Interdiffusion in Intermetallics

Recently, Tiwari and Mehrotra asserted that the vacancy flux in interdiffusion is driven by a vacancy concentration gradient and also that interdiffusion in intermetallics cannot proceed by the six-jump cycle, triple defect, and antistructural bridge mechanisms. It is shown that those authors’ arguments are incorrect according to classical diffusion theory, by the numerous simulations that have been performed, and by analysis of these mechanisms.     

Interdiffusion in Co-Mn alloys

Interdiffusion coefficient in cobalt-manganese alloys has been determined by Matano's method in the temperature range between 1133 and 1423 K on (pure Co)-(Co-30.28 at. pct Mn alloy) and (pure Co)-(Co-51.76 at. pct Mn alloy) couples. This, ∼D, has been found to increase with the increase of manganese content. However, the activation energy (∼Q) and frequency factor ( ₀) show a maximum at about 10 at. pct Mn. The concentration dependence of and has been discussed taking into account the thermodynamic properties of the alloy. The difference in between the ferro- and paramagnetic phases in Co-5 at. pct Mn alloy has been found to be 24 kJ/mol, which is larger, than that for the diffusion of Mn⁵⁴ in this alloy. Further it has been found that the Kirkendall marker moves toward manganese-rich side, showing that manganese atoms diffuse faster than cobalt atoms. From the marker shift, the intrinsic diffusion coefficients,D _Co andD _Mn, at 33 at. pct Mn have been determined as follows:D _Co=0.22×10⁻⁴ exp(−263 kJ mol⁻¹/RT) m²/s, andD _Mn=0.98×10⁻⁴ exp(−229 kJ mol⁻¹/RT) m²/s.     

Interdiffusion in the carbides of the Nb-C system

Interdiffusion coefficients in Nb₂C and NbC_1−x were measured using bulk diffusion couples in the temperature range from 1400 °C to 1700 °C. Marker experiments were used to show that carbon is the only component undergoing significant diffusion in both carbides. Carbon concentrations were measured by difference using electron probe microanalysis, and interdiffusion coefficients were taken from Boltzmann-Matano analyses of the resulting concentration profiles. This analysis clearly showed that, in NbC_1−x, interdiffusion coefficient varies with carbon concentration, and is expressed by

Effect of Varying Molar Volume on Interdiffusion Analysis in a Binary System

Metallurgical and Materials Transactions A - There are seven approaches of determination of interdiffusion coefficients with respect to volume-fixed frame given in the literature. These methods are...     

Interdiffusion in ternary Fe-Cr-AI alloys

Interdiffusion coefficient matrices, have been experimentally measured at 31 points in the αδFe phase field of the Fe-Cr-AI ternary equilibrium phase diagram at 900 °C (1173 K). Analyses of the computed matrices were carried out by subjecting each measured -Dⁿ _ij to two consistency tests comprised of Onsager’s and Kirkaldy’s relations. Good consistency with these relationships was obtained in the central region of the ternary phase field, but there were significant deviations near the phase boundaries. These may beattributable to systematic uncertainties in the analytical procedure. The results indicate that falls quickly with increasing C_Cr, with C_Al > 0.2, but is not a strong function of C_Al. Conversely, is not a strong function of C_Al but decreases with increasing C_Cr. formerly with the Lawrence Berkeley Laboratories of the University of California, Berkeley At the time of this research, Dr. Stringer was on sabbatical leave at the Lawrence Berkeley Laboratories, Department of Materials Science and Mineral Engineering, University of California, Berkeley, CA 94720.     

Interdiffusion in copper-rich cu-ag solid solutions

Interdiffusion was studied in the temperature between 974 and 1273 K, using conventional sandwich-type diffusion couples consisting of pure copper and Cu-2.1 at. pct Ag alloy. The interdiffusion coefficient, , increased slightly with increasing the atomic fraction of silver, N_Ag. Values of were well represented by the parameters of ₀ = 0.21 x 10^-4 (m²/s) and ≈ = 184.5 - 143.0 N_Ag (kJ/g-atom) up toNAg = 0.02. The Kirkendall effect during diffu-sion treatments at 1174 K for up to 1.4724 x 10⁶ s was also studied. The marker moved always toward the silver-rich side. The ratio, D*_Ag / D*_Cu,was 5.6 for N_Ag = 0.011, while it was 4.2 for N_Ag = 0.     

