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Tracer diffusion is one of most reliable techniques for providing basic kinetic data in solids. In the present review, selected direct methods, in particular the radiotracer measurements as a superior technique due to its high sensitivity, Secondary-Ion-Mass-Spectroscopy (SIMS) profiling, X-Ray Diffraction measurements and Rutherford Backscattering Spectrometry are presented and discussed. Special attention is put on the radiotracer technique describing the currently used sectioning techniques in detail with a focus on the experimental applications and complications. The relevant experimental results are exemplary shown. Furthermore, the most recent developments and advances related to the combined tracer/inter-diffusion measurements are highlighted. It is shown that this approach offers possibilities to provide the concentration-dependent tracer diffusion coefficients of the constituting elements in multi-component alloys in high-throughput experiments. Possibilities of estimating the tracer diffusion coefficients following different types of diffusion couple methods in binary and multicomponent systems are briefly introduced. Finally, specificity of SIMS analysis of diffusion in fine-grained materials are carefully analyzed. If applicable, a direct comparison of the results obtained by different techniques is given.

Composition-dependent diffusion coefficients are determined in B2-Ni(CoPt)Al system following the pseudo-binary and pseudo-ternary diffusion couple methods, which would not be possible otherwise in a quaternary inhomogeneous material fulfilling the conditions to solve the equations developed based on the Onsager formalism. The end-member compositions to produce ideal/near-ideal diffusion profiles are chosen based on thermodynamic details. The pseudo-binary interdiffusion coefficients of Ni and Al decrease in the presence of Co but increase in the presence of Pt. The pseudo-ternary interdiffusion coefficients indicate that the main interdiffusion coefficients increase significantly in the presence of Pt. Marginal changes of the cross interdiffusion coefficients substantiate a minor change of the diffusional interactions between the components. The thermodynamic driving forces show opposite trends with respect to composition as compared to the changes of the interdiffusion coefficients advocating a dominating role of the Pt(Co)-induced modifications of point defect concentrations. DFT-based calculations revealed that Pt alloying increases the Ni vacancy concentration and decreases the activation energy for the triple defect diffusion mechanism. These findings explain the increase in the thickness of the interdiffusion zone between the B2-Ni(Pt)Al bond coat and the single crystal superalloy Rene N5 because of Pt addition. Furthermore, the EPMA and TEM analyses reveal the growth of refractory elements-enriched precipitates.

Recent advances in the field of diffusion in multiprincipal element systems are critically reviewed, with an emphasis on experimental as well as theoretical approaches to determining atomic mobilities (tracer diffusion coefficients) in chemically complex multicomponent systems. The newly elaborated and augmented pseudobinary and pseudoternary methods provide a rigorous framework to access tracer, intrinsic, and interdiffusion coefficients in alloys with an arbitrary number of components. Utilization of the novel tracer-interdiffusion couple method allows for a high-throughput determination of composition-dependent tracer diffusion coefficients. A combination of these approaches provides a unique experimental toolbox to access diffusivities of elements that do not have suitable tracers. The pair-exchange diffusion model, which gives a consistent definition of diffusion matrices without specifying a reference element, is highlighted. Density-functional theory–informed calculations of basic diffusion properties—asrequired for the generation of extensive mobility databases for technological applications—are also discussed.

Interdiffusion studies conducted in group IVB, VB and VIB metal-silicon systems are discussed in detail to show a pattern in the change of diffusion coefficients with the change in atomic number of the refractory metal (M) component. MSi2and M5Si3phases are considered for these discussions. It is shown that integrated diffusion coefficients increase with the increase in atomic number of the refractory component when the data are plotted with respect to the melting point normalized annealing temperature. This indicates the increase in overall defect concentration facilitating the diffusion of components. This is found to be true in both the phases. Additionally, the estimated ratios of tracer diffusion coefficients indicate the change in concentration of antisite defects in certain manner with the change in atomic number of the refractory components.

