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.     

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.     

Analysis of multicomponent diffusion couples for interdiffusion fluxes and interdiffusion coefficients

A procedure for the analysis of an isothermal, multicomponent, solid-solid diffusion couple is presented for the direct determination of interdiffusion fluxes of all components over the entire diffusion zone and for the evaluation of main and cross interdiffusion coefficients over regions selected in the diffusion zone. The average effective interdiffusion coefficients for the individual components are also determined over the selected compositional ranges. A user-friendly computer program called MultiDiFlux has been developed to carry out all of the analysis and calculations. With the aid of this program, selected diffusion couples in the ternary Cu-Ni-Zn system were analyzed for interdiffusion fluxes and ternary interdiffusion coefficients, and were assessed for up-hill diffusion, zero-flux plane development, and diffusional interactions among components. The interdiffusion coefficients determined over various regions of the diffusion zone are used by the program to regenerate the concentration profiles of the couple.     

A transfer-matrix method for analysis of multicomponent diffusion with any number of components

A transfer-matrix method (TMM) is presented for the development of concentration and flux profiles in multicomponent diffusion involving any numbern of components. From interdiffusion fluxes or concentration gradients available at an initial positionx _s, the authors derive expressions for the transfer matrix and its integral so that the concentrations or interdiffusion fluxes of the components can be obtained at any coordinatex. The TMM requires data for interdiffusion coefficients, which are obtained as average values over selected regions by the method of moments developed by Dayananda. Expressions for the concentrations are also obtained from initial conditions on the fluxes or the concentration gradients. The method is also applicable to the case when all the concentrations are known at two ends of a region over which the diffusion coefficients are considered constant. The integration of the fluxes over time, or over the coordinatex, can be evaluated using the transfer-matrix approach, provided the value of the interdiffusion flux is given at a given coordinate. The TMM is applicable to any number of components and can be regarded as a compact generalization of the solutions available for ternary diffusion couples with constant interdiffusion coefficients. An application of the method is illustrated with the experimental data for a ternary Cu-Ni-Zn diffusion couple, and the results are compared with those based on the Fujita-Gosting solution. 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.     

Phase stability,oxidation, and interdiffusion of a novel Ni−Cr−Al−Ti−Si bond-coating alloy between 900 and 1100°C

A novel, low-expansion experimental Ni–Cr–Al–Ti–Si bond-coating alloy was investigated in the as-cast state concerning its phase stability, oxidation resistance in air, and interdiffusion with single-crystal IN-100 at 900, 1000, and 1100°C. Isothermal oxidative thermogravimetry was employed up to 500 hr. Interdiffusion was compared to a commercial Ni–Co–Cr–Al–Y alloy on IN-100. Oxidized Ni–Cr–Al–Ti–Si specimens and diffusion couples were characterized by metallography, SEM, EDX, XRD, and XRF. The Ni–Cr–Al–Ti–Si alloy provides good oxidation resistance in air at least up to 1000°C. The alloy is an alumina former. Due to its coarse microstructure, other oxides (e.g., rutile) may form and considerably dominate the oxidation behavior. The kinetics of oxidation were correlated with temperature, formation of phases, and morphology of oxides. Interdiffusion fluxes between Ni–Cr–Al–Ti–Si and IN-100 were mainly directed to the superalloy. They were faster than in Ni–Co–Cr–Al–Y/IN-100 diffusion couples.     

Modeling Interdiffusion Processes in CMSX-10/Ni Diffusion Couple

A diffusion couple between directionally solidified nickel and the single crystal Ni-base superalloy CMSX-10 was produced by hot pressing in vacuum. The diffusion couples were heat treated at temperatures between 1050 and 1250 °C. The exposed samples were characterized by SEM/EBSD/EPMA. The interdiffusion results in dissolution of the γ′-Ni₃Al in the superalloy and in growth of nickel grains towards CMSX-10. Rapid diffusion of aluminum from the superalloy into pure nickel leads to a significant formation of pores in the superalloy. The interdiffusion processes were modelled using the finite-element simulation software DICTRA with the databases TCNi5 and MobNi2, tailored specially for Ni-base superalloys. The effect of alloying elements on the interdiffusion profiles is discussed in terms of alloy thermodynamics. The calculated element concentration profiles are in good agreement with the EPMA measurements. The interdiffusion modeling correctly predicts the shapes of the concentration profiles, e.g. kinks on the Al and Ti profiles in the vicinity of the original interface in the joint. The calculation predicts with reasonable accuracy the extent and the location of the Kirkendall porosity.     

