Simultaneous Measurement of Isotope-Free Tracer Diffusion Coefficients and Interdiffusion Coefficients in the Cu-Ni System

A new formalism recently developed by Belova et al., based on linear response theory combined with the Boltzmann–Matano method, allows determination of tracer and interdiffusion coefficients simultaneously from a single, isotope-free, traditional diffusion couple experiment. An experimental methodology with an analytical approach based on the new formalism has been carried out using the model Cu-Ni system to effectively determine tracer diffusion coefficients from an isotope-free diffusion couple experiment. Cu thin films were deposited in between several binary diffusion couples with varying terminal alloy compositions (Cu-25Ni, Cu-50Ni, Cu-75Ni, Ni). Diffusion couples were annealed at 800, 900 and 1000 °C, and the superimposed concentration profiles of thin film and interdiffusion were analyzed for the simultaneous determination of tracer and interdiffusion coefficients. Processed concentration profiles obtained from the diffusion experiments were also fitted with simple Gaussian distribution function. Results were compared to existing literature data obtained independently by radiotracer experiments, and an excellent agreement has been observed.     

Ternary Interdiffusion in <Emphasis Type="Italic">β</Emphasis> (BCC) Phase of the Ti-Al-Nb System

Interdiffusion coefficients are reported at various compositions in the β (BCC) phase of the Ti-Al-Nb system using solid–solid diffusion couples assembled at three different temperatures of 1060 °C, 1100 °C and 1170 °C. The interdiffusion fluxes were determined after fitting the experimental concentration profiles with MultiDiFlux software and the ternary interdiffusion coefficients were evaluated at various compositions using Kirkaldy’s approach. The interdiffusion of Nb was the slowest, while Ti and Al showed similar interdiffusion kinetics. The main interdiffusion coefficients for the three components are positive. The cross interdiffusion coefficients of Ti and Nb are comparable in magnitude to their respective main terms indicating the presence of strong diffusional interactions in this system. The cross coefficient \(\tilde{D}_{\text{TiNb}}^{\text{Al}}\) is positive indicating that the interdiffusion flux of Ti is enhanced down the concentration gradient of Nb. The negative value of the cross-term \(\tilde{D}_{\text{TiAl}}^{\text{Nb}}\) indicates that the interdiffusion flux of Ti is enhanced up the gradient of Al. The tracer diffusion coefficient of Al increases with temperature and decreasing Nb content in binary Ti-Nb alloys. Binary interdiffusivities calculated at Ti-Nb compositions by extrapolation are reasonably consistent with the values reported in the literature.     

Interdiffusion and Atomic Mobilities of fcc Co-V-Mo Alloys: Measurement and Modeling

Based on 18 bulk diffusion couples, the composition-dependent interdiffusion coefficients in the fcc Co-V-Mo alloys at 1273, 1373 and 1473 K were obtained from the intersection points of the diffusion couples by means of EPMA technique coupled with the Whittle and Green method. With the experimentally determined interdiffusion coefficients and the critically reviewed experimental diffusivities available in the literature, the atomic mobilities of fcc Co-V-Mo alloys were assessed by means of Diffusion Controlled Transformation (DICTRA) software. The quality of the assessed atomic mobilities was confirmed by the comprehensive comparisons between various DICTRA-calculated diffusion behaviors and the experimental ones, including concentration profiles and diffusion paths.     

Interdiffusion in the Face-Centered Cubic Phase of the Co-Al-W-Ta System Between 1090 and 1240 °C

Interdiffusion of Al, W, Ta and Co in a Co-base alloy at temperatures between 1090 and 1240 °C has been investigated. The interdiffusion coefficients were found to be close to those reported for these elements in Ni-base alloys. Combining the diffusion simulation software DICTRA with the Ni-base diffusion databases TCNi₅ and MobNi₃, the interdiffusion profiles of Co, Al W, and Ta were modeled for Co9Al8W2Ta/Co diffusion couples annealed at different temperatures and for different times. The results show that interdiffusion in the Co-Al-W-Ta alloys can be modeled reasonably well using the available commercial databases for thermodynamics and kinetics of Ni-base systems.     