Nb-Ti is a widely used superconductor material. However, its use is limited to applications of magnetic field upto 8T (Sharma, 1987). At the present, Nb3Sn intermetallic compound with A15 structure is considered to be one of the most suitable superconductors for the applications where field requirements go beyond the limit of Nb-Ti superconductors. However, intermetallic compounds are in general brittle and cannot be drawn as wire. To circumvent this problem, different manufacturing technologies have been developed for Nb3Sn, such as bronze method, internal tin process, powder metallurgy route, Jelly roll process, ECN technique (Suenaga, 1981; Sharma, 1987) etc. In this chapter, we shall discuss mainly the growth and diffusion mechanism of Nb3Sn fabricated by the bronze technique. In this method, several Nb rods are inserted inside Cu(Sn) bronze alloy and drawn as a multifilamentary wire. The product phase Nb3Sn is grown during the subsequent annealing by solid state diffusion. The efficiency of a superconductor wire largely depends on the presence of microstructural defects, such as grain boundaries and Kirkendall pores, grain size distribution, the variation of chemical composition over the cross section (Suenaga, 1981; Suenaga & Jansen, 1983; Lee & Larbalestier, 2005; Lee & Larbalestier, 2008) and so on. The application of pure Nb3Sn compound has been found to be limited to magnetic fields of 12 T, since the increase in the field drastically reduces the critical current density, Jc. Further improvements have been achieved by alloying Nb3Sn with different elements, such as Ti, Ta, Zr, Mg etc. (Suenaga et al., 1986). Thus, the aim of this chapter is to discuss and analyse various factors which affect the growth of the product phase by diffusion controlled process. The evolution of microstructure is detemined by the thermodynamics and kinetics of the system. The combined thermodynamic-kinetic approach will be discussed, which provides a feasible tool to rationalize the formation of the observed reaction structures.

Estimating the diffusion coefficients experimentally in a four-component inhomogeneous alloy following the conventional diffusion couple method by intersecting three couples at the same composition is difficult unless a small composition range of constant diffusivity is identified. Additionally, the intrinsic diffusion coefficients of the components cannot be estimated in a system with more than two components. To solve these issues, we have followed the pseudo-binary and pseudo-ternary diffusion couple methods for estimating the diffusion coefficients at the equiatomic composition of NiCoFeCr medium entropy alloy. Along with the pseudo-binary interdiffusion coefficients, we have estimated the intrinsic diffusion coefficients of all the components by designing the pseudo-binary couples such that Ni and Co develop the diffusion profiles keeping Fe and Cr constant in one couple and Fe and Cr develop the diffusion profiles keeping Ni and Co constant in another couple. Subsequently, we have proposed the relations for calculating the tracer diffusion coefficients utilizing the thermodynamic details. We have found a good match with the data estimated directly following the radiotracer method at the equiatomic composition. Following, we have produced three pseudo-ternary diffusion couples intersecting at the compositions close to the equiatomic composition. The main pseudo-ternary interdiffusion coefficients of Fe are found to be higher than Ni and Co. Therefore, we have estimated different types of diffusion coefficients highlighting the complex diffusion process in the four-component NiCoFeCr medium entropy alloy.

Diffusion couple technique is an efficient tool for the estimating the chemical diffusion coefficients. Typical experimental uncertainties of the composition profile measurements complicate a correct determination of the interdiffusion coefficients via the standard Boltzmann-Matano, Sauer-Freise or the den Broeder methods, especially for systems with a strong compositional dependence of the interdiffusion coefficient. A new approach for reliable fitting of the experimental profiles with an improved behavior at both ends of the diffusion couple is proposed and tested against the experimental data on chemical diffusion in the system Fe-Ga. An extension of the approach for reliable description of the up-hill diffusion phenomenon in multicomponent systems is presented.

