example

hence, the rate of diffusion. Interstitial diffusion, with a low-activation
energy, usually occurs much faster than vacancy, or substitutional
diffusion. Activation energies are usually lower for atoms diffusing
through open crystal structures than for close-packed crystal structures.
Because the activation energy depends on the strength of atomic bonding,
it is higher for diffusion of atoms in materials with a high melting
temperature (Figure 5-17). We also find that, due to their smaller size,
cations (with a positive charge) often have higher diffusion coefficients
than those for anions (with a negative charge). In sodium chloride, for
instance, the activation energy for diffusion of chloride ions (Cl-) is about
twice that for diffusion of sodium ions (Na+).
Diffusion of ions also provides a transfer of electrical charge; in fact, the
electrical conductivity of ionically bonded ceramic materials is related to
temperature by an Arrhenius equation. As the temperature increases, the
ions diffuse more rapidly, electrical charge is transferred more quickly, and
the electrical conductivity is increased. As mentioned before, some
ceramic materials are good conductors of electricity.
Dependence on Concentration of Diffusing Species
and Composition of Matrix
The diffusion coefficient (D) depends not only on temperature, as given by
Equation 5-4, but also on the concentration of diffusing species and
composition of the matrix. The reader should consult higher-level
textbooks for more information.
Composition Profile [Fick’s Second Law]
Fick’s second law, which describes the dynamic, or non-steady state,
diffusion of atoms, is the differential equation
If we assume that the diffusion coefficient D is not a function of location x
and the concentration (c) of diffusing species, we can write a simplified
version of Fick’s second law as follows
The