Conventional and effective interdiffusion coefficients have been determined in a Cu-Fe-Ni system for 1000°C based on our experimental data [13] on the distribution of concentrations of components in six diffusion couples of this system. The possibilities of applying these coefficients to interpret peculiar features of interdiffusion in ternary systems are analyzed. It has been demonstrated that effective interdiffusion coefficients are in a certain correlation with thermodynamic characteristics of the system.

Interdiffusion in a Cu-Ni-Fe system was studied at a temperature of 1000°C for three different diffusion couples. It has been shown that, in the studied diffusion couples, the distributions of some components of the system have a distinctly nonmonotonous character and, apart from the local extremes of the concentration curves, there are also zero flux planes in five diffusion zones. Special features of the behavior of the concentration curves and diffusion paths are discussed using thermodynamic data for the system. It has been found that diffusion fluxes of the components are unambiguously associated with a derivative of thermodynamic activity by the concentration taken along the diffusion path. There are experimental data in the appendix concerning the concentration profiles for all of the studied components of the diffusion couples.

The isothermal cross section through the ternary phase diagram Nb–Ni–Cr at 1,100 °C was constructed by means of diffusion couples and equilibrated alloys. It was found that nearly 28 at.% of Cr can be dissolved in the μ phase (Nb7Ni6) at this temperature, and the solubility of chromium in NbNi3 is approximately 5 at.%. Under these circumstances the low-temperature (cubic) modification of the NbCr2 Laves phase can dissolve up to 6 at.% of nickel, but further increase of the Ni content (up to approximately 10 at.%) stabilizes the hexagonal (high-temperature) modification of the Laves phase. The presence of this pseudo-ternary compound which is in equilibrium with all binary intermetallics and body-centred cubic (BCC) Nb- and Cr-based solid solutions largely determines the topology of the isotherm at 1,100 °C. The formation of this phase was also observed in the reaction zone between Nb and Ni–Cr solid solution when chromium concentration exceeded 15 at.%.

In a diffusion-controlled interaction, the Kirkendall plane, identified by inert particles placed at the initial interface between the reactants, need not be unique. The Kirkendall plane can microstructurally (spatially) be stable as well as unstable, and can, under predictable circumstances, bifurcate and even trifurcate. The movement of the Kirkendall markers during the interaction can be rationalized using the classical diffusion theory in terms of the Kirkendall velocity construction. The position of a Kirkendall plane is revealed in the reaction zone not only by the presence of inert markers, but also by a different crystal morphology developed on either side of the plane. The role of the Kirkendall plane in the morphogenesis of multiphase interdiffusion systems can be elucidated using equations of the interfacial reactions occurring in the diffusion zone. The appearance of one or more Kirkendall planes, characterized by morphology changes in the reaction layers is related to different nucleation sites of the product grains. The presence or absence of a Kirkendall plane in certain product phases provides insight into the initial stages of the reactive diffusion. Besides, the sometimes observed spatial (and temporal) patterns in a diffusion zone can be interpreted (and globally predicted) as a Kirkendall-effect mediated phenomenon. These conclusions will alter some previous notions about the diffusional growth of reaction layers and will influence the educational treatment in textbooks. It also will have strong technological implications, e.g., in the field of composite materials, thin-film electronic devices, etc.

Formation of diffusion zone morphologies periodic in time and space during metalceramic reactions is considered as a manifestation of the Kirkendall effect. In a diffusion-controlled interaction, the Kirkendall marker plane can bifurcate, which is attributed to diverging vacancies fluxes in the reaction zone. When the Kirkendall plane is present in a phase layer, it attracts in situproduced inclusions of “secondary-formed phase”, which, in turn, can result in a highly patterned microstructure.

A general treatment of a diffusion-controlled growth of a stoichiometric intermetallic in reaction between two two-phase alloys is introduced. A reaction couple, in which a layer of Co2Si is formed during interdiffusion from its adjacent saturated phases is used as a model system. On the basis of chemical reaction equations occurring at the interphase interfaces, data on relative mobilities of diffusing species and the integrated diffusion coefficient in the product phase are deduced. The analysis yields numerical results identical to those calculated from classical Wagner's theory for the case in which the terminal phases of the diffusion couple are initially saturated.

A diffusion-controlled growth of intermetallic phases and the role of the Kirkendall effect in morphological evolution of the product phase layers can be described in terms of an alternative theory considering chemical reactions at the interphase interfaces. Application of this “physicochemical” treatment to diffusional growth of intermediate phases with fairly wide homogeneity ranges is illustrated by the example of interaction in the Ag-Zn system. The model is purely phenomenological, and its use is convenient, since no explicit assumption of the underlying diffusion mechanism is required.

When a moderately stable phase is precipitated out during an internal reaction, the behaviour of the penetrating atoms within the diffusion zone can be interpreted based on thermodynamic considerations. Evidence for "up-hill" diffusion of the penetrating species through the matrix towards the precipitation front during the internal nitridation of Ni-Cr alloys at 1125 degrees C and 6000 bar of N-2-pressure was predicted. Such behaviour of nitrogen is opposite to the boundary conditions in Wagner's description of internal reactions. A volume change associated with die precipitation reaction resulted in a stress gradient between the alloys surface and the internal nitridation front. Stress relief occurred mainly by transport of nickel to the gas/metal interface. Pipe diffusion-controlled creep is the dominant stress accommodation mechanism during nitriding of dilute Ni-Cr alloys at 700 degrees C under a flowing NH3 + H-2 gas mixture.

