5.01

Corrosion and Compatibility

S. Lillard
Los Alamos National Laboratory, Los Alamos, NM, USA

ß 2012 Elsevier Ltd. All rights reserved.

2

5.01.1

Theory

5.01.1.1
5.01.1.2
5.01.1.3
5.01.1.4
5.01.1.5
5.01.1.6
5.01.2
5.01.2.1
5.01.2.2
5.01.2.3
5.01.2.4
References

Introduction
Half Cell Reactions
Cell Potentials and the Nernst Equation

Reference Electrodes and Their Application to Nuclear Systems
The Thermodynamics of Corrosion from Room Temperature to the PWR
Kinetics of Dissolution and Passive Film Formation
Analytical Methods
Introduction
Potentiodynamic Polarization
Electrochemical Impedance Spectroscopy
Mott–Schottky Analysis

Abbreviations
BWR
CNLS

Boiling water reactor
Complex nonlinear least squares fitting of
the data
EC
Electrical equivalent circuit
EIS
Electrochemical impedance
spectroscopy
EPBRE External pressure-balanced reference
electrode
FFTF
Fast Flux Test Facility
HIC
Hydrogen-induced cracking
HIFER Hi-Flux Isotope Reactor
IG
Intergranular

LBE
Lead–bismuth eutectic
PWR
Pressurized water reactor
SCC
Stress corrosion cracking
SS
Stainless steel

Symbols
A
ai
C
ci
CR
E
EW
Ecorr
f

Surface area
Activity of species i
Capacitance
Concentration of species i
Corrosion rate
Potential
Equivalent weight
Corrosion potential
Mass fraction


ƒ
F
i
icorr
ji
k
L
M
MM
n
ND
Q
r
R
Rp
RV
S
t
ti
T
Vo
z
Z
Z0
Z00
jZj
b
ba
bc
d


2
2
3
4
6
8
10
10
11
12
14
16

Fugacity
Faraday’s constant
Current density
Corrosion current density
Square root of À1
Rate constant
Oxide thickness
Molecular weight
Metal cation
Number of electrons
Donor concentration
Reaction quotient
Rate of reaction
Gas constant
Polarization resistance
Solution resistance

Entropy of transport
Time
Transport number of species i
Temperature
Oxygen vacancy
Charge
Impedance
Real part of the impedance
Imaginary part of the impedance
Magnitude of the impedance
Symmetry factor
Anodic Tafel slope
Cathodic Tafel slope
Double layer thickness

1


2

Corrosion and Compatibility
0

DCp Change in standard partial molar heat
capacity
DE0 Standard reduction potential
DG Change in Gibbs energy
DG0 Standard Gibbs energy
DS0 Standard entropy change
«

Electronic charge
Permittivity of space
«0
f
Applied potential
h
Overpotential
u
Phase angle
r
Material density
v
Frequency

5.01.1 Theory
5.01.1.1

Introduction

Mars Fontana identified eight forms of corrosion in
his book Corrosion Engineering1 and it is quite easy
to find examples of almost all of these in nuclear
reactors in both the primary and secondary cooling
water systems. For example, galvanic corrosion in
zirconiumÀstainless steel couples,2,3 crevice corrosion in tube sheets4 and former baffle bolts,5 and
pitting corrosion in alloy 600 steam generator
tubes.6,7 Perhaps the most infamous form of corrosion
observed in nuclear reactors is stress corrosion cracking (SCC), or environmental fracture, as we shall
refer to it here, which has numerous examples in
the literature. Environmental fracture includes both

intergranular SCC (IG), such as that which occurs in
austenitic stainless steel, and hydrogen-induced cracking (HIC), frequently observed in nickel base alloys.
Failure by one of these mechanisms results from an
interplay between stress, microstructure, and the environment (e.g., the electrochemical interface). The goal
of this chapter is not to address each of the corrosion
mechanisms outlined by Fontana individually, that will
be accomplished in the following chapters. Rather,
this chapter is meant to provide the reader with the
fundamental electrochemical theory necessary to
critically evaluate the data and discussions in the
corrosion chapters that follow.
In this section, we will review the fundamental
theory of the electrochemical interface. In the first
three subsections, we review Half Cell Reaction, Cell
Potentials and the Nernst Equation, and Reference
Electrodes in Nuclear Systems. In these sections, we
develop the theory necessary to understand the role of
electrochemical potential in environmental fracture

and corrosion mechanisms. For example, intergranular
stress corrosion cracking (IGSCC) is only observed at
potentials more positive than a critical value while HIC
is only observed at potentials more negative than a
critical value. In the remaining two sections, we review
the Thermodynamics from Room Temperature to the
pressurized water reactor (PWR) and Kinetics of Dissolution and Passive Film Formation. These sections
should help the reader to understand the role of the
passive film in the corrosion mechanism and the competition that occurs between film formation and metal
dissolution rate. As the fundamental role of irradiation
in corrosion and environmental fracture mechanism is

far from well established, in each section, we incorporate empirical irradiation data as examples and discuss
concepts that are more broadly important to nuclear
systems.
5.01.1.2

Half Cell Reactions

The electrochemical interface is characterized by an
electrode (in this case a metal such as a cooling pipe)
and an electrolyte (e.g., the cooling water in a reactor). While the bulk electrolyte contributes to variables such as solution chemistry and ohmic drop
(solution resistance is discussed later in this chapter),
it is the first nanometer of electrolyte that plays the
most important role in electrochemistry. In this short
distance, referred to as the electrochemical double
layer, a separation of charge occurs. It is this separation of charge that provides the driving force
(potential drop) for corrosion reactions. For example,
a 100 mV-applied potential across a typical double
layer will result in an electric field on the order of
106 V cmÀ2. In the model proposed by Helmholtz,8
the double layer may be thought of as capacitor, with
positive charge on the metal electrode and the
adsorption of negatively charged cations on the solution side (Figure 1). The capacitance of the double
layer is equal to that in its electrical analog e0D/d,
where e0 is the permittivity of space, D is the dielectric, and d is the thickness of the layer. For most
electrochemical double layers, C is on the order of
10À6 F cmÀ2.
Electrochemical reactions that take place in the
double layer are reactions in which a transfer of
charge (electrons) occurs. There are two different
types of cells in which electrochemical reactions

may occur9:
Electrolytic cells in which work, in the form of electrical
energy, is required to bring about a nonspontaneous reaction.


Corrosion and Compatibility

Metal

Because the system cannot store charge, the electrons
produced during the anodic reaction must be used.
This occurs at the cathode where typical reactions
may include oxygen reduction:

Excess negative
charge

Excess positive
charge

Bulk solution

+

-

+

-


+

-

+

-

+

-

+

+

-

+

Acid: O2 þ 4Hþ þ 4eÀ ) 2H2 O

-

Base: O2 þ 2H2 O þ 4eÀ ) 4OHÀ
+

-

3


½IIŠ
½IIIŠ

or hydrogen reduction:
2Hþ þ 2eÀ ) H2

fmetal

½IVŠ

From eqns [I] and [III], the general corrosion of an
Fe surface in basic solution may then be written as:
2Fe þ O2 þ 2H2 O ) 2FeðOHÞ2

fsolution
Double
layer
Figure 1 A diagram depicting the separation of charge at
the electrochemical double layer and the associated
potential drop (f).

