Diffusion in grain boundaries and dislocations

It can be seen drat the major difference lies in die activation energy being lower in the grain boundary. Data for a number of metals show that the activation energy for grain boundary diffusion is about one-half of that for volume diffusion. 

A formal derivation of diffusion in a restricted, high diffusivity path which uses no atomic model of the grain boundary is that due to Fisher, who made a flux balance in unit width of a grain boundary having a drickness of 5. There is flux accumulation in the element according to Pick s second law given by 

There is a loss of material along the jc direction at each face of the boundary and into the grains adjacent to the boundary given by 

An approximate, but sufficient, solution of dris equation for the thin tracer him experimental technique shows that the penetration curve has two components Ai, All and b being known constants. 

The hrst term predominates at low values of x and the long tail in the log c vs x plot which is normally used when only volume diffusion is 

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