
Diffusion
in solids is an atomic level transport process driven by chemical potential
gradients. The diffusing material may be an atom of the host lattice (self
diffusion) or an atom of another type (impurity diffusion). The diffusing
species move through the solid using either normal lattice sites or interstitial
sites. When normal lattice sites are used the transport process is mediated
by lattice vacancies. The interstitial process may involve either thermally
produced interstitials of lattice species (self interstitials) or interstitial
impurities.
The
macroscopic transport behavior is described by Fick's Laws. In steady state
diffusion, Fick's first law describes the flux, J, of material. In one
dimension this has the form: J
= D(T) dc/dx
where D(T) is the temperature dependent diffusion coefficient and (dc/dx)
is the concentration gradient of the diffusing species. Fick's second law
describes the change in concentration of the diffusing species as a function
of time in an element of the sample:
(dc/dt) = D(T) (d^{2}c/dx^{2}).
The
temperature dependent diffusion coefficient can be written as:
D(T) = D_{0}exp(Q/kT)
where D_{0} is a material
dependent, temperature independent parameter and Q is the activation energy
of the transport process in electron volts. For metals: 0.5 < Q <
3.0 eV; 10^{7} <
D_{0} < 10^{4}m^{2}/s 