H2O
2H+

ClH2

H2O
H+


H2O

ClH2O

Cl-

5.01.1.3 Cell Potentials and the Nernst
Equation

Oxide
Fe

For any chemical reaction the driving force, the
Gibbs energy, may be written as10:

Figure 2 Diagram of what the anodic and cathodic
reactions may look like on an iron surface depicting the
separation of reactions and ionic conduction.

DG ¼ DG 0 þ RT lnQ

Voltaic cells in which a spontaneous reaction occurs
resulting in work in the form of electrical energy.
Electrolytic cells cover a fairly large number of
electrochemical reactions but may generally be
thought of as ‘plating’ or ‘electrolysis’ type reactions
and will not be treated here. Corrosion reactions are
voltaic cells and will be the focus of this chapter. As in
an electrolytic cell, voltaic cells are characterized by
two separate electrodes, an anode and a cathode. In

corrosion, reactions at the anode take the form of
metal dissolution, the formation of a soluble metal
cation:
Fe ) Feþ2 þ 2eÀ

where Fe(OH)2 is the corrosion product.
An example of what the anodic and cathodic reactions on Fe electrode might look like is presented in
Figure 2. Though the anodic and cathodic reactions
occur at physically separate locations, as shown in
this figure, the reactions must be connected via an
electrolyte (aqueous solution). Figure 2 also suggests
that corrosion reactions are controlled by variables
such as mass transport (diffusion, convection, migration), concentration, and ohmic drop (resistivity of
the electrolyte). These variables will be considered in
our discussion of corrosion kinetics.

H+

Fe2+

e-

½VŠ

½IŠ

½1Š

where DG0 is the standard Gibbs energy, Q is the
reaction quotient equal to the product of the activities (assumed to obey Raoult’s Law for dilute solutions and, thus, equal to the concentration) of the

products divided by the reactants, R is the gas constant, and T is temperature. The electrical potential,
E, is related to the Gibbs energy of a cell by the
relationship:
nFE ¼ ÀDG

½2Š

where n is the number of electrons participating
in the reaction and F is Faraday’s constant. For the
reduction of hydrogen on platinum:
1
þ
þ eÀ ðPtÞ , H2ðgÞ
Haq
2

½VIŠ


4

Corrosion and Compatibility

The reaction quotient, Q (starting conditions) becomes:
Q ¼

½fH2 Š1=2
½Hþ Š

½3Š


where fH2 is the fugacity of hydrogen gas. Substituting
eqns [2] and [3] into eqn [1], we find for the reduction
of hydrogen on platinum that:
"
#
RT ½fH2 Š1=2
0
½4Š
ln
E ¼ DE þ
½Hþ Š
F
where F is Faraday’s constant and DE0 is the standard
reduction potential for the reaction in eqn [VI]. Equation [10] is commonly referred to as the Nernst equation and defines the equilibrium reduction potential of
the half cell and is pH dependent. The Nernst equation
is commonly expressed in its generalized form as:
E ¼ DE 0 þ

RT
ln½Q Š
F

½5Š

5.01.1.4 Reference Electrodes and Their
Application to Nuclear Systems
In Equation [4], all of the parameters are easily
calculated with one exception, DE0. Therefore, we
define DE0 ¼ 0 in eqn [4] for a set of specific parameters and refer to this cell as the standard hydrogen

electrode (SHE): H2 pressure of 1 atm, a pH ¼ 0, and
a temperature of 25  C. This provides a reference
from which we can calculate the standard potentials
for all other reduction reactions using eqn [5]. These
are referred to as standard reduction potentials and a
few examples are provided in Table 1.
While the SHE is the accepted standard, from
a practical standpoint, this reference electrode is
difficult to construct and maintain. As such, experimentalists have taken advantage of a number of other
reduction reactions to construct reference electrodes
for laboratory use. The reaction selected typically
depends on the application. One common reference
electrode is the silver–silver chloride electrode
(Ag/AgCl) which is based on the reduction of Agþ
in a solution of potassium chloride:
Agþ þ eÀ , AgðsÞ

½VIIŠ

Agþ þ ClÀ , AgClðsÞ

½VIIIŠ

and the overall reaction being:
AgðsÞ þ ClÀ , AgClðsÞ þ eÀ

½XIŠ

Table 1
Standard reduction potentials for several reactions important to the nuclear power industry

Reduction reaction

Standard reduction
potential (V)

Au3þ þ 3eÀ ⇄ Au
Cl2 þ 2eÀ ⇄ 2ClÀ
O2 þ 4Hþ þ 4eÀ ⇄ 2H2O
Agþ þ eÀ ⇄ Ag
Fe3þ þ eÀ ⇄ Fe2þ
O2 þ 2H2O þ 4eÀ ⇄ 4OHÀ
AgCl þ eÀ ⇄ Ag þ ClÀ
2Hþ þ 2eÀ ⇄ H2 (NHE)
Ni2þ þ 2eÀ ⇄ Ni
Fe2þ þ 2eÀ ⇄ Fe
Cr3þ þ 3eÀ ⇄ Cr
Zr4þ þ 4eÀ ⇄ Zr
Al3þ þ 3eÀ ⇄ Al
Liþ þ eÀ ⇄ Li

1.52
1.36
1.23
0.80
0.77
0.4
0.22
0.0
À0.25
À0.44

À0.74
À1.53
À1.66
À3.04

The Nernst equation for eqn [XI] is equal to:


½aAgCl Š
RT
0
E ¼ DEAg=AgCl þ
ln
½aAg Š½aClÀ Š
F
0
¼ DEAg=AgCl
À ln½aClÀ Š

½6Š

where aClÀ is the activity of chloride and for which
the concentration (mClÀ ) in molal (mol kgÀ1) is frequently substituted. In the corrosion lab, the reference electrode is constructed by electrochemically
depositing an AgCl layer onto a silver wire. This
wire is then placed in a glass capillary filled with a
solution of potassium chloride the concentration of
which then defines the cell potential (aClÀ in eqn [6]).
One end of the capillary is sealed using a porous frit
(typically a porous polymer) that acts as a junction
between the solution of the reference electrode and

the environment of the corrosion experiment.
While the Ag/AgCl reference electrode construction described above is straightforward for the lab,
there are several obstacles that must be overcome
before it can be used in a nuclear power plant setting,
namely, radiation flux, pressure, and temperature. As it
turns out, the primary impact of ionizing radiation
on laboratory reference electrodes relates to damage
of the cotton wadding and polymer frits used in their
construction and no change in cell potential occurs.11
As such, two approaches based on the Ag/AgCl
reference electrode have been used to measure electrode potential in nuclear power reactors. In the first
approach, an internal reference electrode operates in
the same high-temperature environment as the reactor. In this case, one must consider the solubility of


