Interdiffusion Coefficients Research Articles

Ternary Interdiffusion Coefficients in BCC Ti-Al Based Alloys and Their Application in Simulations of Homogenization and Finite Diffusion Couples

Ternary Interdiffusion Coefficients in BCC Ti-Al Based Alloys and Their Application in Simulations of Homogenization and Finite Diffusion Couples

YX-IDCRC: a general approach for calculating interdiffusion coefficients from raw experimental data and its application

YX-IDCRC: a general approach for calculating interdiffusion coefficients from raw experimental data and its application

Interdiffusion in chalcogenide semiconductor superlattice nanostructures

The diffusion intermixing of layers during annealing of epitaxial superlattice nanostructures based on chalcogenide semiconductors (PbS, PbSe, PbTe, EuS, EuSe, SrS) was studed by X-ray diffraction technique. The interdiffusion coefficients were determined basing on changing of the intensity of near-Bragg reflection satellites in X-ray diffraction pattern. Layer materials in superlattices EuS-PbTe and PbS-PbTe are not intermixed.

Experimental verification of a common assumption in the use of concentration-dependent interdiffusion coefficient

There has generally been a view that concentration-dependent interdiffusion coefficient, D(C), obtained at any diffusion temperature and time is a material constant and can be reliably used to predict diffusion effects at all other isothermal diffusion times. This notion which is implicitly predicated on the assumption that diffusion-induced stress (DIS) rapidly and completely relaxes once formed and does not influence D(C) is experimentally verified in the present work. The results of the study show that reliably computed D(C) from concentration profile obtained at long diffusion time fails to correctly predict concentration profiles at shorter diffusion periods, due to isothermal variation of the D(C) with time. Accordingly, instead of continuing to assume that D(C) is time-independent and can be reliably used to predict diffusion effects at any isothermal diffusion time, without appropriate experimental support, proper experimental verification of this crucial concept in other alloy systems, as done in the present work, is imperative.

Unraveling Interdiffusion Phenomena and the Role of Nanoscale Diffusion Barriers in the Copper-Gold System.

Diffusion is one of the most fundamental concepts in materials science, playing a pivotal role in materials synthesis, forming, and degradation. Of particular importance is solid state interdiffusion of metals which defines the usable parameter space for material combinations in the form of alloys. This parameter space can be explored on the macroscopic scale by using diffusion couples. However, this method reaches its limit when going to low temperatures, small scales, and when testing ultrathin diffusion barriers. Therefore, this work transfers the principle of the diffusion couples to small scales by using core-shell nanowires and in situ heating. This allows us to delve into the interdiffusion dynamics of copper and gold, revealing the interplay between diffusion and the disorder-order phase transition. Our in situ TEM experiments in combination with chemical mapping reveal the interdiffusion coefficients of Cu and Au at low temperatures and highlight the impact of ordering processes on the diffusion behavior. The formation of ordered domains within the solid-solution is examined using high-resolution imaging and nanodiffraction including strain mapping. In addition, we examine the effectiveness of ultrathin Al2O3 barrier layers to control interdiffusion of the diffusion couple. Our findings indicate that a 5 nm thick layer serves as an efficient diffusion barrier. This research provides valuable insights into the interdiffusion behavior of Cu and Au on the nanoscale, offering potential applications in the development of miniaturized integrated circuits and nanodevices.

Bonding mechanism of TC4 titanium alloy/T2 copper vacuum diffusion bonded joint with nickel as transition interlayer