The addition of Pt to the β-NiAl bond coat enhances the service life of the turbine blade in jet engine application. However, it increases the growth of the unwanted precipitate containing an interdiffusion zone between the bond coat and superalloy. The role of Pd and Ir addition is examined in this study by comparing the growth of the interdiffusion zone without compromising the thermal cycle resistance of the oxide layer. The oxide layers on all the bond coats grow with duplex morphology. Ni and Ir-containing precipitates are found inside α-Al2O3 oxide layer on Ir-containing bond coats. The microstructural evolution of the interdiffusion zone is explained with the help of the diffusion path. The addition of Ir is found to decrease the growth of the interdiffusion zone significantly compared to the Pt containing bond coat without compromising the thermal cycle resistance of the oxide layer, which could be considered as an important addition in next-generation turbine blades.

The solid state diffusion-controlled growth of the phases is studied for the Au-Sn system in the range of room temperature to 200 degrees C using bulk and electroplated diffusion couples. The number of product phases in the interdiffusion zone decreases with the decrease in annealing temperature. These phases grow with significantly high rates even at the room temperature. The growth rate of the AuSn4 phase is observed to be higher in the case of electroplated diffusion couple because of the relatively small grains and hence high contribution of the grain boundary diffusion when compared to the bulk diffusion couple. The diffraction pattern analysis indicates the same equilibrium crystal structure of the phases in these two types of diffusion couples. The analysis in the AuSn4 phase relating the estimated tracer diffusion coefficients with grain size, crystal structure, the homologous temperature of experiments and the concept of the sublattice diffusion mechanism in the intermetallic compounds indicate that Au diffuses mainly via the grain boundaries, whereas Sn diffuses via both the grain boundaries and the lattice.

The diffusion-controlled growth and microstructural evolution at the interface of aluminide coatings and different substrates such as Ni-base superalloys and steel are reviewed. Quantitative diffusion analysis indicates that the diffusion rates of components in the β-NiAl phase increases with the addition of Pt. This directly reflects on the growth rate of the interdiffusion zone. The thickness and formation of precipitates increase significantly with the Pt addition. Mainly Fe2Al5phase grows during hot dip aluminization of steel along with few other phases with the very thin layer. Chemical vapor deposition process is being established for a better control of the composition of the Fe-aluminide coating on steel.

The wrong estimation of the diffusion coefficients following the quasi-binary approach and subsequent analysis by Tsai et al. in Co-Cr-Fe-Mn-Ni high entropy alloy are explained. Since this approach, formulated by the present author before the publication by Tsai et al., has potential to emerge as an efficient technique in multicomponent systems, the correct steps of estimation of the diffusion coefficients are explained in detail. At present state, the diffusion data reported in high entropy alloy Tsai et al. has no significance unless estimated again following the correct steps.

The role of Ni addition in Cu on the growth of intermetallic compounds in the Cu–Sn system is studied based on microstructure, crystal structure and quantitative diffusion analysis. The diffraction pattern analysis of intermetallic compounds indicates that the presence of Ni does not change their crystal structure. However, it strongly affects the microstructural evolution and diffusion rates of components. The growth rate of (Cu,Ni)3Sn decreases without changing the diffusion coefficient because of the increase in growth rate of (Cu,Ni)6Sn5. For 3 at.% or higher Ni addition in Cu, only the (Cu,Ni)6Sn5 phase grows in the interdiffusion zone. The elongated grains of (Cu,Ni)6Sn5 are found when it is grown from (Cu,Ni)3Sn. This indicates that the newly formed intermetallic compound joins with the existing grains of the phase. On the other hand, smaller grains are found when this phase grows directly from Cu in the absence of (Cu,Ni)3Sn indicating the ease of repeated nucleation. Grain size of (Cu,Ni)...

The influence of Zr on the growth of V3Ga is studied by a diffusion-couple technique mimicking the bronze method for superconductor production. Systematic quantitative evaluation on critical-current-density-dependent metallurgical parameters is addressed. A mixture of V3Ga and Zr-containing phases develops at the interdiffusion zone. Smaller grains on Zr addition cause higher growth kinetics owing to grain-boundary diffusion of Ga. The grains are oriented randomly irrespective of Zr addition. Refined microstructure, second-phase, and higher growth kinetics suggest a beneficial role of Zr for the better functioning of the superconductor.