Corrosion and Compatibility

Sapphire lid
AgCl pellet

5

Rulon adapter
Compression fitting

Sapphire
container

Pt cap
Ni wire

Alumina
insulators

Ceramic to
metal braze
Restrainer

Ag/AgCl

Kovar
TIG weld
304SS

Seal

Coaxial
cable
Figure 3 Diagram of an internal Ag/AgCl reference
electrode used in BWRs. Top end is inserted into the cooling
loop, while the coaxial cable provides electrical connection.
Reprinted from Indig, M. E. In 12th International Corrosion
Congress, Corrosion Control for Low-Cost Reliability; NACE
International: Houston, TX, 1993; p 4224, with permission
from NACE International.

Ag/Cl complexes that form as a function of temperature eqn [6].12,13 That is, reactions in addition to eqns
[VIII] and [XI] must be considered. From a construction viewpoint, the internal reference electrode
consists of a silver chloride pellet on a platinum foil
(Figure 3).14 External potential measurement is made
via contact with a nickel wire which is connected to an

electrometer via a coaxial cable. The electrode is
housed in a sapphire tube that is sealed via a porous
sapphire cap. In this configuration, there is no internal
electrolyte per se. Upon placing the electrode in a
boiling water reactor (BWR), the porous cap allows
the cooling water to penetrate the electrode and the
potential is determined from eqn [6] and the solubility
of AgCl in high purity water as a function of
temperature.15
In the second approach, an external pressurebalanced reference electrode is used (EPBRE).
In the EPBRE, the reference electrode is maintained
at room temperature and pressure and the corresponding constants are used in eqn [6]. The
reference is connected to the high-temperature environment via a nonisothermal salt bridge sealed with a
porous zirconia plug (Figure 4).16 As a result of this
configuration, the EPBRE is not susceptible to

Compression fitting
1/4ЈЈ NPT
Pure water or
0.01 M KCl
Glass wick
1/4ЈЈ OD SS
tube

Heat-shrinkable
PTFE tube

SS nut
Rulon sleeve
Zirconia plug


Figure 4 A diagram of a pressure-balanced reference
electrode is used in BWRs. Bottom of figure is sealed into
pressure vessel via compression fitting while Ag/AgCl
electrode (top) remains at room temperature and pressure.
Reprinted from Oh, S. H.; Bahn, C. B.; Hwang, I. S.
J. Electrochem. Soc. 2003, 150, E321, with permission from
The Electrochemical Society.

potential deviations owing to the solubility of AgCl
and its complexes as a function of temperature. However, the temperature gradient between the reactor
and the reference electrode results in a junction
potential that must be subtracted from eqn [6]. The
corresponding thermal liquid junction potential
(ETLJ)17 is given by:

ð 
1 T2 tMþ SMþ tClÀ SClÀ
dT
½7Š
ETLJ ¼ À
þ
zMþ
zClÀ
F T1
where t, S, and z represent the transport number, the
entropy of transport, and the charge on the cation,
respectively. The symbol M in eqn [7] represents the
metal in the chloride salt, MCl, and is commonly Li, Na,
or K. In addition to ETLJ, there is also the isothermal

liquid junction potential, EILJ, which arises due to the
differences in cation and anion mobilities through
the porous frits and the fact that the electrolyte in the
external reference (typically KCl) is vastly different
from the reactor cooling water in which it is immersed17:
ð
RT T2 ti
EILJ ¼ À
dln½ai Š
½8Š
F T1 zi


6

Corrosion and Compatibility

where the subscript i denotes a species that may be
transported through the zirconia plug and for a nuclear
power reactor may include species ions as Agþ, ClÀ,
Hþ, OHÀ, Kþ, and B(OH4)À.
It has been shown that both ETLJ and EILJ each
increase by as much as 0.15 V over the temperature
range of 25–350  C. The result is a decrease in the
measured potential of 0.30 V at 350  C. While these
junction potentials can be calculated and used to
correct eqn [7], it has been shown that there is
some deviation at higher temperatures (>200  C)
and an experimental fitting procedure is the preferred method for calibration of the reference
electrode.


reactions with two soluble species
 3þ 
Fe
½11Š
Fe2þ ¼ Fe3þ þ eÀ E 0 ¼ 0:771 þ 0:059log
Fe2þ

solubility of iron and its oxides
Fe ¼ Fe2þ þ 2eÀ E 0 ¼ À0:440 þ 0:0295logðFe2þ Þ

2Fe2þ þ 3H2 O ¼ Fe2 O3 þ 6Hþ þ 2eÀ
E 0 ¼ 0:728 À 0:177pH À 0:059logðFe2þ Þ

An atlas of electrochemical equilibria has been created by M. Pourbaix for metals in aqueous solution at
room temperature.18 This atlas contains potential–
pH diagrams, so-called Pourbaix diagrams, which
define three equilibrium thermodynamic domains
for metals in aqueous solutions: immunity, passivity,
and corrosion. Immunity is defined as the state where
the base metal is stable while corrosion is defined
as the formation of soluble metal cations and passivity the formation of a stable oxide film. Pourbaix’s
derivation requires that the values of the standard
chemical potential, m0, for all of the reacting substances are known for the standard state at the
temperature and pressure of interest. For chemical
reactions at room temperature, the equilibrium conditions are defined by the relationship18:
P 0
nm
½9Š
logK ¼

5708
and for electrochemical reactions at room temperature (Table 1) equilibrium is defined by:
P 0
nm
0
½10Š
E ¼
96485n
where K is the equilibrium constant for the reaction,
m0 is in Joules per mole, v is the stoichiometric coefficient for the species, n is the number of electrons, 5708
is a conversion constant equal to RT/(log10e) where
T is temperature (298.15 K) and R the ideal gas constant (8.314472 J (K mol)À1), and 96 485 is Faraday’s
constant in J (mol V)À1.
As an example of these diagrams, consider the
iron–water system and the solid substances Fe,
Fe3O4, and Fe2O3. Pourbaix18 defined the relevant
equations for this system as:

½13Š

þ
À
Fe þ 2H2 O ¼ HFeOÀ
2 þ 3H þ 2e

E 0 ¼ 0:493 À 0:089pH þ 0:0295log½HFeOÀ
2Š

5.01.1.5 The Thermodynamics of Corrosion
from Room Temperature to the PWR


½12Š

½14Š

þ
À
3HFeOÀ
2 þ H ¼ Fe3 O4 þ 2H2 O þ 2e

E 0 ¼ À1:819 þ 0:029pH À 0:088log½HFeOÀ
2Š

½15Š

reaction of two solid substances
3Fe þ 4H2 O ¼ Fe3 O4 þ 8Hþ þ 8eÀ
E 0 ¼ À0:085 À 0:059pH

