Interdiffusion Experiments Research Articles

High-throughput approach for investigating interdiffusion in medium- and high-entropy alloys

Interdiffusion experiments are usually time-consuming and tedious since diffusion couples must be annealed at several temperatures for a long time. The efforts required to study interdiffusion in multicomponent alloys increase dramatically as multiple diffusion couples are required to cover broad composition ranges and determine the diffusivities of individual elements in different chemical environments. To circumvent this challenge, we present a high-throughput approach applicable to single-phase and compositionally complex alloys, which are assumed to approximate ideal solid solutions. Here, a simple diffusion-multiple experiment combined with a physically based kinetic model is proposed to efficiently determine the diffusion coefficients of the constituent elements in quaternary CrFeCoNi alloys. Compared with tracer diffusivities reported in the literature, the results, thus, obtained do not differ by more than a factor of 2 and were obtained from a single interdiffusion experiment. In contrast, the diffusivities simulated with commercial mobility and thermodynamic databases are strongly overestimated by a factor ranging from 1 to 16. Therefore, our approach enables high-throughput determination of diffusivities and can help in the design of alloys for high-temperature applications where diffusion plays a key role.

Polymer chain transport investigated using surface enhanced Raman spectroscopy: monitoring of diffusion kinetics on meso-structured plasmonic substrates.

We utilize the results of surface-enhanced Raman spectroscopy (SERS)-based interdiffusion experiments on meso-structured substrates to independently validate direct observations of plasmonic enhancements on these elements. The plasmonic enhancement function (PEF) is crucial for accurately determining interdiffusion coefficients using this newly proposed SERS-based methodology. The substrates feature a microscale inverted pyramid geometry, coated with nanoscale sputtered gold. Interdiffusion experiments involve the sequential deposition of polymer bilayers, with deuterated polystyrene (dPS) at the bottom and polystyrene (PS) on top, followed by annealing while periodically acquiring Raman spectra. The temporal evolution of the PS Raman signal reflects not only the interdiffusion process but also plasmonic effects, as the Raman scattering primarily arises from the substrate's plasmonic hotspots. High-resolution finite element (FE) diffusion simulations, combined with experimental SERS data, are used to infer the PEF of the substrate. The derived PEF is consistent with two hotspots located at the apex and vertices of the pyramidal cavity, extending along the edges and spreading into the molecular layer in direct contact with the substrate. This finding is tested against experiments conducted at various diffusion rates, showing excellent agreement. It corroborates recent observations by Steuwe et al. regarding the localization of hotspots on this specific substrate but contradicts other studies that attribute hotspots solely to the micron-scale geometry. This analysis establishes a solid foundation for reliably determining diffusion coefficients using this SERS-based methodology.

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.

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.

Reactive interdiffusion of an Al film and a CoCrFeNi high-entropy alloy at elevated temperatures

The phase evolution of alloys is closely related to atomic diffusion. The influence of reactive diffusion on phase formation in high-entropy alloys (HEAs) is however still unclear. The present work systematically investigates the phase evolution of a multicomponent CoCrFeNi/Al diffusion couple through isochronous-reactive interdiffusion experiments. This provides a direct way to study the influence of enthalpy and entropy on the phase formation and element diffusion behavior. At temperatures below 1173 K, the enthalpy contribution dominates the total energy, leading to the formation of intermetallic compounds. When the temperature is in the range of 1173–1573 K, the entropy of mixing starts to play a more important role. This causes diffusion of Al towards the HEA without phase transformation, forming a more disordered state on the microscale. Even after the system reaches a disordered state, the enthalpy contribution cannot be totally ignored, which is reflected by the uphill diffusion of Ni towards Al. This demonstrates the combined effects of entropy and enthalpy on the phase formation in HEAs at elevated temperatures. Considering the homologous temperature for different equimolar alloys reveals that a multicomponent configuration does not stabilize the disordered state, while the mixing enthalpies between atomic pairs have a large impact on the transition temperature from ordered to disordered state. Finally, it is shown that surface modification of the HEA can be realized through a combination of film deposition and annealing processes. Compared to the HEA matrix, the formation of intermetallic compounds results in a hard surface layer. After the system becomes disordered, the higher hardness of the film side compared to the matrix can be attributed to the lattice distortion induced by Al.

