Interdiffusion Coefficients Research Articles

Interdiffusion behaviors and mechanical properties of Zr-X (X Nb, Ta, Hf) binary systems

The diffusion behaviors and the mechanical properties of Zr-X (X Nb, Ta, Hf) systems have been systematically investigated at the annealing temperature range of 950–1200 °C. Based on the Sauer-Freise method and the Hall method, the interdiffusion coefficients of the Zr-rich alloys were evaluated, and the impurity diffusion coefficients on the Zr-rich side have been extracted by using the Darken equation. The presently obtained interdiffusion coefficients and impurity diffusion coefficients are all in good agreement with experimental data in the literature. According to the Arrhenius regression, the diffusion activation energies of the three systems have been calculated. It can be concluded that the diffusion activation energies of the Zr-Ta system are the largest value. Finally, the hardness and Young’s modulus of the Zr-X have been obtained by using the nanoindentation test. The present results can help the materials design, research and development for the Zr-based alloys. • Interdiffusion coefficients and activation energies are obtained from the measured composition profiles. • Hardness and Young’s modulus of Zr-X (X Nb, Ta, Hf) systems have been obtained. • The solid-solid diffusion couple has been used.

Thermal diffusion behavior of Fe/Cu/Ni multilayer coatings: a molecular dynamics study

In this paper, the thermal diffusion behavior of Fe/Cu/Ni multilayer coatings was investigated by molecular dynamics. The results show that the Fe, Cu, and Ni elements can diffuse each other at 1250 K. Meanwhile, the intrinsic diffusion coefficients and interdiffusion coefficients of the Fe, Cu, and Ni were calculated. Besides, the diffusion mechanism for high melting-point elements of Fe and Ni at 1250 K was analyzed in the paper. According to the simulation result, the Fe and Ni lattices were disturbed by the active Cu particles. Fe and Ni particles at higher energies may move out of their original positions and migrate into the Cu lattice randomly. Thus, the Fe and Ni elements were involved in the thermal diffusion. This can be confirmed by the decrease of the peak and the disappearance of the secondary peak in the radial distribution function curves. However, the position of the curve peaks did not change. Thus, the lattice structure was still maintained during the whole diffusion process. The thermal diffusion of the three elements was carried out by particle substitution at the lattice positions. It was a solid phase diffusion process. Furthermore, there was a clear particle diffusion asymmetry at the original interface of the element. It was consistent with the diffusion asymmetry of diffusion-couple experiments. The primary reason for this diffusion asymmetry was the difference in the interaction potential of the three elements. This asymmetry was ultimately reflected in the intrinsic diffusion coefficient and the interdiffusion coefficient of each element. For the Fe–Cu–Ni ternary system, the largest diffusion coefficient was copper and the smallest was iron at 1250 K.

Physically driven enhancement of the stability of Bi2O3-based ionic conductors via grain boundary engineering

Fast oxygen-ion conductors for use as electrolyte materials have been sought for energy conversion and storage. Bi2O3-based ionic conductors that exhibit the highest known oxygen-ion conductivities have received attention for use in next-generation solid electrolytes. However, at intermediate temperatures below ~600 °C, their conductivities degrade rapidly owing to a cubic-to-rhombohedral phase transformation. Here, we demonstrate that physical manipulation of the grain structure can be used to preserve the superior ionic conductivity of Bi2O3. To investigate the effects of microstructural control on stability, epitaxial and nanopolycrystalline model films of Er0.25Bi0.75O1.5 were fabricated by pulsed laser deposition. Interestingly, in situ impedance and ex situ XRD analyses showed that the grain boundary-free epitaxial film significantly improved the stability of the cubic phase, while severe degradation was observed in the conductivity of its polycrystalline counterpart. Consistently, the cation interdiffusion coefficient measured by the Boltzmann–Matano method was much lower for the epitaxial thin film compared to the polycrystalline thin film. Furthermore, first-principles calculations revealed that the presence of grain boundaries triggered the structural resemblance between cubic and rhombohedral phases, as evidenced by radial distribution functions. Additionally, phase transition energetics predicted that the thermodynamic stability of the cubic phase with respect to the rhombohedral counterpart is reduced near grain boundaries. Thus, these findings provide novel insights into the development of highly durable superionic conductors via microstructural engineering.

