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Electrochimica Acta 56 (2011) 6165– 6183

Contents lists available at ScienceDirect

Electrochimica Acta

jou rn al hom epa ge: www.elsev ier .com/ locate /e lec tac ta

ffects of selected water chemistry variables on copper pitting propagation inotable water

ung Haa,∗, Claes Taxenb, Keith Williamsc, John Scullya

Center for Electrochemical Science and Engineering, Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA, USASWEREA-KIMAB, Stockholm, SwedenDepartment of Physics, University of Virginia, Charlottesville, VA, USA

r t i c l e i n f o

rticle history:eceived 29 January 2011eceived in revised form 1 April 2011ccepted 1 April 2011vailable online 29 April 2011

eywords:opperittingit propagationotable waterorrosion product

a b s t r a c t

The pit propagation behavior of copper (UNS C11000) was investigated from an electrochemical per-spective using the artificial pit method. Pit growth was studied systematically in a range of HCO3

−, SO42−

and Cl− containing-waters at various concentrations. Pit propagation was mediated by the nature of thecorrosion products formed both inside and over the pit mouth (i.e., cap). Certain water chemistry concen-trations such as those high in sulfate were found to promote fast pitting that could be sustained over longtimes at a fixed applied potential but gradually stifled in all but the lowest concentration solutions. Incontrast, Cl− containing waters without sulfate ions resulted in slower pit growth and eventual repassi-vation. These observations were interpreted through understanding of the identity, amount and porosityof corrosion products formed inside and over pits. These factors controlled their resistive nature as char-acterized using electrochemical impedance spectroscopy. A finite element model (FEM) was developedwhich included copper oxidation kinetics, transport by migration and diffusion, Cu(I) and Cu(II) solidcorrosion product formation and porosity governed by equilibrium thermodynamics and a saturationindex, as well as pit current and depth of penetration. The findings of the modeling were in good agree-

ment with artificial pit experiments. Malachite, bronchantite, cuprite, nantokite and atacamite corrosionproducts were both observed in experiment and predicted by the model. Stifling and/or repassivationoccurred when the resistance of the corrosion product layer became high enough to lower the pit bottompotential and pit current density such as 10-5 A/cm2 could be attained with thick and dense layer. Theramifications of these findings towards pit propagation characteristics in potable waters will be discussedwith improved insight into the roles of Cl− and SO4

2− ions.

. Introduction

Pitting corrosion of copper in potable waters has been studiedor several decades due to the wide use of copper as a tubing mate-ial in water distribution systems. Important factors that controlopper pitting corrosion such as surface condition [1–3], composi-ion of copper and alloys [2,4], water chemistry [5–10], pH [11–13],emperature [12,14], and electrochemical potential [15] have beennvestigated. For instance, the open circuit potential was critical toit initiation. Pitting occurred when the electrode potential of theopper became more positive than a critical value [15]. Also, pittingusceptibility was found to be controlled by the presence of aggres-

ive anions such as SO4

2− and Cl− [6–10,14,16–19]. In one study,he aggressive nature of anions towards the breakdown of passivityf copper was shown to be ranked from worst to least harmful in

∗ Corresponding author.E-mail address: hmh2n@virginia.edu (H. Ha).

013-4686/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.oi:10.1016/j.electacta.2011.04.008

© 2011 Elsevier Ltd. All rights reserved.

the order SO42− < Cl− < Br− < NO3

− < ClO4− < I− [6]. One of the first

explanations for pitting was based on the theory that oxygen anionsin the initial cuprous, cupric duplex passive film were replaced bysuch aggressive anions [20,21]. However, this explanation did notexplain the effects of water chemistry on pit stabilization and prop-agation after a pit has already formed. Recently, Cong and Scullydeveloped empirical equations to predict the corrosion potentials,the pitting potentials and the repassivation potentials of copperover a large range of drinking water chemistries and pH levels[22–24]. High OH− and HCO3

− concentration suppressed pittingby raising pitting potentials associated with pit stabilization. Highratios of SO4

2− to OH− and HCO3− promoted pitting by lowering

pitting potentials. These findings were in agreement with a num-ber of previous studies which showed similar trends but offered noquantitative relationships [6–8,16,20,21].

The kinetics of pit propagation also likely depends on manyfactors such as applied potential, pH, temperature and water chem-istry. However, most previous studies of copper pitting combineall of the stages such as potential rise, initiation, stabilization and

6 ica Acta 56 (2011) 6165– 6183

piwaitrlptasctretos[t

cscpariorooCebmppgac

aptpctatpcmrdcs((tiafct

Table 1Composition of high purity grade UNS C11000 copper wire.

(composition as shown in Table 1). The working electrodes wereembedded in Armstrong epoxy resin and then cast in ethylenepropylene diene methylene terpolymer mounting moulds. The

166 H. Ha et al. / Electrochim

ropagation in a single experiment. For instance, exposure stud-es conducted in “piping rigs” which duplicate flow as well as

ater chemistry may be dominated by the propagation stage andssessments are often based on final pit depth [25]. Therefore, thesolated effects of water chemistry variables on are lacking. Never-heless, after long term exposures in cold waters, SO4

2− was ofteneported to be very aggressive to localized copper dissolution anded to the formation of deep pits [6,9,14,16]. In contrast, HCO3

− hadositive effect on preventing pit growth under potentiostatic con-rol and repassivated pits [7,9,16]. Cl− is commonly known as anggressive pitting species [7,8,23,26,27], but in some cases, Cl− wasurprisingly reported to have inhibiting effect on pit propagation inopper [16]. The precise reasons and mechanisms by which each ofhese water chemistry variables controls the pit propagation stageemains largely speculative. For instance, the peculiar mitigatingffect of Cl− on copper pitting corrosion was suggested to be dueo the quantity of scale that was allowed to form on the surfacef copper [17]. More scale formed when Cl− was present. This waspeculatively regarded to be beneficial towards slow pit growth17] without understanding of either the identity or properties ofhe scale that influenced pitting.

Several theories regarding the pit propagation mechanism foropper have been considered but they remain controversial andometimes contradictory trends are observed [13,18,28,29]. Thelassic membrane cell theory, credited to Lucey, proposed that aorous cuprite layer across the pit mouth served the dual role of

diffusion barrier and bipolar electrode. This porous layer wasegarded to be a key component for pit propagation [28,29]. Accord-ng to the theory, the anodic and cathodic reactions taking placen the inner and outer sides of this membrane, respectively, wereesponsible for the self-driven behavior of copper pitting. This the-ry is attractive because it attempts to relate the physical propertiesf the corrosion product layer to the formation of a corrosion cell.learly, the identity of the corrosion product is important. How-ver, Sosa and colleagues found that current carried through theulk metal to a proximate cathode outside the pit accounted forore than 80% of the charge responsible for the mass loss in the

it. This was inconsistent with the membrane cell theory. They pro-osed that a concentration cell rather than the bipolar membraneoverns pitting of copper [18]. However, neither study enumer-ted a strong connection between corrosion product identity andorrosion rates.

