Environmental Engineering Reference
In-Depth Information
sures prevailing in the gas phase [
P
(g)
O
2
]. For an oxide scale with a predominance
of metal vacancies, the metal ions diffuse outward from the M/MO to MO/O
2
(g)
interface. The metal vacancies created at the outer surface migrate in the oppo-
site direction and their equilibrium concentrations at the interfaces are given by
the relevant defect equilibrium as presented in Fig. 5.14a. Since normally
P
(g)
O
2
, the metal vacancies are continuously produced at the MO-O
2
(g)
interface and are consumed or annihilated at the M-MO interface.
On the other hand, oxygen ion vacancies migrate in opposite direction to the
metal ion vacancies and their equilibrium concentrations at the two reaction inter-
faces of the oxide are presented in Fig. 5.14b. In such a system, oxygen vacancies
are continuously created at the M/MO phase boundary and are simultaneously
consumed at the MO-O
2
(g) interface because
P
(d)
O
2
O
2
P
(d)
P
(g)
O
2
.
For thick film or scale formation at relatively high temperatures, of the above-
mentioned two driving forces, the contribution from electrical field to the film
growth process becomes negligible. Therefore, under such a situation, thermally
aided diffusion of ionic or electronic species due to the existence of a chemical
potential gradient provides the major driving force. If the temperature is too low,
diffusion of ions is not easily possible due to lack of thermal activation. Under
such circumstances, Wagner's parabolic law [19] is not satisfied. This indirectly
brings a thought in one's mind regarding two additional factors that need consid-
eration. The first is the type of migrating species (electrons, positive holes, ions,
vacancies, interstitials, etc.) and the second is the necessary thermal energy,
which is again highly dependent on the nature of the product layer, i.e., on some
of its physical and chemical properties. As was pointed out by Wagner, the mi-
grating or diffusing species in a tarnishing or scaling layer are usually the cations,
anions, electrons, or positive holes. The slowest moving species automatically
controls the movement of other species, as otherwise the charge neutrality condi-
tion will not be maintained in the bulk film. The absence of associated species
or defects has also been assumed.
5.5.1 Thick Scale Formation Mechanism; Wagner's
Parabolic Law and Its Applications
The basic assumptions of Wagner's parabolic law [19] are as follows:
1.
Scale should be adherent to the metal substrate, compact and nonporous in
nature such that solid state diffusional transport through the product lattice
remains the main process.
2.
Phase boundary reactions being quite fast, equilibrium attainment at the
metal-scale and scale-gas interfaces is assumed to be true.
3.
Since thick scale formation is being considered, the chemical potential gradi-
ent across it acts as the major driving force, with a minimal contribution
from electrical field gradient.