Investigation of interdiffusion and kirkendall effect in the Co-Ni-Fe system: III. Dependence of diffusion parameters on the initial conditions

Dependences of the parameters of interdiffusion (effective coefficients, diffusion paths, Kirkendall shift) on the variation of the initial compositions of a diffusion couple have been studied on the concrete example of the Co-Fe-Ni system. The experimental results obtained show that the diffusion paths in the three-component system depend substantially on the selection of initial conditions, even when the initial alloys of the “narrower” diffusion couple lie on the diffusion path of the “wider” pair. At the same time, when represented in reduced concentrations, the diffusion paths of all these diffusion couples practically coincide. The latter makes it possible to predict the type of diffusion paths for any diffusion couple whose initial com- position lies in the same concentration region. In one of the diffusion couples studied, the instability of the Kirkendall plane was revealed, which thus far was observed only in binary systems.     

Interdiffusion in multiphase,Al-Co-Cr-Ni-Ti diffusion couples

The interdiffusion in Co matrix/Al particle alloys and Co/Ni-based substrates was studied using electron probe microanalysis and was simulated with the software DICTRA. Alloys were prepared by mixing elemental powders and furnace melting under an inert atmosphere. The phases involved in the study were γ (Ni-based or Co-based), β-CoAl, and γ′. The alloys were single-phase (γ) as well as two-phase (γ + β and γ + γ′). Several equilibrium points in the Al-Co-Cr system were measured and compared with the calculated diagram at 1100 °C. The diffusion couples were prepared to produce combinations of selected alloys and were subjected to annealing at 1100 °C for times up to 72 h. The diffusion calculations made with DICTRA were performed using the TCNI1 thermodynamic database together with mobility data collected from different literature sources. A literature survey on diffusion data of this system was performed, and comparisons with available data were made. The validity of the selected mobility data was checked with the composition profiles measured on some single-phase γ/γ diffusion couples. In the γ + β/γ and γ/γ + γ′ diffusion couples, a regression of the dispersed phase (β or γ′) was observed due to the interdiffusion of Al. From combined experimental and theoretical results, the effects of temperature and coating thickness were determined as an input for a coating lifetime prediction model. Paper presented at Calphad XXXII, La Malbaie, Québec, Canada, May 25–30, 2003.     

Diffusional analysis of a multiphase oxide scale formed on a Mo-Mo3Si-Mo5-SiB2 alloy

Diffusional analyses were performed to understand the oxidation at 1300 °C of a multiphase Mo-13.2Si-13.2B (at.%) alloy. During oxidation, a protective glass scale formed with an intermediate layer of (Mo+glass) between the base alloy and external glass scale. Compositional profiles across the (Mo+glass) layer and the external glass scale were determined, and interdiffusion fluxes and effective interdiffusion coefficients for the various components were determined by using “MultiDiFlux” software. The motion of the (alloy/Mo+glass) and (Mo+glass/glass) interphase boundaries after passivation was examined. Additionally, vapor-solid diffusion experiments at 1300 °C were carried out with single-phase Mo₃Si and T2 specimens in addition to a multiphase Mo-10Si-10B (at.%) alloy. These specimens were exposed to vacuum to induce silicon loss resulting in the formation of a Mo layer. An average effective interdiffusion coefficient of Si in Mo at 1300 °C was estimated from the Mo₃Si-vapor couple to be in the order of 8×10⁻¹⁷ m²/s. 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.     

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.     