The benefits of using the pseudo-binary and pseudo-ternary diffusion couple methods in multicomponent inhomogeneous systems are demonstrated by estimating different types of composition-dependent diffusion coefficients. These are important for understanding the basic atomic mechanism of diffusion and complex compositional evolutions. These were otherwise considered impossible during the last many decades. Without any options previously, sometimes the average values over a composition range of random choice were estimated, which are not the material constants but depend on the composition range and also the end member compositions. The steps and analyses for utilising the pseudo-binary and pseudo-ternary methods are first described in the Ni-Co-Fe-Mo system by producing the ideal diffusion profiles fulfilling the concepts behind these methods. Following, the discussion is extended to the systems related to medium (Ni-Co-Cr) and high (Ni-Co-Fe-Mn-Al) entropy alloys. In fact, this is the first report showing a correct experimental method that should be followed for the estimation of the interdiffusion and intrinsic diffusion coefficients in inhomogeneous high entropy alloys. In the end, the limitations of following these methods because of the generation of non-ideal diffusion profiles are discussed based on experimental results. The steps are also suggested to avoid such complications. These methods are easy to adopt for research engineers. Most importantly, these give an opportunity to validate the data estimated following newly proposed numerical methods by different groups with experimentally estimated diffusion coefficients, which were not possible earlier.

The interdiffusion coefficients can be estimated now purely experimentally from multicomponent diffusion profiles utilizing the recently proposed pseudo-binary and pseudo-ternary diffusion couple methods. One can estimate the composition dependent main interdiffusion coefficients over the composition range and main intrinsic diffusion coefficients at the Kirkendall marker plane from pseudo-binary diffusion couple. On the other hand, main and cross interdiffusion coefficients can be calculated from the pseudo-ternary diffusion couples. In this article, we have first proposed the method of estimation of the tracer diffusion coefficients at the cross of diffusion paths in pseudo-ternary diffusion couples by extending the approach propose by Lane and Kirkaldy in a ternary system but without neglecting the cross phenomenological terms of Onsager formalism. Following, one can even estimate the main and cross intrinsic diffusion coefficients, which is otherwise not possible following the Kirkendall marker experiments in this type of couple. Following we have derived the relation for estimation of the tracer diffusion coefficients at the Kirkendall marker plane in a pseudo-binary diffusion couple. We have chosen NiCoFeCr system to demonstrate the utilization of these methods by comparing the tracer diffusion coefficients estimated directly following radiotracer method. The relations derived in this article help to understand the correlation between estimated data in different types of diffusion couples by neglecting and considering the vacancy wind effect. This method can be now extended to the Al, Ga, Si containing systems in which the estimation of tracer diffusion coefficients following the radiotracer method is difficult/impossible because of various reasons.

We report a rare experimental evidence of an exceptional increase in grain-boundary diffusion-controlled growth kinetics of product phase by grain-refinement due to minor alloying. Ti-addition during growth of V3Ga superconductor by coupling V and Cu(Ga)-solid solution by bronze process increases the critical current density (Jc) significantly. In this manuscript, the exact role of Ti-addition is studied based on systematic and quantitative diffusion-couple experiments that mimic the bronze-method. Metallurgical aspects like microstructural features and growth mechanism are assessed critically. Results are compared when Ti is added either to V or Cu(Ga) and to both for a fixed Ga content. Ti-addition to Cu(Ga) compared to V increases growth kinetics of V3Ga more significantly. Quantitative EPMA-analysis indicates that a mixture of Ti-free and Ti-containing V3Ga phase grows when Ti is added to V. Small precipitates grow along with Ti-containing V3Ga when Ti is added only to Cu(Ga). TEM-study indicates that these precipitates are rich in V and Ti. Much finer grains found in the precipitate-containing region lead to higher growth kinetics due to grain-boundary diffusion. EBSD-analysis shows equiaxed grains and relatively random in orientation because of alloying. This study indicates that Ti-addition to Cu(Ga) is most effective considering metallurgical aspects that influence Jc. Keywords: Superconductor material, Microstructure, Grain size distribution, Grain boundary diffusion, Microtexture

