IN-CREVICE CHEMISTRY MODEL 

DEVELOPMENT FOR NICKEL-BASED ALLOYS 

AND ANALYSIS OF MODEL RESULTS IN VIEW 

OF LITERATURE INFORMATION

Prepared for 

U.S. Nuclear Regulatory Commission 

Contract NRC–02–07–006 

Prepared by 

P. Shukla 

R. Pabalan 

X. He 

Center for Nuclear Waste Regulatory Analyses 

San Antonio, Texas 

September 2011 
ii 

ABSTRACT 

This report documents previously unpublished information on the topic of model development 

for understanding in-crevice chemistry and analysis of model results. 

In the Yucca Mountain Safety Analysis Report, the U.S. Department of Energy assumed that, 

once initiated, the localized corrosion in form of crevice corrosion of Alloy 22 will keep on 

propagating as long as corrosion potential is higher than the crevice corrosion for repassivation 

potential. In order to better understand the propagation behavior of crevice corrosion in 

Alloy 22, the Center for Nuclear Waste Regulatory Analyses staff developed a physico-chemical 

model to determine the chemical environment that could develop inside a crevice. The model 

results indicated that both cations’ and anions’ concentrations are likely to be higher than the 

ions’ concentration in the bulk solution residing outside the crevice. Furthermore, the in-crevice 

solution is expected to be more acidic than the bulk solution. 

Literature information was compiled to understand implications of the model results. 

Specifically, the model results were analyzed in view of the literature information that provided 

corrosion rate of Alloy 22 in different acidic chemical environments. The literature information 

indicated that accelerated corrosion of the alloy will take place in a solution as long as the 

solution pH is below a threshold value, which is predominantly a function of chloride and nitrate 

concentrations, and temperature. The combined analysis of literature information and model 

results indicate that crevice corrosion process is unlikely to stifle due to evolution of in-crevice 

chemical environment. 
iii 

CONTENTS 

Section Page 

ABSTRACT ................................................................................................................................... ii 

FIGURES ..................................................................................................................................... iv 

TABLES ........................................................................................................................................ v 

ACKNOWLEDGMENTS .............................................................................................................. vii 

1 INTRODUCTION ............................................................................................................ 1-1

2 MODEL DEVELOPMENT .............................................................................................. 2-1 

 2.1 Description of the Model ..................................................................................... 2-1 

 2.2 Model Solution Method ....................................................................................... 2-4 

 2.3 Model Parameters .............................................................................................. 2-8 

 2.4 Model Results ..................................................................................................... 2-8 

3 LITERATURE INFORMATION ....................................................................................... 3-1 

4 

5 SUMMARY AND CONCLUSIONS ................................................................................. 4-1 

6 

5 REFERENCES ............................................................................................................... 5-1 
iv 

FIGURES 

Figure Page 

2-1 Schematic Diagram of the Crevice Corrosion Process for a Nickel-Based 

 Alloy ............................................................................................................................... 2-1 

2-2 Potentiodynamic Polarization Curve for Alloy 22 in 1.0 M NaCl Solution at 

 95 °C [203 °F] ................................................................................................................. 2-8 

2-3 Electrode Potential (V − Φ ) as a Function of Distance From Crevice Mouth ................. 2-9 

2-4 Concentration of Nonreacting Species (Chloride, Nitrate, and Sodium) as a 

 Function of Distance From Crevice Mouth ................................................................... 2-10 

2-5 Concentration of Nickel and Nickel Hydroxide Ions as a Function of Distance 

 From Crevice Mouth ..................................................................................................... 2-10 

2-6 Concentration of Hydrogen and Hydroxyl Ions as a Function of Distance 

 From Crevice Mouth ..................................................................................................... 2-11 

2-7 Concentration of (a) Nickel and Nickel Hydroxide Ions and (b) Hydrogen and 

Hydroxyl Ions as a Function of Distance From Crevice Mouth for eq,Ni K equal to 

1.38 × 10−10 mol/cm3

 .................................................................................................... 2-12 

2-8 Distributions of (a) Electrode Potential with Respect to Standard Hydrogen 

Electrode; (b) Sodium, Chloride, and Nitrate Ions’ Concentrations; (c) Nickel and 

Nickel Hydroxide Ions’ Concentrations; and (d) Hydrogen and Hydroxyl Ions’ 

Concentrations as a Function of Distance From Crevice Mouth for i equal 

to 10!4

 A/cm2 ................................................................................................................ 2-13 
v 

TABLES

Table Page 

2-1 Chemical Composition of Mill-Annealed Alloy 22 (in Weight Percent) ........................... 2-2 

2-2 Values of Parameters in Eqs. (2-4), (2-6), and (2-10) .................................................... 2-8 

2-3 Diffusion Coefficients and Bulk Concentrations of Various Species in the Model .......... 2-8 

3-1 Critical pH in NaCl Solution for Alloy 22 Samples .......................................................... 3-2 

3-2 Gray, et al., (2006b) Reported Corrosion Rate and Corrosion Potential Data 

 for Alloy 22 in Different Solutions ................................................................................... 3-3 
vi 

ACKNOWLEDGMENTS 

This report describes work performed by the Center for Nuclear Waste Regulatory 

Analyses (CNWRA) for the U.S. Nuclear Regulatory Commission (USNRC) under Contract 

No. NRC–02–07–006. The activities reported here were performed on behalf of the USNRC 

Office of Nuclear Material Safety and Safeguards, Division of High-Level Waste Repository 

Safety. This report is an independent product of CNWRA and does not necessarily reflect the 

view or regulatory position of USNRC. 

The authors gratefully acknowledge H. Jung for his technical review, T. Mintz for his 

programmatic and editorial reviews, and A. Ramos for his administrative support. 

QUALITY OF DATA, ANALYSES, AND CODE DEVELOPMENT 

DATA: All CNWRA-generated original data contained in this report meet the quality assurance 

requirements described in the Geosciences and Engineering Division Quality Assurance 

Manual. Sources for other data should be consulted for determining the level of quality for those 

data. Computational calculations have been recorded in CNWRA Scientific Notebook 1003E 

(Shukla, 2009). 

ANALYSES AND CODES: This report includes results of calculations performed using 

OLI Analyzer Studio (OLI Systems, Inc., 2010)—commercially available software maintained in 

accordance with CNWRA Technical Operating Procedure (TOP)–018, Development and Control 

of Scientific and Engineering Software. Other computations and plotting were accomplished 

using Matlab® (The MathWorks, Inc., 2008). 

References 

OLI Systems, Inc. “A Guide to Using OLI Analyzer Studio Version 3.1.” Morris Plains, 

New Jersey: OLI Systems, Inc. 2010. 

The MathWorks, Inc. “MATLAB Version 7.7.0.471 (R20008b).” Natick, Massachusetts: The 

MathWorks, Inc. 2008. 

Shukla, P. Scientific Notebook No. 1003E. San Antonio, Texas: CNWRA. 2009. 
1-1

1 INTRODUCTION 

This report is part of the knowledge management activities for the U.S. Nuclear Regulatory 

Commission high-level waste repository safety program. The two main purposes of this report 

are (i) to document a previously unpublished description of a physico-chemical process model 

developed to estimate the concentration of chemical species inside a crevice and (ii) to 

complete the evaluation of a set of model results for in-crevice chemistry of Alloy 22 by 

comparing the results with information obtained from the open literature. 