Influence of solute-source composition on composition-dependent interdiffusion coefficient

The validity of a long-held implicit assumption that the composition-dependent interdiffusion coefficient is a material parameter that is isothermally constant, irrespective of solute-source composition, is studied theoretically and experimentally. Solute concentration distributions under the influence of diffusion-induced stress generation and relaxation are numerically simulated, and the results are used to compute and compare composition-dependent interdiffusion coefficients under different solute-source compositions. The results of both the theoretical and experimental analyses show that solute-source concentration can significantly change the composition dependency of interdiffusion coefficient, in contrast to what is often implicitly assumed. Accordingly, the use of concentration-dependent interdiffusion functions, obtained from pure-metal/pure-metal diffusion couples, to predict or analyze diffusion effects when the solute-source is an alloy instead of a pure-metal can be grossly inaccurate.

A physics-informed neural network-based numerical inverse method for optimization of diffusion coefficients in NiCoFeCr multi principal element alloy

The composition-dependent pseudo-binary (PB) interdiffusion coefficients and the main intrinsic diffusion coefficients of all the components at the near equiatomic composition of NiCoFeCr system are estimated following the PB diffusion couple method. These are otherwise impossible to estimate directly following the conventional method. Subsequently, a physics-informed machine learning based numerical inverse method is used to optimize the diffusion parameters in two steps. Initially, optimization is done by developing a good match with the diffusion profiles and estimated interdiffusion coefficients over whole composition range of the diffusion couples. However, a mismatch was found in the extracted intrinsic diffusion coefficients. Therefore, the second level of optimization is done with estimated intrinsic diffusion coefficients at the Kirkendall plane as constraints demonstrating the need for these diffusion parameters for generating a reliable mobility database. The direct estimation and optimization of diffusion coefficients without using thermodynamic details is an added advantage, especially in multicomponent alloy systems.

Microstructure evolution and interdiffusion of PtAl coated a third generation single crystal superalloy during thermal exposure

Microstructure evolution and elemental interdiffusion of PtAl coated third generation single crystal superalloy at 1000 °C and 1100 °C have been investigated. Interdiffusion coefficients and elemental diffusion fluxes are determined by HitDIC software based on the numerical inverse method. The interdiffusion zone (IDZ) with σ and R topologically close-packed (TCP) phases and secondary reaction zone (SRZ) with σ and P phases are formed after exposure at 1000 °C and 1100 °C. Interdiffusion flux of Al is the largest, followed by Pt, Ni, Co and Ta. However, most of the inward diffused Al is absorbed by IDZ, and the enrichment of Ta in IDZ/SRZ primarily accounts for the formation of SRZ. The increasing outward diffusion of refractory elements, such as Re, W and Ta mainly leads to larger thickness of SRZ at 1100 °C. Moreover increasing interdiffusion of Al and Ni further promotes the growth of SRZ and transformation from β-NiAl to γ′-Ni3Al phases. The content of reserved Al in the β layer is the same after thermal exposure at both temperatures, due to the effect of Pt.

Disparity in the concentration dependence of interdiffusion coefficient under 1D and 2D diffusion interface migration

The common assumption that the concentration dependence of interdiffusion coefficient (D(C)) is an isothermally constant material parameter that is independent of geometry is theoretically and experimentally investigated, using the cases of 1D and 2D diffusion interface migration in the planar and cylindrical systems, respectively. The theoretical results, which are experimentally validated, show that the D(C) can change with diffusion geometry, in contrast to what is commonly assumed.

Experimental diffusion research and assessment of diffusional mobility in HCP Mg–Al-Ga ternary alloys

