under high field conditions. Accurate phase equilibria and interdiffusion coefficients are of great significance for designing novel Nb3Sn superconductors. However, the related experimental information is still in a state of scarcity because of the difficulty in fabrication of Nb-Sn alloys caused by the large difference in melting points of Nb and Sn. In this paper, a simple but pragmatic approach was first proposed to prepare the Nb/Sn liquid-solid reactive diffusion couples (LSDCs) at 1100 °C and 1200 °C, of which the phase identification of the formed layer and the measurement of composition-distance profiles were conducted. The formed layer in Nb/Sn LSDCs was confirmed to be Nb3Sn compound. While the measured composition profiles were employed to determine the phase equilibria according to the local equilibrium hypothesis and the interdiffusion coefficients with an aid of the latest version of HitDIC software. The determined phase equilibria of Nb3Sn, (Nb) and liquid show good agreement with the assessed phase diagram. While the calculated interdiffusion coefficients and activation energy for diffusion in Nb3Sn are consistent with both experimental and theoretical data in the literature. Moreover, the growth of the formed Nb3Sn layer in Nb/Sn LSDCs was also found to be diffusion controlled. All the obtained phase equilibria and interdiffusion coefficients are of great value for further thermodynamic and kinetic modeling of the Nb-Sn system. Furthermore, it is anticipated that the presently proposed approach of fabricating liquid-solid reactive diffusion couple should serve as a general one for various alloy systems with large differences in melting points. [ABSTRACT FROM AUTHOR]

Highlights: [•] Interdiffusivities in Cu-rich fcc Cu–Al–Si alloys at 1073K were determined. [•] The present results were compared with experimental data in boundary binary systems. [•] The present results were validated by thermodynamic constraints and Fick’s law. [•] The sign of ternary cross diffusivities was predicted in terms of thermodynamics. [Copyright &y& Elsevier]

Abstract: In rapid phase transformations, interfaces are often driven far from equilibrium, and the chemical potential may exhibit a jump across the interface. We develop a model for the description of such situations in the framework of the phase-field formalism, with separate concentration fields in each phase. The key novel feature of this model is that the two concentration fields are linked by a kinetic equation which describes the exchange of components between the phases, instead of an equilibrium partitioning condition. The associated rate constant influences the interface dissipation. For rapid exchange between the phases, the chemical potentials are equal in both coexisting phases at the interface as in previous models, whereas in the opposite limit strong non-equilibrium behavior can be modeled. This is illustrated by simulations of a diffusion couple and of solute trapping during rapid solidification. [Copyright &y& Elsevier]

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: 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. [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: A systematical investigation of the diffusivities in an Al–Fe–Ni melt was presented. Based on the experimental and theoretical data about diffusivities, the temperature- and composition-dependent atomic mobilities were evaluated for the elements in Al–Ni, Al–Fe, Fe–Ni and Al–Fe–Ni melts via an effective approach. Most of the reported diffusivities can be reproduced well by the obtained atomic mobilities. In particular, for the first time the ternary diffusivity of the liquid in a ternary system is described in conjunction with the established atomic mobilities. The effect of the atomic mobilities in a liquid on microstructure and microsegregation during solidification was demonstrated with one Al–Ni binary alloy. The simulation results indicate that accurate databases of mobilities in the liquid phase are much needed for the quantitative simulation of microstructural evolution during solidification by using various approaches, including DICTRA and the phase-field method. [Copyright &y& Elsevier]

Abstract: 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. [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: 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]

Abstract: 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 and , the magnetic contribution to the Gibbs energy is taken into account. The sublattice model is employed to describe (the high-temperature form of the Co2Si phase), (the low-temperature form of the Co2Si 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. [Copyright &y& Elsevier]

