Diffusion in grain boundary

An expression for creep may be given in terms of shear-strain rate and shear stress, when both lattice- and grain-boundary diffusion are involved in the deformation. For most poly crystalline materials, diffusion in grain boundaries is more rapid than in the lattice. 

Figure C2.11.6. The classic two-particle sintering model illustrating material transport and neck growtli at tire particle contacts resulting in coarsening (left) and densification (right) during sintering. Surface diffusion (a), evaporation-condensation (b), and volume diffusion (c) contribute to coarsening, while volume diffusion (d), grain boundary diffusion (e), solution-precipitation (f), and dislocation motion (g) contribute to densification.

Diffusion in the bulk crystals may sometimes be short circuited by diffusion down grain boundaries or dislocation cores. The boundary acts as a planar channel, about two atoms wide, with a local diffusion rate which can be as much as 10 times greater than in the bulk (Figs. 18.8 and 10.4). The dislocation core, too, can act as a high conductivity wire of cross-section about (2b), where b is the atom size (Fig. 18.9). Of course, their contribution to the total diffusive flux depends also on how many grain boundaries or dislocations there are when grains are small or dislocations numerous, their contribution becomes important. 

Fig. 7.37 Diffusion coefficients for some impurities in NiO grain boundaries compared with the corresponding lattice diffusivities (the grain boundary width is assumed to be I nm) (after...

Dienes 16) has calculated the energy of activation required for self-diffusion in graphite. For vacancy diffusion, E = 160 kcal. per mole. The treatment is not applicable to diffusion along grain boundaries or pores. 

Short-circuit diffusion along grain boundaries has been studied extensively via experiments and modeling. Because diffusion along dislocations and crystal surfaces is comparatively less well characterized, particular attention is paid to grainboundary transport in this chapter. However, briefer discussions of diffusion along dislocations and free surfaces are also presented. 

There are many situations, particularly at low temperatures, where short-circuit diffusion along grain boundaries and free surfaces is the dominant mode of diffusional transport and therefore controls important kinetic phenomena in materials ... 

Mass diffusion between grain boundaries in a polycrystal can be driven by an applied shear stress. The result of the mass transfer is a high-temperature permanent (plastic) deformation called diffusional creep. If the mass flux between grain boundaries occurs via the crystalline matrix (as in Section 16.1.3), the process is called Nabarro-Herring creep. If the mass flux is along the grain boundaries themselves via triple and quadjunctions (as in Sections 16.1.1 and 16.1.2), the process is called Coble creep. 

Obsidian and flints are natural glasses. Such samples show a uniform diffusion in any direction. In contrast, the diffusion of F into meteorites must be a function of the grain size of the material. The apparent diffusion is a mixture of volume diffusion and grain-boundary diffusion. Grain-boundary diffusion is much faster... 

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