½16Š

2Fe3 O4 þ H2 O ¼ 3Fe2 O3 þ Hþ þ 2eÀ
E 0 ¼ 0:221 À 0:059pH

½17Š

An example of a simplified Pourbaix diagram for Fe
at room temperature based on the reactions in eqns
[11]–[17] is presented in Figure 5, where Eq. [12]
corresponds to figure line 23, [13] to line 28, [14] to

line 24, [15] to line 27, [16] to line 13 and [17] to line
17. Note that Eq. [11] is the boundary between Fe2þ
and Fe3þ and was not drawn in the original figure.
In addition to the lines separating the domains for Fe,
Pourbaix diagrams will typically include the domains
associated with water stability (oxidation and reduction) represented by the dashed lines marked a and b
in Figure 5. Upon inspection of this diagram one
would conclude what is know from experience with
Fe: that iron is passive in alkaline solutions and at
higher applied potentials owing to oxide film formation while at more acidic solutions Fe is susceptible to
corrosion owing to Fe2þ. It is worth noting again that
these potential–pH domains are defined solely by the
thermodynamic stability of the species within them
and these diagrams do not consider kinetics which
will be addressed later in this chapter. This is important as while a species/reaction may be thermodynamically stable it may be kinetically hindered.
While the use of Pourbaix diagrams to characterize room temperature corrosion reactions is


Corrosion and Compatibility

1.5

Fe3+

1.5

Fe3+
20

7


20

1.0

1.0
b

Fe2O3

Fe2+

0

EH2 (200 ЊC) (V)

28

2

EH (25 ЊC) (V)

0.5

a
26

-0.5

17

Fe3O4

23

0.5

0

Fe2+

26

13

-1.0

HFeO-2

17

Fe3O4

23
27
24

Fe

Fe2O3
a


-0.5

13

-1.0

b

28

Fe

HFeO22-

-1.5

-1.5
0

5

10

15

pH

widespread, these diagrams and the method for generating them as presented thus far cannot be used at
the higher temperatures associated with nuclear power

reactors. This is due to the lack of standard potentials
at elevated temperature as required by eqns [9] and
[10] (e.g., the application of Table 1 to higher temperature). In the absence of these high-temperature thermodynamic data, Townsend19 used an extrapolation
method introduced by Criss and Coble (the correspondence principle). The method allows for empirical
entropy data of ionic species at 25  C to be extrapolated to higher temperatures. In this method, the standard Gibbs free energy is calculated from the
relationship:
ð

ÀT

ðT
250

0

T

250

DC p ðT ÞdlnT

0

DC p ðT ÞdT
½18Š
0

where DS is the standard entropy change and DC p is
the change in standard partial molar heat capacity. The
potential–pH diagram for the Fe–H2O system and the

solid substances Fe, Fe3O4, and Fe2O3 at 200  C calculated by Townsend is presented in Figure 6. In comparison with the diagram at 25  C (Figure 5), the
Fe2O3 and Fe3O4 regions are extended to lower pH
and potentials. As a result the area associated with
corrosion at lower solution pH is decreased. However,
0

24

5

10

15

pH

Figure 5 A simplified potential–pH diagram for the
Fe–H2O system and the solid substances Fe, Fe3O4, and
Fe2O3 at 25  C based on the reactions in eqns [11]–[17].
Reprinted from Townsend, H. E. Corrosion Sci. 1970,
10, 343, with permission from Elsevier.

DðDG 0 Þ ¼ À DT DS 0 ð250 Þ þ

0

29

27


Figure 6 The potential–pH diagram for the Fe–H2O
system and the solid substances Fe, Fe3O4, and Fe2O3 at
200  C. Most dramatic influence of increased temperature is
the presence of a large region of soluble species (corrosion)
at high pH. Reprinted from Townsend, H. E. Corrosion Sci.
1970, 10, 343, with permission from Elsevier.

the most notable change in the diagram is at high pH
where the area associated with corrosion owing to the
soluble HFeOÀ
2 has increased dramatically. The Criss
and Coble method is limited, however, to the
150–200  C range and, to extend the Pourbaix to the
temperatures of power reactors, Beverskog used a
Helgeson–Kirkham–Flowers model to extend the
heat capacity data to 300  C.20
Thus far, we have described a method for generating electrochemical equilibria diagrams and regions
of passivity, corrosion, and immunity for pure metals
from 25 to 300  C. From an engineering standpoint,
we would like to know this information for structural
alloys such as austenitic stainless steels and super
nickel alloys. At temperatures near 25  C, the predominant oxide responsible for passivity is Cr2O3 and it is
sufficient to rely only on the Cr potential–pH diagram
for alloys with a high Cr content. However, at higher
temperatures other oxides form such as Fe(Fe,Cr)2O4,
(Cr,Fe)2O3, (Cr,Fe,Ni)3O4, and (Cr,Fe,Ni)2O3, and it is
desirable to know the thermodynamic stability of the
alloy. Beverskog has developed the ternary potential–
pH diagrams for the Fe–Cr–Ni–H2O–H2 system for
temperatures up to 300  C using heat capacitance data

and the revised Helgeson–Kirkham–Flowers model
described above.21 However, Fe–Cr–Ni phases lack
thermodynamic data and the ternary oxides were,


8

Corrosion and Compatibility

npH
2

H2CrO4(aq)
HCrO4-

Potential (VSHE)

1

CrO42-

where ia is the anodic current density, ka is the rate
constant, co is the concentration of oxidized species,
and DGa is the change in free energy for the anodic
reaction. Substituting G2a À G1a in eqn [20] for DGa in
eqn [19], we express the anodic reaction rate as22:


ð1 À bÞnF


½21Š
ia ¼ nFka cR exp
RT

Cr(OH)2+
0
NiCr2O4(cr)
Cr2+

FeCr2O4(cr)

-1

Cr2O3(cr)
Cr(cr)
-2

0

2

4

6
pH300 ЊC

8

decreasing the barrier, that is, not all of the applied
potential is dropped across the electrochemical double layer. The rate (ra) of this reaction is expressed in

the same, Arrhenius, form as for chemical reactions:


DGa
½20Š
ra ¼ ia =nF ¼ ka co exp À
RT

10

Figure 7 Potential–pH diagram for chromium species in
Fe–Cr–Ni at 300  C. Concentration of aqueous species is
10À6 molal. Reprinted from Beverskog, B.; Puigdomenech, I.
Corrosion 1999, 55, 1077, with permission from NACE
International.