Vacuum diffusion bonding of TC4 titanium alloy (TC4) to T2 copper (T2) using nickel foil as transition interlayer was explored. Ti3Ni, Ti2Ni, TiNi, AlNi2Ti and TiNi3 phases arose at the TC4/Ni bonded interface, and Cu-Ni solid solution appeared in the Ni/T2 interface. Thereinto, AlNi2Ti was a kind of discontinuous nano precipitated phase, which distributed between TiNi and TiNi3 phases. The crystallographic orientations of Ti2Ni, TiNi, AlNi2Ti and TiNi3 phases were (201), (020), (11¯1) and (031), respectively. The interplanar spacing of (031), (11¯1) and (020) was correspondingly d(031) = 0.144 nm, d11¯1 = 0.275 nm and d(020) = 0.137 nm. The lattice mismatch between TiNi3 and TiNi was calculated to be 2.5 %, with low strain energy. The order of effective formation enthalpies for TiNi3, TiNi and Ti2Ni phases formed between titanium and nickel was ∆H′NiTi2 > ∆H′NiTi > ∆H′Ni3Ti. The growth activation energy of TiNi3, TiNi and Ti2Ni phases was correspondingly 35.8 kJ/mol, 180.6 kJ/mol and 347.1 kJ/mol. When welding at 880 °C for 60 min, the highest shear strength of the joints could achieve 150 MPa. The joints fractured along the Ni/T2 interface, the fracture surface of joint was composed of elongated dimples and cellular pits, presenting a shear ductile fracture mode. FCC-Cu, FCC-Ni and (Ni, Cu)ss phases were detected on TC4 and T2 fracture surfaces by XRD. The interdiffusion coefficient ratio of (Ni in Cu)/(Cu in Ni) and (Ni in Ti)/(Ti in Ni) decreased gradually with increasing temperature.

Experimental and simulation-based engineering of calcium alginate self-healing asphalt capsules

An emerging technology to mitigate the cracking of asphalt pavements is the use of self-healing capsules embedded in asphalt mixtures. In this study, self-healing capsules were fabricated by encapsulating asphalt rejuvenators with calcium alginate shells. While past studies have used a “brute force” design process for such capsules, the design and formulation of these can be optimized through careful consideration of chemical interactions and crack healing mechanisms. In this study, experiments and molecular dynamics (MD) simulation were used to engineer capsule–rejuvenator formulations to mitigate premature failure of capsules and improve self-healing efficiency. To explore the thermodynamic process, the inter-diffusion coefficient and blending degree between materials in the capsule system were evaluated at different temperatures and capsule designs to determine the ratio of capsules which survive mixing and compaction through molecular scale studies. MD provided an understanding of healing behavior by simulating and quantifying the fracture–healing–fracture process of the binder–capsule system. The experiments verified the MD model by quantifying oil release percentage from micro-extraction and recovery and fine aggregate matrix (FAM) healing efficiency. The research revealed that the interaction between asphalt binder, rejuvenator, and capsules highly depended on their chemical compositions and that the dose of capsule content influences the penetration degree, and structural failure process. Polymeric capsules experienced significant premature failure and content release at high temperatures (160 °C) compared to intermediate temperatures (25 °C) due to enhanced thermal movement. To optimize capsule performance, rejuvenators C and E, which had higher viscosities, required 30%–40% calcium alginate, while rejuvenator A with lower viscosity needed 40%–60% calcium alginate. Rejuvenators with more asphaltenes were more sensitive to the capsule shell protection effect, and strengthened healing efficiency, while rejuvenators with more aromatics resulted in better wetting and diffusion processes during healing. The healing index, derived from FAM experimental healing test and validated by simulations, indicated that approximately 40% shell material effectively prevented capsule breakage and resulted in a 50% reduction in healing capacity. This research therefore established a framework for engineering a combination of capsules for use at pavement scale based on an understanding of chemical interactions, mechanical properties, and experimental verification.

