Experimental Composition Profiles Research Articles

High-throughput determination of accurate interdiffusivity matrices and atomic mobilities in fcc Co-Mn-X (X = Fe, Ni) alloys

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.

Atomic mobilities, diffusion coefficients, and kinetic coefficients in Ti-rich Ti–Mo–Nb system

Diffusion coefficient is an important physical property to control the microstructure, thus the establishment of atomic mobility databank for Ti-based alloy systems is vital to the design of novel Ti alloys. In the present work, ternary Ti–Mo–Nb diffusion couples within the single bcc phase were prepared and measured after annealing at 1273 K for 25 h, and interdiffusion coefficients of bcc Ti–Mo–Nb alloys at 1273 K were determined from the experimental composition profiles by using Matano–Kirkaldy method. Subsequently, the atomic mobility parameters of bcc Ti–Mo–Nb system under the CALculation of PHAse Diagrams (CALPHAD) framework were assessed by using recently proposed diffusion models, which were verified by the comparisons between the experimental interdiffusion coefficients/composition profiles and the model-predicted results. Moreover, diffusion models were carefully discussed for the ternary assessment. Finally, relationships among atomic mobility, kinetic coefficient, and diffusion coefficients were discussed and demonstrated via ternary contour maps. The present work contributes to the development of diffusion databank for computational design of biomedical Ti alloys.

Experimental determination and high-throughput calculation of the interdiffusion coefficient matrix and atomic mobility in Ag-rich fcc Ag–Sn–Zn alloys

In this paper, 10 groups of ternary Ag–Sn–Zn diffusion couples were prepared under 873, 973 and 1073 K within the fcc single-phase region. The element distribution across the diffusional interface was measured by EPMA, and a high-throughput determination of atomic mobilities in Ag-rich fcc Ag–Sn–Zn alloys was performed by using HitDIC (High-Throughput Determination of Interdiffusion Coefficients, https://hitdic.com/) software in the framework of the numerical inverse method. A self-consistent set of atomic mobility parameters was obtained. Reliability of the evaluated atomic mobility parameters were further verified by reasonably reproducing the experimental composition profiles. Insight into the composition- and temperature-dependence of various diffusion properties in fcc Ag–Sn–Zn alloy were subsequently retrieved and discussed. Furthermore, through the related Arrhenius information, the diffusion frequency factors and diffusion activity energies within the corresponding temperature and the composition range were obtained.

Carbon effect on thermo-kinetics of Co-Cr-Fe-Mn-Ni high entropy alloys: A computational study validated by interdiffusion experiments

Interstitial alloying is nowadays an important direction for further developments of High Entropy Alloys. In this work, the impact of interstitial carbon on the thermodynamics–kinetics coupling in CoCrFeMnNi-based HEAs is studied through CALPHAD and continuum approaches. First, purely thermodynamic characteristics (phase diagrams and chemical potentials) are calculated. Then purely kinetics properties, i.e., carbon-content dependent mobilities of substitutional elements are modeled, based on experimental data. Consequently, a continuum model is applied to combine these properties in order to simulate interdiffusion in carbon-free/carbon-bearing HEA couples, underlining mutual influence of carbon and matrix elements diffusion on each other. The results are benchmarked against the experimental composition profiles and a very good agreement is observed, specially when carbon effect for all elements is explicitly included. A non-monotonous dependence of the chromium up-hill diffusion on the carbon content is explained by a strong thermodynamic interaction between carbon and chromium elements.