Computational Study of Atomic Mobility in Co-Fe-Ni Ternary Fcc Alloys

The generalized Boltzmann-Matano method has been used to evaluate the interdiffusion coefficients at 1100 °C for the fcc phase of the Co-Fe-Ni ternary system from the concentration profiles developed from single-phase diffusion couple. The evaluated interdiffusion coefficients, together with other experimental data in the literature, have been assessed to develop an atomic mobility database for the fcc phase of the Co-Fe-Ni ternary. The atomic mobility database, in conjunction with the CALPHAD-base thermodynamics, has been used to simulate a number of ternary diffusion couple experiments. Comprehensive comparisons between the calculated and experimental data show that excellent agreement is obtained not only for the general diffusion data of ternary diffusion couple, such as the interdiffusion coefficients and the concentration profiles, but also for much of in-depth diffusion behavior, like the diffusion path, the interdiffusion flux and the shift of the Kirkendall plane.     

Interdiffusion and Atomic Mobility Studies in Ni-Rich fcc Ni-Co-Al Alloys

The ternary interdiffusion coefficients in fcc Ni-Co-Al alloys at 1373 K were determined using Whittle and Green method together with electronic-probe microanalysis. With the help of DICTRA software, the experimental diffusion coefficients were critically assessed to obtain the atomic mobilities of Ni, Co and Al in fcc Ni-Co-Al alloys. Comprehensive comparisons between calculated and experimental diffusion coefficients showed that the experimental data could be well reproduced by the atomic mobilities obtained in the present work. The developed diffusion mobilities were further validated by the calculation of the concentration profiles and diffusion paths in diffusion couples.     

Interdiffusion and Phase Growth Kinetics in Magnesium-Aluminum Binary System

Binary interdiffusion data as functions of composition in the Mg-Al system are essential in modeling kinetics of phase transformations in multicomponent Mg and Al alloys. Interdiffusion and phase growth kinetics were studied in the binary Mg-Al system using multiphase diffusion couples assembled between pure Mg and pure Al at 380, 400 and 420 °C. Two phases, Al₃Mg₂ (β) and Mg₁₇Al₁₂ (γ) were formed between Al and Mg at the three temperatures studied. Both β and γ phases were observed to follow parabolic growth with time, which suggests that the growth of the two phases is controlled by bulk diffusion mechanisms. The activation energies for the growth of β and γ phases in the temperature range of 380-420 °C were found to be 37.3 ± 4.1 and 187.7 ± 1.9 kJ/mol, respectively. The interdiffusion coefficients were evaluated as functions of compositions in various phases at the three temperatures studied, which were further utilized for evaluating the activation energies and frequency factors for interdiffusion in each phase. The activation energy for interdiffusion in FCC-Al is found to increase with increasing Mg-content whereas the activation energies for interdiffusion in HCP-Mg and γ phases do not vary significantly with composition.     

On Interdiffusion in FeNiCoCrMn High Entropy Alloy

Interdiffusion was studied in FCC FeNiCoCrMn high entropy alloy (HEA) system with the help of two quinary diffusion couples annealed at 1000 °C for 100 hours. The terminal alloys of the two couples were selected based upon the knowledge of binary thermodynamic interactions so as to have enhancement or reduction of interdiffusion of particular components. Interdiffusion fluxes of nickel and manganese, which have highest negative binary enthalpy of mixing, were observed to be enhanced up the gradients of each other and reduced down the gradients of each other. Regions of uphill interdiffusion observed for chromium and iron and presence of a zero flux plane observed for iron in one of the diffusion couples indicate the existence of strong diffusional interactions in this HEA. Quinary interdiffusion coefficients were also calculated at various compositions of the FeNiCoCrMn system based upon Manning’s model, utilizing the knowledge of tracer diffusivities of constituent elements and thermodynamic factors. The calculated cross interdiffusion coefficients were shown to be consistent with the diffusional interactions observed in the two diffusion couples. Nickel and Manganese, which are slowest and fastest diffusing species in the FeNiCoCrMn HEA and, which also possess highly negative binary enthalpy of mixing were observed to play particularly significant role in determining the diffusional interactions in this HEA system. Validity of the interdiffusion coefficients evaluated by Manning’s approach was established by regenerating the concentration profiles of the experimental diffusion couples based on transfer matrix method (TMM).     