Interdiffusion coefficients in the β-NiAl phase over the homogeneity range are determined by the diffusion couple technique in the temperature range of 1000–1200°C. Intrinsic diffusivities of the species at 1000°C at different compositions are measured by Kirkendall marker experiments. The variations of the molar volume with composition and partial molar volumes of the species, required for the determination of the diffusion parameters, are calculated using lattice parameter and vacancy concentration. Tracer diffusion coefficients of the species were calculated from the knowledge on intrinsic diffusivities and compared with the data available in the literature, which were measured directly by tracer methods. The influence of the vacancy wind effect is determined on the calculated results.

A Kirkendall-effect mediated behaviour of inert ("fiducial") markers situated before the interaction at the original interface of a diffusion couple can be complex in both spatial and temporal domains. It was found that the Kirkendall plane can bifurcate and even trifurcate in a multiphase reaction zone. This can be rationalised in terms of Kirkendall velocity construction as well as from a purely chemical point of view considering diffusion-controlled interactions at the interphase interfaces. The physico-chemical approach is also used to explain significance of the Kirkendall effect in the morphogenesis of interdiffusion systems.

The use of equilibrium thermodynamics in describing interfacial reactions between non-ionic inorganic solids is demonstrated using examples of high-temperature interactions in the Ti–Si–N and Mo–Si–N systems. In the case of a diffusion-controlled process, solid-state reactions can be interpreted with chemical potential (activity) diagrams. The role of volatile reaction products formed during interaction in developing the diffusion zone morphology is analysed. The interfacial phenomena in systems based on dense Si3N4 and non-nitride forming metals can be explained by assuming a nitrogen pressure build-up at the contact surface. This pressure determines the chemical potential of Si at the interface and, hence, the reaction products in the diffusion zone.

The Kirkendall-effect induced migration of inert markers during a diffusion-controlled growth of intermetallic compounds in the Cu/Sn and Au/Sn couples at 215 and 180degreesC were studied. It was shown that the behaviour of markers in the multiphase reaction zones can be rationalized in terms of the Kirkendall velocity construction. Observations on the microstructural features of the product intermetallic layers and the role of the Kirkendall effect in the morphogenesis of the interdiffusion systems are discussed. It was demonstrated that the velocity of markers in a product layer, the appearance of the Kirkendall plane(s), their location(s) and the morphological evolution of the reaction products can also be explained from a purely chemical point of view considering the diffusion-controlled interactions at the interphase interfaces. A representation of the reaction scheme and kinetics of intermetallic growth in each of the two systems is given.

An experimental verification of the phenomenological approach introduced earlier [Phys. Rev. Lett. 86 (2001) 3352] to rationalize possible bifurcation of the Kirkendall plane inside a diffusion-grown compound layer is presented. A reaction couple, in which a single-phased layer of β-NiAl intermetallic is growing during interdiffusion from its adjacent phases is used as a model system. The corresponding Kirkendall velocity diagram was constructed on the basis of inter- and intrinsic diffusion data obtained with the diffusion couple technique. The agreement between the predicted and experimentally determined position of the marker planes was found to be good within the range of uncertainty of the experimental results, which demonstrates the validity of the proposed model. It is observed that the position of a stable Kirkendall plane is characterized not only by the presence of inert markers, but also by a different crystal morphology at both sides of this plane. The bifurcation of the Kirkendall plane within the product layer of β-NiAl is directly related to the growth of grains of this phase at a location in between (and not at) the interfaces with starting materials.

There is now a considerable body of experimental evidence to indicate that in a volumediffusion controlled interaction the Kirkendall plane need not be unique. The Kirkendall plane can microstructurally be stable as well as unstable (it does not exist!). Under predictable circumstances, it can also bifurcate and even trifurcate. This can be rationalised in terms of Kirkendall velocity construction as well as from a purely chemical point of view considering diffusion-controlled interactions at the interphase interfaces. The physico-chemical approach is also used to explain significance of the Kirkendall effect in the morphogenesis of interdiffusion systems.

Effective and partial coefficients of interdiffusion of components in the Co-Fe-Ni system at a temperature of 1100degreesC have been determined from our previous experimental data [4] on the concentration distribution and Kirkendall effect in seven diffusion zones of this system. The possibility of using these coefficients for the interpretation of the processes of interdiffusion in three-component systems and for the calculation of the component concentration profiles for diffusion under specified initial and boundary conditions is analyzed.

It is demonstrated that the formation of reaction zone morphologies periodic in time and space can be considered as a manifestation of the Kirkendall effect accompanying interdiffusion in the solid state. In a diffusion-controlled interaction, the Kirkendall marker plane can bifurcate, which is attributed to diverging vacancy fluxes in the reaction zone. When the Kirkendall plane is present in a phase layer, it attracts in situ-produced inclusions of "secondary-formed phase", which, in turn, can result in a highly patterned microstructure.