High-throughput determination of interdiffusivity matrices and atomic mobilities in Cu-rich fcc Cu-Sn-Zn alloys by using the experimental composition profiles and HitDIC

In this paper, 12 groups of ternary Cu-Sn-Zn diffusion couples at 873, 973 and 1073 K were prepared and their composition profiles were measured. A high-throughput determination of atomic mobilities in Cu-rich fcc Cu-Sn-Zn alloys was performed by using HitDIC (HIgh-Throughput Determination of Interdiffusion Coefficients, https://hitdic.com/) software in the framework of the numerical inverse method. A unified set of atomic mobility parameters were thus acquired and excellent prediction performance towards all the composition profiles of the prepared diffusion couples was achieved. Good consistence between interdiffusion coefficients inferred by the assessed mobility descriptions and those evaluated with Matano-Kirkaldy method were successfully achieved. Reliability and soundness of evaluated mobility descriptions were therefore proved. Exploration of various diffusion properties including interdiffusivity and related Arrhenius information among the concerned temperature and composition range was also carried out. Insight into the composition and temperature-dependence of various diffusion properties in fcc Cu-Sn-Zn alloy were subsequently retrieved and discussed.

Two Types of Liquid Phase Separation Induced by Soft Centrifugation in Aqueous Ethyl Acetate Using Ethanol as Cosolvent.

Water/ethyl acetate/ethanol is widely used as a "green" extractant system. We show that 2 different types of phase separation can be induced upon centrifugation in this ternary system using ethanol as a cosolvent of water and ethyl acetate: centrifuge-induced criticality and centrifuge-induced emulsification. The expected composition profiles of samples after centrifugation can be represented by bent lines in a ternary phase diagram when gravitational energy is added to the free energy of mixing. The experimental equilibrium composition profiles behave qualitatively as expected and can be predicted using a phenomenological theory of mixing. The concentration gradients are small except near the critical point, as expected for small molecules. Nevertheless, they are usable when accompanied by temperature cycles. These findings open new possibilities of centrifugal separation, even if control is delicate during temperature cycles. These schemes are accessible even at relatively low centrifugation speed for molecules that float and sediment with apparent molar masses several hundred times larger than the molecular mass.

High-throughput measurements of interdiffusivities in fcc Co–Ni–Ta alloys at 1373K and 1473K

The composition-dependent interdiffusivities in the fcc Co–Ni–Ta alloys at 1373 K and 1473 K were deduced by using our newly developed numerical inverse scheme that combines two-dimensional (2D) simulations with diffusion triple experiments. This approach largely reduced the experimental efforts by analyzing only one single-phase diffusion triple at each temperature yet covering a much wider composition range than diffusion couples. The reliability of the high-throughput results was firstly verified by reproducing the experimental 2D composition profiles in each triple. In order to further validate the deduced interdiffusivities, several traditional one-dimensional (1D) diffusion couples were also devised, and the widely recognized Sauer-Freise method and Whittle-Green method were then employed to calculate the interdiffusivities for the binaries and at the intersection points within the ternary composition range, respectively. The interdiffusivities extracted from the inverse scheme agree well with those from the traditional approaches, which strongly proves the applicability of the present new scheme. Besides, the constructed main interdiffusivity planes at 1373 K and 1473 K provide an overview of the diffusion behavior in the fcc Co–Ni–Ta system and promote further kinetic studies.

Growth interruption strategies for interface optimization in GaAsSb/GaAsN type-II superlattices

Recently, GaAsSb/GaAsN type II short-period superlattices (SLs) have been proposed as suitable structures to be implemented in the optimal design of monolithic multi-junction solar cells. However, due to strong surface Sb segregation, experimental Sb composition profiles differ greatly from the nominal square-wave design. In this work, the improvement of the interface quality of these SLs in terms of compositional abruptness and surface roughness has been evaluated by implementing different growth interruption times under Sb4/As4 (soaking) and As4 (desorption) overpressure conditions before and after the growth of GaAsSb layers, respectively. The combined effects of both processes enhance Sb distribution, achieving squarer compositional profiles with reduced surface roughness interfaces. It has been found that the improvement in compositional abruptness is quantitatively much higher at the lower interface, during soaking, than at the upper interface during desorption. Conversely, a larger decrease in surface roughness is achieved at the upper interface than at the lower interface. Fitting of the Sb segregation profiles using the 3-layer kinetic fluid model has shown that the increase in Sb incorporation rate is due to the decrease in segregation energy, presumably to changes in the surface reconstruction of the floating layer at the surface.