It is in this work that the diffusion behavior in HCP Mg–Ga binary alloys at temperatures from 673 K to 873 K and in Mg–Al-Ga ternary alloys in 673–723 K was investigated by the solid-state diffusion couple experiments. The inter- and impurity diffusion coefficients were then extracted from the composition profiles acquired by electron probe microanalysis (EPMA) via the Sauer-Freise, Whittle-Green and Hall methods, respectively. The extracted impurity diffusion coefficient of Ga in pure HCP-Mg follows an Arrhenius relation with the pre-exponential factor D0 = 1.4 × 10−5 m2/s and activation energy Q = 116869 J/mol. The interdiffusion coefficients of the Mg–Ga binary alloys were found to increase with increasing the Ga content. Whereas in the Mg–Al-Ga ternary, the average main interdiffusion coefficients D˜GaGaMg within the investigated composition space is 5.4 times larger than that of D˜AlAlMg at 673 K and 4.6 times at 723 K, respectively, revealing that Ga is a much faster diffuser than Al in the ternary alloys. The main interdiffusion coefficients D˜GaGaMg and D˜AlAlMg, as well as the impurity diffusion coefficients DAl(Mg−Ga)∗ and DGa(Mg−Al)∗ exhibit increasing composition trends as the content of diffusing species increases, either Al or Ga. Close inspection suggests that Ga has significant effect on the diffusion of Al while the Al effect is minor on Ga. The diffusion coefficients extracted in this work, together with other selected diffusion data in literature, were critically evaluated to assess the diffusional mobility for the HCP Mg–Al-Ga ternary alloys. The optimized parameters of diffusional mobilities enable such diffusion behaviors as composition profiles and diffusion paths to be well represented and then predicted, in most cases, consistent with the experimental findings and therefore validating the mobility parameters assessed in this work.

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

The Co–Cu–Fe ternary system was thermodynamically reassessed with the CALPHAD method in the present work. The miscibility gap of the fcc phase at 1373 K was experimentally determined. The phase relationship among the liquid, Cu-rich and Cu-depleted fcc phases was established. Based on the new experiment data and available data in the literature, the thermodynamic optimization of the Co–Cu–Fe system was carried out. The experimental phase equilibria over the whole composition range can be reproduced. Additionally, in order to optimize the temperature-dependent mobility parameters, the interdiffusion coefficients at 1373 K and 1473 K were measured with the diffusion-couple method. Based on the updated thermodynamic description and atomic mobilities in the binary subsystems, the atomic mobilities of Co, Cu and Fe in the fcc phase were re-optimized. The measured composition profiles and diffusion paths of diffusion couples can be well reproduced using the present mobility parameters.

Automated Development of an Accurate Diffusion Database in Fcc AlCoCrFeNi High-Entropy Alloys from a Big Dataset of Composition Profiles

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.

Influence of Nb, Ta and Zr on the Interdiffusion Coefficients and Solid Solution Strengthening of γ-TiAl Single Phase Alloys

The alloying elements Nb, Ta and Zr improve the creep properties of fully lamellar γ/α2 titanium aluminides significantly. Since high temperature deformation mainly occurs in the γ-phase of γ/α2 titanium aluminides, the diffusivity and the solid solution hardening effect of these three elements in the γ-phase is studied by analyzing the concentration gradients of the alloying elements and the resulting hardness across the interdiffusion zone of diffusion couples by energy dispersive X-ray diffraction and nanoindentation. The results reveal that Zr has the highest interdiffusion coefficient but also the largest solid solution hardening coefficient. The mechanical properties of single γ-phase Ti-54Al-5X alloys were investigated by strain rate jump tests. The addition of 5 at.% Nb or Ta lead to an increased strength compared to a binary γ-Ti-54Al alloy. The Zr-containing γ-TiAl alloy reveals the highest strength at 750 °C and 900 °C, which is discussed to be due to the strong solid solution hardening effect of Zr. However, in comparison to the other alloys, Ti-54Al-5Zr shows quite brittle behavior up to 900 °C. The lower diffusivity of Ta compared to Nb leads to a higher strength of the Ta-modified alloy at 900 °C.

Recent Advances in Understanding Diffusion in Multiprincipal Element Systems

Recent advances in the field of diffusion in multiprincipal element systems are critically reviewed, with an emphasis on experimental as well as theoretical approaches to determining atomic mobilities (tracer diffusion coefficients) in chemically complex multicomponent systems. The newly elaborated and augmented pseudobinary and pseudoternary methods provide a rigorous framework to access tracer, intrinsic, and interdiffusion coefficients in alloys with an arbitrary number of components. Utilization of the novel tracer-interdiffusion couple method allows for a high-throughput determination of composition-dependent tracer diffusion coefficients. A combination of these approaches provides a unique experimental toolbox to access diffusivities of elements that do not have suitable tracers. The pair-exchange diffusion model, which gives a consistent definition of diffusion matrices without specifying a reference element, is highlighted. Density-functional theory–informed calculations of basic diffusion properties—asrequired for the generation of extensive mobility databases for technological applications—are also discussed.

