Environmental Engineering Reference
In-Depth Information
or nonprotective oxide scale growth on the metal substrate. However, it was not
until 1933 and subsequently in 1936 that the pioneering theoretical relation for
the parabolic film/scale growth process was proposed by C. Wagner [19] for a
number of metal-oxidant systems at high temperatures. He proposed that for
thick scale formation, the reactions at metal-oxide and oxide-oxygen interfaces
are fast enough and migration of ionic or electronic species through the reaction
product layer should be the rate-limiting process for subsequent thickening of the
film/scale. This mathematical formulation marked the beginning of theoretical
developments in the field of oxidation and tarnishing reactions of metals and
alloys. It was rightly pointed out by Wagner that the migration mechanism must
be closely related to the types and concentrations of point defects in the growing
product lattice and is controlled by the difference in electrochemical potentials
between the metal/scale and scale/gas phase boundaries. It is also known from
the chemical physics of semiconductors and ionic compounds that the presence
of a favorable electrical field across the growing layer tends to increase the mobil-
ity of ions and electrons via lattice imperfection and complementary electronic
defect in the crystalline solids of the reaction product. Thus, measurements of
electrical conductivity, Hall coefficient, and thermoelectric power of the solid
reaction product with identification of the relative position of an inert marker
within the compact scale would provide enough information as to the kind and
extent of lattice defects present in product compounds. These would help in draw-
ing conclusions about the type and extent of migration process for ions and elec-
trons in the scaling layer.
Through an elaborate mathematical treatment, Wagner could correlate the par-
abolic rate constant with some of the physical parameters of the scale that are
highly dependent on the types and concentrations of point defects in the growing
film/scale. In deriving the parabolic law for thick film or scale growth process,
he considered the diffusing species to be essentially induced to migrate through
the growing film by the action of two kinds of driving forces. The first one is a
chemical potential gradient that is set up across the layer as a result of attainment
of equilibrium conditions at the two reaction interfaces, i.e., metal/scale and
scale/gas, respectively. The second is an electrical potential gradient that arises
due to the formation of negatively charged ionized species of the oxidant at the
outer interface of the scale at the expense of electrons available from the metal
through the conduction band of the product layer. The occurrence of such chemi-
cal potential gradients or concentration gradients is schematically illustrated in
Fig. 5.14a and 5.14b for oxide scales having a predominance of metal vacancies
and oxidant vacancies, respectively. The partial pressures of oxygen at the metal-
oxide interface as depicted in Fig. 5.14a and 5.14b refer to the equilibrium disso-
ciation pressure of the oxide in contact with the metal substrate [
P
(d)
O
2
], whereas
the corresponding ones at the oxide-oxygen interface refer to the oxygen pres-
