Diffusion in Solids High-Diffusivity Paths

In general, the diffiisivity scales with the relative degree of constraint facing atoms in the close-packed 3D lattice. Thus, the following relationship is often a good rule 

The relative contribution of grain boundary versus bulk diffusion can be determined by taking a ratio of the two terms in Equation 4.84  

Question The goal of this problem is to use the simple grain bulk/grain boundary diffusion model discussed above to estimate the temperature above which bulk diffusion becomes more important than grain boundary diffusion. 

Solution (a) Inserting the equation for diffusivity (Equation 4.81) into the equation comparing the relative contributions from bulk-grain boundary diffusion (Equation 4.85) gives 

The purpose of this chapter was to introduce the basic concepts and tools used to understand and model the rate (or speed) of diffusion processes. The main points introduced in this chapter include the following  

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