Combination of nonlinear adaptive filters (CNAF) is gaining popularity as an effective solution to enhance the filter performance by addressing compromises with respect to parameter and structure settings. However, most existing algorithms study the optimal choice of different filters while neglecting the internal structure optimization of filters. This limitation restricts the performance of CNAF. In this work, we propose a new scheme of the CNAF from the perspective of diffusion adaptive over network. Instead of combining the filters in a parallel manner, we consider to organize the candidate filters in a network manner. Specifically, a network with two subnetworks is constructed, and nodes in each subnetwork serve as linear adaptive filters and nonlinear adaptive filters respectively. A generalized CNAF (GCNAF) is obtained by linking the nodes of the network. The proposed GCNAF allows information exchange and sharing among nodes, so as to enhance the performance of the combined filters. As a result, search direction of each filter is also adjusted by combining those of other filters via the diffusion over networks. We show some representative, state-of-the-art combined adaptive filters are special cases of the proposed framework. Simulations with an acoustic problem demonstrate the effectiveness of the proposed GCNAF. [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]

The interdiffusion coefficients in binary face-centered cubic (fcc) Ni–X (X = Rh, Ta, W, Re and Ir) alloys at 1473, 1523, 1573 and 1623 K were measured by using semi-infinite diffusion couples together with the Sauer–Freise method. A scientific method was employed to evaluate the errors of the determined interdiffusivities by considering the error propagation. The measured interdiffusion coefficients agree in general with the literature data. In order to find out the possible substitutional element for Re in Ni-based superalloys, a comprehensive comparison among the interdiffusion coefficients in fcc Ni–X (X = Nb, Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir and Pt) alloys with 6 wt% X at 1473–1623 K was conducted. The comparison results indicate that fcc Ni-6 wt% Os alloys exhibit the lowest diffusion coefficient, followed by Ni-6 wt% Re and Ni-6 wt% Ir alloys. The further analysis on the variation of interdiffusion coefficient with its influence factors including alloying concentration, temperature, atomic number, activation energy, atomic radius and compressibility was also performed. [ABSTRACT FROM AUTHOR]

Based on the recently developed pragmatic numerical inverse method for determining the composition-dependent interdiffusivities in a ternary system by using a single diffusion couple, high-throughput determination of the interdiffusivities in Cu-rich fcc Cu–Ag–Sn alloys at 1073 K was performed in the present work. The composition-dependent interdiffusivity matrices along the entire diffusion paths of five fcc Cu–Ag–Sn diffusion couples were obtained. The reliability of the interdiffusivities determined by the pragmatic numerical inverse method was first validated by Fick’s second law applied to numerical simulation of composition profiles and interdiffusion fluxes for each diffusion couple. The excellent agreement between the simulated results and the experimental data was obtained. In order to further validate their reliability, the traditional Matano–Kirkaldy method was employed to evaluate the interdiffusivities at the intersection point of the diffusion paths for every two diffusion couples. The good agreement between the interdiffusivities determined by the pragmatic numerical inverse method and those by the traditional Matano–Kirkaldy method was also observed. These facts indicate that the interdiffusivities determined by the pragmatic numerical inverse method are reliable. [ABSTRACT FROM AUTHOR]

• Six groups of fcc NiCrFe/LEA(MEA, HEA) diffusion couples were prepared. • Their composition profiles were experimentally measured by EPMA technique. • Interdiffusivities and tracer diffusivities in fcc NiCoCrFe system were evaluated. • Interdiffusivities of Co, Cr and Fe in MEAs and HEAs are lower than those in LEAs. • Sluggish diffusion in Co-Cr-Fe-Cr HEAs is not exist on absolute temperature scale. Six groups of fcc solid/solid diffusion couples, including Ni-Cr-Fe/ low-entropy (pure Ni, and NiCo, NiCr, and NiCoCr) alloys, Ni-Cr-Fe/ medium-entropy (CoCrNi) alloys, and Ni-Cr-Fe/ high-entropy (CoCrFeNi) alloys, were prepared, and their composition profiles were experimentally measured. Concentration-dependent interdiffusion and tracer diffusion coefficients in fcc Ni-Co-Cr-Fe system at 1473 K were retrieved with the aid of High-throughput Determination of Interdiffusion Coefficients (HitDIC) software and their reliability was validated. In most cases, D ˜ C r C r N i > D ˜ F e F e N i > D ˜ C o C o N i . The comprehensive comparison between the interdiffusivities/tracer diffusivities in the NiCo, NiCr, NiCoCr low-entropy, CoCrNi medium-entropy, and CoCrFeNi high-entropy alloys and those reported data available in the literatures indicates that the interdiffusivities Co, Cr, and Fe in low-entropy alloys are the largest than those in the other two types of alloys. While the tracer diffusivity in Co-Cr-Fe-Ni HEAs may have no sluggish phenomenon when the absolute temperature is used. [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: Based on critical review of interdiffusivities, tracer diffusivities and impurity diffusivities available in the literature, atomic mobilities of fcc Al-Zn and Ni-Zn alloys are evaluated by means of the DICTRA software. A comprehensive comparison between the calculated diffusivities and the measured ones, as well as that between the model-predicted concentration profiles and the experimental ones, indicates that the presently obtained atomic mobilities are reliable. It is demonstrated that with fewer adjustable parameters, the presently calculated diffusivities and concentration profiles in fcc Al-Zn alloys yield a comparably good fit to the experimental ones, in comparison with the previous assessment. [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]