Diffusion behavior and mechanical properties of the Mg-Er binary system

The Mg-Er binary system, as a new lightweight alloy material system with important research value and prospects for development and application, has attracted much attention from researchers in the field of materials science. Studies have shown that the addition of the rare earth element Er can improve the mechanical strength and heat resistance of magnesium alloys. However, the specific mechanism of the interaction between Mg and Er and its effect on the mechanical properties still need to be studied in depth. A combination of microscopic morphology characterization and nanoindentation experiments were employed to investigate the binary diffusion behavior and mechanical properties of the Mg-Er system between 748 K and 823 K in this research. The results indicate that the growth constant of the diffusion layer increases with temperature, with Mg24Er5 exhibiting a higher growth constant than the sum of Mg2Er and MgEr. Notably, the Mg2Er phase has the lowest growth activation energy (127.81 kJ/mol), which suggests that it is formed first during the initial growth stage due to its relatively low energy barrier. Moreover, the interdiffusion coefficient of Mg24Er5 was found to be the highest. By calculating diffusion activation energy, this sequence of formation (Mg2Er→Mg24Er5→MgEr) is in agreement with the trend of growth activation energy. Additionally, nanoindentation experiments and first-principles calculations were utilized to derive the mechanical properties of the Mg-Er binary system. The investigations unveil that Mg2Er boasts the highest hardness and Young’s modulus. These findings have significant implications for understanding the correlation between structure and properties for the Mg-Er alloy system.

Determination of interdiffusion coefficients in single crystal superalloys based on solute distribution at the dendritic scale using the Gaussian solution model

Since the initial solute concentration distribution of the sinusoidal solution model shows a significant deviation from the actual concentration distribution of nickel-based single crystal (SX) superalloy dendrites, it is limited to calculate the diffusion coefficient of SX in the homogenization treatment. Therefore, this work proposes a new Gaussian solution model to calculate the diffusion coefficients and the diffusion activation energy of alloying elements in SX superalloy at high temperatures. The diffusion activation energies of W, Ta, and Ti elements in the studied alloy are consistent with the results from other works. This model could more accurately determine the diffusion coefficient of elements during the dendrite homogenization process of SX superalloys since it reflects actual physical processes. Moreover, it has the potential to use in various alloy systems and contributes to the formulation of effective homogenization treatments.

Interdiffusion behaviors and mechanical properties of Zr–Hf system

In this work, Zr–Hf diffusion couples were firstly prepared by Spark Plasma Sintering (SPS) method and the diffusion behavior and mechanical properties of the Zr–Hf system in temperatures range from 1300 to 1600 °C were investigated in detail. The microstructure characterization by SEM and TEM reveals that Zr–Hf diffusion zone form some amorphous and nanocrystalline grains in local area. Then the hardness and Young's modulus of the Zr–Hf system in the diffusion zone were tested and the results show that the hardness and Young's modulus of the alloy system was enhanced by solid solution Hf element, and the maximum hardness and Young's modulus in the diffusion zone reached to 10.74GPa and 203.5GPa, respectively. Finally, based on the profiles of Electron probe microanalysis (EPMA), the interdiffusion coefficient is composition-dependent. The value calculated by Sauer-Freise method is between 10−13 m2/s and 10−11 m2/s, which indicating that SPS diffusion annealing significantly enhances the diffusion rate of the Zr–Hf system. Meanwhile, the current direction has negligible effect on the diffusion of Zr–Hf system and the interdiffusion coefficient decreases slowly with increasing Hf concentration. The diffusion activation energy Q and the frequency factor D0 of the Zr–Hf binary system in this experiment ranges from 196 to 215 kJ/mol and 3.9 × 10−6 to 6.8 × 10−5 m2/s, respectively.

Dissolution and diffusion behavior of solid Mn in Mg melt

Mn is an important alloying element that can improve the mechanical properties and corrosion resistance of magnesium alloys and it belongs to the peritectic reaction type element in Mg melt. In this study, an Mn/Mg solid–liquid diffusion couple was designed to investigate the diffusion behavior of solid Mn in Mg melt at 1023 ∼ 1073 K. The dissolution behavior of Mn in Mg is dominated by Mg elements entering Mn crystal lattice from the original Mn/Mg interface. After 2 h diffusion, the Mn concentration gradient occurs between the new solid–liquid interface and the original Mn/Mg interface, and the concentration of Mn outside the original Mn/Mg interface remains about 2 wt%. For Mn/Mg solid–liquid diffusion at 1023 K∼1073 K for 2 h, the interdiffusion coefficient is in the range from 0.1 × 10-12 to 0.8 × 10-12m2/s.