H‐D Interdiffusion in Single‐Crystal Olivine: Implications for Electrical Conductivity in the Upper Mantle

AbstractKnowledge of water content and distribution in the Earth's mantle is critical to understanding the geochemical evolution and geodynamic processes of the Earth, since water can incorporate into nominally anhydrous minerals at high pressure and dramatically affect the chemical and physical properties of mantle minerals. Hydrogen diffusion controls the transport of water and electrical conductivity in the deep Earth but is not fully understood for olivine, the most abundant mineral in the upper mantle. Here we present new hydrogen self‐diffusion coefficients determined from interdiffusion in H‐ and D‐doped olivine single‐crystal couples at the upper mantle conditions (3–13 GPa and 1,000–1,300 K). Present activation enthalpy for hydrogen migration is significant smaller than previous work determined within a limited measured temperature range. Parallel interdiffusion experiments with diversified water concentrations demonstrated that hydrogen diffusivity strongly accelerated by the water content in olivine. The geometric average diffusion coefficient on olivine is showed as a function of temperature and water content: . Combined with the Nernst‐Einstein relation, the present results can constrain the contribution of water to the electrical conductivity on olivine. It suggests that in situ conductivity measurements on hydrous olivine at low temperatures (<1,000 K) produced too low activation enthalpy to extrapolate to the higher temperatures. Comparison with previous results by conductivity measurements on single‐crystal olivine suggests that the literature data except for Dai and Karato (2014) might overestimate water effect on conductivity because of heterogeneity of synthetic single crystals. Because of a change of dominant hydrogen diffusion mechanism at high temperature, this study suggests that the modeling of mantle conductivity with a high activation enthalpy from diffusion data is more trustworthy. Considering a reevaluated activation enthalpy on hydrogen diffusion and water solubility in olivine, comparisons between present conductivity model and geophysical observations suggest that hydration of olivine cannot account for extremely high conductive values (10−2–10−1 S/m) observed in the oceanic asthenosphere.

Interdiffusion and atomic mobilities in fcc Ag–Mg and Ag–Mn alloys

On the basis of Ag/Ag–Mg and Ag/Ag–Mn semi-infinite diffusion couples together with electron probe microanalysis technique, the interdiffusion coefficients in fcc phases of Ag–Mg and Ag–Mn alloys were measured between 873 and 1173 K via the Sauer-Freise method. A statistic method was applied to evaluate the errors of the identified interdiffusivities in terms of the propagation of errors. Based on available thermodynamic information and the experimental interdiffusion coefficients, the atomic mobilities for the fcc Ag–Mg and Ag–Mn systems are obtained by using the DICTRA software package. The quality of the assessed atomic mobilities was confirmed by the comprehensive comparisons between calculated concentration profiles and the experimental data.

Interdiffusion and Atomic Mobilities in fcc Co-Cr-Mo Alloys

The diffusion couples of Co-Cr-Mo ternary alloys were prepared and annealed at 1473 K for 72 h in order to determine the interdiffusion coefficients by using the electron probe microanalysis combined with Whittle and Green method. The experimental interdiffusion coefficients were critically assessed to the atomic mobilities by means of DICTRA software package. Good agreements were obtained from comprehensive comparison between the model-predicted diffusion properties and the experimental data, meanwhile, considered that the calculated diffusion coefficients were within the acceptable uncertainty of the experimentally measured diffusion coefficients, which verified the reliability of the atomic mobilities. The diffusion phenomena, such as diffusion paths and the concentration-distance profiles in the Co-Cr-Mo ternary system can be reasonably described by the presently obtained atomic mobilities.