Interdiffusion in copper-base Cu-AI solid solutions

Interdiffusion in couples consisting of pure copper and a Cu-12.2 at. pet A1 alloy has been studied in the temperature range between 977 and 1277 K. Concentration of aluminum was determined by EPMA. The interdiffusion coefficient increased with the atomic fraction of aluminum, N_ai, in solid solution: D₀(m²/s) = 0.43 × 10^-4 and Q (kJ/tool) =194000 — 180000 N_a1 The Kirkendall effect has also been studied in the temperature range from 977 to 1277 K. The markers moved toward the aluminum-rich side. The ratio of the tracer-diffusion coefficient of aluminum, D _* ^Al , to that of copper, D _* ^Cu , at the marker position where N_a1 = 0.073, was estimated at 1.7 to 3.7; this ratio showed a tendency to increase with temperature.     

Interdiffusion in the Ni-Cr-Co-Mo system at 1300 °C

Interdiffusion was investigated with solid-solid diffusion couples in theα (fcc) region of the quaternary Ni-Cr-Co-Mo system at 1300 °C for the determination of diffusion paths and diffusional interactions among the components. The concentration profiles for a given couple exhibited a common cross-over composition, Y_c, which reflected the relative depths of diffusion in the terminal alloys. Interdiffusion fluxes were calculated directly from the concentration profiles, and the quaternary interdiffusion coefficients were calculated at selected compositions. Ni and Co exhibited uphill diffusion against their individual concentration gradients in a direction opposite to the interdiffusion of Cr. Quaternary diffusion paths were presented as a set of partial diffusion paths on the basis of relative concentration variables.     

Compendium About Multicomponent Interdiffusion in Two Dimensions

Interdiffusion between dissimilar solids can change the properties of joined materials. Although much work has been done to study experimentally and theoretically interdiffusion in one-dimensional (1-D) diffusion couples, studying interdiffusion in two-dimensional (2-D) or three-dimensional (3-D) solids remains a challenge. In this article, we report an experiment and develop a model to study interdiffusion in a multicomponent system of 2-D geometry. The results (concentration maps and profiles) are compared with data obtained by modeling and numerical simulations. It is assumed that the system satisfies Vegard’s rule and diffusion coefficients are composition dependent. To model the multidimensional diffusion with a drift, we take benefit of the concept of the drift potential. A nonlinear parabolic-elliptic system of strongly coupled differential equations is formulated and the implicit difference method, preserving Vegard’s rule, is applied in the simulations.

     

Interdiffusion of cadmium and nickel

Conclusions In an experimental investigation, the partial heterodiffusion coefficients of cadmium and nickel were determined for an annealing temperature of 270°C. It was established that the diffusion rate of cadmium markedly exceeds that of nickel. This difference accounts for the appearance of pores, inand an increase in volume of, compacts from mixed nickel and cadmium powders during sintering.Translated from Poroshkovaya Metallurgiya, No. 5 (149), pp. 87–92, May, 1975.     

Ti-Al系中TiAl和Ti_3Al相层生长动力学和互扩散

本文研究了Ti衬底与A1膜(1.25～1.35μm)间,在温度580～800℃反应时,金属、TiAl及Ti_3Al相层生长规律,并用Boltzmann-Matano-Heumann和Wagner方法计算了Al在化合物中的互扩散系数和扩散激活能,找出了扩散系数随温度和时间的变化规律,计算结果表明,A1在TiAl及Ti_3A1中的扩散激活能分别为0.82±0.1eV和0.65±0.1eV。     

Interdiffusion in the TiO2 oxidation product of Ti3Al

Oxidation experiments have been conducted on Ti₃Al in the temperature range 1023 to 1273 K in a one-atmosphere pure oxygen environment. The oxidation products were analyzed using the scanning electron microscope (SEM), energy-dispersive spectrometer (EDS), and X-ray diffraction (XRD) techniques and found to be predominantly TiO₂ (rutile). The oxidation rate was observed to obey the parabolic rate law. Diffusivity data were obtained using the parabolic rate constant for interdiffusion of Ti and O in the oxide layer. Parabolic rate constants were calculated from oxidation rate data, and Valenci equations for flat sheets were used to calculate diffusion coefficients. The activation energy, Q, was found to be 295.43±5.90 kJ/mol, and the frequency factor, D ₀, was calculated to be 0.68±0.01 m²/s for oxygen in the TiO₂. The activation energy obtained in this study matches closely with that of oxygen diffusion in TiO₂ reported in the literature.     