Measurement of Diffusion Coefficients and Assessment of Atomic Mobilities in HCP Mg-Ag-Sn Alloys

Reliable thermodynamic and kinetic databases are essential for designing and developing novel magnesium (Mg) alloys for elevated-temperature applications in the automotive and aerospace industries. This study investigated diffusion behaviors of HCP Mg-Ag-Sn alloys by four sets of three diffusion couples annealed at 450, 500, and 550 °C, respectively. Interdiffusion and impurity diffusion coefficients at the three annealing temperatures were extracted using the forward-simulation method. The determined diffusion coefficients, combined with prior results in the literature, were then used to assess atomic mobilities for the HCP phase of the Mg-Ag-Sn system. This assessment was conducted using the DICTRA and the TCMG5 thermodynamic database within the Thermo-Calc software. Comprehensive comparisons between calculated and experimental diffusion coefficients yielded an excellent agreement. The atomic mobilities were also further validated by appropriate predictions of concentration profiles and diffusion paths observed in independent diffusion couple experiments performed at 525 °C for 18 hrs. It has been found that the addition of Sn and Ag both increase the diffusivity of Ag in HCP Mg and Sn in HCP Mg in the stable temperature range of HCP Mg, respectively. This improved understanding of the kinetics in the Mg-Ag-Sn ternary system is essential for controlling diffusion-dependent properties such as coarsening and, therefore, the mechanical properties of Mg-Ag-Sn alloys at elevated temperatures.

Wettability, imbibition and interdiffusion of lithium-based water-in-salt electrolytes in nanoporous carbon in relation to energy storage: A neutron radiography study

Superconcentrated lithium salt electrolytes, or lithium-based Water-in-Salt (WiS) electrolytes emerge as alternative electrolytes in supercapacitors and advanced batteries, such as the Li–O2 ones, especially when combined with a mesoporous carbon with very high surface area. In this work, we analyze the wettability, imbibition, and diffusivity of very concentrated lithium salts in a bimodal mesoporous carbon with pores of 5 nm and 25 nm in diameter. For the first time a neutron radiography technique is used to determine the imbibition and interdiffusion of lithium salts in mesoporous carbon. We found that a 20 m LiTFSI aqueous solution wets the surface of graphite and mesoporous carbon better than water. As a consequence, this WiS electrolyte is embedded rather fast in the mesoporous carbon by the action of capillary forces, exhibiting an intrinsic permeability K = (1.16 ± 0.03).10−18 m2. Finally, by resorting to the different cross-section of the 6Li and 7Li isotopes for the neutron capture, we could analyze the diffusion of LiCl in D2O confined in the mesoporous carbon. The interdiffusion coefficient of the confined LiCl is 5.0 10−7 cm2 s−1, corresponding to a tortuosity coefficient τ = 1.32. This moderate confinement effect results from the strong ion association of the LiCl that precludes the electrostatic interactions of Li+ ions with the negative charge on the pore walls. In summary, the combined properties of the lithium-based WiS electrolytes and the mesoporous carbon allow us to glimpse their use in supercapacitors and Li–O2 batteries.

Interdiffusion Studies in Alloy 617 and 10Cr Steel Joints Using Diffusion Couple Approach and Simulations