Assessment of atomic mobilities for fcc Co–Ti–V alloys

Based on the experimental interdiffusion coefficients from our previous work and the critically reviewed experimental diffusivities available in the literature, the atomic mobilities of Co, Ti and V in fcc Co–Ti–V alloys were assessed by means of DICTRA (DIffusion Controlled TRAnsformation) software. Askill's empirical relations were utilized to assess the self-diffusion coefficients of fcc Ti and fcc V. Comprehensive comparisons between the DICTRA-calculated diffusivities and the experimental data indicate that the presently obtained atomic mobilities can reproduce most of the diffusivities in binary and ternary systems. In addition, a further verification on the obtained atomic mobilities was carried out through comparing the DICTRA-simulated concentration profiles/diffusion paths of the diffusion couples with the corresponding experimental ones. This work contributes to the establishment of a kinetic database for multi-component cemented carbide.

Supercritical fluid in the mantle transition zone deduced from H–D interdiffusion of wadsleyite

Knowledge of the distribution of water in the Earth's mantle is key to understanding the mantle convection and geochemical evolution of the Earth. As wadsleyite and ringwoodite can incorporate large amounts of water in their crystal structures, proton conduction has been invoked to account for the widespread conductive anomalies observed in the mantle wedge, where descending slab stagnates at the transition zone. However, there is a lot of controversy on whether proton conduction by itself is able to explain such anomalies, because of large discrepancy in the extent of the water effect deduced from previous electrical conductivity measurements on hydrous polycrystalline wadsleyite and ringwoodite. Here we report the hydrogen self-diffusion coefficient obtained from H–D interdiffusion experiments in wadsleyite single-crystal couples. Our results demonstrate that the effect of water on the electrical conductivity of wadsleyite is limited and hydrous wadsleyite by itself is unable to explain conductive anomalies in the transition zone. In contrast, the expected hydrogen effective diffusion does not allow the wide propagation of water between the stagnant slab and surrounding mantle, probably leading to persistence of local water saturation and continuous release of supercritical fluids at the stagnant slab roof on geological time scales. This phenomenon provides an alternative explanation for both the high-conductivity and seismic-velocity anomalies observed in the mantle wedge at the transition-zone depth.

Interdiffusion Studies in β- and γ′-Intermetallic Phases of the Binary Ni-Al System

A critical review of interdiffusion processes in the binary β-NiAl and γ'-Ni3Al intermetallic compounds is presented. The molar volume changes associated with interdiffusion and partial molar volumes of the reacting species, required for the determination of the diffusion parameters, are found using lattice parameter data and, in the case of NiAl, the available information about vacancy concentration within homogeneity range of the β-phase. The presented treatment is purely phenomenological, and its use is convenient since no exlicit assumption of the underlying mechanisms required. A critical analysis of diffusion data for β-NiAl and γ'-Ni3Al ordered phases is followed by discussion of error sources encountered in the interdiffusion experiments. From Kirkendall marker experiments with incremental diffusion couples, information about relative mobilities of species in the intermetallic phases can be obtained, and tracer diffusion coefficients can be deduced using pertinent thermodynamic data on the nickel aluminides. Contribution of the vacancy wind effect to the calculated tracer diffusivities can also be estimated. The Kirkendall plane bifurcation in the Ni41.7Al58.3/Ni72.24Al27.76reaction couple, in which a single-phased layer of β-NiAl intermatallic is formed during interdiffusion from its adjacent phases, is directly related to the growth of grains of the reaction product at a location in between interfaces with starting materials. This diffusion phenomenon can be rationallised using a corresponding Kirkendall velocity diagram. Changes in magnitude and sign of the difference in intrinsic mobilities of the components inside the homogeneity range of the β-NiAl lead to a velocity curve that makes bifurcation of the Kirkendall marker plane possible.

