text: Early diffusion models postulated that atomic motion in substitutional alloys occurs via a direct exchange mechanism, in which atoms migrate by switching positions with atoms on adjacent lattice sites.  Such a mechanism implies that the atomic fluxes of two different materials across an interface must be equal, as each atom moving across the interface causes another atom to move across in the other direction.
  Another possible diffusion mechanism involves lattice vacancies. An atom can move into a vacant lattice site, effectively causing the atom and the vacancy to switch places. If large-scale diffusion takes place in a material, there will be a flux of atoms in one direction and a flux of vacancies in the other.
  The Kirkendall effect arises when two distinct materials are placed next to each other and diffusion is allowed to take place between them. In general, the diffusion coefficients of the two materials in each other are not the same. This is only possible if diffusion occurs by a vacancy mechanism; if the atoms instead diffused by an exchange mechanism, they would cross the interface in pairs, so the diffusion rates would be identical, contrary to observation. By Fick's 1st law of diffusion, the flux of atoms from the material with the higher diffusion coefficient will be larger, so there will be a net flux of atoms from the material with the higher diffusion coefficient into the material with the lower diffusion coefficient. To balance this flux of atoms, there will be a flux of vacancies in the opposite direction—from the material with the lower diffusion coefficient into the material with the higher diffusion coefficient—resulting in an overall translation of the lattice relative to the environment in the direction of the material with the lower diffusion constant.
  Macroscopic evidence for the Kirkendall effect can be gathered by placing inert markers at the initial interface between the two materials, such as molybdenum markers at an interface between copper and brass. The diffusion coefficient of zinc is higher than the diffusion coefficient of copper in this case. Since zinc atoms leave the brass at a higher rate than copper atoms enter, the size of the brass region decreases as diffusion progresses. Relative to the molybdenum markers, the copper-brass interface moves toward the brass at an experimentally measurable rate.