In the steam turbine circuit of advanced ultra supercritical power plants dissimilar joints of alloy 617 and 10Cr steel are unavoidable due to economic reasons. In these joints diffusional interaction causing change in microstructure is identified as possible reason for failure during service. To investigate the interdiffusion driven structural changes, alloy 617/10Cr steel diffusion couples were fabricated. To achieve good metallurgical bond between Fe- and Ni-based alloys and to study diffusional transformations under accelerated conditions, diffusion couples were prepared by annealing in the temperature range of 1000-1100 °C for 3-8 h. For all conditions heat treatment interaction zones were wider in alloy 617 (150-200 μm at 1050 °C, 8 h) than in 10Cr steel (15-16 μm at 1050 °C, 8 h) and the phase stability at the interface was studied using electron microprobe and x-ray diffraction. Average effective interdiffusion coefficients were calculated using Dayananda’s approach. While the diffusivities of substitutional solutes were similar in alloy 617 (0.31-0.42 × 10−15 m2/s at 1050 °C), they differed in 10Cr steel in the following sequence: D~Cr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ilde{D}_{{{\ ext{Cr}}}}$$\\end{document} > D~Fe\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ilde{D}_{{{\ ext{Fe}}}}$$\\end{document}≈D~Ni\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ilde{D}_{{{\ ext{Ni}}}}$$\\end{document} > D~Co.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ilde{D}_{{{\ ext{Co}}}}.$$\\end{document} Further, multicomponent interdiffusion profiles were predicted using homogenization model in DICTRA and an integrated approach combining DICTRA with Thermo-Calc helped in understanding the experimental observations on the interface microstructure.

An experimental estimation method of diffusion coefficients in ternary and multicomponent systems from a single diffusion profile

Until recently, it was textbook knowledge that the diffusion coefficients could not be estimated in a multi-component system following the widely practised diffusion couple method. The recently proposed constrained diffusion couple method largely solved the problems. The need to produce two intersecting diffusion paths in a multi-component space with very well-controlled compositions of the diffusion couple end members may be tricky in certain situations, depending on the complications of diffusion paths. In this study, we have shown the estimation of all types of diffusion coefficients from a single diffusion profile without neglecting Onsager's cross terms in concentrated ternary Ni-Co-Fe, Fe-rich quaternary Fe-Ni-Co-Cr and concentrated Ni-Co-Fe-Cr-Al quinary alloys. This is applicable in ternary and multicomponent component systems (n≥3) at a stable Kirkendall marker plane position. One can even estimate the impurity diffusion coefficients utilizing the composition profiles at the ends of the diffusion couples following the Hall method, which has been rarely practised in multicomponent systems until now. We have further demonstrated the importance of estimating the tracer and intrinsic diffusion coefficients in a concentrated or multi-principal element alloy in which interdiffusion coefficients can be vague and misleading for understanding the elements' diffusional interactions and relative mobilities. We have also shown the importance of considering the vacancy wind effect in concentrated alloys. The method proposed in this study will help to generate a mobility database with relative ease in various multicomponent systems important for various applications, which was considered impossible until recently.

The Preparation of Ti–Ta Impedance-Graded Coatings with Limited Diffusion by Cold Spraying Combined with Hot Isostatic Pressing

Ti–Ta impedance-graded coatings were prepared using cold spraying combined with hot isostatic pressing. Compared to the general Ti–Ta binary diffusion couple, the interdiffusion coefficient of as-sprayed Ti–Ta can be increased by approximately 25 times at 1100 °C due to grain refinement at the interface of the cold-sprayed particles. By the control of interdiffusion, pure Ta and pure Ti regions can remain in the materials after hot isostatic pressing at 900 °C. Hot isostatic pressing with capsulate reduced the porosity of the material efficiently to less than 0.02%. The strength of the as-sprayed Ti–Ta composite coating was significantly improved to 990.1 MPa, and the fracture strain reached 11.5%. The strengthening mechanism of Ti–Ta composite coatings relies primarily on the hindrance of dislocation slip by phase interfaces between α and β. Moreover, the macroscopic interfacial bonding strength of the graded material exceeds 881 MPa, which is comparable to that of bulk materials.

Interdiffusion in BCC_B2 Ni–Ti–V alloys at 1223K–1323K

Establishing a Ni–Ti–V system diffusion kinetics database contributes to a better understanding of the precipitation processes in shape memory alloys. In this paper, eleven sets of BCC_B2 Ni–Ti–V single-phase diffusion couples were prepared and annealed at temperatures of 1223 K, 1273 K, and 1323 K. The composition-distance curves were determined using the electron probe microstructure analysis technique. The interdiffusion coefficients were extracted using the HitDIC software, which is based on the numerical inverse method. The software demonstrated high accuracy in predicting the composition curves of the prepared diffusion couples. The interdiffusion coefficients inferred from the HitDIC software and the ones calculated by the Matano-Kirkaldy method achieved good agreement. This demonstrates the reliability and rationality of the evaluated interdiffusion coefficients. This study also investigated the composition and temperature dependencies of interdiffusion coefficients.