Interdiffusion coefficient and atomic mobility for fcc Ag-Cu-Mg phase at 1073 K

In this work, the interdiffusion coefficient and atomic mobility for the fcc Ag-Cu-Mg phase at 1073 K were investigated by combining diffusion couple experiments and calculations. Based on the experimental composition profiles, the diffusion coefficients at the intersections of the diffusion paths were calculated using the Matano-Kirkaldy method. Using the thermodynamic descriptions available in the literature, the atomic mobilities for the fcc Ag-Cu-Mg phase were automatically optimized by numerical inverse method integrated with the CALTPP (CALculation of ThermoPhysical Properties) program. Moreover, the obtained atomic mobilities were confirmed to be reliable by good agreements between the model-simulated and the measured composition profiles. In addition, three-dimensional surfaces were presented for the interdiffusion coefficient, activation energy, and frequency factor. The presently obtained atomic mobilities can be incorporated into the diffusion database for Ag-based alloys, which can contribute to microstructure simulation and materials design.

Automation of diffusion database development in multicomponent alloys from large number of experimental composition profiles

Nowadays, the urgency for the high-quality interdiffusion coefficients and atomic mobilities with quantified uncertainties in multicomponent/multi-principal element alloys, which are indispensable for comprehensive understanding of the diffusion-controlled processes during their preparation and service periods, is merging as a momentous trending in materials community. However, the traditional exploration approach for database development relies heavily on expertize and labor-intensive computation, and is thus intractable for complex systems. In this paper, we augmented the HitDIC (high-throughput determination of interdiffusion coefficients, https://hitdic.com) software into a computation framework for automatic and efficient extraction of interdiffusion coefficients and development of atomic mobility database directly from large number of experimental composition profiles. Such an efficient framework proceeds in a workflow of automation concerning techniques of data-cleaning, feature engineering, regularization, uncertainty quantification and parallelism, for sake of agilely establishing high-quality kinetic database for target alloy. Demonstration of the developed infrastructures was finally conducted in fcc CoCrFeMnNi high-entropy alloys with a dataset of 170 diffusion couples and 34,000 composition points for verifying their reliability and efficiency. Thorough investigation over the obtained kinetic descriptions indicated that the sluggish diffusion is merely unilateral interpretation over specific composition and temperature ranges affiliated to limited dataset. It is inferred that data-mining over large number of experimental data with the combinatorial infrastructures are superior to reveal extremely complex composition- and temperature-dependent thermal–physical properties.

Experimental measurement of diffusion coefficients and assessment of diffusion mobilities in HCP Mg–Li–Al alloys

An atomic mobility database was established for the ternary HCP Mg–Li–Al system as a part of an ongoing effort to enable rapid development of novel lightweight Mg alloys. Three sets of three diffusion couples were assembled and annealed at temperatures ranging from 400 to 500 °C. Li concentration profiles were measured using a combination of Auger electron spectroscopy (AES) and inductively coupled plasma optical emission spectrometry (ICP-OES), while Al composition profiles were acquired using electron probe microanalysis (EPMA). The forward-simulation analysis (FSA) was employed to extract both interdiffusion and impurity diffusion coefficients from the collected experimental composition profiles. These measured diffusivity data were used to assess and iteratively optimize mobility parameters for the Mg–Li–Al system using the diffusion module within the Thermo-Calc Software package (DICTRA). The reliability of the assessed mobility parameters was further confirmed by two validation diffusion couples that were annealed at 425 and 475 °C for 96 and 48 h, respectively. It was observed that additions of Li increased the diffusivity of Al in HCP Mg, whereas additions of Al decreased the diffusivity of Li in HCP Mg.

