Diffusion zone, interface

Strictly speaking, the validity of the shrinking unreacted core model is limited to those fluid-solid reactions where the reactant solid is nonporous and the reaction occurs at a well-defined, sharp reaction interface. Because of the simplicity of the model it is tempting to attempt to apply it to reactions involving porous solids also, but this can lead to incorrect analyses of experimental data. In a porous solid the chemical reaction occurs over a diffuse zone rather than at a sharp interface, and the model can be made use of only in the case of diffusion-controlled reactions. 

FIGURE 19.12 Considerations for the interpretation of SSITKA data. Case 1 Three formates can exist, including (a) rapid reaction zone (RRZ)—those reacting rapidly at the metal-oxide interface (b) intermediate surface diffusion zone (SDZ)—those at path lengths sufficient to eventually diffuse to the metal and contribute to overall activity, and (c) stranded intermediate zone (SIZ)—intermediates are essentially locked onto surface due to excessive diffusional path lengths to the metal-oxide interface. Case 2 Metal particle population sufficient to overcome excessive surface diffusional restrictions. Case 3 All rapid reaction zone. Case 4 For Pt/zirconia, unlike Pt/ceria, the activated oxide is confined to the vicinity of the metal particle, and the surface diffusional zones are sensitive to metal loading. 

Evidence for this hypothesis can be formd in the rough correlation between 5 Mo and [Mo] in suboxic sediments (Siebert et al. 2003) Higher [Mo] is associated with 5 Mo approaching the seawater value, as expected from mass balance in a closed reservoir (the reservoir is the diffusive zone beneath the sediment-water interface in suboxic settings see following section). 

The meehanism of Mo removal in suboxie systems is unelear, and so the fundamental nature of this fraetionation requires further study. However, the effeet may be rmderstood in terms of a two layer diffusion-reaetion model in whieh a reaetion zone in the sediment (where Mo is ehemieally removed) is separated from seawater by a purely diffusive zone in which there is no chemical reaction (Braudes and Devol 1997). The presence of a diffusive zone is likely because Mo removal presumably occurs in suMdic porewaters that lie a finite distance L below the sediment-water interface (Wang and van Cappellen 1996 Zheng et al. 2000a). If HjS is present in the reactive zone such that Mo is removed below this depth, then Mo isotope fractionation in the diffusive zone may be driven by isotope effects in the reactive zone. 

An important consequence of such a model is that the effect of such sedimentary systems on the ocean Mo isotope budget is not represented by a, but rather by the relative fluxes of the isotopes across the sediment-water interface. This effective fractionation factor, is likely to be smaller than a (Bender 1990 Braudes and Devol 1997) because the diffusive zone acts as a barrier to isotope exchange with overlying waters, approximating a closed system. 

Figure 10-10. Representation of the chemical potential of A during the heterogeneous solid state reaction A+B = AB. a) Diffusion control, b) interface control at b2, c) rate control by rearrangement (relaxation) of A in B in zone A (B), d) simultaneous diffusion and interface control (bj).

When the faster-diffusing component is diffused from the vapor phase into a thin sheet, and the diffusion zone is relatively wide compared to the sheet thickness, the constraints on the expansion parallel to the diffusion interface are greatly reduced. Large specimen expansions normal to the diffusion direction have then been observed [5]. 

As a consequence of the time pulsing of one inlet flow rate, one of the feed lamellae and the diffuse zone penetrate also the inlet region of the other fluid, i.e. generating a tri-lamellae peak here. The diffuse interface is now no longer symmetric with regard to the channel width (as for constant flows), but is curved and changes with time. Thereby, material transport is done, the diffuse zone becomes broader... 

The structure of the diffuse weld interface resembles a box of width X, with fractal edges containing a gradient of interdiffused chains as shown by Wool and Long. When the local stress at a crack tip exceeds the yield stress, the deformation zone forms and the oriented craze fibrils consist of mixtures of fully entangled matrix chains and partially interpenetrated minor chains. 

Figure 5.4 Nucleation barrier of AI9C02 nucleus formation at the Al-Co interface calculated by the transversal mode without shape optimization for different diffusion zone widths.

As a result of the simulation, the widening of the A/B diffusion zone is observed and small voids start forming at the pure B/aUoy interface. In the process of a computer experiment, the voids expand, leaving between themselves the bridges of pure B. At high temperature, we observed the subsequent coalescence of voids into a single spherical void in the center of the nanoparticle (Figure 7.23). These simulation results correlate with experiments on the formation of cobalt selenides and sulfides [4, 5, 30]. 

Diffusion processes taking place in such systems have to be regarded as processes that take place in thin Aims, and not in bulk samples. Reactive diffusion in thin Aims differs from that in the bulk case IMCs are formed in sequence ( one by one ), so that the phase spectrum of the diffusion zone differs from the full list of stable intermediate phases. Besides, the growth of new phase layers very often demonstrates a linear time dependence rather than a parabolic one. The best known theory providing an explanation for this fact was offered by Gosele and Tu [9]. However, it was shown that the linear stage of intermetallic layer growth may also be caused by a finite relaxation rate of nonequilibrium vacancies at these interfaces [lOj. 

Let us ensure that by changing the initial concentration of the BC alloy, one can control the phase composition of the diffusion zone. We proceed from the flux balance equations at the interfaces t) p, p — y, and y — a ... 

The concentration profile obtained by this model is linear in the diffusion zone, with an increasing slope for a consumed species and a decreasing one for a produced species, if the origin of the axis Ox is the reaction interface. Other types of models can be developed - particularly those of mixed diffusion, as several species can coexist in the same medium (for instance, air, a nitrogenous compound, oxygen, water vapor, in an H2/air fuel cell). 

The structure of the metal-solution interface can be represented by a series of capacitors (Figme B.1.4) with charges distributed over several planes metal surface, internal Helmholtz plane, external Helmholtz plane, and in the diffuse zone. This leads to the built-up of a difference in potential between the metal and the solution. This difference is generally called the absolute potential of the metal with respect to the solution, or Galvani potential. 

At subcritical potentials a single oxidation process with participation of only electronegative component takes place on the surface of the alloy. The surface layer is saturated with nonequilibrium defects (mainly vacancies), maintains morphological stability and represents a diffusion zone in which the atomic fraction of the noble component gradually increases as we approach the interface with the solution [6-9], According to the volume-diffusion model [10, 11], the formation of such zone is limited by the time-dependent interdiffusion of alloy components for the vacancy mechanism. 

The existence of an inter-diffusion zone at the interface, called an interphase, may also favour adhesion. We have already met this phenomenon when discussing metal-oxide interfaces. When a reactive wetting induces atomic displacements, the wetting angle is small... 

At the silicon nitride-titanium nitride interface a diffusion zone of interaction is observed. 

Most phenomena occur at the internal interface (A/B) however, in the case of decomposition, it is necessary to evacuate gas through layer B, which involves necessarily a diffusion zone (see Chapter 13). If there is gaseous emission, the process of adsorption-desorption is regarded as always present whereas in a gas-solid contact, it is necessary to consider the desorption of produced gas, located either on the surface of A if the gas diffuses through pores of B or on the stuface of B if the gas is produced at this interface after diffusion of point defects in B. 

The ojgrgen vacancy thus created diffuses from the rich vacancy zone (interface c) toward the poor vacancy zone (interface b), where the exchange of oxygen with AO lattice occurs as follows ... 

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