Interface Growth Kinetics

A. A. Chernov, 2004, Notes on interface growth kinetics 50 years after Burton, Cabrera and Frank , J. Cryst. Growth 264,... 

More recently, simulation studies focused on surface melting [198] and on the molecular-scale growth kinetics and its anisotropy at ice-water interfaces [199-204]. Essmann and Geiger [202] compared the simulated structure of vapor-deposited amorphous ice with neutron scattering data and found that the simulated structure is between the structures of high and low density amorphous ice. Nada and Furukawa [204] observed different growth mechanisms for different surfaces, namely layer-by-layer growth kinetics for the basal face and what the authors call a collected-molecule process for the prismatic system. 

Measurements of overall reaction rates (of product formation or of reactant consumption) do not necessarily provide sufficient information to describe completely and unambiguously the kinetics of the constituent steps of a composite rate process. A nucleation and growth reaction, for example, is composed of the interlinked but distinct and different changes which lead to the initial generation and to the subsequent advance of the reaction interface. Quantitative kinetic analysis of yield—time data does not always lead to a unique reaction model but, in favourable systems, the rate parameters, considered with reference to quantitative microscopic measurements, can be identified with specific nucleation and growth steps. Microscopic examinations provide positive evidence for interpretation of shapes of fractional decomposition (a)—time curves. In reactions of solids, it is often convenient to consider separately the geometry of interface development and the chemical changes which occur within that zone of locally enhanced reactivity. 

Torres, F. E., Russel, W. B., and Schowalter, W. R., Floe structure and growth kinetics for rapid shear coagulation of polystyrene colloids. J. Colloid Interface Sci. 142, 554-574 (1991a). Torres, F. E., Russel, W. B., and Schowalter, W. R., Simulations of coagulation in viscous flows. J. Colloid Interface Sci. 145, 51-73 (1991b). 

Equation (6.11) is valid for the initial particle growth. Interface control of the growth kinetics would lead to a linear rate law. Details can be found, for example, in [H. Schmalzried (1981)]. 

S.D. Peteves and R. Abbaschian. Growth-kinetics of solid-liquid Ga interfaces. 1. Experimental. Metall. TYans. A, 22(6) 1259—1270, 1991. 

The authors further note that although visual observations have shown that hydrate crystallizes at the solution-gas interface, this may also be because of nucleation and subsequent growth within a thin solution layer adjacent to the solution-gas interface. For kinetic reasons, the supersaturation in the thin solution layer can be locally high, and therefore hydrate nucleation and subsequent growth in this layer would in fact be more probable than in the bulk of the solution. 

Growth kinetics of the NiBi3 layer at the nickel-bismuth interface... 

As only the Bi atoms are diffusing and experimental NiBi3 layer thicknesses are large enough, its growth kinetics at the Ni-Bi interface is described by simplified equations (1.32) and (1.33) ... 

Note that even in those cases where multiple compound layers were present at the A-B interface, two layers were dominating. For example, G. Hillmann and W. Hofmann and O. Taguchi et al. observed the formation of all six intermetallics shown on the equilibrium phase diagram in the reaction zone between zirconium and copper, with two Cu-rich compounds occupying more than 90 % of the total layer thickness and layer-growth kinetics deviating from a parabolic law. When investigating... 

In the great majority of cases, a line of the markers located in the zinc phase displaces a few micrometres aside from a line located in the other phases, indicative of the crack formation at the interface with zinc. To understand the further course of the reaction-diffusion process after the rupture of any reaction couple, it is necessary first to analyse the growth kinetics of the same compound layer in different reaction couples of a multiphase binary system. This will be done in the next chapter. 

It is most convenient to compare the growth rates of the layer of the same chemical compound in various reaction couples with the rate of its growth at the interface of elementary substances. Therefore, let us first briefly analyse the case in which the ArBs compound layer is formed at the A-B interface (Fig. 4.1). To avoid considerable changes in the designations of the reaction-diffusion constants describing the layer-growth kinetics, the numeration of the interfaces of the ArBs layer, shown in Fig. 3.1, will be retained. 

The melting points of the components of a reaction couple are most frequently different. Therefore, there is a certain range of temperature, in which one of the components is in the solid state, while the other in the liquid state. If soluble, the solid substance will dissolve in the liquid phase. The dissolution process should clearly affect the growth kinetics of a chemical compound layer at the solid-liquid interface. 

When studying the growth kinetics of the intermetallic layers, after the run the crucible, together with the flux, the melt and the solid specimen, was shot into cold water to arrest the reactions at the transition metal-aluminium interface. Note that the solid specimen continued to rotate until solidification of the melt, ft is especially essential in examining the formation of the intermetallic layers under conditions of their simultaneous dissolution in the liquid phase (with undersaturated aluminium melts). The time of cooling the experimental cell from the experimental temperature down to room temperature did not exceed 2 s. 

Growth kinetics of intermetallic layers at the transition metal-liquid aluminium interface... 

In contrast to the Fe2Al5 layer (see Fig. 1.2), the M0AI4 layer is seen to have relatively even interfaces with both initial phases. In the case of the Mo-saturated aluminium melt, its growth kinetics follows the parabolic law jc2 = 2k t (Fig. 5.14). In the 750-850°C range the temperature dependence of the growth-rate constant, ku is described by the equation ... 

Fig. 5.14. Growth kinetics of the MoA14 layer at the interface of molybdenum with Mo-saturated liquid aluminium and the temperature dependence of its growth-rate constant.309 1, 75 0°C 2, 800 3, 850.

Although there are no essential differences in the processes of formation of the layers of chemical compounds at the interface of either two solid substances, or a solid and a liquid, or a solid and a gas, nevertheless in the latter case the experimentally observed layer thickness-time dependences are more diversified and complicated than in the first two cases since the growth kinetics of compound layers in the solid-gas systems are usually investigated by thermogravimetry over a comparatively long time range. 

Nevertheless, in this book the number of the theoretically substantiated kinetic equations, for the experimentalist to use in practice, appears to exceed that resulting from purely diffusional considerations. Whether the experimentalist will be pleased with such an abundance of equations is a wholly different question. Still, for many researchers in the field it is so tempting to employ the only parabolic relation and then to discuss in detail the reasons for (unavoidable and predictable) deviations from its course. Note that unlike diffusional considerations where each interface is assumed to move according to the square root of the time, in the framework of the physicochemical approach the layer-growth kinetics are not predetermined by any additional assumptions, except basic ones, but immediately follow in a natural way from the proposed mechanism of the reaction-diffusion process. 

The growth of layer i — 1, on the other hand, will require an analogous decomposition of layer i by solid-state reaction at the interface xt = 0. This will lead to a negative contribution to the growth kinetics of layer i. Thus, from the time-dependence of the cation interstitial balance at the interfaces we can write the net growth rate of any inner layer i as... 

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