Below the melting point, a pure metal is a crystal. Each atom vibrates around its lattice site. If you look at one atom, its motion is chaotic; the atom jiggles rapidly, once in this direction and then in another. Its vibration amplitude also changes from time to time. But if you look at many atoms, they appear to be a periodic lattice. That is, if you find one atom at a point, you'll almost certainly find another atom any multiple of the lattice spacing away. Well, almost. The crystal is imperfect. It has defects: vacancies, dislocations and grain boundaries. They are the imperfections in the nearly perfect crystal.

Next consider the motion of the vacancies. A tiny fraction of lattice sites are vacant. A vacancy can switch site with a neighboring atom. The vacancy may inject into the crystal from one surface, diffuse through the crystal, and emit from the crystal at another surface. In this lecture we assume that vacancies are the only defects in the crystal. That is, the solid is a single crystal and has no grain boundaries or dislocations. Vacancies can only be created and annihilated at the surface of the crystal.