Diffusion Kirkendall effect

An example where one metal melts before the densihcation process, is the formation of bronze from a 90 10 weight percentage mixture of copper and tin. The tin melts at a temperature of 505 K, and the liquid immediately wets the copper particles, leaving voids in the compact. The tin then diffuses into the copper particles, leaving further voids due to dre Kirkendall effect. The compact is therefore seen to swell before the hnal sintering temperature of 1080 K is reached. After a period of homogenization dictated by tire criterion above, the alloy shrinks on cooling to leave a net dilatation on alloy formation of about 1%. 

It is particularly helpful that we can take the Cu-Ni system as an example of the use of successive deposition for preparing alloy films where a miscibility gap exists, and one component can diffuse readily, because this alloy system is also historically important in discussing catalysis by metals. The rate of migration of the copper atoms is much higher than that of the nickel atoms (there is a pronounced Kirkendall effect) and, with polycrystalline specimens, surface diffusion of copper over the nickel crystallites requires a lower activation energy than diffusion into the bulk of the crystallites. Hence, the following model was proposed for the location of the phases in Cu-Ni films (S3), prepared by annealing successively deposited layers at 200°C in vacuum, which was consistent with the experimental data on the work function. 

In formulating Eqn. (5.101) and the following flux equations we tacitly assumed that they suffer no restrictions and so lead to the individual chemical diffusion coefficients >(/). If we wish to write equivalent, equations for,/(A) and/(B), and allow that v(A) = = v(B), then according to Eqn. (5.103), /(A) /(B) since Ve(A) = ]Vc(B)j. However, the conservation of lattice sites requires that j/(A) j = /(B), which contradicts the previous statement. We conclude that in addition to the coupling of the individual fluxes, defect fluxes and point defect relaxation must not only also be considered but are the key problems in the context of chemical diffusion. Let us therefore reconsider in more detail the Kirkendall effect which was introduced qualitatively in Section 5.3.1. It was already mentioned that this effect played a prominent role in understanding diffusion in crystals [A. Smigelskas, E. Kirkendall (1947) L.S. Darken (1948)]. 

Several points are to be noted. Firstly, pores and changes of sample dimension have been observed at and near interdiffusion zones [R. Busch, V. Ruth (1991)]. Pore formation is witness to a certain point defect supersaturation and indicates that sinks and sources for point defects are not sufficiently effective to maintain local defect equilibrium. Secondly, it is not necessary to assume a vacancy mechanism for atomic motion in order to invoke a Kirkendall effect. Finally, external observers would still see a marker movement (markers connected by lattice planes) in spite of bA = bB (no Kirkendall effect) if Vm depends on composition. The consequences of a variable molar volume for the determination of diffusion coefficients in binary systems have been thoroughly discussed (F. Sauer, V. Freise (1962) C. Wagner (1969) H. Schmalzried (1981)]. 

The Kirkendall effect in metals shows that during interdiffusion, the relaxation time for local defect equilibration is often sufficiently short (compared to the characteristic time of macroscopic component transport) to justify the assumption of local point defect equilibrium. In those cases, the (isothermal, isobaric) transport coefficients (e.g., Dh bj) are functions only of composition. Those quantitative methods introduced in Section 4.3.3 which have been worked out for multicomponent diffusion can then be applied. 

The Kirkendall effect alters the structure of the diffusion zone in crystalline materials. In many cases, the small supersaturation of vacancies on the side losing mass by fast diffusion causes the excess vacancies to precipitate out in the form of small voids, and the region becomes porous [11], Also, the plastic flow maintains a constant cross section in the diffusion zone because of compatibility stresses. These stresses induce dislocation multiplication and the formation of cellular dislocation structures in the diffusion zone. Similar dislocation structures are associated with high-temperature plastic deformation in the absence of diffusion [12-14]. 

J. Bardeen and C. Herring. Diffusion in alloys and the Kirkendall effect. In J.H. Hol-lomon, editor, Atom Movements, pages 87-111. American Society for Metals, Cleveland, OH, 1951. 

The Kirkendall effect can be studied by embedding an inert marker in the original step-function interface (x = 0) of the diffusion couple illustrated in Fig. 3.4. Show that this marker will move in the F-frame or, equivalently, with respect to the nondiffused ends of the specimen, according to... 

It has sometimes been claimed that the observation of a Kirkendall effect implies that the diffusion occurred by a vacancy mechanism. However, a Kirkendall effect can be produced just as well by the interstitialcy mechanism. Explain why this is so. 

The difference in diffusivities of the components in a growing chemical compound layer is often connected, especially in the literature on physics and metallurgy and especially in relation to intermetallics, with the Kirkendall effect. From historical and scientific viewpoints, in many cases this does not seem to be sufficiently substantiated. 

The Kirkendall effect arises from the different values of the self-diffusion coefficients of the components of a substitutional solid solution, determined by Matano s method. Matano s interface is defined by the condition that as much of the diffusing atoms have migrated away from the one side as have entered the other. If DA = DB, its position coincides with the initial interface between phases A and B. If I)A f DB, it displaces into the side of a faster diffusant (see Fig. 1.22c). Note that KirkendalFs discovery only relates to disordered phases. It was indeed a discovery since at that time most reseachers considered the relation l)A = DB to hold for any solid solution of substitutional type. KirkendalFs experiments showed that in fact this is not always the case. 

