The diffusion coefficient in solids at different temperatures is generally found to be well predicted by the Arrhenius equation:
where
*D is the diffusion coefficient (in m/s),
*D is the maximal diffusion coefficient (at infinite temperature; in m/s),
*E is the activation energy for diffusion (in J/mol),
*T is the absolute temperature (in K),
*R ≈ 8.31446J/(mol⋅K) is the universal gas constant.
Diffusion in crystalline solids, termed lattice diffusion, is commonly regarded to occur by two distinct mechanisms, interstitial and substitutional or vacancy diffusion. The former mechanism describes diffusion as the motion of the diffusing atoms between interstitial sites in the lattice of the solid it is diffusion into, the latter describes diffusion through a mechanism more analogue to that in liquids or gases: Any crystal at nonzero temperature will have a certain number of vacancy defects (i.e. empty sites on the lattice) due to the random vibrations of atoms on the lattice, an atom neighbouring a vacancy can spontaneously "jump" into the vacancy, such that the vacancy appears to move. By this process the atoms in the solid can move, and diffuse into each other. Of the two mechanisms, interstitial diffusion is typically more rapid.