thus, not considered. The diagrams assumed that the
metallic elements in the alloy had unit activity, that is,
equal amounts of iron, chromium, and nickel. An
example of the potential–pH diagram for chromium
species in Fe–Cr–Ni at 300  C and aqueous species
with a concentration of 10À6 molal is presented in
Figure 7. Unlike the Fe diagram, where the presence
of soluble HFeO2À
2 species increased with temperature
(Figure 6), the diagram for Cr in Fe–Cr–Ni is dominated by passive region where the stable oxides of
Cr2O3, FeCr2O4, and NiCr2O4 are formed.
5.01.1.6 Kinetics of Dissolution and
Passive Film Formation
The study of dissolution kinetics, corrosion rate,

attempts to answer the question: ‘‘What are the relationships that govern the flow of current across a
corroding interface and how is this current flow
related to applied potential?’’ Consider the anodic
dissolution of a metal with an activation barrier
equal to G1a ¼ nFE (eqn [2]). If we increase the driving
force (potential) from its equilibrium condition, E0, to
a new value, f, the new barrier is given by the
relationship22:

where  (the overpotential) represents a departure
from equilibrium and is equal to f À E0. We can derive
a similar expression for the cathodic reaction22:


bnF

½22Š
ic ¼ nFkc co exp À
RT
where ic is the cathodic current density, kc is the rate
constant, and co is concentration of oxidized species.
Combining eqns [21] and [22] and rearranging them,
we can write an expression for the total current, i:
 



ð1 À bÞnF
bnF
 À exp À


½23Š
i ¼ io exp
RT
RT
where io is the exchange current density and is equal to
Àb Àb
nFkcc1Àb
o ka cR . This expression is commonly referred
to as the Butler–Volmer equation.
To apply eqn [23] to corrosion reactions, we need
to be able to relate  to the corrosion potential, Ecorr ,
that is, as it stands the Butler–Volmer equation is
derived for equilibrium conditions. Returning to our
definition of the overpotential  ¼ f À E0, by both
subtracting and adding Ecorr from the right side of
this definition, inserting the resulting expression back
into eqn [23] and rearranging we find22:


ð1 À bÞF
ðEcorr À Ea Þ
icorr ¼ ia exp
RT


bF
¼ ic exp À ðEcorr À Ec Þ
½25Š
RT


½19Š

For small applied potentials around Ecorr , the Stern–
Geary approximation of eqn [24] is used23:


ba þ bc
ðf À Ecorr Þ
½26Š
i ¼ 2:303icorr
ba bc

where b is the symmetry factor and reflects the fact
that not all of the increase in potential goes to

where ba and bc are defined as the anodic and
cathodic Tafel slopes (discussed in Section

Ga2 ¼ Ga1 À ð1 À bÞnF ðf À E0 Þ


0.4

0.1

0.35

0
Current density (A m-2)


Potential (V vs. SCE)

Corrosion and Compatibility

0.3
0.25
0.2
Beam on at 100 nA
~540 s

0.15
0.1

0

500

1000
Time (s)

1500

2000

5.01.2.2) having units of volts and are empirical factors related to the symmetry factor by the relationships22:
RT
ð1 À bÞnF

bc ¼ À2:303


RT
bnF

Beam = 35 na
Beam = 62 na
Beam = 100 na

-0.1
-0.2
Increasing radiation flux
Increasing cathodic reaction rate

-0.3
-0.4
-0.5

Figure 8 Influence of proton irradiation on the Ecorr of a
SS 304L electrode in dilute sulfuric acid, pH ¼ 1.6. The
increase is caused by the production of water radiolysis
products.

ba ¼ 2:303

9

½27Š
½28Š

As it relates to the nuclear power industry, eqn [24] not

only relates the corrosion rate (icorr) to the applied
potential, f, but it can also help us to rationalize
other processes such as the influence of water radiolysis
products on corrosion rate. For example, it is generally
observed that ionizing radiation (g, neutron, proton,
etc.) increases Ecorr potential (Figure 8) and corrosion
rate at Ecorr .24 The flux of ionizing radiation on the
cooling water results in radiolysis, the breaking of
chemical bonds. During the course of water radiolysis,
a wide variety of intermediate products are formed,
such as O2À, eaq, and the OH radical.25 The vast majority of these species have very fast reaction rates so that
the end result is a handful of stable species. These
stable products are typically oxidants, such as O2, H2,
and H2O2. That is, these products readily consume
electrons (eqns [II]–[IV]) and increase cathodic reaction rate (Figure 9). From eqn [25] we see that an
increase in the cathodic reaction rate, ic, necessarily
results in an increase in corrosion rate, icorr , consistent
with the observation described.
While the development of dissolution kinetics is
straightforward, the kinetics associated with passive

-0.6
-0.2

-0.1

0
0.1
0.2
0.3

Potential (V vs. SCE)

0.4

0.5

Figure 9 Influence of proton irradiation on the cathodic
reactions on a Au electrode in dilute sulfuric acid, pH ¼ 1.6.
The increase is caused by the production of water radiolysis
products.

film formation and breakdown are less well understood yet equally as important to our understanding
of corrosion mechanisms. One such example is the
case of localized corrosion where the probability for
a pit to transition from a metastable to a stable state is
governed by the ability of the active surface to repassivate. Another example is the initiation of SCC where
passive film rupture results in very high dissolution
rates and, correspondingly, crack advance rate which is
controlled by the activation kinetics described above as
the bare metal dissolves.26–28 During the propagation
stage of SCC, the crack tip must propagate faster than
(1) the oxide film can repassivate the surface and (2)
the corrosion rate on the unstrained crack sides so that
dissolution of the walls does not result in blunt notch.
To evaluate the role of repassivation kinetics
in SCC and corrosion mechanisms in general, investigators set about measuring three critical experimental parameters, namely film: ductility,29,30 bare
surface dissolution rates,31–33 and passive film formation rates34,35 for various alloys. Each of these techniques involves the depassivation of a metal electrode
using a tensile frame or a nano-indenter (in the case
of ductility studies) or scratching/breaking an electrode (bares surface current density and repassivation
studies) and measuring the resulting current transient

as a function of time. An example of a current transient for SS 304L in chloride solution is presented
in Figure 10. The surface was under potentiostatic
control and was bared using a diamond scribe. The
data were collected using a high-speed oscilloscope.


10

Corrosion and Compatibility

7.0 ϫ 10−4
6.0 ϫ 10−4

Current (A)

5.0 ϫ 10−4

td

tr

0

0.002 0.004 0.006 0.008
Time (s)

4.0 ϫ 10−4
3.0 ϫ 10−4
2.0 ϫ 10−4
1.0 ϫ 10−4

0.0
0.01

0.012

Figure 10 Scratch test current transient from a SS 304L
electrode in 0.1 M NaCl. The transient is characterized by a
growth period, td, and a repassivation period, tr.