Measurement of the diffusion coefficient in Mg–Sn and Mg–Sc binary alloys

Abstract Diffusion coefficients in the hexagonal close-packed (hcp) Mg–Sn and Mg–Sc solid solutions and the body-centered cubic (bcc) Mg–Sc solid solution were re-evaluated via a method combing diffusion couple experiments, error function expansion fitting, and Sauer–Freise/Hall numerical calculation. The interdiffusion coefficients in hcp Mg–Sn alloys were found to gently rise as the content of Sn increases. The new experimental data amended the compositional dependency of Mg–Sn interdiffusion coefficients and gave rise to a new set of mobility parameters. The interdiffusion coefficients in Mg–Sc alloys were determined at 773 K, 803 K, and 848 K. They showed a slightly parabolic composition dependence in the hcp phase but a monotonic decreasing trend with the increase in Sc content in the bcc phase. The experimental results in this work enriched the determined diffusion coefficients in Mg alloys and effectively justified the assessed mobility parameters in assessments.

The relationship between inter-diffusion and self-diffusion of different liquid metals studied by molecular dynamics simulations

Long-capillary simulation method was used to calculate the inter-diffusion coefficient using nonequilibrium molecular dynamics simulations. The inter-diffusion coefficient of the binary Al80Ni20, Al80Cu20, La80Ni20 and La80Al20 melts were calculated over a wide temperature range. We found that the relationship between inter- and self-diffusion coefficients of Al80Cu20 melts can be well expressed by Darken equation, which agreed with the previous results. For Al80Ni20, La80Ni20 and La80Al20 melts, dynamic cross correlation factor S was needed to correlate the Darken equation. S of Al80Ni20 and La80Ni20 ranged from 0.68 to 0.92, while that of La80Al20 was larger than 1. The effect of pressure on S was further investigated. We found that S of Al80Ni20 under 30 GPa was about 0.46 at 2000K and it was much lower than that of zero pressure, which means that the pressure had a great influence on S. Our investigations provided an improved understanding of cross correlation factor S.

Composition-dependent interdiffusivity matrices of ordered bcc_B2 phase in ternary Ni–Al–Ru system at 1273∼1473 K

Abstract In this paper, 5 Ni–Al–Ru ternary and 2 NiAl/RuAl binary equilibrium alloys were prepared, and their lattice parameters were evaluated by using the X-ray diffraction technique. The relation between the lattice parameters and Ru content satisfies Vegard’s law, confirming that a continuous single bcc_B2 phase exists between NiAl and RuAl in the ternary Ni–Al–Ru system. After that, three diffusion couples located in the bcc_B2 phase region were prepared at 1273, 1373 and 1473 K, respectively. With the presently measured concentration profiles, the composition-dependent interdiffusivity matrices along the entire diffusion paths were efficiently determined by using the High-throughput Determination of Interdiffusion Coefficients (HitDIC) software. The obtained interdiffusivities show a good agreement with the limited experimental data in the literature. Furthermore, the present results show that the addition of Ru to bcc_B2 NiAl alloys can significantly inhibit the interdiffusion rate of Ni, indicating that the bcc_B2 Ru-containing NiAl bond coats can serve as a potential diffusion barrier for Ni-based superalloy substrate.

Investigation of interdiffusion behavior in the Ti–Zr–Cu ternary system

Abstract The interdiffusion behavior of diffusion couples Ti-25Zr/Cu, Ti-50Zr/Cu and Ti-75Zr/Cu (at.%) at 973–1073 K was investigated by using electron probe microanalysis. The results show that the diffusion paths in all diffusion couples deviate away from the faster-diffusing Cu–Ti side. The diffusion paths pass the tie-line, across or parallel to, corresponding to the different diffusion layer structures and phase morphologies. The average effective interdiffusion coefficients and activation energies of Cu in both solid solutions and intermetallic compounds were determined. The diffusion coefficients of Cu in β(Ti, Zr) solid solution increase slightly and then decrease with the increase in Zr content, while the diffusion coefficients of Cu in Cu(Ti,Zr)2 intermetallic compound decrease with the increase in Zr content. The diffusion coefficients of Cu in Cu51Zr14 are the largest among all the intermetallic compounds in diffusion couples.