The long lifetime of Alloy 22 (Ni–22Cr–13Mo–4Fe–3W) waste packages is an important attribute 

of the proposed high-level waste repository at Yucca Mountain, Nevada (DOE, 2002) to isolate 

nuclear waste from the geosphere. The chemical degradation (i.e., corrosion) of the waste 

package material is considered to be an important process that could limit the life of waste 

package materials. More specifically, the localized corrosion in form of crevice corrosion is one 

of the degradation processes that could limit the life of the waste package. In the Yucca 

Mountain Safety Analysis Report (DOE, 2008), the U.S. Department of Energy (DOE) assumed 

that, once initiated, the crevice corrosion of Alloy 22 will keep on propagating as long as 

corrosion potential is higher than the crevice corrosion for repassivation potential. To evaluate 

whether crevice corrosion would continue to propagate or stifle, the Center for Nuclear Waste 

Regulatory Analyses (CNWRA) staff developed a physico-chemical model to determine a range 

of chemical environments that could develop inside a crevice. 

Nickel-based alloys, such as Alloy 600 and C–276, exhibit superior localized corrosion (Kirk and 

Othmer, 1997) resistance compared to iron-based alloys, such as stainless steel. Nickel-based 

alloys can be susceptible to localized corrosion in the form of crevice corrosion when the 

corrosion potential is greater than the repassivation potential in a given environment 

(Gordon, 2002). The severity of localized-corrosion-induced damage on the metal surface is 

dependent on the evolution of the crevice region chemical environment. Several experimental 

studies have been conducted to determine the metal dissolution rate in the crevice region (Dunn 

et. al., 2005; He and Dunn, 2007; He, et al., 2007; Hua and Gordon, 2004; Priyantha 

et al, 2005). However, the experimental studies do not provide a description of the chemical 

environment that would develop inside a crevice because of the restricted geometry of the 

crevices. Furthermore, the experimental studies provide only limited term propagation rate data 

of the localized corrosion front. 

Few studies have been conducted to determine the evolution of the chemical environment 

inside a crevice of nickel and nickel-based alloys. Harb and Alkire, (1991) developed a process 

model to simulate the dissolution of a hemispherical corrosion pit on nickel in 0.5 M NaCl. The 

model accounted for multiple species in solution, reaction equilibria, migration, and surface 

kinetics. In particular, the Harb and Alkire model accounted for complexation of nickel with 

chloride. The model results indicated the buildup of nickel and chloride ions inside the pit. 

Hoffmeister (2004) determined the distribution of dissolved oxygen concentration, chloride 

concentration, and pH of the in-crevice solution. However, Hoffmeister’s work was based upon 

empirical correlations developed from experimental studies. Watson and Postlethwaite, (1990) 

developed a physico-chemical process model to determine the chemical environment inside a 

crevice for Inconel 625 in chloride-containing solutions. Evitts, et al. (1993) simulated the 

Watson and Postlethwaite model for Inconel 625 at high temperatures to determine the effect of 

corrosion on the initiation of crevice corrosion. To the authors’ best knowledge, no study has 

been reported that illustrates the range of chemical solutions that could develop inside a crevice 

on Alloy 22 in the proposed repository environments. 
1-2

The following approach is adopted to evaluate whether localized corrosion would continue to 

propagate or stifle. The physico-chemical model to determine the chemical environment range 

in a crevice is developed by imposing the mass balance for reacting and nonreacting chemical 

species, and by imposing charge conservation. More specifically, the model considers the 

transport of two nonreacting anionic species into a crevice and accounts for a metal dissolution, 

water dissociation, and a metal hydroxide formation reactions inside the crevice. The model 

equations are solved using an iterative method in which the governing equations for potential 

and chemical species’ distributions are solved independently. The model is implemented for 

Alloy 22 in the proposed repository environment. Model results are presented for different 

parameters’ values related to the metal dissolution and metal hydroxide reactions. Following 

the modeling work, literature information is compiled on Alloy 22 corrosion in chemical 

solutions suggested by the model results. The model results and literature information on 

Alloy 22 corrosion are analyzed to assess the stifling of the localized corrosion process. To 

the authors’ best knowledge, this approach for evaluating crevice corrosion stifling has not been 

presented elsewhere. 

The report is organized into four chapters. Chapter 1 introduces the technical background and 

motivation for this topic. Chapter 2 provides a detailed description of the physico-chemical 

process model. Chapter 3 summarizes the information compiled from the open literature that 

was used to understand the corrosion rate of Alloy 22 in the chemical solutions that were 

representative of the in-crevice chemistry indicated by model results. Chapter 4 develops a 

combined analysis of model results and literature information and presents the conclusions. 
2-1

2 MODEL DEVELOPMENT 

2.1 Description of the Model

The physico-chemical model is developed for a rectangular crevice of length L, width a, and unit 

depth. A schematic diagram representing the crevice region and outside the crevice region is 

presented in Figure 2-1. 

A nickel-based alloy is assumed to be immersed in a solution containing chloride, nitrate, and 

sodium ions. It is assumed the primary metal dissolution reaction in the crevice is the 

dissolution of nickel, represented by the following chemical equation 

+ − Ni → Ni + 2e 2 (2-1)

Chemical composition of a typical mill-annealed Alloy 22 is provided in Table 2-1 (Chiang, 

et al., 2007). Most nickel-based alloys, such as Alloy 22, also contain chromium and iron in 

substantial amounts, and dissolution of chromium and iron are also likely in the crevice 

environment according to the following chemical equations 

+ − Cr → Cr + 3e 3 (2-2)

+ − Fe → Fe + 2e 2 (2-3)

However, insight gained regarding the in-crevice chemistry by just considering dissolution of the 

nickel is expected to be the same as one obtained by considering dissolution of nickel, 

chromium, and iron. This point is further explained in this section. 

The corrosion current density associated with the dissolution of nickel is given by the 

following equation 

i 2+ = i exp[ ] β ( ) V − Φ Ni

(2-4)

Figure 2-1. Schematic Diagram of the Crevice Corrosion Process for a Nickel-Based 

Alloy. The Anodic Reaction in the Crevice Region, Which Is Directly Under the Crevice 

Former, Is the Nickel Dissolution, Whereas Cathodic Reaction in the Cathodic Region Is 

the Oxygen Reduction. 
2-2

Table 2-1. Chemical Composition of Mill-Annealed Alloy 22 (in Weight Percent) 

Ni* Cr* Mo* W* Fe* Co* Si* Mn* V* P* S* C* 

56.472 22.15 12.90 2.81 3.82 1.37 0.01 0.30 0.15 0.012 0.002 0.004 

*Ni—nitrogen; Cr—chromium; Mo—molybdenum; W—tungsten; Fe—iron; Co—cobalt; Si—silicon; 

Mn—manganese; V—vanadium; P—phosphorous; S—sulfur; C—carbon 

where 

2 + Ni i — corrosion current density associated with the dissolution of nickel (A/cm2

) 

i — equilibrium current density (A/cm2

)

β — inverse of Tafel slope (V-1) 

V — metal potential (V) 

Φ — solution potential (V) 

The dissolved nickel ion hydrolyzes to form nickel hydroxide and hydrogen ions according to the 

following reversible chemical reaction 

+ + + Ni + H2O ⇔ NiOH + H 2 (2-5)

The equilibrium constant for Eq. (2-5) is represented by the following equation 

+

+ +

= 2 Ni

NiOH H

Ni Keq, C

C C

(2-6)

where 

eq,Ni K — equilibrium constant of the hydrolysis of the nickel ions (mol/cm3

) 

+ NiOH C — concentration of NiOH+

 ions (mol/cm3) 

+ H C — concentration of H+

 ions (mol/cm3) 

2+ Ni C — concentration of Ni2+ ions (mol/cm3

) 

Similar to hydrolysis of nickel ions, the hydrolysis of chromium and iron ions would also result in 

formation of hydrogen ions according to the following chemical reactions 

+ + + Cr + H O ⇔ CrOH + H 2

2

3 (2-7)

+ + + Fe + H2O ⇔ FeOH + H 2 (2-8)

The resulting effect of the above two chemical reactions is additional formation of hydrogen 

ions, which is already included in the model by considering hydrolyses of nickel ions. Thus, 

exclusion of chromium and iron dissolution reactions [Eqs. (2-2) and 2-3)], and corresponding 

metal ions’ hydrolyses reactions [Eqs. (2-7) and 2-8)] in the model is not expected to limit the 

model’s ability in providing insight regarding the in-crevice chemistry. 

