Kirkendall effect has been studied experimentally as well as theoretically for decades already. There are theoretical indications, that the Kirkendall effect must operate from the beginning of the diffusion process but there are practically no measurements on this short time and length scale. For that reason, diffusion on the nanometer scale was investigated experimentally in different binary systems in thin film geometry. We followed the diffusion process as well as the Kirkendall effect by different methods (TEM, SNMS and synchrotron X-ray waveguide technique). Investigations were performed in systems with complete solubility (Bi-Sb, Cu-Ni, Bi-Sb) as well as in systems forming intermetallic phase (Fe-Sb, Fe- Pd). It was found that with these methods the Kirkendall shift can be well followed on the nano-scale. In Fe-Sb system even the bifurcation of the Kirkendall plane was observed.

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Hot section components in gas turbines can be NiCoCrAlY-coated to provide the component with an Al reservoir that maintains a protective oxide layer on its surface. Over the service life of the component, the coatings degrade by composition and phase changes due to oxidation/hot-corrosion, and multicomponent interdiffusion from and into the superalloy substrate. In this study, the rate of Al interdiffusion into selected Ni-base superalloys using various diffusion couples of two-phase NiCoCrAlY (beta + gamma) and single beta-phase NiAl with the selected alloys is measured. The diffusion couples were examined with an emphasis on the composition-dependence of Al interdiffusion. Microstructural analysis of the NiCoCrAlY vs. superalloys couples is performed to examine the dependence of coatings lifetime on the superalloy composition. The beta-NiAl diffusion couples were analyzed to determine the integrated, apparent and average effective interdiffusion coefficient as a function of superalloy's composition. Concentration profiles were obtained by EPMA of the NiAl vs. superalloy diffusion couples. Findings of this study show that the lifetimes of NiCoCrAlY are heavily dependent on superalloy compositions. The rate of interdiffusion in the diffusion couples is affected by the refractory precipitate phase microstructure structures in the interdiffusion zones as well as by component interactions. The results of the beta-NiAl diffusion couples show that increasing concentrations of Cr, Mo and Ti in the superalloy increase the Al effective interdiffusion coefficient into the superalloy, while increasing concentrations of Al, Ta and W reduce it. Thus NiCoCrAlY-superalloy systems may be designed to produce optimal microstructures in the interdiffusion zone and minimize Al interdiffusion by consideration of these diffusional interactions.

Diffusion plays a significant role in most materials systems by controlling microstructural development. Consequently, the overall properties of a material can be largely dependent upon diffusion. This study investigated the interdiffusion behavior of three binary systems, namely, Mo-Zr, Fe-Mo, and Fe-Zr. The main interest in these particular metals is for application in nuclear fuel assemblies. Nuclear fuel plates generally consist of two main components which are the fuel and the cladding. Due to diffusional interactions that can occur between these two components, a third is sometimes added between the fuel and cladding to serve as a diffusion barrier layer. Fe, Mo, and Zr can act as either cladding or barrier layer constituents and both Mo and Zr also serve as alloying additions in uranium based metallic fuels. Therefore, a fundamental understanding of the diffusional interactions in these systems is critical in predicting the performance and lifetime of these fuels. In order to study this diffusion behavior, a series of solid-to-solid diffusion couples were assembled between Fe, Mo, and Zr. These couples were then diffusion annealed isothermally for various predetermined times over a range of temperatures, including some both above and below the allotropic transformation temperatures for Fe and Zr. Following the diffusion anneal, the couples were water quenched, cross-sectioned, and prepared for microstructural and compositional characterization. A combination of scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), and electron probe microanalysis (EPMA) were used to obtain micrographs showing the microstructure and to collect compositional data for identifying intermediate phases and determining concentration profiles across the interdiffusion zone. Based on this characterization, the phases that developed in the diffusion zones were identified. In the Mo-Zr system, a large Zr solid solution layer developed in the couples annealed iv at and above 850C and a thin (~1-2 m) layer of Mo2Zr formed in all couples. Growth constants and concentration dependent interdiffusion coefficients were calculated for the Mo2Zr and Zr solid solution phases, respectively. In the Fe-Mo system, both the -Fe2Mo and -Fe7Mo6 phases were observed in couples annealed at 900C and below while -Fe7Mo6 and -Fe solid solution layers were observed in couples annealed above 900C. The relevant growth constants and activation energies for growth were calculated. In the Fe-Zr system, the couple annealed at 750C developed an FeZr2 and an FeZr3 layer while the couple annealed at 850C developed an Fe2Zr and Fe23Zr6 layer in the diffusion zone. The results of this analysis were then compared to available information from literature and the corresponding binary phase diagrams for each system. The results are discussed with respect to the effects of the allotropic transformations of Fe and Zr on the interdiffusion behavior in these systems.