Grain refinement and enhanced diffusion of W[sbnd]Cu gradient material processed by high pressure torsion with floating cavity

High-pressure torsion (HPT)processing with floating cavity was carried out under the applied pressure of 1.5 GPa with the revolution from 5 to 20 turns at the temperature of 300 °C, and the WCu gradient material with noble bonding interface and significant grain refinement was successfully obtained. The microstructure evolution and atomic diffusion around the bonding interface were analyzed by electron backscatter diffraction (EBSD), transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDS) in a field emission scanning electron microscope (SEM). The mechanism of large shear strain on the microstructure evolution and diffusion ability of tungsten and copper at the interface was investigated. The results show that HPT processing with floating cavity can effectively refine microstructure of tungsten and copper to submicron. After 5 turns of HPT deformation, the grain size of copper was significantly refined to 0.59 μm but experiences slight increases to 0.8 μm with the additional revolution number to 20 turns, and the ultrafine equiaxed grains with relatively straight grain boundaries and few dislocations within grains were formed under the continuous dynamic recrystallization mechanism. However, the microstructure of tungsten was continuously refined within 20 turns of HPT processing due to the accumulation shear deformation, and a lamellar microstructure was formed along the WCu bonding interface with a gradient distribution in the width of banded grains from 0.06 μm at the interface to 0.33 μm towards the tungsten matrix. In addition, with the increase of torsion strain, the diffusion lengths of tungsten and copper gradually increasing to 1.6 μm and 6.2 μm, the interdiffusion coefficient of tungsten in copper remained basically constant, while the value of copper in tungsten increases continuously. The high density of defects and ultrafine grains with high angle boundaries introduced by large shear deformation of 20 turns of HPT processing play roles in the rapid diffusion paths to accelerate the atom diffusion and the interdiffusion coefficient of tungsten and copper is enhanced by 0.48– 1.79× 108 times compared to the lattice diffusion.

Quantification of Ag/Ni Auger electron spectroscopy depth profiles upon preferential sputtering with non-stationary roughness

The measured Auger electron spectroscopy (AES) depth profiles of the as-deposited Ag/Ni multilayers demonstrate a strong preferential sputtering effect. In the framework of the Mixing-Roughness-Information depth (MRI) model, the influence of preferential sputtering on the “measured” depth profile is quantitatively evaluated. The mass conservation upon AES preferential sputtering is verified and applied to obtain the true layer thickness from the measured depth profiling data (i.e. intensity or composition as a function of sputtering time). Meanwhile the influences of preferential sputtering and non-stationary roughness effects on the depth resolution are also quantitatively evaluated. Based on the developed model, the measured AES depth profiles of the Ag/Ni multilayers as-deposited and annealed at different temperatures are fitted and the interdiffusion coefficients are obtained accordingly.

Ex-situ study of diffusion in liquid Al–Cu melts under a transverse magnetic field using X-ray imaging

ABSTRACT Al–Cu melts were used to study interdiffusion under a transverse magnetic field (TMF) using X-ray imaging. A novel gravity-assisted automatic docking device was used to create a long capillary of the diffusion couple. Compared with the results acquired using energy-dispersive spectroscopy, X-ray imaging is more convenient and accurate to determine concentration profiles along long capillaries using the numerous gray value intensities in the imaging. Because a TMF can inhibit melt convection, the interdiffusion coefficient (D AlCu) was reduced after applying a TMF of 2 T. Our results demonstrate that the application of X-ray imaging is an efficient way to study ex-situ diffusion in liquid melts.

Diffusivities and atomic mobilities in BCC Ti-Rich Ti–V–Cr ternary alloys

In this work, we investigate ternary diffusion behaviors in BCC Ti–rich Ti–V–Cr alloys at 1373 K and 1473 K using the diffusion couple technique. We extract the inter-diffusion coefficients by the Whittle-Green method and obtain the impurity diffusion coefficients using the Hall method. Based on a thermodynamic description and validated binary mobility parameters, we evaluate the ternary diffusion coefficients and optimize the atomic mobility parameters of the Ti–V–Cr ternary alloy system in the DICTRA diffusion Module of Thermo-Calc software. Finally, we simulate the composition profiles and diffusion paths using our optimized atomic mobility parameters and find agreement between our simulated and experimentally observed results, providing evidence of the accuracy of our mobility parameters.