Diffusion along interfaces

The role of grain boundary diffusion in stress relaxation in a thin polycrystalline film on a substrate is considered here, as a vehicle for illustrating the 

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Solid-solid noncatalytic reactions are important in ceramics manufacture. It appears that diffusion resistances may be important to some extent in all such systems. The diffusion process itself is hard to define in solid-solid systems, since at least two possibilities exist volume diffusion in the solid and surface diffusion along interfaces and crystal boundaries. Little is known about the kinetics of solid-solid reactions at the reacting interface because most measurements include diffusion effects. 

Secondly, based on Pick s first law, diffusion along interface of the grain contacts is defined in terms of the diffusive mass flux, dM iffldt, as (Yasuhara et al., 2003) ... 

Diffusion along interfaces But consistency of these two results requires that... 

Fig. 46 Schematic diagram of elemental process during transition from Hex cylinder to bcc sphere (i) undulation of interface (a, b), (ii) break-up of cylinders into ellipsoids (b, c), (iii) relaxation of domains from ellipsoids into spheres (c, d), and (iv) relaxation in junction distribution to attain uniform distribution (d, e). Pole where concentration of junction points is low may work as memory of grain conservation upon reverse transition from bcc sphere to Hex cylinder. Small arrows in part (b) indicate diffusion of chemical junctions along interface in process (ii). From [136], Copyright 2000 American Chemical Society...

Figure 12. Modeling and measurement of oxygen surface diffusion on Pt. (a) Model I adsorbed oxygen remains in equilibrium with the gas along the gas-exposed Pt surface but must diffuse along the Pt/YSZ interface to reach an active site for reduction. Model II adsorbed oxygen is reduced at the TPB but must diffuse there from the gas-exposed Pt surface, which becomes depleted of oxygen near the TPB due to a finite rate of adsorption, (b) Cotrell plot of current at a porous Pt electrode at 600 °C and = 10 atm vs time. The linear dependence of current with at short times implies semi-infinite diffusion, which is shown by the authors to be consistent only with Model II. (Reprinted with permission from ref 63. Copyright 1990 Electrochemical Society, Inc.)...

Since diffusion along the interface is negligible compared with that normal to the interface, the convective diffusion equation can be approximated by... 

Fig. 4.13. Schematic diagram to illustrate the process of intermetallic-layer formation in the Ni-Zn diffusion couple (a) before and (b) after its rupture along interface 4.

Adhesion promoters were first used to treat glass fibers and other fdlers before they are incorporated into liquid resin to make composite materials. In the fiber industry, adhesion promoters are also known as finishes. Certain finishes have been specially developed to match a fiber with a resin matrix. Without adhesion promoters, the interfacial resin-glass fiber adhesion is weak, and water can diffuse along the interface with catastrophic results on the end properties of the composite. 

The temperature distribution during crack propagation is shown in Fig. 15. As the crack advances, the heat continues to diffuse along the normal to the craze surfaces but the size of the hot zone remains comparable to that of the craze thickness. The maximum temperature increase is located at the crack/craze interface, where the craze thickening and related heat flux into the bulk are maxima. At this location, the temperature reaches the glass transition temperature Tg but plasticity is not enhanced in the bulk, which remains primarily elastic during crack propagation. 

Redox processes are important for elements which can exist in more than one oxidation state in natural waters, e.g. Fe and Fe, Mn, and Mn. These are termed redox-sensitive elements. The redox conditions in natural waters often affect the mobility of these elements since the inherent solubility of different oxidation states of an element may vary considerably. For example, Mn is soluble whereas Mn is highly insoluble. In oxic systems, Mn is precipitated in the form of oxyhydr-oxides. In anoxic systems, Mn predominates and is able to diffuse along concentration gradients both upwards and downwards in a water column. This behaviour gives rise to the classic concentration profiles observed for Mn (and Fe) at oxic-anoxic interfaces as illustrated in Figure 2. 

Chromia is thought to grow via outward diffusion of cahons from the metal to the oxide/ gas interface. When the scale formation proceeds by diffusion along short-circuit paths such as grain boundaries in the oxide layer, Eq. 1 describes the usual diffusion controlled oxidation kinetics ... 

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