Diffusion coefficients and atomic mobilities in the BCC phase of the Al–Nb–V system

Diffusion coefficients in the BCC phase of the Al–Nb–V ternary system are studied for the first time, including an assessment of the atomic mobilities. Ternary interdiffusion coefficients are obtained from the intersecting diffusion paths of several sets of diffusion couples that are annealed at both 1100 °C and 1200 °C. Existing experimental data from the pertinent binary systems are also employed for the assessments of atomic mobilities using the 1-parameter Z-Z-Z binary diffusion coefficient model developed by Zhong et al [1]. Interdiffusion coefficients in the BCC region of the Al–V system are also extracted through a forward-simulation analysis and incorporated into the mobility modeling. A complete description of diffusion in the BCC phase of the Al–Nb–V system is presented following the Binary and Cross-Binary Parameters Only (BCBPO) model developed by Zhong and Zhao [2]. Our data will be valuable input to diffusion-related simulation of refractory high entropy alloys containing aluminum.

Effect of Relative Mass on Ion Velocity Cross-Correlations in Ionic Liquids and Molten Salts: Different Perspectives in Different Reference Frames.

In electrolytes, the self- and interdiffusion coefficients, transport numbers, and electrical conductivity can be used to determine velocity cross-correlation coefficients (VCC) that are also accessible through molecular dynamics simulations. In an ionic liquid or molten salt, there are only three, corresponding to correlations between the velocities of distinct ion pairs (cation-anion, cation-cation, and anion-anion) averaged over both the ensemble and time, calculable from experimental ion self-diffusion coefficients and the electrolyte conductivity. Most usually, the mass-fixed frame of reference (with velocities relative to that of the center of mass of the system) is used to discuss the VCC and the distinct diffusion coefficients (DDC) derived from them. Recent work in the literature has suggested a dependence of the DDC on the ratio of the anion to cation mass. Here, we demonstrate, using our own and literature transport property data for a large number of ionic liquids and molten salts, that the trends observed depend on the particular choice of velocity reference frame, mass-, number-, or volume-fixed. The perception of ion-ion interactions may be distorted in the mass- and volume fixed frames when the co-ions have very different masses or volumes, particularly for systems containing light lithium ions.

Diffusivities and Atomic Mobilities in BCC Ti-Fe-Cr Alloys.

In this research, the diffusion behaviors within the Ti-Fe-Cr ternary system were examined at the temperatures of 1273 K and 1373 K through the diffusion couple technique. This study led to the determination of both ternary inter-diffusion and impurity diffusion coefficients in the body-centered cubic (bcc) phase for the Ti-Fe-Cr alloy, utilizing the Whittle-Green and Hall methods. The statistics show that the average diffusion coefficients D˜FeFeTi and D˜CrCrTi measured at 1273 K were 1.34 × 10-12 and 3.66 × 10-13, respectively. At 1373 K, the average values of D˜FeFeTi and D˜CrCrTi were 4.89 × 10-12 and 1.43 × 10-12. By adopting the CALPHAD method, a self-consistent database for atomic mobility in the bcc phase of the Ti-Fe-Cr system was established. This database underwent refinement by comparing the newly acquired diffusion coefficients with data from the existing literature. Diffusion simulations for the diffusion couples were performed, drawing on the established database. The error between the simulated diffusion coefficient and the experimental measurement data is within 15%, and the simulated data of the component distance distribution and diffusion path are in good agreement with the experimental data. The simulations generated results that aligned well with the observed experimental diffusion characteristics, thereby affirming the reliability and accuracy of the database.