Determination and assessment of ternary interdiffusion coefficients from individual diffusion couples

Two pairs of diffusion couples were assembled with α (fcc) Cu-Ni-Zn alloys characterized by similar thermodynamic activities for Cu and annealed at 775 °C. One pair of couples exhibited intersecting diffusion paths, and the other pair showed overlapping path segments. They were analyzed for interdiffusion fluxes, zero-flux-planes, and ternary interdiffusion coefficients directly from the concentration profiles. The analysis was based on converting profiles of concentrations to profiles of interdiffusion fluxes and evaluating moments of interdiffusion fluxes for the determination of interdiffusion coefficients over selected composition ranges. For the pair with intersecting diffusion paths, ternary interdiffusion coefficients were determined from the individual couples in the region of their common composition; these coefficients were in agreement with each other and with those determined by the Boltzmann-Matano analysis. For the pair of couples with overlapping diffusion path segments, interdiffusion coefficients calculated from each couple over the common path segment agreed with each other. In addition, the interdiffusion coefficients calculated over various composition regions were used to regenerate the concentration profiles of the individual couples. All calculations were carried out with the aid of a computer program called MultiDiFlux, which was developed by Dayananda and Ram-Mohan as a free educational and research tool for analysis of multicomponent diffusion.     

Effect of Small Amount of Manganese on the Interdiffusivities in Fe-Al Alloys

The ability to weld aluminum and steel sheets depends strongly on the formation of intermetallic phases; a process that is, in turn, controlled by the interdiffusion of iron and aluminum across the welded interface. Understanding the interdiffusion behavior, and how it is influenced by tertiary elements such as manganese, will allow for better prediction of the properties of the spot weld. Hence, interdiffusion coefficients and activation energies for interdiffusion were determined in the α solid solution and B2 intermetallic phases of Fe-Al alloys in the presence of 1.5-2 at.% manganese with pseudo-binary diffusion couples investigated at 900-1095 °C. The interdiffusion coefficients in α were found to increase in the presence of Mn at all temperatures compared with those reported in the binary Fe-Al alloys. The activation energies for interdiffusion in α are correspondingly lower than those in the binary Fe-Al alloys. The increase in the main interdiffusion coefficients in the presence of Mn indicates that diffusional interactions between Fe and Al are increased in the presence of Mn. The expected increase in diffusional interactions of Fe and Al are found to be consistent with the thermodynamic interactions between Fe and Al in the binary Fe-Al and ternary Fe-Al-Mn system as estimated from the literature. The presence of Mn is found to decrease the solubility of Al in the α solid solution, which, in turn, is expected to decrease the growth rate of the intermetallic at the interface between steel and aluminum.     

Interdiffusion and Atomic Mobilities in fcc Co-Ga and Co-V Alloys

On the basis of Co/Co-10Ga, Co/Co-12Ga, and Co/Co-10V (at.%) diffusion couples, interdiffusion coefficients in the face-centered cubic (fcc) phase of the Co-Ga and Co-V binary systems were investigated in the temperature range between 1273 and 1573 K by means of the den Broeder method. Based on available thermodynamic information, the interdiffusion data were assessed to develop the atomic mobilities for the fcc Co-Ga and Co-V alloys using the DICTRA software package, and their validity was tested by simulating concentration–distance profiles.     