There is scarcity of data in literature on rate constant of metal ion hydrolysis reactions, however, 

available data on metal ion hydrolysis suggests that the metal ion hydrolysis reactions are rapid 

compared to metal dissolution reactions, therefore, the nickel ion hydrolysis reaction is judged to 

be rapid compared to the nickel dissolution and transport of nickel ions via diffusion and 

migration (Baes and Mesmer, 1979) in the crevice region. 
2-3

The hydrogen ions, produced ion by Eq. (2-5), equilibrate with the hydroxyl ions according to the 

following water dissociation reaction 

+ − H2O ⇔ H + OH (2-9)

The equilibrium constant for the water dissociation reaction is presented by the 

following equation 

= + − H2O H OH K C C (2-10)

where 

KH2O — equilibrium constant for the water dissociation reaction (mol2

/cm6) 

− OH C — hydroxyl ion concentration (mol/cm3

) 

The ionic species present in the crevice region are sodium, chloride, nitrate, nickel, nickel 

hydroxide, hydrogen, and hydroxyl ions. The steady-state concentration distribution of these 

ionic species in the crevice is represented by the following equation 

− ∇ ⋅ Nk + Rk = 0 (2-11)

where 

Rk — rate of generation of ionic species k (mol/sec-cm3

) 

Nk — flux of ionic species k (mol/sec-cm2

) 

The flux of an ionic species, Nk , in the solution is represented by the following 

Nernst-Plank equation 

k k kFCk Dk Ck N = −z u ∇Φ − ∇ (2-12)

where 

zk — charge number of species k

k u — mobility of species k (cm2

/sec-volt)

F — Faraday constant = 96,486 C/mol 

Ck — Concentration of species k (mol/cm3

) 

Φ — electrolyte potential (volts) 

Dk — diffusion coefficient of species k (cm2

/sec) 

It is assumed that the concentrations of various species inside the crevice are low enough to 

invoke the dilute solution approximation. As a result of the dilute solution approximation, the 

diffusion coefficient and mobility of a chemical species k are related according to the 

following equation 

Dk = ukRT (2-13)

where 

R — universal gas constant = 8.3145 J/K/mol 

T — temperature of the system (K) 
2-4

It is further assumed that the crevice solution is electrically neutral. This ensures that no charge 

separation occurs due to the solution potential gradients in the crevice region 

 k = 0

k

zkC (2-14)

The model is developed for bulk solution containing sodium, chloride, and nitrate ions. The 

nickel and nickel hydroxide ions will diffuse in the bulk solution from the crevice region where 

they are generated. It is assumed that the concentrations of sodium, chloride, nitrate, nickel, 

nickel hydroxide, hydrogen, and hydroxyl ions at the mouth of the crevice are assumed to be 

equal to the bulk solution concentration: 

Ck = Ck ,bulk (2-15)

At the end of the crevice, the flux of the nickel ion concentration is given by the 

following equation: 

F

i

N n

2

+

+ ⋅ = 22

Ni

Ni

 (2-16)

where n



is the outward normal vector. The flux of all other species at the end of the crevice is 

zero. In this model, it is assumed that no cathodic reaction occurs inside the crevice and the 

oxygen reduction reaction is the cathodic reaction that occurs outside the crevice, as depicted in 

Figure 2-1. 

2.2 Model Solution Method 

Because the width of a crevice is negligible compared to the length of a crevice, it is assumed 

that concentration gradients across the width of the crevice are also negligible compared to 

those along the length of the crevice. This assumption is consistent with the approach Alkire 

and Siittari (1979) adapted to model potential and concentration distributions inside a pit where 

pit radius was one third of the pit’s depth. Under this assumption, the governing equation for 

concentration distribution labeled Eq. (2-12), can be rewritten as 

a

N N R sk ∇ ⋅ k = k + (2-17)

where 

a — width of the crevice (cm) 

Nsk — flux of the species k at the metal-solution interface (mol/sec-cm2

) 

Note that the operator ∇ is equal to dx

d where x denotes the distance down the crevice from 

the crevice mouth. The flux of the nickel ions at the metal-solution interface in the crevice 

region is given by the following equation 

F

i

N n s 2

+

+ ⋅ = 22

Ni

Ni

 (2-18)

where n



is the outward normal vector. The flux of all other species at the metal-solution 

interface is zero. 
2-5

The diffusion and migration of the ionic species in the crevice region generates current. The 

total current density is defined by 

=

=

N

k

kNk i F z

1

(2-19)

and the divergence of the current is given by 

Fa

i

i

2

+

∇ ⋅ = 2 Ni (2-20)

Insertion of Eqs. (2-12) and (2-17) in Eq. (2-18) yields 

() ( ) Fa

i

F z D C

N

k

i i i

1 2

+

∇ ⋅ ∇Φ +  ∇ ⋅ ∇ = − =

2 Ni κ (2-21)

where 

=

κ =

N

k

2 k k k

RT

z D C F

1

2

(2-22)

Rearrangement of Eq. (2-21) yields 

 ( ) =

κ∇ Φ + ∇Φ ⋅∇κ = − − ∇ ⋅ ∇ + N

k

F k Dk Ck 2Fa

i

1

z 2 2 Ni (2-23)

Based upon the stoichiometry of homogeneous chemical reactions given by Eqs. (2-5) and 

(2-9), it is recognized that 

+ + + = 0 Ni NiOH R 2 R (2-24)

Inclusion of Eq. (2-24) in the model ensures that there is instantaneous equilibrium between 

nickel and nickel hydroxide ions. Furthermore, the generation rate of nickel ions will balance 

hydrogen and hydroxyl ions. Therefore 

+ + + − − = 0 Ni H OH R 2 R R (2-25)

Inclusion of Eq. (2-25) ensures that the hydrogen ions are in equilibrium with nickel and hydroxyl 

ions throughout the crevice region. 

