Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

# Microstructural effects

If a material contains grains, the grains will act as diffusion pathways, along which diffusion is faster than in the bulk material.

Consider a cylindrical grain of radius r and grain boundary thickness δ

The area of the grain boundary in the cross section is 2π r δ.

Every grain boundary is shared between two grains, so the total grain boundary area associated with one grain is π r δ.

The ratio of the area of the grain boundary to the bulk is:

$\frac{{\pi r\delta }}{{\pi {r^2}}} = \frac{\delta }{r} = \frac{{2\delta }}{d}$

The overall flux through unit cross-sectional area is the sum the fluxes through the bulk and the grain boundary:

$J = {J_\rm{b}} + {J_\rm{gb}}\frac{{2\delta }}{d}$

The derivation for this equation is here

Therefore:

${D_{{\rm{measured}}}} = {D_{\rm{b}}} + {D_{{\rm{gb}}}}\frac{{2\delta }}{d}$

It is important to realise that δ is very small, therefore grain boundary diffusion only becomes significant when Dgb >> Db, i.e. at low temperatures.

The following animation shows the effect of microstructure on diffusion at various temperatures:

Dislocations have a similar effect, providing fast diffusion paths due to the disruption in the lattice, again with only a significant effect at low temperatures.