The transient is characterized by two separate processes, anodic dissolution and repassivation represented by td and tr in Figure 10. To analyze the
repassivation rates, the period tr is typically fit to an
expression and evaluated as a function of solution pH
or electrode potential. The most prolific work in this
field is probably on the alloy SS 304L. For this alloy, it
has been proposed that the kinetics of film growth are
controlled by ion migration under high electric
field.36–38 The kinetics of high-field film growth
were first proposed by Cabrera and Mott39 to obey
the kinetic relationship:
 
BV
½29Š
i ¼ Aexp
L
where i is the current density, V is the voltage, L is the
oxide thickness, and A and B are constants.

5.01.2 Analytical Methods
5.01.2.1


Introduction

In this section, we will review the principle analytical
methods used to probe the electrochemical interface.
In the Section 5.01.2.2 Potentiodynamic Polarization, we discuss linear polarization resistance and
the practical application of corrosion kinetics, eqns
[25] and [26]. In that section, we also describe the
salient points of the anodic polarization curve. In the
Section 5.01.2.3 Electrochemical Impedance Spectroscopy, we introduce an ac method for interrogating
the electrochemical interface. This technique is

probably the most versatile experimental method
available to scientists and researchers. As it relates
to nuclear reactors, this technique has the ability to
subtract out the contribution of the solution resistance to polarization resistance measurements which,
if not accounted for in highly resistive cooling water
measurements will result in nonconservative corrosion rates. In the final section, we introduce a more
seldom used technique, Mott–Schottky analysis.
While this is by no means a common experimental
method, it provides a conduit for the reader to
become familiar with defects in the oxide film, their
transport and ways to quantify it. This has particular
interest here as ionizing radiation may promote corrosion rates by increasing transport of these defects
through the passive oxide film.
Regretfully, the scope of this chapter is limited,
and we are not able to discuss the step-by-step details
of the experimental methods that are used to make
corrosion measurements. A comprehensive guide
to experimental methods in corrosion has been
published by Kelly et al.40 as well as Marcus and

Mansfeld41 while a more broad description of electrochemical methods has been published by Bard and
Faulkner.42 The reader is also encouraged to become
familiar with the equipment that is used to make
electrochemical measurements and a good introductory chapter on this topic has been presented by
Schiller.43 The most important instrument is, no
doubt, the potentiostat. While this instrument is the
cornerstone of corrosion science, it does have its pitfalls including bandwidth limitations and the potential for ground loop circuits when used in conjunction
with other equipment such as load frames, autoclaves
and cooling loops. The latter can be overcome using
proper instrumentation such as potentiostat with a
floating ground, or isolation amplifiers.
To investigate the influence of the neutron flux
on corrosion rates and mechanisms, real-time in-situ
corrosion measurements are often made ‘in-reactor’
or at neutron facilities such as Oak Ridge National
Lab’s Hi-Flux Isotope Reactor (HIFER) and Argonne
National Lab’s Fast Flux Test Facility (FFTF). Alternately, neutron damage can be simulated using ion
beams. As it relates to ion irradiation, this method
provides opportunities for studying the interaction
of the components of reactor environments (radiation, stress, temperature, aggressive media) that are
not possible with in-reactor or neutron irradiation
facilities. For a full discussion of this topic, see
Chapter 1.07, Radiation Damage Using Ion
Beams. To summarize these experiments, controlled


Corrosion and Compatibility

environmental cells are coupled to accelerator beamlines to study the interaction of the environment and
irradiation on structural materials. Corrosion at the

substrate–environment interface is studied in real
time by numerous electrochemical techniques
including those described below. With respect to
dose, light ions can be used to reach doses up
to $10 dpa in several days. However, the depth of
penetration is low (tens or micrometers), which puts
unrealistic limitations on electrochemical cell construction. Heavy ion irradiation can reach several
hundred displacements per atom in a matter of days
but the penetration depth is much less.
5.01.2.2

Potentiodynamic Polarization

During our development of Butler–Volmer reaction
kinetics, we introduced the Stern–Geary approximation and defined Tafel slopes within the context of the
symmetry factor without much further explanation.
To understand the empirical source of the Tafel
slopes, we rearrange eqn [26] to define the polarization resistance Rp in units of O cmÀ2:
Rp ¼

ba bc
DE
¼
2:303icorr ðba þ bc Þ Di

½30Š

The Tafel slopes can be obtained from a plot of
potential as a function of the logarithm of current
density as shown for the cathodic curve in Figure 11

where bc has units of volts. A similar anodic plot can
be generated to obtain ba. It is important to realize
that these slopes are frequently not equal as they are
related to separate mechanisms on the electrode surface. From a plot of both the anodic and cathodic
Tafel slopes, we can also obtain icorr (Figure 11).
With knowledge of icorr , ba, and bc, the polarization
iOH2
EH

+

+

H

2

h(mv)
20

10
Slope =

Applied current
curve

Ecorr
+

M


20

20

iapp(cathodic)

icorr

E
iOM

resistance can then be determined from eqn [30]. For
small voltage perturbations, the slope of a plot of
applied potential (DE ) versus the change in current
density (Di ) is equal to Rp (Figure 12), often referred
to as the linear polarization resistance as the slope is
only linear for small voltage perturbations around Ecorr .
Errors not accounted for in eqn [30] include
uncompensated solution resistance (RO) and choosing
a scan rate that is too fast. From a reactor standpoint,
the value of RO in the cooling water or a simulant
where the resistivity is high may be a significant
contribution to the measured Rp and, therefore, result
in a nonconservative corrosion rate, that is, the calculated corrosion rate will be too low. For a complete
standardized method of conducting potentiodynamic
polarization resistance measurements and data analysis, the reader is referred to the appropriate ASTM
standards G3, G59, and G102.44–46
Potentiodynamic polarization curves can also be
used to assess corrosion rate as well as determine if a

material is passive, active, or susceptible to pitting
corrosion in a given environment. Consider the curve
in Figure 13. It plots the applied potential as a
function of the log of the absolute value of the current
density. The corrosion potential and corrosion current density are shown at the intersection of the
cathodic and anodic curves. Mass loss (m, in grams)
for a given period of exposure can then be

40
H+

/H2

11

DE
Diapp

40
iapp(anodic)

-10

Tafel region

M

- EM/M+
log iapplied


Figure 11 Diagram depicting the cathodic polarization of
an electrode near Ecorr. Tafel extrapolation showing the
determination of icorr is also presented. Reprinted from
Fontana, M. G. Corrosion Engineering; McGraw Hill:
New York, 1986, with permission from McGraw Hill.

-20
h(mv)
Figure 12 Diagram depicting the linear polarization for an
electrode about Ecorr. Slope, DE/Di, is equal to the
polarization resistance. Reprinted from Fontana, M. G.
Corrosion Engineering; McGraw Hill: New York, 1986, with
permission from McGraw Hill.


12

Corrosion and Compatibility

positive hysteresis in the reverse portion of the curve
that is not observed in the case of solution oxidation
or transpassivity.