The presence of bifurcation of the Kirkendall marker plane, a very special phenomenon discovered recently, is found in a technologically important Cu Sn system. It was predicted based on estimated diffusion coefficients; however, could not be detected following the conventional inert marker experiments. As reported in this study, we could detect the locations of these planes based on the microstructural features examined in SEM and TEM. This strengthens the concept of the physicochemical approach that relates microstructural evolution with the diffusion rates of components and imparts finer understanding of the growth mechanism of phases. The estimated diffusion coefficients at the Kirkendall marker planes indicates that the reason for the growth of the Kirkendall voids is the nonconsumption of excess vacancies which are generated due to unequal diffusion rate of components. Systematic experiments using different purity of Cu in this study indicates the importance of the presence of impurities on the growth of voids, which increases drastically for greather than 0.1 wt percent impurity. The growth of voids increases drastically for electroplated Cu, commercially pure Cu and Cu(0.5 at percent Ni) indicating the adverse role of both inorganic and organic impurities. Void size and number distribution analysis indicates the nucleation of new voids along with the growth of existing voids with the increase in annealing time. The newly found location of the Kirkendall marker plane in the Cu3Sn phase indicates that voids grow on both the sides of this plane which was not considered earlier for developing theoretical models.

High entropy alloys (HEAs) are considered as a novel class of materials with a large number of components available in nearly equatomic proportions. One of the characteristic properties of HEAs was believed to be so-called "sluggish" diffusion. The faith on this myth instead of rigorous experimental analysis played such a dominant role that the first set of data on interdiffusion, in fact based on an improper analysis, were cited in hundreds of articles to state the presence of sluggishness of diffusion rates in high entropy alloys. In this review, the recent data on atomic diffusion in HEAs are critically discussed. The discussion is focused on tracer diffusion which is already measured dominantly for polycrystalline, but in some cases for single crystalline high-entropy alloys. Alternatively, a rigorous analysis of the interdiffuson experiments, which provide the diffusion rates of chemical species, too, becomes more and more sophisticated for three and more elements in an alloy and it is challenging to derive physically sound quantities from a general multicomponent diffusion experiment. Most promising in this case is the diffusion couple technique, especially the so-called pseudo-binary approach. This approach is analyzed with a focus on the applicability and the possible errors induced if up-hill diffusion appears. It is shown that atomic diffusion in HEAs cannot a priori be considered as sluggish and both atomic interactions as well as correlation effects are responsible for the observed trends. Even if estimated on the same homologous scale, the diffusion retardation induced by a "high entropy" in FCC crystals is not simply proportional to the number of alloying components and it is shown to be similar to that induced by the L12 ordering in a binary system. Furthermore, the importance of cross-correlations in diffusion of different species in HEAs is highlighted., 50 pages; 14 figures

