Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-16 GTBL042-Callister-v2 September 17, 2007 17:32

Revised Pages

692 • Chapter 16 / Corrosion and Degradation of Materials

Metal

(M)

Oxide scale

(MO)

Gas

(O 2 )

M2+

e–

O2–

M M2+ + 2e– 21 O 2 + 2e– O2–

Figure 16.24 Schematic

representation of processes

that are involved in gaseous

oxidation at a metal surface.

and takes place at the scale–gas interface. A schematic representation of this metal–

scale–gas system is shown in Figure 16.24.

For the oxide layer to increase in thickness via Equation 16.28, it is necessary

that electrons be conducted to the scale–gas interface, at which point the reduction

reaction occurs; in addition, M^2 +ions must diffuse away from the metal–scale inter-

face, and/or O^2 −ions must diffuse toward this same interface (Figure 16.24).^5 Thus,

the oxide scale serves both as an electrolyte through which ions diffuse and as an

electrical circuit for the passage of electrons. Furthermore, the scale may protect the

metal from rapid oxidation when it acts as a barrier to ionic diffusion and/or electrical

conduction; most metal oxides are highly electrically insulative.

Scale Types

Rate of oxidation (i.e., the rate of film thickness increase) and the tendency of the

film to protect the metal from further oxidation are related to the relative volumes of

Pilling–Bedworth the oxide and metal. The ratio of these volumes, termed thePilling–Bedworth ratio,

ratio may be determined from the following expression:^6

P–B ratio=

AOρM

AMρO

(16.32)

Pilling–Bedworth

ratio for a divalent

metal—dependence

on the densities and

atomic/formula

weights of the metal

and its oxide

whereAOis the molecular (or formula) weight of the oxide,AMis the atomic weight

of the metal, andρOandρMare the oxide and metal densities, respectively. For metals

having P–B ratios less than unity, the oxide film tends to be porous and unprotective

because it is insufficient to fully cover the metal surface. If the ratio is greater than

(^5) Alternatively, electron holes (Section 12.10) and vacancies may diffuse instead of electrons
and ions.
(^6) For other than divalent metals, Equation 16.32 becomes
P–B ratio=
AOρM
aAMρO
(16.33)
Pilling–Bedworth
ratio for a metal that
is not divalent
whereais the coefficient of the metal species for the overall oxidation reaction described by
Equation 16.31.