Differences in corrosion products deposited at the pit forming cover or “cap” covering the pit mouth were observed in bothractice and laboratory experiments [4,13,16,30,31]. In some cases,he molecular identity, location (inside/outside pits), amount androperties of the corrosion product have not been identified nororrelated with pits growth rates. Other attempts to characterizehe corrosion products formed at pits led to some understandingbout their structure and composition. In one case of copper tubeshat failed in drinking water distribution system, the corrosionroduct layer was studied by diffraction and comprised of threeomponents: the cap, characterized by two basic copper sulfateinerals, the cuprite membrane and the cuprite and copper chlo-

ide crystals inside the pit [13,30]. In the most advanced study toate, artificial copper pits were grown in simulated drinking waterontaining Cl−, SO4

2− and HCO3−. The molecular identity of corro-

ion products was found using in situ Raman spectroscopy. CupriteCu2O), eriochalcite (CuCl2·2H2O), atacamite and/or botallackiteCu2Cl(OH)3) and brochantite (Cu4(SO4)(OH)6) were all found inhe pit cap [16]. These authors linked the fast pit growth kineticsn SO4

2− waters with the high solubility of copper sulfate species

nd the slow pit growth kinetics in Cl− and HCO3

− waters with theormation of voluminous corrosion product caps [16]. However noonnections between the corrosion product identity, their proper-ies and pit growth rates were made. To gain more understanding

Elements Cu B Ca Fe Si Ag

% Balanced <1 ppm 2 ppm <1 ppm 1 ppm <1 ppm

regarding the mechanism of pitting propagation, an investigation ofthe parameters controlling pit propagation is needed that connectsthe properties of corrosion product caps with growth in isolatedpits.

In the present study, the pitting propagation behavior of copper(UNS C11000) was isolated from the other stages and investigatedfrom an electrochemical perspective using the artificial pit method[32]. Pit growth was studied systematically using a range of diluteHCO3

−, SO42− and Cl− containing waters under potentiostatic con-

trol at a fixed anodic potential representative of a well passivatedpipe [22]. The potentiostat provided nearly infinite cathodic cur-rent enabling study of the pit anode in isolation. The effect ofwater composition on pit growth kinetics was elaborated for thefirst time by making connection between corrosion product prop-erties including ionic resistance, morphology, structure as well aschemical identity and subsequent pit growth rate. In situ electro-chemical impedance spectroscopy (EIS) was used for analysis ofthe corrosion product resistivity. EIS is capable of interrogatingthe electrical properties of films in situ using frequency specificinformation that enables separation of solution phase, film, chargetransfer and diffusional resistances [33]. Chemical identity wasaddressed through energy dispersive X-ray spectroscopy (EDS) andmicro Raman spectroscopy analysis. Raman analysis is a molecularspectroscopy tool that provides complimentary information aboutthe nature of the corrosion product (i.e. chemical formula) [34–37]that is not obtainable with EDS. Further, a micro Raman systemutilizing laser beam of micrometer size was used to improve thespatial resolution of the analysis in comparison with conventionalRaman [16,38–41] so that each layer of a multi-layers corrosioncap over a small pit could be investigated. A quantitative finite ele-ment model (FEM) was employed to study pit propagation. Thismodel included copper oxidation kinetics, transport by migrationand diffusion, Cu(I) and Cu(II) solid corrosion product formationof various types governed by the equilibrium thermodynamics ofchemical precipitation. The onset of precipitation was controlledby a saturation index. Outputs included pit current in response toa fixed applied potential mediated by reaction rate and corrosioncap resistance. Depth of penetration was taken into account. Othermodel outputs included corrosion product identity, formation loca-tion and volume. These were typically in good agreement withexperimental findings. Other publications will address the effectsof applied potentials and switching of water chemistry during pitgrowth.

2. Experimental procedure

2.1. Materials

The working electrodes for artificial single pit experiments weremade from 250 �m diameter1 copper wires of grade UNS C11000

1 The merit of using small-sized specimens is the ease of converting the entirespecimen cross-section into a single pit of known area that simplifies the analysisin comparison to the formation of multiple pits at different times on a large planarelectrode. The other advantage of using a small electrode is to reduce the IR dropassociated with the low conductivity of test solution and corrosion product.

H. Ha et al. / Electrochimica Ac

Table 2Equivalent ionic conductances of selected ions.

Ions � (S cm2 /eq)

Na+ 50.11HCO3

− 41.5SO4

2− 80.0Cl− 76.34

s1jw

2

ws1pdtc

�

wccelt

2

ftcP(ftw

scmpoVcA+a

TC

OH− 197.6H+ 349.8

pecimens were ground with silicon carbide paper to a final finish of200 grit to expose a circular flush cross section of ca. 5 × 10−4 cm2

ust before each experiment. Then the specimens were degreasedith methanol and rinsed with deionized water.

.2. Electrolyte

Solutions containing HCO3− with addition of SO4

2− and/or Cl−,hich are commonly observed in potable waters, were used in this

tudy. The concentrations of the anions in each solution were either0−4, 10−3 or 10−2 M with unit anion ratios. The solutions were pre-ared by adding analytical grade of NaHCO3, Na2SO4 and NaCl toeionized water of 18.2 MS/cm conductivity. No attempt to con-rol pH was performed. The conductivities of the solutions werealculated as follow:

bulk =∑

�iziCi (1)

here �bulk is solution conductivity (S/cm), � is equivalent ioniconductance (S cm2/eq), z is ionic charge (eq/mol), C is ionic con-entration (mol/cm3) and i represents each ionic species in thelectrolyte. The equivalent ionic conductances used in our calcu-ation are shown in Table 2 [42]. The theoretical conductivities ofhe test solutions are shown in Table 3.

.3. Electrochemical methods

A conventional three-electrode electrochemical cell was usedor all electrochemical experiments. A nickel ribbon was solderedo the nonexposed end of single copper wires to make an electricalonnection. The counter electrode was a platinum–niobium mesh.otentials were measured by either a saturated calomel electrodeSCE) for chloride-containing solutions or a saturated mercury sul-ate electrode (MSE) for chloride-free solutions, separated from theest solution by a bridge with a Luggin capillary. All the potentialsere reported vs. SCE.