Thermodynamic assessment of the Co–Fe–Ni system and diffusion study of its fcc phase

A specially designed diffusion triple and three diffusion couples were assembled to respectively determine isothermal sections of the Co–Fe–Ni alloy system at 1073 K and 1173 K. The binary thermodynamic parameters of the fcc and bcc phases in the Fe–Ni system were modified and further used to reassess the Co–Fe–Ni system above 873 K, neglecting the low-temperature ordered phases. Based on the present thermodynamic data, the atomic mobilities of Fe–Ni fcc phase were assessed to reproduce the literature data as well as the present extracted interdiffusion coefficients from two Fe–Ni diffusion couples. Furthermore, nine ternary Co–Fe–Ni diffusion couples annealed at 1173 K were scanned by using electron probe microanalysis and used to deduce the interdiffusion coefficients. Based on these coefficients and experimental data from 1373 K to 1588 K in the literature, the atomic mobilities of Co, Fe, and Ni coupled with the present thermodynamic description were assessed by means of DICTRA software, and verified by comparing with experimental composition profiles and diffusion paths. Although interdiffusion coefficients are treated as solvent-dependent so three sets of interdiffusion coefficients can be deduced from the same sets of ternary experimental data, the assessed atomic mobilities are unique and applicable in the whole composition range. This methodology is especially vital when studying diffusion behaviors for multi-principal element alloys (also known as complex concentrated alloys, or high entropy alloys).

A novel computational framework for establishment of atomic mobility database directly from composition profiles and its uncertainty quantification

In this work, a novel computational framework for establishment of atomic mobility database directly from the experimental composition profiles and its uncertainty quantification was developed by merging the Bayesian inference with the Markov chain Monte Carlo algorithm into the latest version of the HitDIC software. By treating the simulation of composition profiles with the composition-dependent coefficients as the forward problem, the inverse coefficient problem that provides the potential way to compute the atomic mobilities directly from composition profiles can be postulated. The values and uncertainties of the atomic mobility parameters of interest were assessed by means of Bayesian inference, where the composition profiles were consumed directly. Benchmark tests that consider the number of diffusion couples and the noise levels were conducted. Practical application of the current framework in determination of atomic mobility descriptions of fcc Ni-Ta and Ni-Al-Ta alloys was performed. Further discussion about the results of the benchmark tests and practical study case indicated that the present computational framework together with numbers of composition profiles from the multiple diffusion couples can help to establish the high-quality atomic mobility database of the target multicomponent alloys.

Liquid phase axial mixing in distillation column packed with structured packing: Effect on column performance

We present values of the Bodenstein number, BoL, characterizing liquid phase axial mixing, for the atmospheric distillation of three binary mixtures of primary alcohols and a mixture of cyclohexane/n-heptane, all of which were distilled in a column packed with Mellapak 250.Y or Mellapak 452.Y. In addition, volumetric mass transfer coefficients (kLa, kGa) were evaluated from the experimental composition profiles along the distillation column. To describe the distillation process, axial mixing in the phases was considered and modelled as axial dispersion. The results of our modelling call for a reassessment of the relative importance of the process-affecting phenomena. In particular, while vapour phase mass transfer resistance was confirmed as most important, liquid phase axial mixing is shown to have a significant impact under all conditions. For the C6/C7 mixture on Mellapak 452.Y, liquid phase mass transfer resistance was negligible when axial mixing was taken into account. Conversely, non-zero liquid phase mass transfer resistance was found for the alcohol mixtures in all cases. However, our investigation revealed that this is most likely a relic of the usage of the simplistic plug flow model.

Simulation of reaction-diffusion between substrate and coating during vapor deposition processes

This work presents simulations of the solid state diffusion and reactions during deposition processes. Two cases are studied where the diffusion in and between coating and substrate is simulated. The processes simulated are in one case directed vapor deposition of Al and Ni on a precoated nickel-base superalloy, and in the other case chemical vapor deposition aluminization of a nickel-base superalloy. The simulations result in composition and phase-fraction profiles, which are presented and compared with experimental composition profiles. The simulation results are generally in good agreement with the experimental profiles.