The divergence of flux of nickel and nickel hydroxide ions can be combined to yield 

( ) 2Fa

i

N N +

∇ ⋅ + + + = 2

2

Ni

Ni NiOH

(2-26)

and the divergence of flux of nickel, hydrogen, and hydroxyl ions can be combined to yield 

( ) Fa

i

N N N

2

+

∇ ⋅ + + + − − = 2

2

Ni

Ni H OH (2-27)

The concentration of nickel hydroxide in Eq. (2-24) is substituted with nickel and hydrogen ion 

concentration using Eq. (2-6). Similarly, the hydroxyl ion concentration in Eq. (2-25) is 

substituted with hydrogen ion concentration using Eq. (2-10). 
2-6

The nonreacting species are chloride, nitrate, and sodium ions. The divergence of flux of 

chloride and nitrate ions are given by 

∇ ⋅ - = 0 Cl N (2-28)

and 

∇⋅ - = 0 NO3N (2-29)

The concentration boundary conditions for these governing equations at the mouth of the 

crevice are given by Eq. (2-15). The electrolyte potential at the mouth of the crevice is assumed 

to be zero; that is 

Φ = 0 (2-30)

At the end of the crevice, the electrolyte potential is represented by 

κ∇Φ +  ∇ = +

=

2 Ni F z D C i

N

k

k k k

1

(2-31)

Using Eq. (2-12), the boundary conditions for Eqs. (2-26) and (2-27) at the end of the 

crevice are 

( ) F

i

N N n

2

+

+ + + ⋅ = 22

Ni

Ni NiOH

 (2-32)

and 

( ) F

i

N N N n

2

+

+ + + − − ⋅ = 22

Ni

Ni H OH

 (2-33) 

The flux boundary conditions at the end of the crevice for chloride and nitrate ions are 

N − ⋅ n = 0 

Cl (2-34) 

and 

N ⋅ n = 0  - NO3 (2-35) 

An iterative procedure was used to solve Eqs. (2-23), (2-26), (2-27), (2-28), and (2-29), and 

the electroneutrality condition provided in Eq. (2-14), subjected to boundary conditions given 

by Eqs. (2-15) and (2-30)–(2-35). The governing equations are second-order ordinary 

differential equations with fixed boundary values at the mouth and at the end of the crevice. 

The equations were solved using the two-point boundary values solver function in MATLAB®

(The MathWorks, Inc., 2008). 

In the initial iteration, first, Eq. (2-23) is solved for potential distribution inside the crevice 

subjected to the boundary conditions given by Eqs. (2-30) and (2-31). The concentration 

distributions of various species inside the crevice is assumed to be equal to the bulk 

concentration. The solution of Eq. (2-23) provides the distributions of Φ , ∇Φ , and ∇ Φ

2 inside 

the crevice. Second, the distributions of concentrations of chloride and nitrate ions are obtained 

by solving Eqs. (2-28) and (2-29) subjected to the boundary conditions given by Eqs. (2-15), 

(2-34), and (2-35). The solution of Eqs. (2-28) and (2-29) also provides the values of ∇ − Cl C , 

- NO3

∇C ,∇ − Cl C

2 , and - NO3

C

2 ∇ along the length of the crevice. Third, the distributions of nickel and 

hydrogen ion concentrations are obtained by solving Eqs. (2-26) and (2-27) subjected to the 

boundary conditions given by Eqs. (2-15), (2-32), and (2-33). The solution of Eqs. (2-26) 
2-7

and (2-27) also provides the values of∇ 2+ Ni C ,∇ + H C , ∇ 2+

2

Ni C , and ∇ + H C

2 along the length of the 

crevice. Fourth, the distributions of concentrations of nickel hydroxide and hydroxyl ions and 

∇ + NiOH C , - OH ∇C ,∇ + NiOH C

2 , and - OH C2 ∇ are obtained using Eqs. (2-6) and (2-10). Fifth, the 

electroneutrality condition given by Eq. (2-14) is used to obtain the sodium ion concentration 

distribution, ∇ + Na C and ∇ + Na C

2 inside the crevice. 

In the subsequent iterations, first, Eq. (2-23) is solved for potential distribution inside the crevice 

subjected to the boundary conditions given by Eqs. (2-30) and (2-31). The calculated values of 

concentration distribution from the previous iteration of various species are used to calculate κ

in Eq. (2-23). Similarly, the calculated values of ∇Ck and Ck

2 ∇ from the previous iteration are 

used to calculate ∇κ and  ( ) =

∇ ⋅ ∇

N

k

F k Dk Ck

1

z

,

 which are part of Eq. (2-23). The second, third, 

fourth, and fifth steps in the initial iteration are repeated to obtain the concentration distributions, 

∇Ck and Ck

2 ∇ using the calculated values of Φ, ∇Φ , and ∇ Φ

2 from the first step. The 

calculated values of the potential and concentration distributions are compared with the values 

from the previous iteration. If the absolute difference in potential and concentration distributions 

is less than a specified tolerance limit, the iterative procedure is terminated. 

2.3 Model Parameters 

The model is executed for the free corroding condition under which the metal potential, denoted 

by V, is equal to zero in Eq. (2-4). The value of the passive current density (i ), inverse of the 

Tafel slope (β) in Eq. (2-4), and equilibrium constants ( eq,Ni K ,KH2O ) in Eqs. (2-6) and (2-10) are 

provided in Table 2-2. 

The value of the passive current density is obtained from experimental data collected for 

Alloy 22 in 1.0 M NaCl solution for this study. A cyclic polarization curve was obtained for the 

alloy in the solution according to ASTM G61 (ASTM International, 2003) at 95 °C [203 °F]. The 

polarization curve is presented in Figure 2-2. As seen in the figure, the measured current 

density is independent of potential in the forward scan; however, current density is a strong 

function of potential in the reverse scan. The data suggests that the metal surface was covered 

with a passive film while the alloy sample was anodically polarized in the forward scan. The 

current density is a strong function of potential in the reverse scan because original film was no 

longer in the passive state to protect the metal surface from corrosion. As seen in the figure, 

the passive current density is approximately equal to 2 × 10−6

 A/cm2 at an electrode potential 

equal to zero and the calculated value of the inverse of the Tafel slope (β) is 0.06 V−1

. The 

value of passive current density is the same as the one adopted by Watson and Postlethwaite, 

(1990). No assumption has been made regarding the presence or absence of passive film in 

the crevice region. 

The values of equilibration constants for nickel ion hydrolysis reaction is adopted from Malki, 

et al. (2008), whereas, the dissociation constant for water is calculated using a thermodynamic 

calculator. These values are listed in Table 2-2. The values of diffusion coefficients of 

different species are calculated using the chemical thermodynamic simulator13 (OLI Systems, 

Inc., 2010) and are provided in Table 2-3. The bulk concentrations of various chemical species 

also are provided in Table 2-3. The model is simulated for a 5-cm [1.97-in]-long and 0.5-mm 

[197-mils]-high crevice. 
2-8

Figure 2-2. Potentiodynamic Polarization Curve for Alloy 22 in 1.0 M NaCl 

Solution at 95 °C [203 °F] 

Table 2-2. Values of Parameters in Eqs. (2-4), (2-6), and (2-10) 

Parameter Values

i (A/cm2) 2 × 

10−6

β ( V-1) 0.06 

eq,Ni K (mol/cm3

) 1.38 × 

10−13

KH2O (mol2

/cm6) 10−20

Table 2-3. Diffusion Coefficients and Bulk Concentrations of Various Species in the Model 

Species 

Diffusion coefficient (cm2

/sec) 

at 95 °C 

Concentration 

(mol/L) 

H+ 17.0 × 10−5 10−8

OH+ 11.9 × 10−5 10−6

Na+ 3.95 × 10-5 Estimated using 

Eq. (2-14) 

Cl− 5.45 × 10−5

 0.5 

NO3

− 4.86 × 10−5

 0.1 

Ni2+ 2.18 × 10−5 10-6

NiOH+ 2.15 × 10−5 10-6

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-8 -7 -6 -5 -4 -3 -2

log (i (A/cm2

))

Eletrode Potential (VSCE)

start end
2-9

2.4 Model Results 

The calculated values of electrode potential (V − Φ ) are presented in Figure 2-3. As seen in the 

figure, the electrode potential becomes more cathodic with increasing distance. The electrode 

potential at the tip of the crevice is 9 mV more cathodic than at the mouth of the crevice. The 

calculated values of the nonreacting chemical species (chloride, nitrate, and sodium) are 

presented in Figure 2-4. As seen in the figure, the chloride, nitrate, and sodium ion 

concentrations increase with distance from the crevice mouth. Note that the ratio of nitrate to 

chloride ions remains constant throughout the crevice. This observation can be explained by 

analyzing the governing equations for the concentration distribution of chloride and nitrate inside 

the crevice. Because the divergence of flux of nitrate and chloride ions is zero throughout the 

crevice, the steady-state flux of nitrate and chloride ions is constant throughout the crevice, and 

the transport properties, such as mobility and the diffusion coefficient of nitrate and chloride 

ions, have no impact on the steady-state concentration distribution inside the crevice. In fact, 

the concentration distribution of nitrate and chloride ions is only dependent on the gradient of 

potential distribution, ∇Φ , inside the crevice. 