Artificial pits were initiated and stabilized by applying a con-tant potential of +0.5 VSCE for either 1 or 3 h depending on the aniononcentration of the test solution, i.e. longer initiation time forore diluted solutions, to obtain a characteristic pit depth (x2/G; x-

it depth; G-pit diameter) in the range of 0.5–70 �m. Examinationf pit propagation with different initial pit depths was performed.ariation in initial pit depth showed little effect on pit propagation

ompared to corrosion product identity as will be shown below.fter pit initiation and stabilization, the potential was switched to0.3 VSCE to allow the pit to propagate for a period of 100 h. Suchn open circuit potential is readily achieved in these waters when

able 3alculated conductivity of test solutions.

Solution Conductivity of solutions (S/cm)

10 mM 1 mM 0.1 mM

HCO3− + SO4

2− 3.52 × 10−3 3.52 × 10−4 3.52 × 10−5

HCO3− + Cl− 2.19 × 10−3 2.19 × 10−4 2.19 × 10−5

HCO3− + SO4

2− + Cl− 4.78 × 10−3 4.78 × 10−4 4.78 × 10−5

ta 56 (2011) 6165– 6183 6167

chlorinated [23]. Polarization curves of Cu in different waterchemistries were published elsewhere [22,23]. As a frame of ref-erence for artificial pit studies, pitting potentials decreased withincreasing sulfate and chloride concentrations and ranged fromabout +0.5 to 0.0 VSCE but strongly depended on the chemical com-positions of potable waters. Repassivation potentials ranged from0.1 to −0.1 VSCE.

Electrochemical impedance spectroscopy was performed onactively growing artificial pit electrodes during pit propagation at1, 3, 5, 10, 20, 50 and 100 h. The electrode potential during EIS mea-surements was kept at +0.3 VSCE and a cyclic voltage perturbationof ±40 mV was swept from 100 kHz to 10 mHz. The pit Ohmic resis-tance and polarization resistance were obtained by fitting the EISdata to a Randles circuit. The pit Ohmic resistance is the sum ofthe Ohmic resistance of bulk solution outside the pit, the Ohmicresistance of the solution inside the pit and Ohmic resistance ofcorrosion product deposited at the pit.

2.4. Scanning electron microscopy/X-ray energy dispersivespectroscopy

Morphology and chemistry of corrosion products on specimensafter pit growth experiments were analyzed with scanning elec-tron microscopy (SEM) and energy dispersive X-ray spectroscopy(EDS). A JOEL 6700F SEM operated at 15 kV was used in all experi-ments. This voltage provided a kinetic energy for the electron beamtwo times higher than the highest energy of the excited X-rayK� from the samples (i.e. Cu K� = 8.04 keV). After artificial pittingexperiments, the specimens were rinsed in deionized water andair dried. To characterize the structure and composition of the cor-rosion product inner layers, different preparation methods wereemployed. The cross sections perpendicular to the axis of the pitswas exposed by scrapping off the top cap with a razor blade or withan adhesive tape. The cross sections parallel to the long axis of thepit were exposed by grinding the specimens parallel to the wireaxis after casting the whole exposed specimen including the corro-sion products in epoxy for preservation purposes. The final grindingintersected the intact wire, the pit and the corrosion product capover pits.

2.5. Raman spectroscopy

Raman spectroscopy of the corrosion products covering pits wasobtained with a green light excitation of 514.53 nm from an Arlaser source. The scattered light was collected in the backscatter-ing geometry by a single-axis spectrometer and a notch filter (JobinYvon Horiba, T64000) equipped with a charge-coupled devicedetector. In all measurements, the laser power coming out at thesource never exceeded 0.5 W. A grit setting of 600 gr/mm was usedand the spectra were collected for at least 10 min at ambient tem-perature of approximately 22 ◦C. Experiments were carried out inmicro-Raman configuration with a 20× objective lens. The laserbeam spot size was approximately 50 �m. This spot was focusedat various locations on corrosion products both inside and outsidepits.

3. Computational modeling of corrosion product formation

The model used finite element software to describe pitting cor-rosion of copper in waters of different chemistries. The model tookwater composition, temperature, electrochemical potential andgeometrical restrictions as inputs. A cylindrical pit geometry and a

potential dependent pit dissolution law were assumed. A potentialwas applied between the mouth of the pit and the actively corrod-ing pit bottom. The output from the model was the pitting currentas function of time, local concentrations of dissolved species and the

6168 H. Ha et al. / Electrochimica Ac25

0 μm

Copper

Inert material

Stagnant solu�on laye r

Reference electrode

Solu�on influence d by

convec�on

Remote counter

electrodePit dept h

Fig. 1. Schematic of an electrochemical setup to study pitting corrosion with a250 �m diameter cylindrical copper electrode in an inert material. The copper metalconstitutes the working electrode that is polarised to fixed potentials relative to arifi

do

3

cwTTta

wcomnbtaptFaco

b

c

Fw

eference electrode. The blue volume indicates the fraction of the geometry thats covered by the FEM-model (For interpretation of the references to color in thisgure legend, the reader is referred to the web version of this article.).

istribution of solid precipitates and scales when supersaturationf dissolved species was achieved.

.1. Model geometry and boundary conditions

Fig. 1 shows the model geometry. A 250 �m diameter copperylindrical electrode embedded in an inert material served as theorking electrode. The initial depth of penetration was assigned.

he growth in depth could be accounted for through Faraday’s law.he corrosion current passed between the copper metal and a dis-ant counter electrode. A reference electrode was located on thexis of symmetry at some distance from the copper surface.

Fig. 2 illustrates how the boundary conditions for the modelere developed taking advantage of the radial symmetry assuming

onstant solution composition and copper corrosion as a functionf radial position. There were no fluxes across the axis of sym-etry. Thus all fluxes were set to zero across this boundary but

o constraints were imposed on any concentrations. At the loweroundary to the right in Fig. 2, bulk conditions were assumed. Thushe concentrations for all species considered in the model werettributed a predetermined value determined by the solution com-osition for the bulk solution. No constraints of the fluxes acrosshe boundary were imposed. The boundaries to the lower left inig. 2 were assumed to be inert. Thus all fluxes were set to zerocross these boundaries but no constraints were imposed on anyoncentrations. The boundary conditions were the same for the axis

f symmetry.

The corroding copper metal is represented by the left handoundary in Fig. 2. This boundary was a source of Cu+ and Cu2+ ions.

