On the Spatial Stability and Bifurcation of the Kirkendall Plane during Solid-State Interdiffusion

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.     

The Kirkendall effect in binary diffusion couples

The understanding of the phenomenological process related to the position of the Kirkendall plane is still lacking. In this study some aspects of Kirkendall and lattice plane migration in binary diffusion couples are studied by means of numerical simulations by the bi-velocity method. The simulations are performed using constant and composition dependent intrinsic diffusion coefficients. The results show that the position and stability of the Kirkendall plane as well as a number of other interesting features can be predicted using the entropy–density curve calculated by the bi-velocity method.     

The Kirkendall effect in single-phase multicomponent systems: dependence on drift and entropy distribution

This paper concerns interdiffusion in a diffusion couple and determination of the Kirkendall plane. The “entropy density” model is proposed in which the entropy is used to predict the position of the Kirkendall plane in a multicomponent system. It is shown that the marker position depends on the drift velocity and pressure field only. Application of the model is presented for ternary CoFeNi diffusion couples of three various initial compositions. The concentration profiles and entropy densities are calculated for each diffusion couple. The positions of the Kirkenadl planes are determined and compared with those obtained by velocity-curve and trajectory methods.     

The generalization of the Boltzmann–Matano method

The phenomenological Boltzmann–Matano (B–M) analysis allows approximating the concentration dependent interdiffusion coefficients related to infinite binary diffusion couple experiments. However, the complete understanding of the phenomenological process related to the Kirkendall plane position coupled with the B–M method is still lacking. A purpose of the present study is to generalize the Boltzmann–Matano analysis and propose a method of estimating the unique intrinsic diffusion coefficients of components from the experimental concentration profile and the positions of Matano and Kirkendall planes in multicomponent systems. The proposed physico-chemical approach is used to approximate the intrinsic diffusivities in a single phase of Ni–Pd binary and Cu–Fe–Ni ternary diffusion couples.     

Comparison of Monte Carlo simulations and macroscopic theories of diffusion in systems with non-ideal sources and sinks for vacancies

A new concept of generation and annihilation of vacancies at non-ideal dense sources and sinks for vacancies is incorporated into the standard Monte Carlo model for vacancy-mediated diffusion. This model enables to treat the vacancy wind as well as the deformation of the specimen and the shift of the Kirkendall plane. The Monte Carlo model is used for testing the recent macroscopic theories of diffusion by Darken [Trans. Am. Inst. Min. Eng. 175 184 (1948)], Manning [Phys. Rev. B 4 1111 (1971)] and Moleko et al. [Phil. Mag. A 59 141 (1989)]. The agreement with the self-consistent Moleko et al. theory is excellent. On the other hand, the agreement with the classical Darken theory frequently used in the open literature for the explanation of the Kirkendall effect is rather poor.     

A pseudobinary approach to study interdiffusion and the Kirkendall effect in multicomponent systems

Interdiffusion studies become increasingly difficult to perform with the increasing number of elements in a system. It is rather easy to calculate the interdiffusion coefficients for all the compositions in the interdiffusion zone in a binary system. The intrinsic diffusion coefficients can be calculated for the composition of Kirkendall marker plane in a binary system. In a ternary system, however, the interdiffusion coefficients can only be calculated for the composition where composition profiles from two different diffusion couples intersect. Intrinsic diffusion coefficients are possible to calculate when the Kirkendall markers are also present at that composition, which is a condition that is generally difficult to satisfy. In a quaternary system, the composition profiles for three different diffusion couples must intersect at one particular composition to calculate the diffusion parameters, which is a condition that is almost impossible to satisfy. To avoid these complications in a multicomponent system, the average interdiffusion coefficients are calculated. I propose a method of calculating the intrinsic diffusion coefficients and the variation in the interdiffusion coefficients for multicomponent systems. This method can be used for a single diffusion couple in a multicomponent pseudobinary system. The compositions of the end members of a diffusion couple should be selected such that only two elements diffuse into the interdiffusion zone. A few hypothetical diffusion couples are considered in order to validate and explain our method. Various sources of error in the calculations are also discussed.     

Mechanistic Insights into a Non‐Classical Diffusion Pathway for the Formation of Hollow Intermetallics: A Route to Multicomponent Hollow Structures

Hollow nanostructures are used for various applications including catalysis, sensing, and drug delivery. Methods based on the Kirkendall effect have been the most successful for obtaining hollow nanostructures of various multicomponent systems. The classical Kirkendall effect relies on the presence of a faster diffusing species in the core; the resultant imbalance in flux results in the formation of hollow structures. Here, an alternate non‐Kirkendall mechanism that is operative for the formation of hollow single crystalline particles of intermetallic PtBi is demonstrated. The synthesis method involves sequential reduction of Pt and Bi salts in ethylene glycol under microwave irradiation. Detailed analysis of the reaction at various stages indicates that the formation of the intermetallic PtBi hollow nanoparticles occurs in steps. The mechanistic details are elucidated using control experiments. The use of microwave results in a very rapid synthesis of intermetallics PtBi that exhibits excellent electrocatalytic activity for formic acid oxidation reaction. The method presented can be extended to various multicomponent systems and is independent of the intrinsic diffusivities of the species involved.     