Chemical diffusion in the iridium-richA1 andL12 phases in the Ir-Nb system

The diffusion in iridium-rich Ir-Nb alloys has been studied by single-phase interdiffusion experiments. The chemical diffusion coefficient has been measured for the primary fcc solid-solution and theL1₂ ordered compound Ir₃Nb in the temperature range between 1650 and 1950 °C, using Ir/Ir-8Nb and Ir-26Nb/Ir-28Nb diffusion couples, respectively (numbers indicate mol%). While the chemical diffusion coefficient in the solid-solution phase is close to the tracer self-diffusion coefficient of pure iridium, the diffusion in the compound phase is extremely slow: the chemical diffusion coefficient is 1/40 to 1/50 of that in the solid solution. The low diffusion rate in the compound must be beneficial for high-temperature performance of refractory superalloys based on the Ir-Nb system. 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.     

Intrinsic diffusion simulation for single-phase,multicomponent systems

A one-dimensional, finite difference simulation based on Darken’s treatment of intrinsic diffusion for single-phase, multicomponent systems is described. For the study of intrinsic diffusion using semi-infinite diffusion couples for binary systems, the input to the simulation includes the initial concentration distributions, the molar volume and the intrinsic diffusion coefficients for the two components as a function of composition. The simulation provides as the output all the results that are obtained from a typical interdiffusion experiment including the concentration profiles, the Kirkendall shift and interdiffusion fluxes of the components as a function of position and time. In addition, the intrinsic and vacancy fluxes, and the lattice shifts and lattice velocity profiles are also obtained at all positions within the diffusion zone. Since the simulation can handle variations in molar volume, information regarding fluxes and mean velocities in various reference frames are also provided. The internal consistency of the simulation is tested with the aid of an analytical model for a binary system where the interdiffusion coefficient and the ratio of the intrinsic diffusion coefficients are constant.     

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.     

Interdiffusion in γ (face-centered cubic) Ni-Cr-X (X=Al, Si, Ge, or Pd) alloys at 900 °C

Interdiffusion in nickel (Ni)-chromium (Cr) (face-centered cubic γ phase) alloys with small additions of aluminum (Al), silicon (Si), germanium (Ge), or palladium (Pd) was investigated using solid-to-solid diffusion couples. Ni-Cr-X alloys having compositions of Ni-22at.% Cr, Ni-21at.%Cr-6.2at.%Al, Ni-22at.%Cr-4.0at.%Si, Ni-22at.%Cr-1.6at.%Ge, and Ni-22at.%Cr-1.6at.%Pd were manufactured by arc casting. The diffusion couples were assembled in an Invar steel jig, encapsulated in Ar after several hydrogen purges, and annealed at 900 °C in a three-zone tube furnace for 168 h. Experimental concentration profiles were determined from polished cross sections of these couples by using electron probe microanalysis with pure element standards. Interdiffusion fluxes of individual components were calculated directly from the experimental concentration profiles, and the moments of interdiffusion fluxes were examined to determine the average ternary interdiffusion coefficients. The effects of ternary alloying additions on the diffusional behavior of Ni-Cr-X alloys are presented in the light of the diffusional interactions and the formation of a protective Cr₂O₃ scale. This article was presented at the Multicomponent-Multiphase Diffusion Symposium in Honor of Mysore A. Dayananda, which was held during TMS 2006, the 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 of Germanium in Binary and Multicomponent Nickel Alloys

Interdiffusion and impurity diffusion of Ge is studied in Ni and multicomponent alloys over the temperature range of 1150-1250 °C. The diffusion is investigated using diffusion couples, which are evaluated using microprobe measurements. The interdiffusion coefficients are calculated with the den Broeder method, while the impurity diffusion coefficients are determined with the Hall method. A model for the diffusion simulation software DICTRA is developed by mobility assessments. Further on, the diffusion of Ge in the multicomponent superalloys PWA1483 and René N5 is investigated. The Ge diffusion coefficient in René N5 is 4.5 × 10⁻¹⁴ m²/s at 1180 °C which is similar to other alloying elements such as Co, Cr, Mo or Ta.     

