106 6·Atoms in Motion that this mode requires less lattice distortions and,thus,less en- ergy than a direct interchange. Self-Diffusion Diffusion involving the jump of atoms within a material con- and Volume sisting of only one element is called self-diffusion.(Self-diffusion can be studied by observing the motion of radioactive tracer Diffusion atoms,that is,isotopes of the same element as the nonradioac- tive host substance.)Diffusion within the bulk of materials is called volume diffusion. Grain Grain boundaries are characterized by a more open structure Boundary caused by the lower packing at places where two grains meet. They can be represented by a planar channel approximately two Diffusion atoms wide,as schematically depicted in Figure 6.2.Grain boundaries therefore provide a preferred path for diffusion.The respective mechanism is appropriately called grain boundary dif- fusion.It generally has an activation energy of only one-half of that found for volume diffusion since the energy of formation of vacancies Ef(see above)is close to zero.This amounts to a dif- fusion rate that may be many orders of magnitude larger than in the bulk,depending on the temperature.However,grain boundaries represent only a small part of the crystal volume,so that the contribution of grain boundary diffusion,at least at high temperatures,is quite small.As a rule of thumb,volume diffu- sion is predominant at temperatures above one-half of the melt- ing temperature,Tm,of the material,whereas grain boundary dif- fusion predominates below 0.5 Tn. Surface Further,free surfaces provide an even easier path for migrating Diffusion atoms.This results in an activation energy for surface diffusion that is again approximately only one-half of that for grain bound- FIGURE 6.2.Schematic representation of a pla- nar diffusion channel between two grains. (Grain boundary diffu- sion.)that this mode requires less lattice distortions and, thus, less en￾ergy than a direct interchange. Diffusion involving the jump of atoms within a material con￾sisting of only one element is called self-diffusion. (Self-diffusion can be studied by observing the motion of radioactive tracer atoms, that is, isotopes of the same element as the nonradioac￾tive host substance.) Diffusion within the bulk of materials is called volume diffusion. Grain boundaries are characterized by a more open structure caused by the lower packing at places where two grains meet. They can be represented by a planar channel approximately two atoms wide, as schematically depicted in Figure 6.2. Grain boundaries therefore provide a preferred path for diffusion. The respective mechanism is appropriately called grain boundary dif￾fusion. It generally has an activation energy of only one-half of that found for volume diffusion since the energy of formation of vacancies Ef (see above) is close to zero. This amounts to a dif￾fusion rate that may be many orders of magnitude larger than in the bulk, depending on the temperature. However, grain boundaries represent only a small part of the crystal volume, so that the contribution of grain boundary diffusion, at least at high temperatures, is quite small. As a rule of thumb, volume diffu￾sion is predominant at temperatures above one-half of the melt￾ing temperature, Tm, of the material, whereas grain boundary dif￾fusion predominates below 0.5 Tm. Further, free surfaces provide an even easier path for migrating atoms. This results in an activation energy for surface diffusion that is again approximately only one-half of that for grain bound￾Self-Diffusion and Volume Diffusion Grain Boundary Diffusion Surface Diffusion 106 6 • Atoms in Motion FIGURE 6.2. Schematic representation of a pla￾nar diffusion channel between two grains. (Grain boundary diffu￾sion.)