Solid-state diffusion high-diffusivity paths

Key features of nanostructures that typically are exploited are a high surface area, a short solid state diffusion path, a high aspect ratio (ID materials), fast electron separation and transport, and fast switching of surface charges (inch oxidation state of the entire bulk nanostructure or its surface). Except for these conventional features, specific features to the nanoscale, namely quantum size effects, such as band-gap-widening or ballistic electron transport " may be the target of electrochemical processing. 

One limit of behavior considered in the models cited above is an entirely bulk path consisting of steps a—c—e in Figure 4. This asymptote corresponds to a situation where bulk oxygen absorption and solid-state diffusion is so facile that the bulk path dominates the overall electrode performance even when the surface path (b—d—f) is available due to existence of a TPB. Most of these models focus on steady-state behavior at moderate to high driving forces however, one exception is a model by Adler et al. which examines the consequences of the bulk-path assumption for the impedance and chemical capacitance of mixed-conducting electrodes. Because capacitance is such a strong measure of bulk involvement (see above), the results of this model are of particular interest to the present discussion. 

Solid-State Diffusion Coefficient 343 Temperature Dependence 343 Values of D for Lattice Diffusion 345 High Diffitsivify Paths 346... 

Numerous chemical reactions or micro-structural changes in solids take place through solid state diffusion, i.e. the movement and transport of atoms in solid phases. In crystalline solids, the diffusion takes place because of the presence of defects. Point defects, e.g. vacancies and interstitial ions, are responsible for lattice diffusion. Diffusion also takes place along line and surface defects which include grain boundaries, dislocations, inner and outer surfaces, etc. As diffusion along linear, planar and surface defects is generally faster than in the lattice, they are also termed high diffiisivity or easy diffusion paths. Another frequently used term is short circuit diffusion. 

Since ferrites possess a very high melting temperature, both reaction and densification usually take place in the solid state. Initial formation of the product occurs at the contact surface between particles of the two reactants. As reaction proceeds, the product layer becomes thicker, increasing the length of the diffusion paths of the reactants and thus... 

A small particle size of the reactant powders provides a high contact surface area for initiation of the solid state reaction diffusion paths are shorter, leading to more efficient completion of the reaction. Porosity is easily eliminated if the initial pores are very small. A narrow size... 

All solid state reactions, whether alloying or oxidation/reduction reactions, involve the formation of one or more product phases between the reactants. Without mechanical alloying, the reactant phases become separated and the reaction rate is determined by the contact area and the diffusion path length through the product phases. Diffusion through the product phases is invariably the rate-controlling process, and consequently high temperatures are required for flie reaction to occur at a measurable rate. 

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