Phase boundary advancement

The crystals do not precipitate in the entire glass mass simultaneously at certain points nuclei first appear which then grow into the ambient melt. The nucleation rate is expressed by the number of nuclei created in a unit volume within a unit period of time. The rate of growth is given by the velocity at which the phase boundary advances into the melt, usually in cm s or in pm min . ... 

From what has already been said, we can see that phase boundary advancement from these nuclei is another important factor in reactions in... 

Extensive studies of crazes and their behavior imder loads have been conducted by Kramer and co-workers (30-40). We know from this work that there are two unique regions within the craze (1) the craze/bulk interface, a thin (10-25 nm) strain-softened polymer layer in which the fibrillation (and thus craze widening) takes place and (2) the craze midrib, a somewhat thicker (50-100 nm wide) layer in the craze center, which forms immediately behind the advancing craze. The relative position of the midrib does not change as the craze widens. By contrast, as the phase boundaries advance, continuously new locally strain-softened regions are generated, while strain-hardened craze fibrils are left behind. 

When the rate of advance of the phase boundary is limited by the removal of latent heat or impurities, then the diffusion field modifies the interfacial values of the relevant field variables and therefore the growth shape. The physical picture is as follows As a phase boundary advances, latent heat and/or impurities are emitted at the front. Their build up occurs over a characteristic dimension, or boimdary layer, that depends on their respective diffusivities and the rate of advance. The motion itself is limited by the speed with which this excess is depleted by diffusion. These diffusion-limited xt gimes are generally studied using non-geometric formulations. The reason is that the... 

These considerations have so far been restricted to small-amplitude deviations of h x) from a straight horizontal line. Since a phase boundary typically advances in the normal direction, we must make a correction for the case of an inclined interface ... 

In addition to the above, there are further possibihties. When the rate of guest diffusion between individual layers is very large compared with the rate of nucleation at the edge of the crystal, there exists a situation in which the individual layers appear to fill instantly. In this case, when Avrami kinetics are applied to the system, the diffusion process being observed is not the diffusion of guest species between the layers, but the diffusion of filled layers parallel to the c-axis. Such ID processes will consist of nucleation followed by diffusion control in the vast majority of cases, although phase boundary control is also possible if the rate of advancement of the phase boundary is also very rapid with respect to nucleation. In this case, instantaneous nucleation is not a possibility [18]. 

Hasse et al. [366] have used in situ AFM for the detection of silver nucleation at the three-phase junction of the type metal-silver halide-electrolyte solution. At this phase boundary, electrochemical reduction of submicrometer size silver halide crystals immobilized on the surface of gold and platinum electrodes took place. Following nucleation, the reaction advanced until the entire surface of the silver hahde crystals was covered with 20 atomic layers of silver. Then, reduction was terminated. The obtained silver layer could be oxidized and the next layer of silver halide crystals became accessible for further reduction. 

Let us conclude this section with a few general remarks. If we assume phase boundary rate control, the rate of advance is co-determined by the interface mobility, which in turn is related to the mobilities of the atoms in the interface. We note that 1) the directional dependence of mobilities or diffusivities in the interface may be quite pronounced (depending on 5) and 2) the mobilities or diffusivities depend on the component chemical potentials, which change over time at the interface until diffusion control eventually becomes rate determining. 

Quite recently there was an important advance toward a deeper understanding of the nature of catalytic processes. The mobility of electrons at surfaces and the exchange of electrons at phase boundaries between catalyst and substrate were investigated and rules for these processes formulated. 

The thermodynamic definition of the spinodal, binodal and critical point were given earlier by Eqs. (9), (7) and (8) respectively. The variation of AG with temperature and composition and the resulting phase diagram for a UCST behaviour were illustrated in Fig. 1. It is well known that the classical Flory-Huggins theory is incapable of predicting an LCST phase boundary. If has, however, been used by several authors to deal with ternary phase diagrams Other workers have extensively used a modified version of the classical model to explain binary UCST or ternary phase boundaries The more advanced equation-of-state theories, such as the theory... 

A solidified body is maintained by cooling at x = 0 at the constant temperature i90, which is lower than the solidification temperature E, Fig. 2.35. Only onedimensional heat conduction in the x-direction will be assumed. At the phase boundary x = s, which is moving to the right, the solid is touching the liquid which has already been cooled to the solidification temperature. By advance of the phase boundary, or in other words by solidifying a layer of thickness ds, the enthalpy of fusion is released and must be conducted as heat to the cooled surface of the solid at x = 0. 

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