The effect of surface contact conditions on grain boundary interdiffusion in a semi-infinite bicrystal

The Kirkendall effect is conditioned by active diffusion as well as by active sources and sinks for vacancies. In the case of grain boundaries under the condition of negligible bulk diffusion, the Kirkendall effect is highly localized and responsible for the formation of an extra material wedge in the grain boundary, which may lead to high stress concentrations. The Kirkendall effect in grain boundaries of a binary system is described by a set of partial differential equations for the mole fraction of one of the diffusing components and for the stress component normal to the grain boundary completed with the respective initial and boundary conditions. The contact conditions of the grain boundary with the surface layer acting as source of one of the diffusing components can be considered as equilibrium ones ensuring the continuity of generalized chemical potentials of both diffusing components. Thus, the boundary conditions are determined by the difference in chemistry (i.e. how the thermodynamic parameters depend on chemical composition) of the grain boundaries and of the surface layer. The simulations based on the present model indicate a drastic influence of the chemistry on the grain boundary interdiffusion and Kirkendall effect.     

Interdiffusion induced defect microstructures of Co(1-x)O near confined zirconia particles

Diffusion couples of metal alloys were commonly used to study Kirkendall pore formation and amorphization near the interface of composition discontinuity. In this work, yttria-partially stabilized zirconia (Y-PSZ) powders mixed with Co(1-x)O (1:99 molar ratio, denoted as Z1C99) were sintered and annealed at 1600 degrees C for 1-75 h to study interdiffusion-induced defect microstructures of Co(1-x)O near confined Y-PSZ particles. Analytical electron microscopic analysis indicated a much larger flux of Co(2+) from Co(1-x)O into Y-PSZ compared to the reverse flux of Zr(4+) and Y(3+). In addition, there is a significant inward flux of oxygen from Y-PSZ into Co(1-x)O. A net vacancy flux in the opposite direction of ion flux then caused the formation of Kirkendall pores and dislocations in Co(1-x)O near corrugated Y-PSZ/Co(1-x)O interface. Amorphous regions and [111] faulting were also found in Co(1-x)O near Kirkendall pores, which can be rationalized by diffusion-induced amorphization and assembly of cation vacancies along close-packed [111] planes vulnerable to crystallographic shear, respectively. Y-PSZ particles were found to migrate-coalesce as corrugated slabs and rods at Co(1-x)O grain boundaries and junctions, respectively, when the composite with more Y-PSZ additive (Z(1)C(89)) was annealed.     

Interdiffusion in the Co-Ni system-I concentration penetration curves and interdiffusion coefficients

The interdiffusion in the Co-Ni system has been investigated in the temperature range of 950 to 1150 °C, by means of diffusion specimens of pure Co and Ni. The concentration curvesN(x, t) obtained with the aid of an JXA-3 A JEOL electron microprobe were evaluated using the smoothing cubic spline method by means of the Boltzmann-Matano equation. The obtained interdififusion coefficient values ¯D increase with the increasing Ni concentration and satisfy the Arrhenius equation at temperaturesH 990 °C. At lower temperatures the influence of high diffusivity paths may be effective, resulting in higher ¯D values. No expressive influence of atomic (Ni₃Co) or magnetic order on the interdiffusion has been detected. The activation enthalpyH values were found almost concentration independent. A Kirkendall effect study has been carried out with positive results which are presented in Part II of this paper. A new method for the determination of diffusants concentration in the Kirkendall plane was proposed. With the use of this method and of Darken equations the intrinsic diffusion coefficients were calculated. These results are given in Part III.     

Long-range chemical interaction in solid-state synthesis: The Kirkendall effect and solid-state reactions in Cu/β-CuZn and Cu/Fe/β-CuZn film systems

The results of the experimental investigations of the solid-state reaction of Cu with β brass, which is associated with the Kirkendall, in Cu/β-CuZn and Cu/Fe/β-CuZn film systems are reported. It has been shown that the initiation temperature of the solid-state synthesis of α brass at the Cu/β-CuZn interface is about 200°C. The chemically inert Fe barrier layers 420 and 850 nm in thickness between the Cu and β-CuZn films do not suppress the solid-state synthesis of the α brass, but increase the initiation temperature to about 250°C. This behavior indicates that the chemical interaction between the Cu and Zn atoms through the chemically inert Fe layer is long-range. The X-ray photoelectron investigations reveal the migration of Zn atoms from the β-CuZn layer through the Fe barrier to the Cu layer. The results are interpreted under the assumption that the migration of Zn atoms in the Kirkendall is initiated by the strong chemical interaction between the Cu and Zn atoms in the Cu and β-CuZn layers, which is due to the synthesis of α brass, rather than by the diffusion random walk, as is commonly accepted at present.     