Combined interdiffusion and self-diffusion analysis in Al-Cu liquid diffusion couple

In this paper, a recent combined isotope and interdiffusion analysis is adapted to the case of binary liquid alloys. Shear-cell interdiffusion experiments with a layer enriched in 65Cu sandwiched between the interdiffusion couple ends have been performed on liquid Al-Cu that is suitable for demonstration of the application of this analysis. (Note that the analysis is not limited to the use of the shear-cell technique.) The self-diffusion coefficient of Cu is then obtainable as a function of composition. Results of the new analysis are in good agreement with an independently measured Cu self (tracer) diffusion coefficient at two compositions.

Selection of healing agents for a vascular self-healing application

To increase the durability and reliability of thermosets, self-healing via a vascular network, is developed. A judicious choice of healing agents proves to be necessary to achieve the best recovery of properties. Four low viscosity two-component epoxy-amine healing systems were compared, to check which glass transition temperature range would be best to recover mechanical properties (Tg ranging from −8 to 68 °C). Interdiffusion experiments show that all systems react sufficiently slowly at room temperature to allow interdiffusion of epoxy and amine over more than 1 mm before the diffusion is stopped by vitrification. Swelling tests revealed that most of the selected healing agents diffuse into the surrounding matrix and swell it. This might be beneficial for crack closure and improved adhesion between healing system and matrix. Flexural tests demonstrated that, the higher the glass transition temperature of the fully cured healing system, the higher the healing capability.

Analysis of diffusion in high entropy alloys

High-entropy alloys (HEAs) are a class of multicomponent alloys consisting of five or more principal elements with equal (or nearly equal) compositions. Diffusion plays an important role in these alloys and, indeed, if diffusion is rather sluggish, it may be partly responsible for the apparent stability of HEAs. For the understanding of diffusion properties of HEAs, the full diffusion kinetics behaviour of self-diffusion and interdiffusion in HEAs needs to be investigated. This problem is addressed in this paper by extending and applying three diffusion kinetics formalisms, one due to Darken, a combination of one from Manning and one from Holdsworth and Elliott (HE), and a ‘light’ version of one due to Moleko, Allnatt and Allnatt. Recently, an elegant and novel quasi-binary variation of a standard experimental interdiffusion set-up was used in a study of diffusion in a CoCrFeMn0.5Ni alloy [1, 2]. We successfully address these quasi-binary interdiffusion experiments analytically by applying the above random alloy diffusion kinetics formalisms for the case of CoCrFeMn0.5Ni in order to extract self-diffusion coefficients. This success now suggests that the quasi-binary variation of a standard interdiffusion set-up should be used more widely for diffusion studies in multicomponent alloys, especially HEAs.

Composition-dependent tracer diffusion coefficients in the B2 Ni–Al–Ti alloy via a combination of radiotracer and diffusion couple techniques

Tracer (44Ti) and inter-diffusion experiments were performed on identical pseudo-binary diffusion couples of the B2 Ni–Al–Ti system at 1411 K. The molar volume of B2 Ni–Al–Ti alloys was critically assessed via CALPHAD approach. The concentration dependencies of pseudo-binary interdiffusion and 44Ti tracer diffusion coefficients are determined for both, constant and variable molar volumes. The results show that while interdiffusivities are sensitive to uncertainties in molar volume, the tracer diffusion coefficients are not. With a decrease of the molar fraction of Al in the pseudo-binary B2 Ni–Al–Ti alloy, the tracer diffusion coefficient of Ti is first decreased and then increased with a minimum around the composition corresponding to 48 at.% of Al and 3.5 at.% of Ti.