A pseudo ternary diffusion couple technique in a multicomponent system by simplifying the mathematical complications of Onsager formalism is proposed for the estimation of composition dependent values of the interdiffusion coefficients. This is otherwise impossible following the conventional method in a system with more than three components. Other alternative methods estimate the average diffusion coefficients over a composition range of random choice and lack physical significance. This method can be followed in a multicomponent system with any number of components on the condition that only three components develop diffusion profiles keeping others as constant. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The interdiffusion coefficients are estimated either following the Wagner's method expressed with respect to the composition (mol or atomic fraction) normalized variable after considering the molar volume variation or the den Broeder's method expressed with respect to the concentration (composition divided by the molar volume) normalized variable. On the other hand, the relations for estimation of the intrinsic diffusion coefficients of components as established by van Loo and integrated diffusion coefficients in a phase with narrow homogeneity range as established by Wagner are currently available with respect to the composition normalized variable only. In this study, we have first derived the relation proposed by den Broeder following the line of treatment proposed by Wagner. Further, the relations for estimation of the intrinsic diffusion coefficients of the components and integrated interdiffusion coefficient are established with respect to the concentration normalized variable, which were not available earlier. The veracity of these methods is examined based on the estimation of data in Ni-Pd, Ni-Al and Cu-Sn systems. Our analysis indicates that both the approaches are logically correct and there is small difference in the estimated data in these systems although a higher difference could be found in other systems. The integrated interdiffusion coefficients with respect to the concentration (or concentration normalized variable) can only be estimated considering the ideal molar volume variation. This might be drawback in certain practical systems. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Major drawback of studying diffusion in multi-component systems is the lack of suitable techniques to estimate the diffusion parameters. In this study, a generalized treatment to determine the intrinsic diffusion coefficients in multi-component systems is developed utilizing the concept of a pseudo-binary approach. This is explained with the help of experimentally developed diffusion profiles in the Cu(Sn, Ga) and Cu(Sn, Si) solid solutions. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Interdiffusion study is conducted in the Ni-Zr system in the temperature range of 750-850 A degrees C. Five intermetallic compounds, Ni5Zr, Ni7Zr2, Ni10Zr7, NiZr and NiZr2 are found to grow in the interdiffusion zone. Integrated diffusion coefficients are estimated for different phases. Activation energy is found to be lowest for Ni10Zr7 (178 +/- A 8 kJ/mol) and highest for NiZr (323 +/- A 6 kJ/mol). Tracer diffusion coefficients are estimated at the location of the Kirkendall marker plane in the Ni7Zr2 phase. Ni is found to have 10 times higher diffusion rate compared to Zr in this phase. Higher diffusion rate of Ni compared to Zr is found, which is expected because of higher number of Ni-Ni bonds compared to Zr-Zr bonds in this phase.

When one starts to analyze the evolution of the interfacial reaction product layers between dissimilar materials it is often found out that as the number of interacting species grows, the complexity of the analysis increases extremely rapidly. It may even appear that the task is just too difficult to be completed. In this article we present the thermodynamic-kinetic method, which can be used to rationalize the evolution of interfacial reaction layers and bring back the physics to the analyses. The method is conceptually very simple. It combines energetics—what can happen—with kinetics—how fast things take place. Yet the method is flexible enough that it can utilize quantitative and qualitative data starting from the atomistic simulations up to the experiments carried out with bulk materials. Several examples about how to utilize this method in material scientific problems are given.

Thermodynamics and diffusion kinetics determine the microstructure of a given reaction couple between dissimilar materials under specific conditions. The microstructure, in turn, affects strongly the performance of multimaterial assemblies under different stress and environmental states. Hence it is shown here how the combination of thermodynamics and kinetics (namely the thermodynamic-kinetic method) can be used to rationalize the evolution of microstructure between dissimilar materials. The relevant thermodynamic considerations are given first, before moving to the foundations of diffusion kinetic considerations most relevant for the thermodynamic-kinetic method. The method itself is then briefly discussed, before finalizing this chapter with a couple of case studies from the field of electronics.

Diffusion couple method is one of the well-established techniques for estimation of the diffusion coefficients. In this chapter, the concept and definition of different types of diffusion coefficients are described along with experimental methods, tricks and the analysis in binary and pseudo-binary (multicomponent) systems. Experimental results in various systems are introduced. In the end, physical significance of the data estimated is described.