The concentration of nickel and nickel hydroxide ions as a function of distance is presented in 

Figure 2-5. As seen in the figure, the nickel ion concentration increases with distance from the 

crevice mouth, whereas the nickel hydroxide ion concentration first increases with distance up 

Figure 2-3. Electrode Potential (V − Φ ) as a Function of Distance From Crevice Mouth. 

The Potential Values Are With Respect to Standard Hydrogen Electrode.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 -9.0

-8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

Distance from Crevice Mouth (cm)

Electrode Potential (mV)
2-10

Figure 2-4. Concentration of Nonreacting Species (Chloride, Nitrate, and Sodium) as a 

Function of Distance From Crevice Mouth

Figure 2-5. Concentration of Nickel and Nickel Hydroxide Ions as a Function of Distance 

From Crevice Mouth

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Distance from Crevice Mouth (cm)

Concentration (mol/L)

ClNO3

-

Na+

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 10-6

10-5

10-4

10-3

10-2

10-1

Distance from Crevice Mouth (cm)

Concentration (mol/L)

Ni2+

NiOH+
2-11

to 1.0 cm [0.4 in] and then decreases with distance. The nickel ions are generated in the 

crevice as the potential becomes more cathodic. However, the nickel hydroxide ion 

concentration is determined by the equilibrium between the nickel, nickel hydroxide, and 

hydrogen ions. 

The concentration of hydrogen and hydroxyl ions as a function of distance is presented in 

Figure 2-6. As seen in the figure, the hydrogen ion concentration increases with distance from 

the crevice mouth, whereas the hydroxyl ion concentration decreases with distance from the 

crevice mouth. The hydrogen ions are generated as nickel ions react with water to produce 

nickel hydroxide and hydrogen ions. An increased concentration of nickel ions corresponds to 

an increase in hydrogen ion concentration. Because the product of hydrogen and hydroxyl ion 

concentration is constant, the hydroxyl ion concentration decreases with distance from the 

crevice mouth. This result also indicates that the crevice solution is more acidic than the bulk 

solution due to generation of hydrogen ions. 

The effect of different parameters’ values on potential and concentration distributions was also 

studied. Two parameters, eq,Ni K and i , were independently varied. The value of eq,Ni K was 

increased by three orders of magnitude and set to 1.38 × 10−10 mol/cm3

. The values of 

remaining parameters were the same as listed in Tables 2-2 and 2-3. It was observed that the 

electrode potential distribution was not affected by the change in eq,Ni K . Similarly, the 

concentration distributions of nonreacting species (i.e., sodium, nitrate, and chloride ions) were 

also not affected by the change in eq,Ni K . However, the concentration distributions of nickel and 

nickel hydroxide, hydrogen, and hydroxide ions are affected by the eq,Ni K value. The 

concentration distributions of nickel and nickel hydroxide ions are presented in Figure 2-7(a), 

Figure 2-6. Concentration of Hydrogen and Hydroxyl Ions as a Function of Distance 

From Crevice Mouth

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 10-8

10-7

10-6

Distance from Crevice Mouth (cm)

Concentration (mol/L)

H+

OH-
2-12

Figure 2-7. Concentration of (a) Nickel and Nickel Hydroxide Ions and (b) Hydrogen and 

Hydroxyl Ions as a Function of Distance From Crevice Mouth for eq,Ni K Equal to 

1.38 × 10−10 mol/cm3

. Remaining Parameters’ Values Were the Same as Listed in 

Tables 2-2 and 2-3.

and of hydrogen and hydroxide ions are presented in Figure 2-7(b). Consistent with increased 

value of eq,Ni K , the nickel hydroxide concentrations are higher along the crevice length compared 

to the eq,Ni K value of 1.38 × 10−13 mol/cm3

. Similarly, the hydrogen ion concentrations are also 

higher for the increased value of eq,Ni K . These simulation results also confirm that the model 

generates consistent results. 

The model results for i equal to 10−4

 A/cm2 are presented in Figure 2-8. All other parameters’ 

values are the same as listed in Tables 2-2 and 2-3. The selected value of i equal to 10−4

A/cm2

 is 50 times larger than i equal to 2 × 10−6 A/cm2. As a result, the nickel dissolution rate is 

also higher. The model results reflect the higher dissolution rate of nickel. The electrode 

potential distribution is presented in Figure 2-8(a). As seen in the figure, the electrode potential 

varies between 0 to −90 mV with respect standard hydrogen electrode along the length of the 

crevice. The potential distribution in Figure 2-8(a) for i equal to 10−4

 A/cm2 is steeper than for i

equal to 2 × 10−6

 A/cm2 (see Figure 2-3). The steeper potential distribution is also reflected in 

larger concentrations of nonreacting species (i.e., sodium ion, chloride, and nitrate), which are 

presented in Figures 2-8(b), along the length of the crevice. Similarly, the higher value of i

result in higher values of nickel and nickel hydroxide ions along the length of the crevice. The 

concentration distributions of nickel and nickel hydroxide ions are presented in Figure 2-8(c). 

The larger value of i results in higher dissolution rates of nickel, and thus, the higher 

concentration of nickel and nickel hydroxide ions along crevice length than for i equal to 

2 × 10−6

 A/cm2 (see Figure 2-4). The higher concentrations of nickel hydroxide also results in 

higher values of hydrogen ion concentrations, which are presented in Figure 2-8(d), along the 

length of the crevice. 

The following bullets provide a summary of the model results: 

• The in-crevice solution is acidic compared to the bulk solution 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 10-6

10-5

10-4

10-3

10-2

10-1

Distance from Crevice (cm)

Concentration (mol/L)

Ni2+

NiOH+

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 10-9

10-8

10-7

10-6

10-5

Distance from Crevice (cm)

Concentration (mol/L)

H+

OH-
2-13

(a) (b) 

(c) (d) 

Figure 2-8. Distributions of (a) Electrode Potential with Respect to Standard Hydrogen 

Electrode; (b) Sodium, Chloride, and Nitrate Ions’ Concentrations; (c) Nickel and Nickel 

Hydroxide Ions’ Concentrations, and (d) Hydrogen and Hydroxyl Ions’ Concentrations as 

a Function of Distance From Crevice Mouth for i Equal to 10−4

 A/cm2. Remaining 

Parameters’ Values Are the Same as Listed in Tables 2-2 and 2-3.