Self-assembly of block copolymers via micellar intermediate states into vesicles on time scales from milliseconds to days

Block copolymer micelles and vesicles are mostly prepared by the solvent mixing method, where the block copolymer is first dissolved in a common solvent for both blocks, which is then mixed with a selective solvent, mostly water, to induce self-assembly into the desired structure. Using a combination of microfluidic flow-focusing and capillary interdiffusion experiments combined with in-situ small-angle X-ray scattering (SAXS) and cryo-transmission electron microscopy (cryo-TEM) we investigated the structural evolution during solvent mixing from single block copolymers into spherical and cylindrical micellar intermediate structures into vesicles. We find that micelle formation is very fast and diffusion-limited, occurring on time scales of a few milliseconds. The development of an ordered lyotropic micellar phase is completed within 1 s. The structural transformation into cylindrical micelles occurs over several hours, which subsequently evolve into vesicles over time scales of days. Whereas the first two steps are transport-limited, the two latter processes involve large activation energies related to micellar fusion against the sterically stabilizing micellar coronas, which corresponds to much longer time scales of self-assembly.

Reaction-induced surface reconstruction of silver in contact with zirconium

In the case of solid state diffusion between two metals the effect of the initial surfaces of the metals on the intermetallic compounds (IMC) formation is not well understood, particularly when the surfaces are not flat and the contact time is relatively short. Here we demonstrate that in the case of Ag/Zr couple the early stage of IMCs formation starts at the Ag/Zr contact points and is the place of complex surface reconstruction of Ag in direct connection to the reaction/diffusion at these Ag-Zr contact points. The effect of incomplete contact has been studied by micromachining a regular pattern on the Zr surface prior to interdiffusion experiments. The nucleation and growth of AgZr2 and AgZr occurred along the contact points and led to silver surface reconstruction with the formation of preferential {111} and {100} surface facets. A mechanism explaining this new phenomenon is developed based on the minimisation of Gibbs energy and the diffusion rates of both Ag and Zr atoms.

Ni–Cu interdiffusion and its implication for ageing in Ni-coated Cu conductors

Abstract After heat treatment at 400 °C the effective resistivities of typical Ni-coated Cu conductor wires increased by up to 6.9% as a result of Ni–Cu interdiffusion. Direct Ni–Cu interdiffusion experiments were performed between metal foils at temperatures of 400–600 °C for times up to 192 h. Calculated activation energies were in range 80–90 kJ mol −1 , consistent with a grain boundary diffusion mechanism. Analysis of published Ni–Cu interdiffusion coefficients suggested a clear dependence on grain size and grain shape. A concentric circle model was developed to simulate changes in composition and effective resistivity in the Ni–Cu wires as a function of time. It was predicted that it would take 1.4 × 10 5 h at 400 °C for 10% increase in the effective resistivity of an AWG18-Class27 conductor wire. Good agreement between simulated and experimental data for effective resistivity was only achieved by employing effective diffusion coefficients corrected for microstructural effects.

Interdiffusivities and atomic mobilities in FCC Co–Mo–W alloys

By employing six groups of bulk diffusion couples together with electron probe microanalysis technique, the composition dependence of ternary interdiffusion coefficients in Co-rich fcc Co–Mo–W alloys at 1373K was determined via the Whittle and Green method. The experimental interdiffusion coefficients were critically assessed to obtain the atomic mobilities of Co, Mo and W in fcc Co–Mo–W alloys by using the DICTRA (Diffusion-Controlled TRAnsformations) software package. Comprehensive comparisons between the calculated and experimental data show that a good agreement is obtained for diffusivities in binary Co–Mo and ternary Co–Mo–W systems. In addition, a further verification of the obtained atomic mobilities was carried out through comparing the model-predicted concentration profiles/diffusion paths of several diffusion couples with the corresponding experimental data. The results indicate that the atomic mobilities can reproduce the experiment data reasonably well. This work contributes to the establishment of a Co-based kinetic database for computational design of superalloys.

Experimental investigation and computational study of atomic mobility in fcc ternary Co–Cr–W alloys

The interdiffusion coefficients in fcc Co–Cr–W alloys at 1373K 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.