Corrodin g opper metal

Symmetry axis (rota �onal)

Insula�on

Bulk proper�es of the sol u�onTotal conc entra �on fixed

Pola riza�on vol tage

ig. 2. Illustration of the boundary conditions for the model of pitting corrosionith cylindrical growth.

ta 56 (2011) 6165– 6183

The boundary conditions were fluxes for these two components.The magnitude of each flux was influenced by the polarization volt-age according to rate expressions for potential dependent copperoxidation as described below. Under some circumstances, molecu-lar oxygen from the bulk solution might reach the corroding coppermetal surface. A potential dependent reduction rate for oxygen oncopper metal was assumed. Thus, also the flux of oxygen and ofhydroxide ions, might have a non-zero value at this boundary. In thevolume enclosed by the boundaries the conditions were governedby local aqueous equilibrium, conservation of mass formulated bythe transport equations and by precipitation of solids. The onlyreaction between aqueous species considered slow, compared todiffusion, was the oxidation of aqueous Cu+ to aqueous Cu2+ bymolecular oxygen.

3.2. Mathematical equations of the model

The mass transport equations were established with a cor-rection for the non-linear behavior of solution conductivity withconcentration as follows:

ji = −Ci × Di

(1Ci

× ∂Ci

∂x+ 1

�i× ∂�i

∂x

)− Ci

(Di − kD ×

√I

1 + √I

)

× ziF

RT

∂˚

∂x(2)

where j is the flux (mol/m2/s), C is the concentration (mol/m3), Dis the diffusivity (cm2/s), � is the activity coefficient, I is the ionicstrength of the solution, kD is a constant, x is the distance from thepit mouth (x > 0 means outside the pit, x < 0 means inside the pit)and i represents for the ionic species in the electrolyte. Thus, thedriving force may be regarded as having three components; theconcentration gradient, the gradient in the activity coefficient andthe gradient in the electrical potential.

The mass conservation equations were established for a porousmedium filled with electrolyte. The assumption was that the con-duction path was via electrolyte inside the pores rather than viathe solid phase. The equations have the form:

Porosity × ∂ci

∂t= ∂(ji × Porosity)

∂x(3)

Eq. (3) was used to calculate the time derivative of the concentra-tions where the fluxes, ji, are given by Eq. (2).

The transport equations were applied to groups of aqueousspecies rather than to individual species. In an equilibrium sys-tem a species such as H+ or Cu2+ might not be conserved. Rapidreactions with OH− or with SO4

2− might convert one species toanother. However, the total concentration species such as Cu2+

were conserved, barring precipitation reactions. For instance, in asystem including ions and aqueous complexes such as Cu+, Cu2+,H+, OH−, Na+, SO4

2−, HCO3−, H2CO3(aq), CuSO4(aq), CuCO3(aq) and

Cu(OH)2(aq), Eqs. (2) and (3) were applied to the total concentra-tions of Cu2+, [Cu2T], the total concentration of H+, [HT], and thetotal concentration of HCO3

−, [CO2T] as follow:

[Cu2T] = [Cu2+] + [CuSO4(aq)] + [CuCO3(aq)]

+ [Cu(OH)2(aq)] (4)

[HT] = [H+] − [OH−] + [H2CO3(aq)] −[CuCO3(aq)]

−2[Cu(OH)2(aq)] (5)

[CO2T] = [HCO3−] + [H2CO3(aq)] + [CuCO3(aq)] (6)

[Cu1T] = [Cu+] + [CuCl(aq)] + [CuCl2−] (7)

ica Ac

[

Mts

sbssdrt

F

wotiiatt

2

T

S

wc

F

sr

C

C

O

a

I

w(hc((aa

I

w(hc

H. Ha et al. / Electrochim

ClT] = [Cl−] + [CuCl(aq)] + 2[CuCl2−] (8)

eanwhile, Na+ did not take part in any equilibrium reactions inhis system and Eqs. (2) and (3) could be directly applied to thepecies concentration of Na+.

Precipitation reactions of Cu2+ with the anions available in theolutions were considered inside the volume constrained by theoundaries. Table 4 shows all species existed in the water con-idered in this study and selected solid corrosion products. Theelection of solid corrosion products was based on experimentalata and field tests results [4,5,13,16,20,30,43,44]. Precipitationeaction rates were treated with rate constants and a driving forcehat is proportional to the saturation index for the solid compound:

= k(SI1/n − 1) (9)

here F is the precipitation reaction rate, k is the rate constantf the precipitation reaction, n is the number of copper cation inhe chemical formula of the corrosion product, SI is the saturationndex for the solid compound which was calculated by multiply-ng the stability constant for the solid with the ratio of the reactantnd product activities rise to their stoichiometries in the precipi-ation reaction. For instance, cuprite (Cu2O) was formed followinghe reaction:

Cu+ + H2O → Cu2O(s) + 2H+ (10)

he saturation index for cuprite was calculated by

ICuprite = KCuprite ×a2

Cu+

a2H+

(11)

here Kcuprite is a constant. Therefore the precipitation rate foruprite was expressed as

Cuprite = kCuprite(SI1/2Cuprite − 1) (12)

The electrochemical reactions considered were the anodic dis-olution of copper metal to Cu+ and Cu2+ and the oxygen reductioneaction:

u(s)k1f↔k1b

Cu+ + e− (13)

u(s)k2f↔k2b

Cu2+ + 2e− (14)

2 + 4e− + 2H2OkO2−→4OH− (15)

The current density of reaction 13 was conventionally writtens:

1 = F × k10(10E−E01

b1a − aCu+ × 10− E−E01b1c )[A/m2] (16)

here F is Faraday constant, k10 is the rate constant of reaction (13)mol/s m2), E is the pit bottom potential (VSCE), E01 is the standardalf cell potential of reaction (13) (VSCE), b1a and b1c are the Tafelonstants for the oxidation of Cu(s) and reduction of Cu+ in reaction13), respectively (V/decade), aCu+ is the activity of Cu+. Reaction14) involved adsorbed Cu+ which acted as a precursor intermedi-te, therefore the current density for reaction (14) was expresseds:

2 = 2 × F × k20(aCu+(ads) × 10E−E02

b2a − aCu2+ × 10− E−E02b2c ) [A/m2]

(17)

here F is Faraday constant, k20 is the rate constant of reaction 14mol/s m2), E is the pit bottom potential (VSCE), E02 is the standardalf cell potential of reaction (14) (VSCE), b2a and b2c are the Tafelonstants for the oxidation of Cu+ and reduction of Cu2+ in reaction

ta 56 (2011) 6165– 6183 6169

(14), respectively (V/decade), aCu2+ is the activity of Cu2+, aCu+(ads)is the activity of Cu+(ads) and is calculated by:

aCu+ads = 10E−E010.059 (18)

The values k20 = 0.1 mol/s m2 was determined from literatures [45].Reaction (13) is known to be very fast and behaved as a local equi-librium. A value k10 = 0.1 mol/s m2 was found to be sufficiently highto make reaction (13) behave as at equilibrium.