• If nitrate and chloride are nonreacting, the ration of nitrate to chloride is the same as in 

the bulk 

• An increase in i and eq,Ni K results in an increase in pH of in-crevice solution 

The model does not account for water reduction and hydrogen ion reduction reactions, which 

are expected to occur at cathodic potentials and in low pH solution. Similarly, the nitrate 

reduction reactions, which is expected to occur in low pH solutions, is not accounted for in the 

model. The model also does not account for complexation of chloride with nickel ions. Harb and 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 -90

-80

-70

-60

-50

-40

-30

-20

-10

0

Distance from Crevice Mouth (cm)

Electrode Potential (mV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Distance from Crevice Mouth (cm)

Concentration (mol/L)

ClNO3

-

Na+

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 10-6

10-5

10-4

10-3

10-2

10-1

100

101

Distance from Crevice Mouth (cm)

Concentration (mol/L)

Ni2+

NiOH+

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 10-9

10-8

10-7

10-6

10-5

Distance from Crevice Mouth (cm)

Concentration (mol/L)

H+

OH-
2-14

Alkarie (1991) considered complexation of nickel ions with chloride while simulating the increvice chemistry according to the following chemical reaction 

+ − ⇔ + Ni + Cl NiCl 2 (2-35)

Harb and Alkarie, (1991) reported that the equilibrium constant for the reaction is approximately 

equal to 0.3 M−1

. This indicates that the reactant concentrations dominate at equilibrium. 

Therefore, most of the chlorides do not complexate with nickel ions. Moreover, the model 

predicted concentration of the nickel ions is an order of magnitude less than chloride 

concentration. For this reason, the complexation of nickel ions with chlorides is expected to be 

limited by the nickel ion concentration. Thus, the impact on chloride concentration due to the 

complexation reaction is not expected to exceed more than 30 percent. Thus, the model 

predicted chloride concentrations are expected to be approximately 30 percent more than 

expected chloride concentration if the complexation reaction was considered in the model. 

Even though the model does not account for the nitrate reduction and nickel ion complexion 

reaction, the model predicted results are not far off from the expected values. Therefore, the 

ratio of nitrate to chloride is expected to be close to the bulk value. The model results are only 

indicative of evolution of in-crevice chemistry. 
3-1

3 LITERATURE INFORMATION 

As indicated by the model results, the in-crevice solution is expected to be more acidic that the 

bulk solution, and concentrations of nitrate and chloride is likely higher than the bulk. Moreover, 

the ratio of nitrate to chloride concentrations is not expected to be significantly different than the 

bulk. For this reason, literature information on corrosion of Alloy 22 in acidic chemical solutions 

containing chloride and nitrate was sought, and is provided next. 

Llyod, et al. (2003) conducted polarization experiments on Alloy 22 in 1 M NaCl plus 0.1 M 

H2SO4 solution at various temperatures. The objective of the study Llyod, et al. (2003) 

conducted was to understand the effect of solution chemistry and temperature on stability of 

passive film of Alloy 22 in the solution. The calculated pH of the solution is 0.7. The test 

solutions were deaerated with ultrahigh purity argon for at least 20 minutes prior to starting the 

experiment, and this purge was continued throughout each experiment. Llyod, et al. (2003) 

conducted potentiostatic and potentiodynamic experiments at various temperatures. In the 

potentiostatic experiment, the Alloy 22 samples were polarized up to 700 mV with respect to 

Ag/AgCl reference electrode. The authors measured current density as a function of time in the 

potentiostatic experiments and measured current density as a function potential in the 

potentiodynamic experiments. Both experiments were conducted at various temperatures 

ranging from 25 to 85 °C [185 °F]. The authors reported that the Alloy 22 maintained low 

passive current density with a maximum of 2.0 × 10−6 A/cm2 even at potential as high as 700 mV 

with respect to Ag/AgCl reference electrode at 85 °C [185 °F]. The authors concluded that even 

though the chemical composition of the passive film changed in the potentiostatic experiments 

at different temperatures, the film did not cease to exist at the metal surface. 

Gray, et al. (2006a) tested the passivity of Alloy 22 over a broad range of pH and anion 

concentrations encompassing the aggressive solutions that may exist in these localized 

environments. The authors conducted experiments in 1 to 4 molal NaCl solution with varying 

amounts of acid. The authors used either HCl or H2SO4 or HNO3 to adjust the pH of the NaCl 

solution. The amount of a selected acid was added such that the pH of the NaCl solution varied 

in the range of 2 to −1. The test solutions were purged with dissolved nitrogen to remove 

oxygen from the solution. 

Gray, et al., (2006a) compared Alloy 22 corrosion rates as a function of pH for the different 

acids at 60 and 90 °C [140 and 184 °F] in a 1 molal NaCl , and 90 °C [184 °F] in a 4 molal NaCl 

solution. The authors defined passive film breakdown when corrosion rate equals or surpasses 

100 μm/yr, and also critical pH when below which corrosion rate surpasses 100 μm/yr. The 

authors reported that the critical pH value changed with acid type and temperature. The 

authors’ reported experimental results are summarized in Table 3-1. 

Gray, et al. (2006a) reported that no critical pH was observed when acidity of the 1 and 4 molal 

NaCl solutions were adjusted using HNO3. The authors conducted the measurements in the pH 

range of 2 to −0.7 for 1 molal NaCl solution at 60 and 90 °C [140 and 194 °F ], and in the pH 

range of 3 to −0.4 for 4 molal NaCl solution at 90 °C [194 °F ]. 

Gray, et al. (2006a) further reported that the breakdown of the passive film was evident in the 

corrosion potential of Alloy 22 samples in the test solutions. When pH of the 1 and 4 molal NaCl 

solutions were adjusted using HCl or H2SO4 , the corrosion potentials of the Alloy 22 samples 

remained virtually unchanged, whereas, the corrosion potential increased with decreasing pH 

when HNO3 was used to the adjust pH of adjusted 1 and 4 molal NaCl solutions. Because the 
3-2

Table 3-1. Critical pH in NaCl Solution for Alloy 22 Samples 

Acid Used to Adjust 

the pH 

Salt 

Concentration 

in Solution 

Temperature (°C) 

[°F] Critical pH* 

HCl 

1 molal NaCl 60 [140] 0.5 

1 molal NaCl 90 [194] 0.75 

4 molal NaCl 90 [194] 2.5 

H2SO4

1 molal NaCl 60 [140] 0.5 

1 molal NaCl 90 [194] 0.6 

4 molal NaCl 90 [194] 2.5 

*Critical pH, as defined by Gray, J.J., J.R. Hayes, G.E. Gdowski, B.E. Viani, and C.A. Orme. “Influence of Solution 

pH, Anion Concentration, and Temperature on the Corrosion Properties of Alloy 22.” Journal of the Electrochemical 

Society. Vol. 153, No. 3. pp. B61–B67. 2006, below which the Alloy 22 corrosion rate surpasses 100 μm/yr. 

corrosion potentials of the Alloy 22 samples did not change with decreasing pH in HCl or H2SO4 

adjust 1 and 4 molal NaCl, the rate of hydrogen ion reduction reaction increased with 

decreasing pH. As a result, the oxidation rates of metal species present in Alloy 22 also 

increased with decreasing pH. Thus, the overall corrosion rate increased with pH decrease. 