Epit
Potential

Erepass

5.01.2.3 Electrochemical Impedance
Spectroscopy

Eflade

ba
ipass

icorr

bc

Ecorr

Log current density
Figure 13 Diagram depicting the potentiodynamic
polarization of an electrode far from Ecorr. Relevant
potentials and currents are defined in the text.

determined from the corresponding icorr using
Faraday’s Law, for a pure metal40:
icorr t EW
½31Š
FA
where t is time in seconds, icorr has units of A (cmÀ2),
A is surface area, and EW is equivalent weight and is
equal to molecular weight (M) divided by the number of electrons in the reaction. Similarly, for an alloy:
m¼

EW ¼ P

1
n

i
i fi =Mi

½32Š

where the subscript i denotes the alloying element of
interest and f is the mass fraction of that element
in the alloy. From Faraday’s law, it is also possible to
calculate corrosion rate, the penetration depth owing
to corrosion over a period of time in units of mm
yearÀ1 (CR):
CRmm yearÀ1 ¼

3:27 Â 103 icorr EW
r

½33Š

where r is the material density in g cmÀ3.
Other critical parameters in Figure 13 include
the Flade potential (EFlade) which marks the critical
potential necessary for passive film formation, the
passive current density (ipass), the pitting potential
(Epit), and the repassivation potential (Erepass). With
respect to EFlade, this active to passive transition is not
observed for materials that are spontaneously passive
in a given environment such as SS in a BWR. In
such a case, the current would be limited by the
film dissolution current (ipass). As it relates to Epit,
the onset of localized corrosion is characterized by a

sharp increase in current at a given potential. As such,
materials that are more susceptible to pitting have
lower Epit values. Pitting is also characterized by a

While potentiodynamic polarization is typically considered a destructive technique, that is, it alters the
surface of the corrosion sample, electrochemical
impedance spectroscopy (EIS) is a powerful nondestructive technique for obtaining a wealth of data
including Rp.47 Further, this technique has the ability
to subtract out the uncompensated solution resistance (RO) from the measurement which, for highly
resistive reactor cooling water environments, is a
significant advantage.
In EIS, a small sinusoidal voltage perturbation
(10 mV) is applied across the electrode interface
over a broad frequency range (mHz to MHz). By
measuring the transfer function of the applied voltage
to the system current, the system impedance may be
obtained. For corrosion systems, the impedance (Z)
is a complex number and may be represented in
Cartesian coordinates by the relationship:
ZðoÞ ¼ Z0 þ Z00

½34Š

where o is the applied frequency in radians, Z0 is the
real part of the impedance, and Z00 is the imaginary
part of the impedance, and the magnitude of the
impedance jZj is given by:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
½35Š
jZj ¼ ðZ0 Þ2 þ ðZ00 Þ2

In its simplest form, the electrochemical interface can
be thought of as an electrical equivalent circuit (EC):
a resistor (R) with an impedance Z(o) ¼ R and a
capacitor (C) with Z(o) ¼ 1/joC where j is the square
root of À1.48 Thus, the impedance of a resistor is
purely real and independent of frequency while the
impedance of a capacitor is purely imaginary and
inversely proportional to frequency. With respect to
the electrochemical interface, the polarization resistance is in parallel with the double layer capacitance
(Cdl, owing to adsorption of charged anions/cations
in the electrolyte). These two components act in
series with the solution resistance, RO as seen in the
EC in Figure 14. This circuit is referred to as a
simple Randles circuit and represents an ideal interface. Commonly, however, Cdl does not behave as an
ideal capacitor and its impedance is better represented by the expression


Corrosion and Compatibility

13

-6 ϫ 104

Rp
RW

-5 ϫ 104
-4 ϫ 104

Figure 14 Simplified Randles equivalent circuit of an

electrochemical interface where Rp is the polarization
resistance, Cdl is the double layer capacitance, and RO is the
geometric resistance associated with the solution
resistance.

ZЈЈ (W)

Cd1

-3 ϫ 104

-2 ϫ 104
-1 ϫ 104

0

105

0

1 ϫ 104 2 ϫ 104 3 ϫ 104 4 ϫ 104 5 ϫ 104 6 ϫ 104
ZЈ (W)

Rp + RW

Figure 16 Nyquist format for data in Figure 15 where
Rp ¼ 5 Â 104 O, Cdl ¼ 4 Â 10À6, and RO ¼ 200 O.

104
|Z| (W)


ZðoÞ ¼ 1=Cð j oÞa
103

RW
102
10-3 10-2 10-1 100 101 102
(a)
Frequency (Hz)

103

104

105

0
-10

Q (Њ)

-30
-40
-50

-70

wmax

-80

-90
10-3 10-2 10-1 100 101 102
(b)
Frequency (Hz)

where a is typically found to be between 0.5 and 1.
The element that represents this behavior is known
as a constant phase element (Ccpe).49
The response of a simple Randle’s circuit as a
function of frequency is shown in Figure 15(a) and
15(b). These plots are referred to as the Bode magnitude plot (eqn [35]) and the Bode phase plot50 where
the phase angle, y, is equal to:
 00 
Z
½37Š
y ¼ tanÀ1
Z0
This phase angle is a result of the double layer
capacitance where the current leads the applied ac
voltage perturbation as is the case for pure capacitors.
The parameters Rp and RO may be determined graphically from the Bode magnitude plot as shown in
Figure 15(a) while Cdl is determined from the graphical parameter omax (converted to radians, 2pf) in
Figure 15(b) and the relationship40:
1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ Rp =RO
½38Š
Cdl ¼
omax Rp

-20


-60

½36Š

103

104

105

Figure 15 (a) Bode magnitude and (b) Bode phase plots.
Data were generated from an electrical equivalent of a
simplified Randles circuit (Figure 13) where Rp ¼ 5 Â 104 O,
Cdl ¼ 4 Â 10À6, and RO ¼ 200 O.

Alternately, the data may be presented using the
Nyquist format which plots the imaginary impedance
as a function of the real impedance as seen in
Figure 16 (sometimes referred to as a Cole–Cole
plot). As graphical analysis is somewhat imprecise,
commercially available complex nonlinear least
squares fitting of the data (CNLS) is commonly
used to obtain these parameters (Figure 17).


14

Corrosion and Compatibility


|Z| exper.
|Z| fit

102

ROX

0

RW

-10

|Z| (W m2)

-30

Q exper.
Q fit

-40
-50

100

Q (degrees)

-20
101


-60

COX
Figure 19 Equivalent circuit of an oxide-covered metal in
liquid PbBi eutectic (LBE) where Rox is the resistance of the
passive film, Cox is the double layer capacitance of the
oxide, and RO is the geometric resistance associated with
the LBE.

-70
10-1
10-3

10-2

10-1

100

101

102

-80
103

Frequency (Hz)
Figure 17 Bode magnitude and Bode phase plots for SS
304L during proton irradiation in a pressurized deionized
cooling water loop at 125  C showing experimental data and

complex nonlinear least squares fit of equivalent circuit in
Figure 14.

