A microstructure is not as homogeneous as we think from a larger length scale. If it is possible to delve into the microscale, we can encounter various features like grain boundaries and dislocations. Diffusion through these features would be dif­ferent from the diffusion that takes place through the lattice interior or the bulk of the crystal.

2.3.6.1 Grain Boundary Diffusion

We have discussed the characteristics of grain boundaries in Section 2.2. Even though we have not fully covered grain boundary models, we can easily develop a picture of grain boundary where atoms are more loosely packed compared to the crystal interior. Grain boundary in itself is typically only a few atomic diameters in thickness. Naturally, it leads us to believe that atomic migration rates are greater in grain boundaries than in the grain interior or single crystals. In order to under­stand the effect of grain boundaries, one needs to compare the diffusion results between a single crystal and a polycrystalline material. Let us take an example involving the diffusion in single crystal and polycrystalline silver. The data were plotted as log(D) versus 1/T (a schematic plot is shown in Figure 2.51 without actual experimental data). The plot is a straight line for the single crystal across the temperature range studied, but the curve for the polycrystal coincides with the sin­gle crystal at the higher temperature range. However, with decreasing temperature, the diffusivity in the polycrystal silver becomes higher. It can only happen if the

grain boundary activation energy is lower than that for bulk diffusion. Equa­tion (2.50) expresses the diffusion data in single-crystal silver crystal, whereas Eq. (2.51) shows the diffusivity data in polycrystalline silver.

D = 0.9 exp(—1.99 eV/fcT) cm2 s—1 (2.50)

and

D = 0.9 exp(—1.01 eV/fcT) cm2 s—1. (2.51)

The equations above reflect the fact that at lower temperatures, the lower acti­vation energy for grain boundary diffusion lowers the overall activation energy and thus grain boundary diffusion becomes more dominant at lower tempera­tures. However, as the temperature is increased, the contribution of bulk diffu­sion becomes more dominant. That is why at higher temperatures, the grain boundary diffusion contribution becomes negligible compared to the bulk diffu­sion. Thus, one cannot see much change at all in the position of the curves (Figure 2.49) in the higher temperature range. For example, the grain boundary activation energy for bulk diffusion in aluminum is taken as 142kJmol—1, whereas the grain boundary activation energy for aluminum is only 84 kJ mol—1. However, grain boundary activation energy has been variously taken as 0.35­0.60 times the activation energy for lattice diffusion. It is worth noting that poly­crystals are generally composed of small grains oriented randomly with one another. Thus, when the diffusion rates are measured, it gives an average value of measurement over several grains, thus simulating a macroscopic isotropy of diffusion, even though diffusion in each grain (single crystal) in essence is highly anisotropic.

2.3.6.2 Dislocation Core Diffusion

Dislocation core structure is quite different from the lattice crystal structure. Diffusion along the dislocation core may provide a faster diffusion path and contribute to the overall diffusion, especially at lower temperatures. This type of diffusion is also known as pipe diffusion. Activation energy for the dislocation core diffusion is generally close to the activation energy for grain boundary diffusion.