Determination of the interface parameter in terahertz quantum-cascade laser structures based on transmission electron microscopy

We have determined the interface profiles of GaAs/Al0.25Ga0.75As and GaAs/AlAs terahertz quantum-cascade laser structures using transmission electron microscopy (TEM). The experimental composition profiles are directly extracted from the analysis of the diffracted intensity distribution of g002 dark-field TEM images. Simulated composition profiles, which have been obtained using a Fourier-transform-based model, are in remarkably good agreement with the experimental results so that the determined interface parameter can be used for designing terahertz quantum-cascade lasers. Due to the interface grading, these actual profiles reveal a significantly lower aluminum content of the Al0.25Ga0.75As and AlAs barriers than the nominal values.

Diffusion in the Ti-Al-V System

Diffusion in the Ti-Al-V system is studied and a CALculation of Phase Diagrams (CALPHAD) diffusion mobility description is developed. Diffusion couple experiments are performed to obtain diffusion paths in the hcp phase at 923 K, 1023 K and 1123 K. The diffusion coefficient of V in the hcp-Ti phase is found to decrease with increasing Al alloying. A forward-simulation analysis is used to evaluate the impurity diffusion coefficient for Al and V diffusion in the hcp Ti-V and the Ti-Al systems which are used as input in the mobility modeling. The composition dependency for the diffusion in the hcp phase in the ternary system is accounted for and a CALPHAD diffusion mobility description is obtained by directly optimizing the mobility parameters as a function of the experimental composition profiles from the diffusion couples. Both experimental data and previous diffusion mobility descriptions in the literature for the bcc Ti-Al-V phase are adopted. A complete description of diffusion in both the hcp and bcc phases for the Ti-Al-V system is presented with the aim to be used for design of Ti alloys and processes.

Application of distribution functions in accurate determination of interdiffusion coefficients

Diffusion couple technique in combination with the Boltzmann-Matano method is the widely used approach to evaluate the interdiffusion coefficients in the target systems. However, the quality of the evaluated interdiffusion coefficients due to the Boltzmann-Matano method strongly depends on the fitting degree of the utilized continuous function to the discrete experimental composition profiles. In this paper, the application of different types of distribution functions is proposed to solve this problem. For the simple D-c relations, the normal, pseudo-normal, skew normal, pseudo-skew normal distributions can be employed, while for the complex D-c relations, the superposed distributions should be used. Even for the cases with uphill diffusion, the combined superposition of distributions may be chosen. Through validation in several benchmarks and real alloy systems, accurate diffusion coefficients are proved to be successfully obtained by using the distribution functions. It is anticipated that the Boltzmann-Matano method together with the distribution functions may serve as the general solution for determining the accurate interdiffusion coefficients in different materials.

HitDIC: A free-accessible code for high-throughput determination of interdiffusion coefficients in single solution phase

In this paper, a free-accessible code for High-throughput Determination of Interdiffusion Coefficients (HitDIC, https://hitdic.com/) based on the numerical inverse method is introduced. HitDIC is developed to robotize the procedures to retrieve the reliable composition-dependent interdiffusivities from the experimental composition profiles of single or multiple diffusion couples by minimizing the misfit between the experimental and model-predicted compositions profiles. The code is an efficient C++ implementation and provided as a free-accessible one, as well as demos and assistant toolkits. The underlying physics and mathematics of the modules of HitDIC, (i.e., database, simulation, error and minimization modules) are also demonstrated. Such an implementation is further proved to be feasible and reliable according to the results and discussion of the benchmarks and real cases. Moreover, some hints for the usage of HitDIC are also given.

Diffusion study in bcc_A2 Fe-Mn-Si system: Experimental measurement and CALPHAD assessment

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 1373K 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.