Corrosion rate (mm year −1)

6.0

5.0

4.0

3.0
Photons
Neutrons
2.0

1.0

Protons

0

20

100 120
40
60
80
Flux (particles m–2 per proton)


140

Figure 18 Corrosion rate as a function of particle flux
for a SS 304L electrode during proton irradiation in a
pressurized deionized cooling water loop at 125  C.

EIS has been used successfully to investigate the
passive films on Zr alloys,51–53 SS 304L,54 and nickel
base alloys55 in environments that simulate reactor
cooling water systems. In addition, it has also been
used to measure the real-time corrosion rates of
materials during irradiation. Lillard et al.56,57 measured the corrosion rate of materials as a function of
immersion time in a deionized water cooling loop
during proton irradiation. In that work, radiationhardened probes made from Alloy 718, SS 304L,
and Al 60 601 were exposed to a proton beam at

various current densities. The impingement of the
beam on the probes resulted in a mixed neutron,
photon, and proton flux. It was shown that corrosion
rate was almost linear with photon and neutron flux
as compared to proton flux where anomalies existed
at intermediate fluxes (Figure 18). The data were
ultimately used to extrapolate lifetimes for accelerator materials.
In other studies, EIS has also been applied to
investigate passive films on metals in sodium (Na)cooled and lead–bismuth (LBE) systems that simulate reactor environments. The equivalent circuit
(EC) used to model the data is similar to the simplified Randles circuit; however, in this case, there is no
electrochemical double layer, only the impedance
and capacitance associated with the oxide
(Figure 19). In this EC, Rox is the dc resistance of
the oxide, Cox is the oxide capacitance, and RO is the

geometric resistance associated with the liquid metal
(Na or LBE). In one such study, Isaacs investigated
the capacitance of anodized films on Zr in liquid Na.
In that study, it was shown that both Rox and Cox were
a function of Na temperature between 50 and 400  C.
Lillard et al.58 reported similar trends for HT-9 in
LBE. At constant temperature, Rox and Cox for HT-9 in
LBE were a function of immersion time (Figure 20).
The data were used to calculate oxide thickness as a
function of time. In addition, Rox was related to ionic
transport through the film and corrosion rates were
calculated using Wagner’s oxidation theory. Upon irradiation in a proton beam, this rate fell even further.59
Additional information about leadÀeutectic coolants
may be found in Chapter 5.09, Material Performance in Lead and Lead-bismuth Alloy.
5.01.2.4

Mott–Schottky Analysis

The formation and growth of passive oxide films is
driven, fundamentally, by interfacial reactions and
defect, electron and ion transport processes. Yet the


Corrosion and Compatibility

105

ROX

15


5.5 ϫ 1010

101

5.0 ϫ 1010

104

Prior to irradiation

Fit

Beam on

Fit

10–1

101

1 C-2 (cm4 F-2)

ROX (W cm−2)

Rp = 0.9 ´ t1.7
102

COX (nF cm–2)


100
103

4.5 ϫ 1010
4.0 ϫ 1010
3.5 ϫ 1010

10–2
COX

100
10–1
–50

0

50
100
Immersion time (h)

150

3.0 ϫ 1010
10–3
200

2.5 ϫ 1010
-0.2

0


0.2

0.4

0.6

0.8

1

Potential (V vs. SCE)

Figure 20 Impedance capacitance for the oxide on
an HT-9 steel as a function of immersion in liquid PbBi
eutectic. Reprinted from Lillard, R. S.; Valot, C.;
Hanrahan, R. J. Corrosion 2004, 60, 1134, with
permission from the author.

Figure 21 Mott–Schottky plots for a SS 304L electrode in
dilute sulfuric acid, pH ¼ 1.6. Before and after proton
irradiation. Reprinted from Lillard, R. S.; Vasquez,
G. J. Electrochem. Soc. 2008, 155, C162, with permission
from the author.

nature and relative importance of these processes
are still far from being understood. Key to oxide
growth, and, therefore, passivation, is the mobility of
these defects, specifically vacancies. Under irradiation, however, the defect properties of the oxide
are undoubtedly changed, and the extent of corrosion is related both to the microstructure and transport properties of defects. One way to probe the

transport properties of the oxide film is by using
Mott–Schottky theory.
Returning to our discussion of EIS above, the
oxide capacitance may be obtained at high frequency
from the relationship

depends on what type of semiconductor the oxide is
(p vs. n) and this effects the sign of the slope.
Lillard used Mott–Schottky analysis to examine
the influence of proton irradiation on defect generation and transport in the oxide film on SS 304L.61
The passive film on SS 304L is an n-type semiconducting oxide and the major defect is the oxygen
vacancy which acts as an electron donor. According
to the Point Defect Model62 for oxide growth, oxygen
vacancies are produced at the metal–film interface by
the injection of a metal atom into the oxide lattice:

Z00 ðoÞ ¼ 1=oC or C ¼ 1=oZ00 ðolim Þ

½39Š

By measuring Z00 as a function of applied dc voltage
at the high frequency limit (olim) and calculating the
film capacitance from eqn [39], it is possible to evaluate donor concentration (ND) in the oxide film from
the well-known Mott–Schottky relationship:


1
ÀkT
½40Š
¼

2=ee
N
U
À
U
0
D
fb
C2
q
where e0 is the permittivity of space and is equal to
8.854 Â 10À14 F cmÀ1, e is the electronic charge and
is equal to 1.602 Â 10À19 C, U is the applied potential
in V, Ufb is the flatband potential in V, kT/q is equal to
25 mV at 25  C, and ND is the donor concentration
(oxygen vacancies) in cmÀ3.60 ND is the slope of a plot
of 1/C2 versus applied potential. The type of defect

m ! MM þ ðx=2ÞVo þ xeÀ

½41Š

where m is a metal atom, MM is a metal cation, Vo is a
oxygen vacancy, eÀ is an electron, and x is the stoichiometric coefficient. In pH 1.6 H2SO4, it was found
that the cation vacancy concentration in the oxide
increased from 2.94 Â 1021 in the absence of irradiation to 3.41 Â 1021 during irradiation (Figure 21).
It was proposed that the film on SS 304L is composed
of an inner Cr-rich p-type semiconductor and an
outer Fe-rich n-type semiconductor. This bilayer
film results in a p–n junction where the two layers

meet. On the p side of the junction, there is a surplus
of holes, while on the n side of the junction, a surplus
of electrons exists. The energy bands are such that
it is ‘uphill’ (an increase in energy) for electrons
moving across the junction (from the n side to the
p side). On a related topic, a discussion of defects in
bulk oxides can be found in Chapter 1.02, Fundamental Point Defect Properties in Ceramics.


16

Corrosion and Compatibility

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