Magnesium (Mg) is a light-weight metal that has extraordinary physical and chemical properties for many potential applications in automobile, military, and electronics. Aluminum alloys, because of its light-weight, high strength and corrosion resistance have a wide range of commercial applications. Given these two, sometime competing, alloy systems, there are now many applications where the metallurgical compatibility of Mg- and Al-alloys are required for engineering applications. One such case is the development of diffusion barrier for U-Mo metallic fuel in Al-alloy cladding, where Mg, with its complete immiscibility with U and Mo is being considered as the diffusion barrier. While negligible diffusional interaction between Mg and U-Mo alloys have been reported, diffusional interaction between the Mg and Al-alloy cladding has not been investigated. In this study, solid-to-solid diffusion couples were assembled using discs of pure Mg (99.999 %) and AA6061 Al-alloy. After preparation, Mg was diffusion bonded to AA6061 in sealed quartz capsule at 300°, 350°, and 400°C for 720, 360, and 240 hours, respectively. Scanning electron microscopy was used to inspect the interdiffusion zone, while phase identification was performed using X-ray energy dispersive spectroscopy. One specific phase that exists in the binary Mg-Al system, labeled “ε” was observed and characterized by transmission electron microscopy. From the preceding data, the growth rates as well as interdiffusion coefficients of the intermetallic phases were extracted and compared to previous investigations using pure Mg and Al.

Interdiffusion in multicomponent-multiphase alloys is commonly encountered in many materials systems. The developments of multicomponent-multiphase alloys require control of microstructure through appropriate heat treatment, involving solid-state transformations, precipitation processes, and surface modification, where the interdiffusion processes play a major role. In addition, interdiffusion processes often control degradation and failure of these materials systems. Enhanced performance and reliable durability always requires a detailed understanding of interdiffusion. In this study, ternary and quaternary interdiffusion in Ni-Cr-X (X = Al, Si, Ge, Pd) at 900°C and 700°C, Fe-Ni-Cr-X (X = Si, Ge) at 900°C, and Ni3Al alloyed with Ir, Ta and Re at 1200°C were examined using solid-to-solid diffusion couples. Interdiffusion fluxes of individual components were calculated directly from experimental concentration profiles determined by electron probe microanalysis. Moments of interdiffusion fluxes were examined to calculate main and cross interdiffusion coefficients averaged over selected composition ranges from single diffusion couple experiments. Consistency in the magnitude and sign of ternary and quaternary interdiffusion coefficient were verified with interdiffusion coefficients determined by Boltzmann-Matano analysis that requires multiple diffusion couples with intersecting compositions. Effects of alloying additions, Al, Si, Ge and Pd, on the interdiffusion in Ni-Cr-X and Fe-Ni-Cr-X alloys were examined with respect to Cr2O3-forming ability at high temperature. Effects of Ir, Ta and Re additions on interdiffusion in Ni3Al were examined with respect to phase stability and site-preference. In addition, a numerically refined approach to determine average ternary interdiffusion coefficients were developed. Concentrations and moments of interdiffusion fluxes are employed to generate multiple combinations of multicomponent interdiffusion coefficient as a function of moments. The matrix of multicomponent interdiffusion coefficients corresponds to the lowest order of the moment. It yields real and positive eigen values which provides reliable average interdiffusion coefficients for the selected composition range.