Interdiffusion Coefficients in FCC Co-Rich Co-Ti-V Alloys at 1273, 1373 and 1473 K

Based on 18 bulk diffusion couples, the composition-dependent interdiffusion coefficients in the FCC Co-rich Co-Ti-V alloys at 1273, 1373 and 1473 K were obtained from the intersection points of the diffusion couples by means of EPMA technique applied to Whittle and Green method. The reliability of the experimental interdiffusivities is validated via thermodynamic constraints. Taking Co as the solvent element, the present results show that when the temperature is from 1273 to 1473 K, the ternary interdiffusion coefficients increases from 10^?16 to 10^?14 m²/s and the diffusion of Ti is generally faster than V. The ternary main interdiffusion coefficients of \(\tilde{D}_{\text{TiTi}}^{\text{Co}}\) and \(\tilde{D}_{\text{VV}}^{\text{Co}}\) at different compositions of Ti and V at 1473 K were compared with the values obtained for boundary binary Co-Ti and Co-V systems in the literature. A composition-dependent decreasing-increasing tendency was found for \(\tilde{D}_{\text{VV}}^{\text{Co}}\).     

Intrinsic diffusion and Kirkendall effect in Ni–Pd and Fe–Pd solid solutions

Intrinsic diffusion and the Kirkendall effect in the Ni–Pd (at 900–1200°C) and Fe–Pd (at 1100°C) solid solution systems were investigated. The diffusion couple technique including incremental and “multi-foil” couples was employed. A theoretical analysis of the Kirkendall effect, which manifests itself by migration of inert markers inside the interdiffusion zone, was performed for a binary solid solution system. It was demonstrated that depending upon the relative mobilities of the components in different parts of the interaction zone of such binary diffusion couples, the appearance of two or more “Kirkendall” planes as marked by inert particles can be expected. This phenomenon, which indeed was predicted and found in the multiphase Ni/Ti diffusion couple, was not observed in the experiments on the single-phase Ni–Pd and Fe–Pd systems. The diffusion process in these binary systems exhibiting a minimum in the liquidus curve was found to show special features with respect to the concentration dependence of the diffusion coefficients.     

Interdiffusion in the f.c.c. Phase of Cu-Mn Binary Alloys

Interdiffusion coefficients are calculated in the Cu-Mn binary system from 450 to 925?°C. Starting from the diffusion couples between pure Cu and Mn, the solubility limit of the manganese in copper is determined and the interdiffusion characteristics in the f.c.c. solid solution of Cu-Mn alloys are analysed. The interdiffusion coefficients in this binary system are calculated by the den Broeder method. The interdiffusion coefficients are strongly dependent on the composition: their values lie between approximately 10^?14 and 4?×?10^?9?cm²?s in this temperature range. The Vignes and Birchenall method is used to determine the impurity diffusion coefficients of manganese in pure copper. These coefficients are compared with the tracer diffusion coefficients of Mn⁵⁴ in copper from the literature. Activation energies, which lie from 155 to 180?kJ/mol, are of a vacancy controlled diffusion mechanism.     

Interdiffusion and Diffusion Mobility for Fcc Ni-Co-Mo Alloys

Ternary fcc Ni-Co-Mo diffusion couples annealed at 1273 and 1473 K have been scanned to measure composition profiles by using electron probe microanalysis. The interdiffusion coefficients were extracted using the Whittle–Green method from the measured composition profiles of the ternary diffusion couples. Based on the diffusion coefficients reported in the literature and data determined in the present work, the diffusion mobilities for fcc Ni-Co-Mo alloys were assessed. In addition, diffusion paths and composition profiles were simulated with presently assessed mobility parameters. In general, reasonable agreements have been reached and the resulted mobility database can be used to investigate the diffusion behavior of the ternary fcc Ni-Co-Mo alloys in wide composition and temperature ranges.     

