Chapter 3 derived the diffusion equation with the assumption of random atom jumps. Solutions to the diffusion equation were presented, but the reader was warned that these solutions require a constant diffusion constant D, and this is rarely true as an alloy evolves during a phase transformation. There are other risks in using the diffusion equation when atom motions occur by the vacancy mechanism, where a mobile vacancy rearranges atoms in its wake. This chapter explains the nonrandomness of atom jumps with a vacancy mechanism, and these nonrandom characteristics occur even when the vacancy itself moves by random walk. Furthermore, in an alloy with chemical interactions strong enough to cause a phase transformation, the vacancy frequently resides in energetically favorable locations, so any assumption of random walk may be seriously in error.

When materials with different diffusivities are brought into contact, their interface is displaced with time because the fluxes of atoms across the interface are not equal in both directions. Other phenomena such as stresses and voids may develop during interdiffusion. An applied field can bias the diffusion process towards a particular direction, and such a bias can also be created by chemical interactions between atoms. Chapter 9 ends with two other topics of diffusion – one is atom diffusion that occurs in parallel with atom jumps forced without thermal activation, and the second is a venerable statistical mechanics model of diffusion that has components used today in many computer simulations of diffusion.