The diffuse-interface phase-field model is a powerful method to simulate and predict mesoscale microstructure evolution in materials using fundamental properties of thermodynamics and kinetics. The objective of this dissertation is to develop phase-field model for simulation and prediction of interdiffusion behavior and evolution of microstructure in multiphase binary and ternary systems under composition and/or temperature gradients. Simulations were carried out with emphasis on multicomponent diffusional interactions in single-phase system, and microstructure evolution in multiphase systems using thermodynamics and kinetics of real systems such as Ni-Al and Ni-Cr-Al. In addition, selected experimental studies were carried out to examine interdiffusion and microstructure evolution in Ni-Cr-Al and Fe-Ni-Al alloys at 1000°C. Based on Onsager’s formalism, a phase-field model was developed for the first time to simulate the diffusion process under an applied temperature gradient (i.e., thermotransport) in single- and two-phase binary alloys. Development of concentration profiles with uphill diffusion and the occurrence of zeroflux planes were studied in single-phase diffusion couples using a regular solution model for a hypothetical ternary system. Zero-flux plane for a component was observed to develop for diffusion couples at the composition that corresponds to the activity of that component in one of the terminal alloys. Morphological evolution of interphase boundary in solid-to-solid two-phase diffusion couples (fcc-γ vs. B2-β) was examined in Ni-Cr-Al system with actual thermodynamic data and concentration dependent chemical mobility. With the instability introduced as a small initial compositional fluctuation at the interphase boundary, the evolution of the interface morphology was found to vary largely as a function of terminal alloys and related composition-dependent chemical mobility. In a binary Ni-Al system, multiphase diffusion couples of fcc-γ vs. L12-γ′, γ vs. γ+γ′ and γ+γ′ vs. γ+γ′ were simulated with alloys of varying compositions and volume fractions of second phase (i.e., γ′). Chemical mobility as a function of composition was employed in the study with constant gradient energy coefficient, and their effects on the final interdiffusion microstructure was examined. Interdiffusion microstructure was characterized by the type of boundaries formed, i.e. Type 0, Type I, and Type II boundaries, following various experimental observations in literature and thermodynamic considerations. Volume fraction profiles of alloy phases present in the diffusion couples were measured to quantitatively analyze the formation or dissolution of phases across the boundaries. Kinetics of dissolution of γ′ phase was found to be a function of interdiffusion coefficients that can vary with composition and temperature. The evolution of interdiffusion microstructures in ternary Ni-Cr-Al solid-to-solid diffusion couples containing fcc-γ and γ+β (fcc+B2) alloys was studied using a 2D phase-field model. Alloys of varying compositions and volume fractions of the second phase (β) were used to simulate the dissolution kinetics of the β phase. Semi-implicit Fourier-spectral method was used to solve the governing equations with chemical mobility as a function of compositions. The simulation results showed that the rate of dissolution of the β phase (i.e., recession of β+γ twophase region) was dependent on the composition of the single-phase γ alloy and the volume fraction of the β phase in the two-phase alloy of the couple. Higher Cr and Al content in the γ alloy and higher volume fraction of β in the γ+β alloy lower the rate of dissolution. Simulated results were found to be in good agreement with the experimental observations in ternary Ni-CrAl solid-to-solid diffusion couples containing γ and γ+β alloys. For the first time, a phase-field model was developed to simulate the diffusion process under an applied temperature gradient (i.e., thermotransport) in multiphase binary alloys. Starting from the phenomenological description of Onsager’s formalism, the field kinetic equations are derived and applied to single-phase and two-phase binary system. Simulation results show that a concentration gradient develops due to preferential movement of atoms towards the cold and hot end of an initially homogeneous single-phase binary alloy subjected to a temperature gradient. The temperature gradient causes the redistribution of both constituents and phases in the two-phase binary alloy. The direction of movement of elements depends on their atomic mobility and heat of transport values.

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After a few remarks about the history of diffusion in solids we remind the reader to some basics of diffusion such as tracer diffusion, interdiffusion, high- diffusivity paths, and basic diffusion mechanism in solids. We then summarize self-diffusion in cubic, hexagonal metals and metals with phase transformations. Then we summarize diffusion of substitutional impurities (solutes) in metals and remind the reader to the phenomena of slow solute diffusion in aluminium and of fast solute diffusion in polyvalent metals. We finish the part on solute diffusion with some remarks on interstitial impurities We start the part on intermetallic alloys by reminding the reader to some of the more frequent structures. We consider examples of the influence of order-disorder transformation on diffusion. We then discuss diffusion in cubic B2-structured phases and in B2-, L12 - and DO 3- intermetallics, We then discuss uniaxial L1 0 -intermetallics and C11 b-structured molybdenum disilicide. We finish with some remarks diffusion in the cubic Laves phase Co2 Nb.:1. Introduction – some historical remarks 2. Some basics 2.1 Tracer diffusion 2.2 Interdiffusion 2.2.2 The ‘random alloy’ approximation for interdiffusion 2.2.1 Boltzmann-Matano method 2.3 High-diffusivity paths in solids 2.4 Diffusion mechanisms in solids 3. Self-diffusion in metals 3.1 Cubic metals 3.2 Uniaxial metals 3.3 Metals with phase transitions 4, Impurity diffusion in metals 4.1 Diffusion of substitutional impurities 4.2 Slow impurity diffusion in aluminium 4.3 Fast impurity diffusion in polyvalent metals 4.4 Diffusion of fast diffusing interstitial impurities and of hydrogen 5. Diffusion in Intermetallics 5.1 Some structures of intermetallics 5.2 Influence of order-disorder transitions on diffusionThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/1 5.3 Diffusion in B2 phases and B2-intermetallics 5.4 Diffusion in L12-intermetallics 5.5 Diffusion in DO3-intermetallics 5.5 Diffusion in L10-intermetallics 5.6 Diffusion in C11b-structured molybdenum disilicide 5.6 Diffusion in the Laves phase Co 2Nb