Defects assist the diffusion process, whereas driving forces influence the rate of diffusion depending on the thermodynamics of alloying, diffusion mechanisms, diffusion paths, and defect production. Different types of diffusion are defined based on defects assisting the diffusion process and whether atomic transport occurs in the absence or presence of an additional driving force different from purely entropic one. In this chapter, different types of zero-dimensional (point defects), one-dimensional (edge and screw dislocations), two-dimensional (grain and phase boundaries, surfaces), and three-dimensional (voids) defects are introduced. The origins of internal (chemical) and external (electric current) driving forces are discussed. Based on defect types and driving forces, different types of diffusion coefficients are introduced.

The diffusion couple technique is a unique and powerful experimental method which provides a framework to determine interdiffusion coefficients in solid solution systems and integrated diffusion coefficients for stoichiometric compounds. From simple marker experiments with incremental diffusion couples, information about relative mobilities of species in solid solution and intermetallic phases can be obtained, and tracer diffusion coefficients can be deduced if pertinent thermodynamic data are at hand. The diffusion couple technique is also a valuable approach in phase diagram studies and establishing composition–structure–property relationships in multicomponent systems. The efficiency of the method is very high. Yet, it is not without shortcomings. A number of error sources that may appear when the diffusion couple technique is used as “a research tool” are discussed in detail.

The growth rates of the product phases Cu3Sn and Cu6Sn5 in the Cu-Sn system are affected differently by the addition of Au, Pd and Pt in Cu. The addition of 8 at.% of Au and Pd in Cu produce different (and additional) phases in the interdiffusion zone of ternary Cu(Au)/Sn and Cu(Pd)/Sn diffusion couples, respectively, when compared to the binary Cu/Sn diffusion couple. The addition of Au has very little effect; however, the addition of Pd and Pt significantly increases (both size and number) the formation of the Kirkendall voids. This study clearly indicates that addition of these components (i.e., inorganic impurities) have similar detrimental role like organic impurities in Cu on the growth of the Kirkendall voids, which leads to the degradation of flip-chip bonding in an electronic component.

The solidestate growth of intermediate phases in the Cu-Sn and Ni-Sn systems is investigated in the temperature range of room temperature to an elevated temperature. In the Cu/Sn diffusion couples, Cu6Sn5 and Cu3Sn grow at temperatures >= 100 degrees C and only the Cu6Sn5 phase is found at lower temperatures. The integrated interdiffusion coefficients are estimated in the temperature range of 125-215 degrees C because of the observation of parabolic growth. The activation energies are estimated to be 64 +/- 4 and 75 +/- 6 kJ/mol for Cu3Sn and Cu6Sn5, respectively. In the Ni/Sn diffusion couples, only Ni3Sn4 grows at higher temperatures. At 50-100 degrees C, metastable NiSn4 phase is found along with an equilibrium Ni3Sn4 phase. At room temperature, only the metastable NiSn4 phase is found. The activation energy for the integrated interdiffusion coefficient of Ni3Sn4 is estimated as 71.6 +/- 5.3 kJ/mol, which is similar to the values estimated in the CueSn system. The growth rate of the product phases, for electroplated couples, is found to be a little higher in the Ni-Sn system as compared to the CueSn system. During storage at room temperature and service at elevated temperatures, the phases in the Ni-Sn system have comparable growth rate when compared to the same in CueSn system. (C) 2017 Elsevier B.V. All rights reserved.

Microstructure plays an important role in controlling many physical and mechanical properties. In this chapter, a physicochemical model is described which can be used for estimating the diffusion parameters along with an additional ability to predict or explain the microstructural evolution because of reaction–diffusion in an interdiffusion zone between dissimilar materials. Diffusion rates of components can be estimated without even using any Kirkendall markers but just by analyzing microstructural features, which is elucidated with experimental results. This is important since inert markers cannot be used to understand the growth process in thin films, nanomaterials and material in applications.