Ti-Zr二元合金在β相区的互扩散行为研究

通过扩散偶技术,利用电子探针(EPMA)研究了Ti-Zr二元合金在β相区(950至1150℃)的互扩散行为。采用Den Broeder方法及Hall修正法计算了Ti-Zr二元合金的互扩散系数,其范围为10-14～10-12m2/s;计算了扩散激活能Q和频率因子D0,两者均随Zr浓度的增加呈现先增加后减小的规律,其峰值均出现在50at%Zr浓度附近。用Vignes-Birchenall方法计算了Ti-Zr二元合金在扩散组元极限浓度处的杂质扩散系数,并与用Hall修正方法计算的互扩散系数进行了对比,二者结果比较接近。     

An examination of a multicomponent diffusion couple

New expressions relating the interdiffusion flux of a component to its own concentration gradient in a multicomponent diffusion couple have been derived and applied to a diffusion couple investigated in the Cu-Ni-Zn system. From these relations, effective interdiffusion coefficients were determined at selected sections in the diffusion zone directly from the locations of the sections relative to the Matano plane. The Cu-Ni-Zn couple was analyzed for interdiffusion fluxes and interdiffusion coefficients with the aid of “MultiDiFlux” program developed for the analysis of interdiffusion in multicomponent systems. The couple was examined for zero-flux plane development, interdiffusion against activity gradients, and diffusion path representation. Diffusion path slopes at selected sections in the diffusion zone were related to the interdiffusion coefficients; slopes at path ends were determined from eigenvectors evaluated from limiting ratios of interdiffusion fluxes. Expressions for internal consistency among the concentration profiles or flux profiles of the individual components were also developed in terms of the terminal alloy compositions and applied to the Cu-Ni-Zn couple in the diffusion zone. This article was presented at the Multicomponent-Multiphase Diffusion Symposium in Honor of Mysore A. Dayananda, which was held during TMS 2006, 135th Annual Meeting and Exhibition, March 12–16, 2006, in San Antonio, TX. The symposium was organized by Yongho Sohn of University of Central Florida, Carelyn E. Campbell of National Institute of Standards and Technology, Richard D. Sisson, Jr., of Worcester Polytechnic Institute, and John E. Morral of Ohio State University.     

Diffusion Research in BCC Ti-Al-Ni Ternary Alloys

Interdiffusion in BCC phase of Ti-Al-Ni ternary system was investigated at 1473 K (1200 °C) by employing the diffusion-couple technique. The raw composition profiles resulting from interdiffusion treatment and retrieved from EMPA were first analytically represented by error function expansion (ERFEX), and the ternary interdiffusion and impurity diffusion coefficients were then extracted by the Whittle-Green and generalized Hall methods, respectively. The obtained main interdiffusion coefficients \( \tilde{D}_{\text{AlAl}}^{\text{Ti}} \) and two cross coefficients, i.e. \( \tilde{D}_{\text{AlNi}}^{\text{Ti}} \) and \( \tilde{D}_{\text{NiAl}}^{\text{Ti}} \), were found to increase with increasing composition of diffusing species, whereas the values of \( \tilde{D}_{\text{NiNi}}^{\text{Ti}} \) show no noticeable compositional dependence. The impurity diffusivities \( \tilde{D}_{{{\text{Al}}\left( {\text{Ti - Ni}} \right)}}^{*} \) and \( \tilde{D}_{{{\text{Ni}}\left( {\text{Ti - Al}} \right)}}^{*} \) increase with decreasing the Ni and Al compositions, respectively. The results imply that Al diffusion in β Ti-Al-Ni alloys would occur via an ordinary vacancy diffusion mechanism, whereas Ni diffusion, at least one order magnitude faster than Al, very likely benefits from interstitial diffusion as Fe and Co anomaly diffuse in BCC Titanium alloys.