The grain boundary diffusion coefficient is the diffusion coefficient of a diffusant along a grain boundary in a polycrystalline solid. It is a physical constant, and it is important in understanding how grain boundaries affect atomic diffusivity. Grain boundary diffusion is a commonly observed route for solute migration in polycrystalline materials. It dominates the effective diffusion rate at lower temperatures in metals and metal alloys. Take the apparent self-diffusion is the same in both types of samples. However, at temperatures below 700 with a single crystal.

Measurement

The general way to measure grain boundary diffusion coefficients was suggested by Fisher., and the depth is a unit length, the diffusion process can be described as the following formula. The first equation represents diffusion in the volume, while the second shows diffusion along the grain boundary, respectively.

is their concentration in the grain boundary.

To solve the equation, Whipple introduced an exact analytical solution. He assumed a constant surface composition, and used a Fourier–Laplace transform to obtain a solution in integral form. The diffusion profile therefore can be depicted by the following equation.

of different boundaries.

• .

• with the length of lattice penetration from the surface far from the boundary.

References

See also

• Kirkendall effect

• Phase transformations in solids

• Mass diffusivity