The oxygen reduction on copper at potentials relevant for pittingcorrosion has been studied by Jiang and Brisard [46]. They reportedfirst order behavior and a four-electron transfer, at least for thehigher potential ranges studied for the oxygen reduction. The high-est potential at which they studied the process was in 0.1 M HClO4solutions. Analysing their data led to an approximated expressionof the rate constant:

kO2 = 1.1 × 10−5 × 10−(E−0.242)/0.18[mol/s] (19)

In the present study a constant value for kO2 of 10−4 mol/s, whichcorresponds to the value at the potential of −0.18 VSCE, was used.The application of the selected value of kO2 at all potentials wouldtherefore seem to overestimate the rate of the reaction. However,because of consumption of O2 by Cu+ in the solution, oxygen onlyrarely reaches the copper surface at significant concentrations andtherefore the error was insignificant.

The FEM model was solved using COMSOLTM software with theinput for the model including applied potential, solution chemistryand composition, initial pit depth and all physical parameters asso-ciated with the ionic species and the solid corrosion products. Theoutcomes were pit current, pit depth, concentration vs. positionsinside and outside of the pit as well as occurrence of precipitation,potential gradient and porosity distribution with time resolution.

4. Results

4.1. Pit growth rate

Fig. 3 shows experimental anodic pit propagation current den-sity vs. time curves during potentiostatic polarization of artificialpits at +0.3 VSCE for 100 h in different bulk water chemistries indi-cated. In all cases, the pitting current densities in HCO3

− + Cl−

solutions were much lower than those in HCO3− + SO4

2− and inHCO3

− + SO42− + Cl− solutions. In the waters of 10 mM concen-

tration, the pitting current density on Cu in solutions containingHCO3

− + SO42− was the highest following by the current den-

sity in HCO3− + SO4

2− + Cl− solution. The pitting current density inwater containing HCO3

− + Cl− was the lowest. In waters of 1 mMand 0.1 mM concentrations, the pitting current densities on Cuin HCO3

− + SO42− and in HCO3

− + Cl− solutions were about thesame. Notably these were at least one order of magnitude higherthan those in solutions containing only HCO3

− + Cl−. The currentdensities were lower with solutions of higher concentration. Theionic conductivities of all test solutions are shown in Table 3. Itcan be seen that the pitting current densities on copper were notproportional to the bulk homogenous ionic conductivity of thetest solutions. Except in 0.1 mM solutions where current densitiestended to rise with time, the pitting current densities tended todecreased with time. Abrupt drops are seen in the HCO3

− + Cl− solu-tions after 22 (10 mM) or 27 (1 mM) h but not in 0.1 mM solutionas indicated by the arrows.

Fig. 4 shows corresponding theoretical i–t curves calculatedfrom the model during potentiostatic polarization at +0.3 VSCE over

the same set of water chemistries. Similar to the experimental data,in waters of the same concentration, the pitting currents on Cu insolutions containing HCO3

− + SO42− or HCO3

− + SO42− + Cl− were

at least one order of magnitude higher than those in solutions

6170 H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183

Table 4Summary of all possible species existed in the system and selected solid corrosion products that were considered in this model. The selection of solid corrosion products wasbased on experimental data and field tests results.

Species in solution Solid corrosion products

Cations Anions Neutrals Carbonate Sulfate Chloride Oxide

H+ OH− H2CO3(aq) Cu2(CO3)(OH)2 Cu4(SO4)(OH)6 Cu2Cl(OH)3 Cu2ONa+ HCO3

− CuCO3(aq) CuCl CuOCu+ CO3

2− Cu(OH)2(aq) CuCl2·2H2OCu2+ SO4

2− CuCl(aq)

cprgidelHssisb

4

f51o

Fm

Cl−

CuCl2−

ontaining HCO3− + Cl−. The decrease in current was due to the

recipitation of corrosion products that leads to an effective ionicesistance increase which decreases E applied at the pit bottom thatoverns the reaction rate via Eq. (16). One interesting feature in the–t curves of artificial pits in HCO3

− + Cl− solutions was a suddenrop of the pitting current density which was also observed in thexperimental i–t curves at 22 and 27 h (Fig. 3). This occurred afteress than 1 h in 10 mM HCO3

− + Cl− solution, less than 5 h in 1 mMCO3

− + Cl− solution and only after 80 h in 0.1 mM HCO3− + Cl−

olution. The sudden current drop occurred sooner for pits grown inolutions of higher concentration because it was easier to achieveonic species supersaturation to form copper chloride containingalts such as atacamite/eriochalcite to plug pits, as will be shownelow.

.2. Impedance measurements in pits

EIS measurements were performed during pit growth in dif-

erent water chemistries at various time points of 1, 3, 5, 10, 20,0 and 100 h. Fig. 5 shows a typical EIS data for a pit grown in0 mM NaHCO3 + 10 mM Na2SO4 solution at the applied potentialf +0.3 VSCE. The low frequency data is assigned to the sum of the

ig. 3. Experimental i–t curves from C11000 copper measured during potentiostatic poeasurements conducted at 1, 3, 5, 10, 20, 50 and 100 h at +0.3 VSCE.

charge transfer resistance and an Ohmic resistance. The tail in theEIS spectrum at high frequencies in the Nyquist plot is assigned toartifact often reported in low conductivity solutions [47,48]. TheOhmic resistance at 100 h is indicated by the arrow in Fig. 5. ThisOhmic resistance was verified by spiking solutions containing pit-free copper electrodes in the same geometry as artificial pits withsupporting electrolyte to shift the point indicated as R�pit. Thevalues of the total pit Ohmic resistance were obtained by fittingthe semi-circle segments in the Nyquist plot to a Randles circuit asshown in Fig. 6a. Fig 6b and c show a good fit between the exper-imental and equivalent electrical circuit model data in Nyquistand Bode plots for an artificial pit grown in 1 mM NaHCO3 + 1 mMNa2SO4 solution at +0.3 VSCE for 100 h. In some experiments, theartifact tail in the spectrum was dominant so that the fitting pro-cedure was not reliable towards establishing R�pit. In that case,the value R�pit could not be obtained and will not be presentedhere.