Interdiffusion in the Ni/TD-NiCr and Cr/TD-NiCr Systems

The diffusion of Ni and Cr into TD-NiCr has been studied over the 900 to 1100°C temperature range. The diffusion couples were prepared by electroplating Cr and Ni on polished TD-NiCr wafers. Concentration profiles produced as a result of isothermal diffusion at 905, 1000, and 1100°C were determined by electron microprobe analysis. The Boltzmann-Matano analysis was used to determine concentration dependent diffusion coefficients which were found to compare favorably with previously reported values. These data suggest that 2 vol pct ThO₂ distribution has no appreciable effect on the rates of diffusion in TD-NiCr with a large grain size. This supports the view that an inert dispersoid in an alloy matrix will not in itself lead to enhanced diffusion unless a short-circuit diffusion structure is stabilized. Formerly Asst. Prof, of Metallurgical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va.     

Confirmation of the Grube-Jedele Procedure in Processing Interdiffusion Data in Binary Alloys

The 1932/1933 experiments of Grube-Jedele (G-J) reveal their discovery that 0–100 at. pct diffusion penetration curves can generate monotone composition-variant interdiffusion coefficients, \( \tilde{D}\left( X \right) \). G-J templated a smoothed infinite couple sectionally and sequentially curve via a set of constant \( \tilde{D} \) error function curves with local 2- and 3-point determined. The first and second derivatives created a monotone sequence of coefficient values. We detail this in processing G-J curves, remarkably revealing as with constant \( \tilde{D} \), that variable \( \tilde{D} \) obtained generates a \(\root{}\of{(t)}\) penetration dependence. This finding was later verified analytically via Ginzburg-Landau’s (G-L) 1950 variational-quantum, lattice-dynamical requirement that \( \tilde{D} \) lies outside the Fickian second derivative. The G-L and G-J procedures and analyses were supported in 1947 by Smigelskas and Kirkendall’s experimental discounting of Boltzmann’s 1897 purely mathematical theorem.     

Interdiffusion in copper(rich)-chromium solid solutions

Abstract

Interdiffusion was studied in copper (rich)-chromium solid solutions in the composition range approximately 0.2 to 0.8 at% Cr and in the temperature range 852°C – 1050°C. Diffusion couples consisted of cylindrical sections of OFHC copper electroplated with pure chromium. The concentration profiles of the diffusion couples were determined using an electron probe micro analyzer, and the diffusion coefficients were determined by fitting the error function solution of the diffusion equation to the experimental curves. The Arrhenius plot of the diffusion coefficients obtained for five different temperatures gives 48.4 ± 1.2 kcal/mole and 1.11_?0.44^+0.78 cm²/sec for the activation energy (E_D) and frequency factor (D_o) respectively (where the limits given are standard deviations for a 99 per cent confidence level), and approximate published chromium tracer diffusion and copper self diffusion results.

Résumé

Les auteurs ont étudié l'interdiffusion dans des solutions solides, riches en cuivre et con tenant environ 0.2 à 0.8% atomique de chrome, pour une gamme de temp;amp;#x00E9;ratures de 852 agrave; 1050°c. Les couples de diffusion étaient des sections cylindriques de cuivre OFHC électroplaqués avec du chrome pur. Les profils de concentration des couples ont été mesurés par microsonde électronique et les coefficients de diffusion ont été déterminés en lissant les courbes expérimentales grâce à la solution de la fonction erreur pour l'équation de diffusion. La courbe déArrhenius des coefficients de diffusion obtenus à cinq températures différentes donne une énergie d'activation (ED) de 48.4 ± 1.2 kcal/mole et un facteur de fréquence (Do) de 1.11 _?0.44^+0.78 cm²/sec. (oú les limites indiquées sont les déviations standards pour un niveau de con fiance de 99%). Ces valeurs sont approximativement égales à celles publiées pour la diffusion de traceur de chrome et pour l'autodiffusion du cuivre.