Kirkendall effect couples

The Kirkendall effect (8) is time and temperature dependent, and with some metal couples, it takes place even at room temperature. For instance, adhesion of solder to gold is damaged by heating to about 150°C for about 5 minutes, due to the formation of Kirkendall voids. Naturally, the formation of Kirkendall voids is accelerated by increased temperature and dwelling time. 

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)]. 

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... 

We need to understand what controls the rate of a phase transformation. We can monitor both chemical and structural changes to address the sometimes subtle question— which change (chemistry or structure) occurs first The answer depends on why the phase change itself occurs. The experimental techniques we use are those given in Chapter 10, so we just give some specific illustrations here. The classical approach used to study the kinetics of solid-state reactions between two ceramic oxides is to react a bulk diffusion couple in much the same way as, for example, when studying the Kirkendall effect in metals. 

Uga] Optical microscopy, SEM, EMPA, Kirkendall effect 1100°C, < 70 at.% Ni, diffusion couples... 

In diffusional processes, such as the classic Kirkendall effect of interdiffusion in a bulk diffusion couple of A and B, the atomic flux of A is not equal to the opposite flux of B. If we assume that A diffuses into B faster than B diffuses into A, we might expect that there will be a compressive stress in B, since there are more A atoms diffusing into it than B atoms diffusing out of it. However, in Darken s analysis of interdiffusion, there is no stress generated in either A or B. But Darken has made a key assumption that vacancy concentration is in equilibrium everywhere in the sample. To achieve vacancy equilibrium, we must assume that lattice sites can be created and/or annihilated in both A and B, as needed. Hence, provided that the lattice sites in B can be added to accommodate the incoming A atoms, there is no stress. The addition of a large number of lattice sites implies an increase in lattice planes if we assume that the mechanism of vacancy creation and/or annihilation is by dislocation climb mechanism. It further implies that lattice planes can migrate. 

Thus, the growth of an external oxide scale by the reaction between a pure metal or a metallic alloy and a gaseous or liquid oxidant phase at high temperature is also a combination of diffusion processes and interfacial reactions, and Fig. 2.1 also applies to such corrosion processes that are formally similar to solid-state reactions in poly-phase and multi-constituent systems. Such a similarity will be considered to extend the treatment of the Kirkendall effect for two-phase diffusion couples to the growth of an oxide scale on a pure metal or on an alloy. The roles of interfaces will be analysed more particularly in relation to some specific topics related to oxide scaling processes such as interface displacement, growth stresses and injection of point defects (vacancy or interstitial). 

The Kirkendall effect is a well-known phenomenon resulting from the difference in intrinsic diffusivities of chemical constituents of substitution solid solutions (non-reciprocal diffusion). Many textbooks provide a detailed and quantitative treatment of this important phenomenon (Philibert, 1991) schematized in Fig. 2.2 for a homogeneous diffusion couple of constituents A and B forming a continuous substitutional solid solution. In Fig. 2.2a, the initial position of the contact surface is marked by fixed inert markers that define the origin, also named the Matano plane (M), of the reference frame centred on the mass or the number of moles this reference frame is conunonly used to define interdiffusion processes and the unique interdiffusion coefficient that permits the characterization of the transport of A and B. Moving inert markers determine the actual position of the initial contact surface (Fig. 2.2b) and therefore visualize the drift of lattice planes within the diffusion zone. They mark the origin, also named the Kirkendall plane, of the lattice-fixed frame of reference that permits the definition of the different intrinsic diffusion coefficients of the A and B constituents. Relative to the Matano plane, this drift of lattice planes is equivalent to a translation of the diffusion couple without apparent deformation and without the action of any externally applied stress or, in other words, to a rigid body translation of the phase lattice. 

The simplest and classical treatment of the Kirkendall effect in binary homogeneous systems assumes that the differences between the intrinsic diffusion fluxes of the two substitutional constituents are compensated by the action of local vacancy sinks and sources that maintains the system in local equilibrium, i.e. in states that can be completely defined by the knowledge of appropriate state variables to permit the calculation of pertinent state functions such as, for example, the chemical potential of system constituents. The drift of lattice planes is one important characteristic of the Kirkendall effect in stress-free homogeneous systems and is a consequence of the action of these vacancy sources and/or sinks distributed along the diffusion zone. As the system remains in local equilibrium by the action of vacancy sinks and sources, the vacancy concentration or molar fraction remains constant and equal to its equilibrium value within the entire diffusion couple. Therefore, no effective gradient of vacancy concentration is established in the diffusion zone. However, the local action of vacancy sinks or sources along the diffusion direction is formally equivalent to a vacancy flux Jy related to the required local density of vacancy sources or sinks ps equal to the flux divergence,... 

Kirkendall effect in a homogeneous binary diffusion couple. 

Specificity of the Kirkendall effect in two-phase diffusion couples... 

One specific aspect of the Kirkendall effect in two-phase systems, emphasized in Section 2.2.2, resides in the need to define one Kirkendall plane, i.e. one lattice-fixed frame of reference, for both phases of such a system. For a diffusion couple between two constituents forming one or several compounds, the Kirkendall planes of all the phases, the reacting phases as well as the product phases, coincide with the initial contact surface at f = 0. These planes tend to separate as the product phases grow and the reacting phases recede. Thus, the behaviour of inert markers located at the initial contact surface is difficult to determine as they can be attached to each of these possible Kirkendall planes. Figure 2.9 shows that 10 pm tungsten wires used as inert markers in a Ti-Ni diffusion couple were broken longitudinally and split in several pieces that mark the Kirkendall planes of the different phases (Bastin and Rieck, 1974). This observation provides an impressive illustration... 

As discussed in Section 7.2.3, radiation can induce segregation of alloy elements at defect sinks such as grain boundaries [101]. Typically, RIS is a result of inverse Kirkendall (IK) effects in which the evolution of defect concentration field drives the evolution of alloy composition field. ID rate theory modeling [44,101] is widely used to describe the coupled evolution between defect flux and composition flux. These rate theory models considered both vacancy-mediated and interstitial-mediated solute transport, as well as point defect recombination and defect loss to dislocations. At steady state, the solute segregation direction depends on the relative diffiisivity of different species-defect coupled diffusion. In austenitic Fe-Cr-Ni alloys, the vacancy-mediated solute diffusion alone is sufficient in describing the RIS trend and the interstitial-mediated solute diffusion is usually assumed to have a neutral contribution to RIS [44]. However, in Fe-Cr F/M alloys, both interstitial- and vacancy-mediated diffusion should be considered [102]. 

---