Different diffusional contributions of the components of a chemical compound to the growth process of its layer at the interface between phases A and B should not be regarded as a manifestation or result of the Kirkendall effect since the fact that these contributions are in general different became known far before discovering this effect, the essence of which consists in different diffusivities of the components of a substitutional solid solution. 

The difference in diffusivities of the components in a growing chemical compound layer is often connected, especially in the literature on physics and metallurgy and especially in relation to intermetallics, with the Kirken-dall effect. From historical and scientific viewpoints, in many cases this does not seem to be sufficiently substantiated. In particular, this is so in the case of formation of chemical compound layers at the interface of initial substances. A brief consideration was presented to show that different dif-fusional contributions of the components to the growth process of a chemical compound layer can hardly be regarded as a manifestation or result of the Kirkendall effect. 

The intrinsic diffusion coefficients, Dk and DB, of a binary alloy A-B express the diffusion of the components A and B relative to the lattice planes [7], Therefore, during interdiffusion, a net flux of atoms across any lattice plane is present, where, normally, the diffusion rates of the diffusing particles A and B are different. Subsequently, this interdiffusion process provokes the shift of lattice planes with respect to a fixed axis of the sample, result which is named the Kirkendall effect [9],... 

Now, we describe the Kirkendall effect [9], The flux, as well as the diffusion coefficient, has to be chosen relative to a frame of reference. In Figure 5.4, the laboratory frame of reference, X, which is the observer frame of reference, and the moving frame of reference, x, which moves with the inert markers, are shown. 

A brass (Cu-Zn) bar, wound with molybdenum wire, was plated with copper metal. The specimen was annealed in a series of steps, in which the movements of the molybdenum wires were recorded. The inert markers had moved from the interface towards the brass end of the specimen, which contained the fastest diffuser - zinc. This is now called the Kirkendall effect. A similar marker experiment had actually been performed by Hartley a year earlier while studying the diffusion of acetone in cellulose acetate (Hartley, 1946), but most metallurgists were not familiar with this work (Darken and Gurry, 1953). 

We report on formation of tin-dioxide nanoislands by molecular-beam deposition of Sn on Si/Si02 substrates followed by thennal oxidation. The microstructure and phase composition of Sn and SnO nanoislands wens studied by TEM. The formation of coreshell Sn02/Sn structures as well as holes in the SnO nanoislands is documented and found to correlate with the thickness of initial Sn layer and with the oxidation temperature. The results are discussed on the basis of the Kirkendall effect with an additional assumption that absorption of oxygen atoms on the oxide surface creates an electric field that promotes the diffusion of metal ions. 

It can be concluded that the formation of the voids in the center of SnOi particles is mainly a result of the Kirkendall effect [8] associated with a faster outward diffusion of Sn atoms as compared to the inward diffiision of oxygen atoms in the process of the surface oxide layer formation. This produces high density of vacancies at the metal side of the metal/oxide interface. Vacancies transform to vacancy clusters which then aggregate into holes. It might be expected from this model that the increase of oxygen content in the ambiance will result in the promotion of an inward diffusion of oxygen atoms into the Sn particles, and therefore, suppress the formation of holes. 

For Al bonds on Au or vice versa, the Kirkendall effect leads to a well known failure mechanism [37]. The Kirkendall effect results from the different diffusion coefficients of Au and Al in different phases of the system AlAu [38]. The Al2Au phase ( purple phase ), which is always present, plays a crucial role. The diffusion coefficient of Al through Al2Au is much higher than that of Au. As a result, voids are created as soon as the temperature reaches the diffusion temperature, which reduces the stability of the bond contact. 

While the thermal oxidation of a compact metal surface is usually limited to the growth of an oxide layer with a thickness of a few of nanometers, bulk metal nanostmctures can be fully converted into the corresponding oxide or chalcogenide. Again the relative diffusion rate of metal atoms and the oxidation agent in the oxide determine the oxidation kinetics and structure formation. A topographic transformation to a metal oxide nanostructure is observed when the mobility of the oxidation agent exceeds the one of the metal atoms. When this is not the case, the so-called nanoscale Kirkendall effect (NKE) responsible for the formation of sophisticated hollow nanostructures, such as nanospheres, nanotubes, and nanopeapods, proceeds [2-5]. 

Hollow Magnetic Nanocrystals Hollow nanoscale stmctures were first obtained by Y. Yin during the sulfurization of cobalt nanocrystals at elevated temperatures [145]. This process was found to lead to the formation of hollow cobalt sulfide nanocrystals such that, depending on the size of the cobalt nanocrystals and the cobalt sulfur molar ratio, different stoichiometries of hollow cobalt sulfide could be obtained. Hollow nanostmctures are usually formed through the nanoscale Kirkendall effect, which is based on the difference in diffusion rates of two species, and results in an accumulation and condensation of vacancies [146]. This phenomenon was first observed by Kirkendall at the interface of copper and zinc in brass in 1947 [147]. As a typical example of the nano-Kirkendall effect, the controllable oxidation of iron nanoparticles by air can lead to the formation of hollow iron oxide nanostructures, as shown in Figure 3.137. During the course of metal nanoparticle oxidation, the outward diffusion of metal occurs much faster in... 

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