The dependence of the Ohmic resistances, R�pit, polarization

resistance, Rp, and their sum, obtained from actively growing pitswith time, is shown in Fig. 7. Both Ohmic and polarization resis-tances changed in the same manner during polarization. The i–tcurves measured during potentiostatic polarization of artificial pits

larization of artificial pits at +0.3 VSCE for 100 h in different water chemistries. EIS

H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183 6171

0 1 2 3 4 510-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

10 mM NaHC O3 + 10 mM Na

2SO

4

10 mM NaHC O3 + 10 mM NaC l 10 mM NaHC O3 + 10 mM Na2SO4 + 10 mM NaC l

i (A

/cm

2 )

Time (hours )0 5 10 15 20 25 30

10-5

10-4

10-3

10-2

10-1

100

i (A

/cm

2 )

Time (hour s)

1 mM NaHC O3 + 1 mM Na2SO4

1 mM NaHC O3 + 1 mM NaC l 1 mM NaHC O

3 + 1 mM Na

2SO

4 + 1 mM NaC l

0 20 40 60 80 10 010-6

10-5

10-4

10-3

10-2

10-1

100

i (A

/cm

2 )

Tim

0.1 mM NaH CO3 + 0.1 mM Na2SO4

0.1 mM NaH CO3 + 0.1 mM NaCl 0.1 mM NaH CO

3 + 0.1 mM Na

2SO

4 + 0.1 mM NaC l

(a) (b)

(c)

ation

iatgt

FNF

Fig. 4. Theoretical i–t curves calculated during potentiostatic polariz

n test solutions corresponding to each R�pit and Rp data set were

lso plotted in the same graphs. At the same solution concentra-ion, the Ohmic resistances and polarization resistances of pitsrown in HCO3

− + Cl− solutions were at least one order of magni-ude higher than those grown in the sulfate-containing solutions.

0 5 10 15 20 25 30

0

-5

-10

-15

-20

-25

-30 1 hour 3 hours 5 hours 10 hours 20 hours 50 hours 100 hours

Z'' (

cm2 )

Z' ( cm2)

(a)5x

5x

5x

5x

Z (

.cm

2

Z'' (

cm)

Z' (k cm )

R pit

ig. 5. EIS spectra of an artificial pit measured at different time points of 1, 3, 5, 10, 20, 5aHCO3 +10mM Na2SO4 solution at the applied potential of +0.3VSCE; (a) Nyquist plot aig. 16a indicates R�pit after 100 hours.

e (hour s)

of artificial pits polarized to +0.3 VSCE in different water chemistries.

Fig. 7 shows that the pitting current is inversely proportional to

the sum of the pit Ohmic resistance and polarization resistance.The slopes of the R�pit and Rp–t and i–t curves of the same testsolution also have inverse relationships. Furthermore, Rp > R�pit in10 mM solutions, but R�pit > Rp in more dilute solutions. This sug-

(b)10-3 10-2 10-1 100 101 102 103 104 105 106

10-1

100

101

102

Fre q (H z)

-80

-60

-40

-20

0

Phase ( o)

0 and 100 h during the course of potentiostatic polarization experiment in 10mMnd (b) Bode plot. The inset in (a) shows the spectra for the first 20 h. The arrow in

6172 H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183

Fig. 6. Fitting of semi-circle segments of EIS spectra measured during artificial pit propagation at +0.3 VSCE in different water chemistries and concentrations; (a) Randlescircuit for fitting, (b) and (c) experimental and fitting curves in Nyquist and Bode plots of an artificial pit grown in 1 mM NaHCO3 + 1mM Na2SO4 solution at +0.3VSCE for 100 h.R ion prc ction

gitab

4p

csicmwwwccmtc1

ascaclptups

uoipeilp

�pit is the Ohmic resistance of the pit including the Ohmic resistance of the corrosapacitance of the copper surface and Rct is the resistance of the charge transfer rea

ests that pit propagation under mixed or Ohmic control was likelynfluenced by the nature of the corrosion products. In summaryhe nature of the corrosion product formed in pits and the pit capre of great importance to pit growth. These issues are consideredelow.

.3. Morphology and chemical identity of corrosion products inits

Fig. 8 shows the morphology of corrosion products on the artifi-ial pits grown potentiostatically at +0.3 VSCE after 100 h in differentolutions. In these micrographs the corrosion product cap was leftn place. The size of the caps varies from 300 �m which was barelyovered the 250 �m diameter of the artificial pit to thousands oficrometers. The cap diameters grown in HCO3

− + SO42− solutions

ere the biggest while the ones grown in HCO3− + Cl− solutions

ere the smallest. Caps grown in lower concentration solutionsere not necessarily smaller. In sulfate-containing solutions, the

aps morphology changed from mushroom-shaped mounds toorral-like plates to thin membranes just enough to cover the pitouth as the concentration of the solutions changed from 10 to 1

o 0.1 mM, respectively. In HCO3− + Cl− solutions, the pit caps were

a. 300 �m. Deposition of granules with size in the range of ca.–20 �m was observed at the top surfaces.

Fig. 9 shows the morphology of the pits grown potentiostaticallyt +0.3 VSCE in different waters after cap removal. In HCO3

− + SO42−

olutions, removal of the caps revealed deep open pits with red,ubic corrosion product crystals (less than 10 �m in size) depositedt the pit bottom and on the pit wall. In HCO3

− + Cl− solutions, theap had strong bond with the copper substrate. The pits were shal-ower, covered by a dense corrosion product layer of small, redarticles (less than 10 �m in size). In HCO3

− + SO42− + Cl− solutions,

he pits were filled with mixture of red and white corrosion prod-cts almost to the pit mouth. The size and the porosity of corrosionroducts decreased as the concentration of HCO3

− + SO42− + Cl−

olutions increased.Analysis on morphology and identities of the corrosion prod-

cts were performed with SEM, EDS and Raman spectroscopyn cross section along the pit axis. In backscattered electronmages, the dark areas are epoxy, the gray areas are corrosionroducts or copper and the bright areas are locations in epoxy

xperiencing excessive charge. The chemical identification processncluded matching the experimental Raman spectra with a col-ection of reference Raman spectra which was selected from allossible combination of copper and anion species in the test solu-

oduct deposited at the pit and the Ohmic resistance of the solution. C is the parallelof copper.

tions [16,34–36,49]. Figs. 10–15 show the structure and chemicalanalysis of the corrosion products deposited inside and out-side of the pits after potentiostatic polarization at +0.3 VSCE for100 h in 10 mM NaHCO3 + 10 mM Na2SO4, 10 mM NaHCO3 + 10 mMNa2SO4 + 10 mM NaCl and 10 mM NaHCO3 + 10 mM NaCl solutions.In all solutions, Raman spectra indicated the formation of an outercorrosion product top layer of malachite (Cu2CO3(OH)2). Howeverin 10 mM NaHCO3 + 10 mM NaCl solution, the malachite top layerwas compact and thin in contrast with a porous and voluminousmalachite layers in 10 mM NaHCO3 + 10 mM Na2SO4 and 10 mMNaHCO3 + 10 mM Na2SO4 + 10 mM NaCl solutions.