Gray, et al. (2006b) conducted additional studies to understand the effect of nitrate and chloride 

concentrations and nitrate to chloride ratio in low pH solution on Alloy 22 corrosion rates. The 

authors conducted experiments with Alloy 22 samples immersed in solution containing NaCl 

and KNO3 salts. The NaCl concentration in the solutions was either 1 or 4 molal. Appropriate 

amounts of KNO3 was added to achieve desired values of [NO3

−

]/[Cl−]. Acidity of a test solution 

was varied by adding an HCl-HNO3 acid solution. The acid solution had the same [NO3

−

]/[Cl−] 

as the test solution whose acidity was varied by adding the acid solution. The corrosion rate of 

Alloy 22 samples were measured as a function of test solutions’ pH. The corrosion potentials of 

the Alloy 22 samples were also recorded. The corrosion experiments were conducted at 60 and 

90 °C [140 to 194 °F] The test solutions were continuously purged with nitrogen to remove 

dissolved oxygen. 

Gray, et al. (2006b) first conducted a control experiment in HCl solution with varying pH at 90 °C 

[194 °F]. The Alloy 22 corrosion rates remained below 20 μm/yr until the HCl solution pH was 

greater than 1. The alloy corrosion rates suddenly increased when pH approximately was equal 

to 1. The measured corrosion potentials of the alloy remained between 0 and −0.2 V versus 

Ag/AgCl in the entire solution pH ranges. The authors concluded that the critical pH in the HCl 

solution was approximately equal to 1. Gray, et al. (2006b) conducted a series of Alloy 22 

corrosion rate measurements in 1 and 4 molal NaCl solutions. Potassium nitrate was added in 

the NaCl solutions to obtain a desired value of [NO3

-

]/[Cl-]. The acidity, and thus pH, of the 

solutions was varied by adding the acid solutions. The authors reported that in 1 molal NaCl 

plus 0.05 molal KNO3 solution with [NO3

-

]/[Cl-] equal to 0.05, corrosion rate first increased and 

then decreased with the solution pH in the range of 0.5 to !0.2. The peak corrosion rate of 

Alloy 22 in the 1 molal NaCl plus 0.05 molal KNO3 solution is between 20 to 40 μm/yr at pH 

approximately equal to 0. The authors concluded that small concentrations of nitrate control the 

runaway corrosion rate, which was observed with the HCl solution, of Alloy 22. Gray, 

et al. (2006b) conducted additional tests in 1 molal NaCl plus 0.2 molal KNO3 and 1 molal NaCl 

plus 0.5 molal KNO3 solutions. The author reported that the transpassive dissolution of the alloy 

took place in both the solutions below pH equal to 1.0. Though, the rate of dissolution, and thus 
3-3

the corrosion rate, was lower in 1 molal NaCl plus 0.5 molal KNO3 solution compared to 1 molal 

NaCl plus 0.2 molal KNO3 solution. The corrosion rate data reported by Gray, et al. (2006b) is 

summarized in Table 3-2. 

Gray, et al. (2006b) also conducted corrosion rate measurements of Alloy 22 in 4 molal NaCl 

solution with varying amount of KNO3. These experiments enabled the authors to evaluate the 

effect of chloride concentration on corrosion rate of Alloy 22 in low pH solutions. The corrosion 

rates of Alloy 22 in 4 molal NaCl plus 0.2 molal KNO3 solution with [NO3

-

]/[Cl-] equal to 0.05 first 

increased and then decreased in the pH range of 1.5 to 0.5. The peak corrosion rate was 

approximately equal to 20 μm/yr at about pH of 1. The corrosion rate of the alloy exponentially 

increased when pH was less than 0.5. The authors concluded that, similar to 1 molal NaCl plus 

0.05 molal KNO3 solution, small additions of nitrate ions control the runaway corrosion of 

Alloy 22 observed in the HCl solution. The authors further concluded that transpassive 

dissolution of the alloy took place in the solution below pH equal to less than 0.5. When 

compared with 1 molal NaCl plus 0.05 molal KNO3, the critical pH for transpassive dissolution 

increased from 0 to 0.5 in the 4 molal NaCl plus 0.2 molal KNO3 solution. Similarly, the critical 

pHs for transpassive dissolution were approximately equal to 1 in 4 molal NaCl plus 0.8 molal 

KNO3 and 4 molal NaCl plus 2.0 molal KNO3 solutions, whereas critical pHs were −0.15 and 

−0.25 in 1 molal NaCl plus 0.2 molal KNO3 and 1 molal NaCl plus 0.5 molal KNO3 solutions, 

respectively. These experiments further affirmed the conclusion that increase in chloride 

concentration results in increase of critical pH for transpassive dissolution. Furthermore, 

presence of nitrate only decreases the critical pH below which transpassive dissolution takes 

place. Thus, in presence of nitrate ions, a more acidic environment is needed to initiate 

transpassive dissolution of the alloy in a solution containing nitrate compared to a solution 

without nitrate. 

The presence of other localized corrosion inhibiting anions, such as sulfate, may also further 

decrease critical pH below which transpassive dissolution takes place. Ilevbare, et al. (2005) 

reported that nitrate is the most effective anion that affects the localized corrosion 

repassivation potential. Brossia and Kelly (1998) reported that nitrate is 65 times more 

effective than sulphate in the inhibition of crevice corrosion on SS 304. Thus, the presence of 

other localized-corrosion-inhibiting anions is not expected to significantly change the critical pH. 

Table 3-2. Gray, et al.* Reported Corrosion Rate and Corrosion Potential Data for 

Alloy 22 in Different Solutions 

Solution 

pH 

Range 

Corrosion Rate 

Data 

Corrosion 

Potential Data Summary 

HCl solution 2 to 1 Below 20 μm/yr until pH 

>1, corrosion rate 

suddenly increased when 

pH ≤1 

Corrosion potential 

remained between 0 

and −0.2 V vs. 

Ag/AgCl 

Critical pH was 

approximately equal to 1. 

1 molal NaCl plus 

005 molal 

KNO3.solution with 

[NO3

−

]/[Cl−] equal to 

0.05. pH was adjusted 

by adding HCl–HNO3

mixture 

2 to −0.25 Corrosion rate first 

increase and then 

decreases with pH in the 

range of 0.5 to −0.2. The 

peak corrosion rate is 

between 20 to 40 μm/yr 

at about pH equal to 0. 

Corrosion potential 

increases with 

decreasing pH. 

Small concentrations of 

nitrate ions control the 

runaway corrosion rate, 

which was observed with 

HCl solution, of Alloy 22. 
3-4

Table 3-2. Gray, et al.* Reported Corrosion Rate and Corrosion Potential Data for 

Alloy 22 in Different Solutions (continued) 

Solution 

pH 

Range 

Corrosion Rate 

Data 

Corrosion 

Potential Data Summary 

1 molal NaCl plus 0.2 

molar KNO3 solution 

with [NO3

−

]/[Cl−] equal 

to 0.2. pH was 

adjusted by adding 

HCl–HNO3 mixture 

2 to −0.4 Corrosion rate remains 

constant till pH is 

lowered to approximately 

−0.15. Corrosion rate 

then increases 

exponentially with 

decreasing pH. 

Corrosion potential 

increases linearly with 

decreasing pH. The 

rate of increase is 

higher when pH is 

below 0.5. 

Alloy 22 sample remains 

passive in the solution till 

the pH is lowered to 

−0.15. 

1 molal NaCl plus 0.5 

molal KNO3 solution 

with [NO3

−

]/[Cl−] equal 

to 0.5. pH was 

adjusted by adding 

HCl–HNO3 mixture 

2 to −0.4 Corrosion rate remains 

constant till pH is 

lowered to approximately 

equal to −0.25. 

Corrosion rate then 

increases rapidly, but not 

exponentially, with 

decreasing pH. 

