Anomalous Kinetics and Regimes of Growth of Intermetallic Phases during Solid State Reactions in Nanosystems

Abstract

Two interesting features of formation and growth of intermetallic phases in nanoscale solid state reactions will be discussed:Linear-parabolic “normal” growth: it will be summarized that at the very early stages of the growth of an already existing new phase (i.e. when nucleation problems can be neglected) the linear kinetics can be observed due to the so-called diffusion asymmetry. Indeed, it was shown that if the ratio of the diffusion coefficients differ by orders of magnitude in the parent materials (and so also in the new phase), during the growth of a phase bordered by parallel interfaces from the parent phases (normal growth geometry), the shift of the individual interfaces can be linear at the beginning and a transition to the parabolic regime can take place even after a shift of several tens of nanometres. In addition, an AB compound in contact with the pure A and B phases can be dissolved if the diffusion in B is much faster than in either A and AB. This means that the thickness of this phase should decrease, or even can be fully dissolved, at the beginning and only after some time—when the composition in B will be high enough allowing the re-nucleation of this AB phase—will the AB phase grow further.The common problem oftwo stages of solid state reactionswill be revisited: usually the growth can be divided into two stages: a) the formation (nucleation) and lateral growth of the new phases and b) the “normal” growth of the already continuous phase. It was concluded in different previous reviews that in stage b) in the majority of cases the parabolic growth was observed in accordance with the above i) point: the linear-parabolic transition length was typically below 1 μm, which was the lower limit of detection in many previous investigations. On the other hand recently the application of the linear-parabolic growth law for the analysis of experimental data obtained in nanoscale reactions became very popular, not making a clear distinction between a) and b) stages. It will be emphasized here that care should be taken in all cases when the experimental methods applied provide information only about the increase of the amount of the reaction product and there is no informationwhere and howthe new phase (s) grow. We have illustrated in a series of low temperature experiments - where the bulk diffusion processes are frozen - that even in this case a full homogeneous phase can be formed by cold homogenization called Grain Boundary Diffusion Induced Solid State Reaction (GBDIREAC). In this case first the reaction starts by grain-boundary (GB) diffusion and nucleation of the new phase at GBs or their triple junctions, then the growth of the new phase happens by the shift of the new interfaces perpendicular to the original GB. This is a process similar to the diffusion induced grain-boundary motion (DIGM) or diffusion induced recrystallization (DIR) phenomena and in this case the interface shift, at least in the first stage of the reaction until the parent phases have been consumed, can be considered constant. This means that the amount of the phase increases linearly with time, giving a plausible explanation for the linear kinetics frequently observed in stage a).