Comparison of experimental and simulated multicomponent Ni-base superalloy diffusion couples

A multicomponent diffusion mobility database for the Ni-rich fcc phase [2002 Cam] is evaluated by comparing diffusion simulations to two experimental multicomponent Ni-base superalloy diffusion couples: Ni/René-88 and IN718/René-88. The diffusion simulations use composition-dependent thermodynamic and diffusion quantities within a finite difference code to simulate single-phase and multiphase planar layers. The multiphase layers consist of a matrix phase and a disperse phase. The calculated composition profiles, interdiffusion coefficients, phase fraction profiles, and location of Kirkendall porosity are compared with experimental results. To treat diffusion in the IN718 alloy, iron and carbon are added to the existing diffusion mobility database using previous assessment work and new assessments of Fe-Al and Fe-Co.     

Phase-field investigation of multicomponent diffusion in single-phase and two-phase diffusion couples

Interdiffusion in hypothetical ternary single-phase and two-phase diffusion couples are examined using a phase-field model by numerically solving the nonlinear Cahn-Hilliard and Ginzburg-Landau equations. For diffusion couples assembled with a regular single-phase solution, constant chemical mobilities were used to examine the development of concentration profiles including uphill diffusion and zero-flux plane. Zero-flux plane for a component was observed to develop for a diffusion couple at the composition that corresponds to the activity of that component in one of the terminal alloys. Experimental thermodynamic parameters and composition-dependent chemical mobilities were used to examine the morphological evolution of the interphase boundary in solid-to-solid, two-phase diffusion couples. Instability at the interphase boundary was introduced initially (t=0) by a small compositional fluctuation at the diffuse interface, and its evolution varied largely as a function of terminal alloys and related composition-dependent chemical mobility. This article was presented at the Multicomponent-Multiphase Diffusion Symposium in Honor of Mysore A. Dayananda, which was held during TMS 2006, the 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.     

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.     

Substrate Effect on the High Temperature Oxidation Behavior of a Pt-modified Aluminide Coating. Part II: Long-term Cyclic-oxidation Tests at 1,050 °C

This second part of a two-part study is devoted to the effect of the substrate on the long-term, cyclic-oxidation behavior at 1,050 °C of RT22 industrial coating deposited on three Ni-base superalloys (CMSX-4, SCB, and IN792). Cyclic-oxidation tests at 1,050 °C were performed for up to 58 cycles of 300 h (i.e., 17,400 h of heating at 1,050 °C). For such test conditions, interdiffusion between the coating and its substrate plays a larger role in the damage process of the system than during isothermal tests at 900, 1,050, and 1,150 °C for 100 h and cyclic-oxidation tests at 900 °C which were reported in part I [N. Vialas and D. Monceau, Oxidation of Metals 66, 155 (2006)]. The results reported in the present paper show that interdiffusion has an important effect on long-term, cyclic-oxidation resistance, so that clear differences can be observed between different superalloys protected with the same aluminide coating. Net-mass-change (NMC) curves show the better cyclic-oxidation behavior of the RT22/IN792 system whereas uncoated CMSX-4 has the best cyclic-oxidation resistance among the three superalloys studied. The importance of the interactions between the superalloy substrate and its coating is then demonstrated. The effect of the substrate on cyclic-oxidation behavior is related to the extent of oxide scale spalling and to the evolution of microstructural features of the coatings tested. SEM examinations of coating surfaces and cross sections show that spalling on RT22/CMSX-4 and RT22/SCB was favored by the presence of deep voids localized at the coating/oxide interface. Some of these voids can act as nucleation sites for scale spallation. The formation of such interfacial voids was always observed when the β to γ′ transformation leads to the formation of a two-phase β/γ′ layer in contact with the alumina scale. On the contrary, no voids were observed in RT22/IN792, since this β to γ′ transformation occurs gradually by an inward transformation of β leading to the formation of a continuous layer of γ′ phase, parallel to the metal/scale interface.     

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).