The solid-state growth of the product phases in bulk and electroplated diffusion couples of the Pd-Sn and the Pt-Sn systems is reported at various temperatures, ranging from room temperature to 215 A degrees C. The growth rate of the product phase in the Pt-Sn system is found to be much lower compared to the Pd-Sn system and the Au-Sn system also, which is currently used in the microelectronics industry. The time dependent experiments indicate that the growth rate in the Pd-Sn system is parabolic in nature, i.e., it is controlled by the diffusion rates of components through the product phases. However, the growth rate is linear and hence reaction-controlled in the Pt-Sn system, which indicates that the formation of the compound is the rate-limiting step rather than the diffusion rates of components. The PdSn4 phase covers almost whole interdiffusion zone in the Pd/Sn couple, while PtSn4 is the only phase found in the Pt/Sn couple. The marker experiments indicate that both PdSn4 and PtSn4 grow mainly by the diffusion of Sn, with negligible diffusion of Pd and Pt, respectively. Furthermore, the analysis considering the same crystal structure (i.e., oC20) of these phases along with the concept of sublattice diffusion mechanism indicates that the diffusion rates of both Pd and Pt are negligible via both the lattice and the grain boundaries.

A study on reactive diffusion is conducted in the Re-Si system. According to the study, ReSi1.8 phase grows with much higher thickness than the Re2Si phase, in the interdiffusion zone of bulk diffusion couples. The activation energy for integrated diffusion of ReSi1.8 is estimated to be 605 +/- 23 kJ/mol. The growth of the Re2Si phase is studied by considering an incremental diffusion couple of Re/ReSi1.8. Analysis based on the calculation of integrated diffusion coefficients indicates the reason underlying the observed high difference between the growth rates of the ReSi1.8 and Re2Si phases.

Based on an interdiffusion study using an incremental diffusion couple in the V-Ga binary system, we have shown that V diffuses via the lattice, whereas Ga does so via grain boundaries, for the growth of the V3Ga phase. We estimate the contributions from the two different mechanisms, which are usually difficult to delineate in an interdiffusion study. Available tracer diffusion studies and the atomic arrangement in the crystal structure have been considered for a discussion on the diffusion mechanisms.

The growth of phases by reactive diffusion in Mo-Si and W-Si systems are compared. The crystal structures of MSi2 and M5Si3 phases (M = Mo, W) are similar in these two systems. However, the diffusion rates of the components change systematically with a change in the atomic number. Integrated diffusion coefficients in both phases increase with an increasing atomic number of refractory elements i.e. from Mo to W. On the other hand, the ratio of diffusivities of the components decreases. This indicates a relative increase in the diffusion rates of the metal components with increasing atomic number and a difference in defects concentrations in these two systems.

The interfacial reactions between several Au(Cu) alloys and pure Sn were studied experimentally at 200A degrees C. Amounts of Cu in the AuSn4 and AuSn2 phases were as low as 1 at.%. On the basis of these experimental results there is no continuous solid solution between (Au,Cu)Sn and (Cu,Au)(6)Sn-5. The copper content of (Au,Cu)Sn was determined to be approximately 7-8 at.%. Substantial amounts of Au were present in the (Cu,Au)(6)Sn-5 and (Cu,Au)(3)Sn phases. Two ternary compounds were formed, one with stoichiometry varying from (Au40.5Cu39)Sn-20.5 to (Au20.2Cu59.3)Sn-20.5 (ternary ``B''), the other with the composition Au34Cu33Sn33 (ternary ``C''). The measured phase boundary compositions of the product phases are plotted on the available Au-Cu-Sn isotherm and the phase equilibria are discussed. The complexity and average thickness of the diffusion zone decreases with increasing Cu content except for the Au(40 at.%Cu) couple.

Experiments are conducted to study interdiffusion in a complete solid solution as well as in ordered phases in the Cu–Pt system. The variation of the interdiffusion coefficient and the activation energy with composition of the solid solution is explained with the help of melting points, vacancy formation energies and thermodynamic factors indicating the driving force for diffusion. Additionally, interdiffusion coefficients are also estimated in the CuPt and Cu3Pt phases at two different temperatures.