In sulfate containing solutions (Figs. 10–13), a porousand thick layer of brochantite (Cu4SO4(OH)6) or posnjakite(Cu4SO4(OH)6·H2O) with a plate-like structure was formed under-neath the malachite top layer. At the pit mouth, a relatively thinand compact layer rich in Cu, C and O was detected by EDS butthe molecular identity could not be resolved by Raman. After100 h growth, the pits were ca. 1000 �m deep and filled withdeposits which their nature depended on the solution chem-istry. Cuprite (Cu2O) was the only corrosion product inside pitsgrown in NaHCO3 + Na2SO4 solution while cuprite and atacamite(Cu2Cl(OH)3) or eriochalcite (CuCl2·2H2O) were found inside pitsgrown in NaHCO3 + Na2SO4 + NaCl solution.

In contrast to sulfate-containing solutions, the corrosion prod-uct layers in 10 mM NaHCO3 + 10 mM NaCl solution (Figs. 14 and 15)was thin and compact. Underneath the malachite top layer, onlycuprite was detected by Raman spectroscopy. However, the exis-tence of Cl detected with EDS and the green color of this layersuggested that atacamite/eriochantite/nantokite might form partof the layer. The pit depth in this solution after 100 h potentiostaticpolarization at +0.3 VSCE was less than 100 �m.

EDS and Raman analysis of corrosion products at the artificialpits are summarized in Table 5. Before cap removal, Cu, C and Owere found by EDS in the top layers of the caps grown in 10 mMconcentration solutions and in 1 mM HCO3

− + 1 mM Cl− solution.The corrosion product was identified as malachite by Raman spec-troscopy. Cu, S, O and trace of C were detected at the top layersof the caps grown in sulfate-containing solutions at 1 mM con-centration and in 0.1 mM HCO3

− + 0.1 mM SO42− solution. Raman

spectroscopy identified the corrosion product as either brochantiteor posnjakite. Cu, Cl and O were detected in the top layers of the caps

grown in chloride-containing solutions at 0.1 mM concentration.

The composition of the corrosion products inside the pit was alsoanalyzed after cap removal. In HCO3

− + SO42− solutions, the corro-

sion products were comprised of Cu, S, O and C (brochantite). In

H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183 6173

Fig. 7. (a)–(c) The dependence of R�pit, Rp, R�pit + Rp and i with time during pit growth at +0.3 VSCE in 10 mM CO3− + 10 mM SO4

2− , 10 mM CO3− + 10 mM SO4

2− + 10 mM Cl−

a − − Rp and

t ectra.

E f 10 or

Hpsw

daH

nd 10 mM CO3 + 10 mM Cl solutions respectively; (d) the dependence of R�pit +ime in 10 and 1 mM solutions. The R�pit and Rp values were extracted from EIS spIS measurement. The numbers 10 and 1 in the legends denote the concentration oepresent HCO3

− , SO42− or Cl− , respectively.

CO3− + SO4

2− + Cl− solutions, the corrosion products were com-rised of Cu, Cl and O (atacamite or eriochalcite). In HCO3

− + Cl−

olutions, Cu, Cl and O were also detected, however only cupriteas found by Raman.

Fig. 16 shows the results of the computational model pre-icting the location and porosity of corrosion products insidend outside pits grown potentiostatically at +0.3 VSCE in 10 mMCO3

− + 10 mM SO42−, 10 mM HCO3

− + 10 mM SO42− + 10 mM Cl−

i with time in 10 mM solutions, (e) and (f) the dependence of R�pit, Rp and i withThe pitting current values were taken from potentiostatic polarization data beforer 1 mM of the test solutions, respectively. The characters C, S and Cl in the legends

and in 10 mM HCO3− + 10 mM Cl−. The predicted pit depth and

the size of the corrosion product cap was reduced when changingthe water chemistry from 10 mM HCO3

− + 10 mM SO42− to 10 mM

HCO3− + 10 mM SO4

2− + 10 mM Cl− and to 10 mM HCO3− + 10 mM

Cl−. Thus the pit was deeper in Fig. 16a compared to Fig. 16c. More-over, as the water chemistry changed the porosity of the corrosionproduct and the location of the denser product changes from out-side to inside the pit. That is, little corrosion product deposited

6174 H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183

Fos

Frcp

ig. 8. SEM micrographs show the morphology of intact pit caps grown potentiostatically af the test solutions in which the pit was grown are labeled in each figure. The numbers

olutions, respectively. The characters C, S and Cl in the labels stand for HCO3− , SO4

2− and

ig. 9. SEM micrographs show the morphology of corrosion products within pits growemoval. The chemistry and concentration of the test solutions in which the pit was grooncentration of 10, 1 and 0.1 mM of the test solutions, respectively. The characters C, S anit mouth in each figure was 250 �m.

t +0.3 VSCE for 100 h in different water chemistries. The chemistry and concentration10, 1 and 0.1 in the labels denote the concentration of 10, 1 and 0.1 mM of the test

Cl− , respectively. An estimation of the size of the cap is shown in each figure.

n potentiostatically at +0.3 VSCE for 100 h in different water chemistries after capwn are labeled in each figure. The numbers 10, 1 and 0.1 in the labels denote thed Cl in the labels stand for HCO3

− , SO42− and Cl− , respectively. The diameter of the

H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183 6175

Table 5Composition of corrosion products at artificial pits grown potentiostatically at +0.3 VSCE for 100 h in different solutions. The analysis was performed with EDS and Ramanspectroscopy at the pit before and after cap removal.

Test solution Before cap removal After cap removal

EDS Raman EDS Raman

10 C + 10 S Cu, C, O Malachite Cu, S, O, C Brochantite1 C + 1 S Cu, S, O, C Brochantite Cu, S, O, C Brochantite0.1 C + 0.1 S Cu, C, O, S Not available Cu, S, O, C Not available10 C + 10 S + 10 Cl Cu, C, O Malachite Cu, Cl,O Atacamite/Eriochalcite1 C + 1 S + 1 Cl Cu, C, O, S Brochantite Cu, Cl,O Not available0.1 C + 0.1 S + 0.1 Cl Cu, Cl,O Not available Cu, Cl,O Not available

hite

hiteailabl

ibsfq

dpSmtsTatmF

5

5

tp

Fg(oi

10 C + 10 Cl Cu, C, O Malac1 C + 1 Cl Cu, C, O Malac0.1 C + 0.1 Cl Cu, Cl,O Not av

nside the pit formed in 10 mM HCO3− + 10 mM SO4

2− solution,ut more was found in 10 mM HCO3

− + 10 mM SO42− + 10 mM Cl−

olution. A compact corrosion product layer with low porosity wasormed in 10 mM HCO3

− + 10 mM Cl− solution. These findings areualitatively similar to Figs. 8 and 9 as well as Figs 10, 12, and 14.

