Lattice Diffusion from Particle Surfaces

As the source of material is the particle surface, there is no shrinkage even though the neck growth occurs by lattice diffusion. Under the same condition as that in Section 4.2.4, the following holds. 

In this mechanism, atoms evaporate from the sphere surface and the evaporated atoms condense in the neck region. When the distance between the 

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Lattice diffusion from particle surface to neck 5 lODlYsVmO X = 1 RT = C,D,a t 3... 

Fig. 5.10 Six distinct mechanisms can contribute to the sintering of a consolidated mass of crystalline particles 1 surface diffusion (5D), 2 lattice diffusion from the surface, 3 vapor transport, 4 grain boundary diffusion, 5 lattice diffusion from the grain boundary, and 6 plastic flow. Only mechanisms i to 5 lead to densification, but all cause the necks to grow and so influence the rate of densification. Reproduced with permission from [24]. Copyright 2007, Springer...

Figure 19.2 shows, at a microscopic level, what is going on. Atoms diffuse from the grain boundary which must form at each neck (since the particles which meet there have different orientations), and deposit in the pore, tending to fill it up. The atoms move by grain boundary diffusion (helped a little by lattice diffusion, which tends to be slower). The reduction in surface area drives the process, and the rate of diffusion controls its rate. This immediately tells us the two most important things we need to know about solid state sintering ... 

At normal temperatures H atoms are very mobile on metal surfaces. We take this into account by the possibility of diffusion steps for the H atoms. A H atom jumps with rate D/z onto the nearest neighbour sites on the lattice. If this site is occupied by N, reaction occurs and an A particle (NH particle) is formed. The same holds if the site is occupied by A or B (NH2) where the products B or NH3 = 0 are formed, respectively. NH3 desorbs immediately from the surface and an empty site is formed. That is we deal with the diffusion-limited reaction system. It is important to note that all the reaction steps discussed above (with the exception of the N2-adsorption) are independent of 7/ and 7m. 

In Fig. 9.16 the coverages of A and B and the production rate Rco2 are shown as a function of Yqo- We assume a large desorption rate kA = 0.05 and no diffusion (D = 0). For curve 1 we have EAA = EAb = 0, which corresponds to the case of the ZGB-model incorporating A-desorption. The value of yi is not shifted by the desorption because at this point too few A particles are present. Complete coverage of the lattice by A does not occur because at every time step A particles have the chance to desorb from the surface. Both facts are in agreement with the corresponding Monte Carlo simulations [15]. 

There is diffusion of salt away from both the solid-liquid interface and the vapor-liquid interface, in each case toward the brine. Water moves counterflow to the salt. Heat must transfer from solid to liquid to gas through stagnant films at the solid surface and through the turbulent liquid. An additional resistance to the formation of ice exists at the ice surface, where water molecules must orient themselves and find positions of low energy before being incorporated into the crystal lattice. When inadequate ice surface or foreign particles exist in the freezer, nucleation may control or affect the rate of ice production. 

The hairy particles stabilized by non-ionic emulsifier (electrosteric or steric stabilization) enhance the barrier for entering radicals and differ from the polymer particles stabilized by ionic emulsifier [35]. For example, the polymer lattices with the hairy interface have much smaller values of both the radical entry (p) and exit (kdes) rate coefficients as compared to the thin particle surface layer of the same size [128,129]. The decrease of p in the electrosterically stabilized lattices is ascribed to a hairy layer which reduces the diffusion of oligomeric radicals, so that these radicals may be terminated prior to actual entry. For the electrostatically stabilized lattices with the thin interfacial layer, exit of radicals occurs by the chain transfer reaction [35]. This chain transfer reaction results in a monomeric radical which then exits out of the particle by diffusing through the aqueous phase and this event is competing with the propagation reaction in the particle [130]. The decrease of kdes in the electrosterically stabilized latex... 

The main act of the electrochemical process, charge transfer, is localized in a very thin double electric layer. This process can take place continuously only when electrically active particles, that is, particles that participate in the charge transfer step are transferred toward the electrode, and the products formed move in the opposite direction - from the surface of the metal phase of the electrode to the solution volume. When electrochemical deposition of metal takes place in simple (noncomplex) salt solutions, there may be no transport of the product, because the metal atoms formed do not participate in the diffusion process, and they form a new solid phase - a crystal lattice. 

This diffuse double-layer approach can be applied to describe the EDL of particles, if charges on particle surface are only permanent structural surface charges originating from isomorphic substitutions of ions in a clay crystal lattice (e.g., montmorillonite, which is a typical example of infinite flat plates with a constant charge density [19]) or they form by the adsorption of potential determining ions (e.g., Ag+ ions on a Agl surface is an example of the case of charged particles with constant potential [1,33,38]) and the diffuse swarm of indifferent electrolyte ions compensates surface charges. 

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