Abstract: The phase equilibria at 950°C of the Co–Mo–Ti system was investigated by a combination of a diffusion couple technique and equilibrated alloys. The samples were examined by means of optical microscopy, scanning electron microscopy, electron probe microanalysis, and X-ray diffraction analysis. The isothermal section of the Co–Mo–Ti system at 950°C consists of 7 three-phase fields and 15 two-phase fields. The following five three-phase equilibria were well determined: (1) TiCo2 (h)+MoCo3 +Mo6Co7, (2) TiCo2 (c)+TiCo2 (h)+TiCo, (3) TiCo2 (h)+TiCo+Mo6Co7, (4) TiCo+Ti2Co+(Mo,Ti), and (5) TiCo+Mo6Co7 +(Mo,Ti). The solubility of Ti in Mo6Co7 was determined to be 23.1at.% Ti. The solubilities of Mo in TiCo2 (h), TiCo2 (c), and TiCo were measured to be 11.4, 4.7, and 5.4at.% Mo, respectively. The solubility of Mo in Ti2Co is about 0.3at.% Mo. The two-phase region of TiCo3 +MoCo3 was found to be very narrow and close to the TiCo3 side. [Copyright &y& Elsevier]

In this paper, we developed a novel analytical approach for description of the diffusion-controlled simultaneous growth of multilayer stoichiometric compounds in binary reactive diffusion couples. The approach was directly extended to describe the compounds with narrow/certain homogeneity ranges. The models were then applied to three different real cases in technically important Co–Si and Cu–In binary systems. The predicted thickness curves/composition profiles revealed a satisfactory agreement with all the experimental data. The successful applications indicate that the approach can serve as an efficient way for describing the multi-layer growth in the joining, coating, and solar cell industries. Image, graphical abstract [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]

Owning the excellent high temperature properties, low cost and density, Al-Co-Cr-Fe-Ni-Ti high-entropy superalloys (HESAs) represent a potential substitute for Ni-based superalloys. In this paper, the composition-dependent interdiffusivity matrices of face centered cubic (fcc) Al-Co-Cr-Fe-Ni-Ti HESAs at 1473 K were first determined via a combination of diffusion multiple technique and HitDIC software based on the numerical inverse method. The correlations between the main interdiffusivities and the components suggest that alloying elements play great impact on diffusion in HESAs. After that, comprehensive comparisons of the interdiffusivities and tracer diffusivities in present fcc HESAs with the literature data in fcc-based pure elements, lower-order alloys and traditional high-entropy alloys were conducted. The results indicate that the sluggish diffusion effect exists for only some of the components in the present HESAs. Moreover, comparisons of the diffusion coefficients between the HESAs and traditional Ni-based superalloys with refractory elements show that the interdiffusivities in the present HESAs are lower than the Ni-based superalloys with most refractory elements, but higher than those with Ir, Re and Os. Furthermore, it is also found that refractory elements need to be added in order to further improve the creep resistance of the HESAs. • Interdiffusivity matrices of Al-Co-Cr-Fe-Ni-Ti HESAs at 1473 K were determined. • Correlations between main interdiffusivities and components were investigated. • Sluggish diffusion does not exist for all the elements in the present HESAs. • Refractory elements need to be added to improve the creep resistance of HESAs. [ABSTRACT FROM AUTHOR]