Modeling of Radiation-Induced Segregation in Fe–Cr–Ni Alloys

Physics of the Solid State - In the model of radiation-induced segregation based on the first and second Fick laws and taking into account the inverse Kirkendall effect, concentration profiles of...     

Kinetic analysis of the instability of hollow nanoparticles

A general method of obtaining hollow nanoparticles by utilizing the Kirkendall effect has been reported recently. We examine here the thermal instability of hollow nanoparticles. The difference of vacancy concentrations at the inner and outer surfaces of a nanoshell will generate an outflux of vacancies and transform it into a solid nanoparticle. Phenomenological as well as kinetic Monte Carlo modeling has been applied to analyse the shrinking kinetics of nanoshells, consisting of either a pure element or an intermetallic compound with large difference of partial diffusivities of the components. Shrinking kinetics and time to collapse to solid particles are demonstrated to be determined mainly by the slow diffusant, making compound nanoshells more stable than anticipated.     

Electromigration revisited: competition between Kirkendall shift and backstress in pure metals and two-phase alloys

The simple phenomenological model and analytical approach of electromigration in the two-phase alloy (solder) under combined influence of the Kirkendall effect, backstress and sedimentation is presented. It is compared with electromigration in pure metal under condition of quasi-equilibrium vacancies (unlimited power of vacancy sinks-sources) and electromigration in pure metal with account of nonequilibrium vacancies.     

Influence of electric transfer on the Kirkendall effect and partial lengths of liquid areas appearing upon contact melting in metallic systems

The results of experimental studies of the influence of electric transfer on the Kirkendall effect in a Bi-Cd system and the partial lengths of contact interlayers of Bi-Cd and In-Zn systems upon contact melting are discussed. It was established that electric current passing across the melt formed upon contact melting considerably affects its rate of growth and contributes also to the velocity of the general shift of the liquid, as determined by the shift of inertial marks.     

NMR study of solid state reaction in Co-Sn multilayers

Amorphization by solid state reaction at room temperature in Co-Sn multilayers with periodicities of 65, 130 and 195 Å and relative Co to Sn ratio varying as 4, 3, 2 has been studied by zero field NMR method. The distribution of⁵⁹Co hyperfine fields and that of NMR enhancement factors were used as a probe of the ferromagnetic part of a sample and its evolution with the annealing time. The critical role of the interface during the first hours of annealing is pointed out. On the long time scale the diffusion process is slowed down by the creation of Kirkendall voids and after 3 months of annealing some crystalline Co is still present.     

Model of phase separation and of morphology evolution in two-phase alloy

Elementary theory of mass-transfer in two-phase alloy under electromigration with account of two competing mechanisms of the fluxes equilibration is presented. These two competing mechanisms are Kirkendall effect and backstress. Various versions of Monte Carlo models for simultaneous simulation of structure evolution kinetics and of mass-transfer kinetics under high-density current are presented. Possibility of self-organization with minimization of Joule heating is demonstrated.     

注氢Fe-1wt%Ni合金中的辐照诱导偏析

利用离子加速器注氢和高压电子显微镜的电子辐照方法,研究了Fe-1wt%Ni铁素体钢中Ni合金元素的辐照诱导偏析现象．实验结果表明,Ni与空位、氢结合成复合体,其扩散机制为逆Kirkendall效应,即Ni的扩散方向与空位的扩散方向一致．在空洞附近富集的Ni会沿{110}平面共格析出．在特定的入射方向的电子衍射图象中,能够观察到由于这种平面共格析出引起的衍射条纹． 关键词：     

MoO2微米空心球的水热合成及合成机理研究

在阳离子表面活性剂的作用下,以钼酸铵为钼源,乙醇作为还原剂合成了微米级MoO2空心球．采用X射线粉末衍射、热重-差热、扫描电子显微镜、透射电镜和X射线光电子能谱对合成的样品进行了表征,并对MoO2空心球可能的形成机理进行了讨论.在MoO2空心球的形成过程中,发现了样品从“大块-实心球-空心球”的形貌转化过程,空心球的形成机理可用微米尺度的Kirkendall效应解释．