Corrosion potential 

increases linearly with 

decreasing pH. The 

rate of increase is 

higher when pH is 

below 1.0. 

Alloy 22 sample remains 

passive in the solution till 

the pH is lowered to 

−0.25. The rate of 

increase is not as high as 

one observed for 

[NO3

−

]/[Cl−] equal to 0.2. 

4 molal NaCl plus 0.2 

molal KNO3.solution 

with [NO3

−

]/[Cl−] equal 

to 0.05. pH was 

adjusted by adding 

HCl–HNO3 mixture 

3 to −0.25 Corrosion rate first 

increase and then 

decreases with pH in the 

range of 1.5 to 0.5. 

The peak corrosion 

rate is approximately 

20 μm/yr at about pH of 

1.0. Corrosion rate 

exponentially increases 

when pH <0.5. 

Corrosion potential 

increases linearly with 

decreasing pH. The 

rate of increase is 

higher when pH is 

below 1.0. 

Similar to 1 molal NaCl 

plus 0.05 molal KNO3

solution, small additional 

of nitrate ions control the 

runaway corrosion rate, 

which was observed with 

HCl solution, of Alloy 22. 

4 molal NaCl plus 0.8 

molar KNO3 solution 

with [NO3

−

]/[Cl−] equal 

to 0.2. pH was 

adjusted by adding 

HCl–HNO3 mixture 

3 to −0.25 Corrosion rate remains 

constant till pH is 

lowered to 1.0. 

Corrosion rate then 

increases exponentially 

with decreasing pH. 

Corrosion potential 

increases linearly with 

decreasing pH. The 

rate of increase is 

higher when pH is 

below 0.5. 

Alloy 22 sample remains 

passive in the solution till 

the pH is above 1.0. 

Transpassive dissolution 

takes place below 

pH 1.0. 

4 molal NaCl plus 2.0 

molal KNO3 solution 

with [NO3

−

]/[Cl−] equal 

to 0.5. pH was 

adjusted by adding 

HCl–HNO3 mixture 

2 to −0.4 Corrosion rate remains 

constant till pH is 

lowered to 1.0. 

Corrosion rate then 

increases exponentially 

with decreasing pH. 

Corrosion potential 

increases almost 

linearly with 

decreasing pH. The 

rate of increase is 

higher when pH is 

below 0.5. 

Alloy 22 sample remains 

passive in the solution till 

pH is above 1.0. 

Transpassive dissolution 

takes place below pH 

1.0. The corrosion rate is 

similar to one observed 

for 4 molal NaCl plus 

0.8 molar KNO3 solution 

with [NO3

−

]/[Cl−] equal 

to 0.2. 

*Gray, J. J., J. R. Hayes, G. E. Gdowski, B. E. Viani, and C. A. Orme. “Inhibiting Effects of Nitrates on the Passive 

Film Breakdown of Alloy 22 in Chloride Environments.” Journal of The Electrochemical Society. Vol. 153, No. 5. 

pp. B156–-B161. 2006. 
4-1

4 SUMMARY AND CONCLUSIONS

A physico-chemical process model for a steady-state chemical environment inside a crevice for 

nickel-based alloys is presented. The model accounts for one heterogeneous and two 

homogeneous chemical reactions. The heterogeneous chemical reaction is the dissolution of 

nickel metal, and two homogeneous chemical reactions are the hydrolysis of nickel ions, 

resulting in formation of nickel hydroxide and hydrogen ions and, the dissociation of water. The 

concentration and potential variations along the crevice width are assumed to be negligible 

compared to the crevice length. The governing steady-state equations for the potential and 

concentration distributions of various species are algebraically simplified and then solved using 

an iterative procedure. 

The model is simulated for parameter values provided in Section 2.3. The calculated results are 

presented in the form of potential and concentration distributions of various species as a 

function of distance from the crevice mouth. The model results indicate that electrode potential 

becomes more cathodic along the crevice length measured from the crevice mouth. The 

calculated potential distribution inside the crevice is consistent with the results presented by 

Song and Sridhar (2008) and Allahar (2003) that showed that the potential becomes more 

cathodic inside a crevice. 

The calculated results also show that the concentrations of nonreacting anionic species 

(chloride and nitrate) increase with distance from the crevice mouth. Note that the ratio of 

concentration of nitrate to chloride ions remains constant throughout the crevice length. This 

result is consistent with the fact that the concentration distributions of nitrate and chloride ions 

are solely dependent upon the gradient of potential inside the crevice and are independent of 

the diffusion coefficient and mobility of the ions. 

The concentrations of nickel and hydrogen ions increase with distance from the crevice mouth. 

The nickel hydroxide ion concentration increases with distance from the crevice mouth up to 

1.0 cm [0.4 in] and then decreases thereafter. The hydroxyl ion concentration decreases with 

distance from the crevice mouth. The concentration profile of nickel ion is consistent with the 

fact that nickel ions are generated by the dissolution of metal throughout the crevice, and nickel 

ions are transported along the crevice depth to balance the ionic charge accumulated because 

of increased concentration of chloride and nitrate ions. The increase of hydrogen ion 

concentration is consistent with the fact that the nickel ions react with water molecules to 

produce hydrogen ions. Therefore, a high concentration of nickel ions corresponds to a high 

concentration of hydrogen ions. The concentration of nickel hydroxide ions is determined by the 

interplay between the equilibrium constants denoted by Ni Keq, and KH2O in Eqs. (2-6) and 

(2-10), respectively. The concentration of hydroxyl ions decrease throughout the crevice 

because the KH2O for the water dissociation reaction is constant throughout the crevice and the 

hydrogen ion concentration increases with distance from the crevice mouth. 

The physico-chemical process model does not account for several heterogeneous reactions, 

such as nitrate and water reduction reactions, and dissolution of other chemical species, such 

as chromium and iron, present in Alloy 22. Moreover, the model also does not account for 

complexation of chloride with nickel ions reaction that Harb and Alkarie (1991) considered. 

Additional analyses using literature information indicated that the exclusion of nitrate reduction 

and the complexation reactions in the model is not expected to significantly alter nitrate to 

chloride ratio compared to the bulk value. 
4-2

The literature information indicated that the transpassive dissolution of Alloy 22 at corrosion 

potential could take place as long as solution surrounding the alloy is acidic enough (i.e., the 

solution pH is below a critical value). Moreover, the presence of nitrate and other localized 

corrosion inhibiting anions is only expected to decrease critical pH below which transpassive 

dissolution takes place. The physico-chemical model results indicate that the in-crevice solution 

is expected to be more acidic than the bulk solution. The actual acidity of the solution will 

depend upon rate of nickel dissolution and nickel ion hydrolysis reactions. The model results 

also indicate that in-crevice solution pH decreases with distance from crevice mouth. This 

suggests that the lowest pH in-crevice solution is expected to reside farthest from the 

crevice mouth. An analysis of model results in view of literature information indicates that more 

acidic chemical environment could evolve inside a crevice than predicted by the model. The 

model is simulated for a fixed value of equilibrium current density (i in Eq. 2-4) associated with 

dissolution of the nickel. The literature information indicates that the corrosion rate of the alloy 

increases with decreasing pH. Therefore, it is most likely that equilibrium current density will 

increase along the crevice from the crevice mouth. This could result in evolution of in-crevice 

solutions with pHs below the threshold pH for transpassive dissolution of the alloy. The 

combined analysis of the model results and literature information suggests that the stifling of 

crevice corrosion solely based upon in-crevice chemistry is not credible. 
5-1 

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