The identity and distribution of corrosion products formed inifferent water chemistries are shown in Fig. 17. The top layer of theit caps in all solutions was malachite. In 10 mM HCO3

− + 10 mMO4

2− solution, brochantite was found as a sublayer underneath thealachite top layer and trace of cuprite was found deposited inside

he pit. In 10 mM HCO3− + 10 mM SO4

2− + 10 mM Cl− solution, aublayer comprised of brochantite and atacamite was predicted.he pit in this solution was filled with nantokite and a smallmount of cuprite. In 10 mM HCO3

− + 10 mM Cl− solution, a mix-ure of cuprite, nantokite and atacamite forming a layer of several

icrometers was predicted. These findings are in agreement withigs. 11, 13 and 15.

. Discussion

.1. Effect of water composition on pit growth kinetics

Both experimental data and model results (Figs. 3 and 4) indicatehat water chemistry and concentration have significant effects onit growth kinetics. At all concentration, the pitting current densi-

ig. 10. SEM photo and EDS analysis on a cross section along a pit axis. The pit wasrown potentiostatically at +0.3 VSCE for 100 h in 10 mM NaHCO3 + 10mM Na2SO4;a) backscattered electron image and (b) EDS spectra. The inset in (a) is a SEM imagef the pit from the top down view after removal of the cap. Points 1, 2 and 3 in (a)ndicate the location where EDS analysis was performed.

Cu, Cl,O CupriteCu, Cl,O Cuprite

e Cu, Cl,O Not available

ties in HCO3− + SO4

2− solutions were several orders of magnitudelarger than those in HCO3

− + Cl− solutions. As the pit grew, pit-ting current densities in HCO3

− + SO42− solutions decreased but

the pit did not repassivate. In HCO3− + Cl− solutions, repassiva-

tion occurred as indicated by abrupt current densities decreasedbelow 10−6 A/cm2 (Fig. 3a). Further, adding sufficient amount ofCl− to HCO3

− + SO42− solutions, e.g. 10 mM, can decrease the pitting

current density by one order of magnitude (Fig. 3a).To elucidate the effect of water composition on the pit propa-

gation, the pit depth during potentiostatic polarization at +0.3 VSCEwas calculated based on the following equation derived from Fara-day’s law:

d =t∫0

A × i(t)z × � × F

dt (20)

where d is the pit depth (cm), A is the atomic weight of cop-per (A = 64 g/mol), i(t) is the pitting current density (A/cm2),t is time (s), z is the number of e− in charge transfer reac-tion associated with copper dissolution (z ≈ 2 [16,24]), � isthe density of copper (� = 8.96 g/cm3), F is Faraday constant(F = 96,500 C/mol/equivalent).

The pit depth vs. time curves were then fitted to a power func-tion d = do × tn, a common empirical growth law in pitting corrosion,where do and n are constants [50–55]. The pit growth rate is pro-portional to the pitting current i, i.e., d′ = do × n × tn−1. Therefore, ifn < 1, the pit growth rate, will decrease with time; if n = 1, the pitgrowth rate will independent of time; and if n > 1, the pit growthrate will increase with time. The product of do and n also deter-mines the magnitude of the pit growth rate and is the dominantterm when t is small. Fig. 18 shows the experimental pit depthvs. time curves plotted together with the fitted curves. The val-ues of the constants do and n are summarized in Table 6. Mostd–t curves can be fitted with one power function, except the d–tcurves in 10 mM HCO3

− + 10 mM Cl− and 0.1 mM HCO3− + 0.1 mM

Cl− solutions which must be fitted with two different powerfunctions.

Fig. 18 shows a good fit between the experimental data andthe empirical power law for pit growth. In most of the cases,the values of n in HCO3

− + SO42− and HCO3

− + SO42− + Cl− solu-

tions were higher than those in HCO3− + Cl− solutions at the

same concentration. This indicates faster pit growth rates in theHCO3

− + SO42− and HCO3

− + SO42− + Cl− solutions in comparison

to those in HCO3− + Cl− solutions during a long term pit growth. In

some cases such as during the first 8 h in 10 mM HCO3− + 10 mM

Cl−, the value of n was 0.708 which was comparable to that in

10 mM HCO3

− + 10 mM SO42−, however the product of do × n in

the former solution was one order of magnitude smaller thanthat in the later case, and the result was a slower pitting rate inthe former solution. After the first 8 h, the value of n in 10 mM

6176 H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183

Point 2

200 40 0 600 800 10 00 1200

inte

nsity

(a.u

)

wavenumber (cm-1)

Experi ment Malachi te (ref erence ) Broch antite (reference)

Point 1

200 40 0 60 0 80 0 100 0 120 0

inte

nsity

(a.u

)

wavenumber (cm-1)

Experi ment Posnja kite (refer ence) Brochantite (r eference )

(b)(a)

Fig. 11. Raman spectra on a cross section along a pit axis. The pit was grown potentiostatically at +0.3 VSCE for 100 h in 10 mM NaHCO3 + 10mM Na2SO4. Points 1 and 2 areindicated in Fig. 10.

Table 6Summary of values for do and n obtained from fitting experimental pit depth vs. time curves with power function d = do × tn; d is pit depth (�m) and t is time (s).

Solution do n do × n

10 mM HCO3− + 10 mM SO4

2− 4.1 × 10−2 0.749 3.1 × 10−2

1 mM HCO3− + 1 mM SO4

2− 8.6 × 10−4 0.971 8.3 × 10−4

0.1 mM HCO3− + 0.1 mM SO4

2− 2.1 × 10−5 1.067 2.2 × 10−5

10 mM HCO3− + 10 mM SO4

2− + 10 mM Cl− 9.2 × 10−2 0.632 5.8 × 10−2

1 mM HCO3− + 1 mM SO4

2− + 1 mM Cl− 1.06 × 10−3 0.966 10−2

0.1 mM HCO3− + 0.1 mM SO4

2− + 0.1 mM Cl− 6.6 × 10−5 1.01 6.67 × 10−5

10 mM HCO3− + 10 mM Cl− 3.1 × 10−3a 2.82b 0.708a 0.026b 2.2 × 10−3 7.3 × 10−2

1 mM HCO3− + 1 mM Cl− 2.2 × 10−2 0.357 7.8 × 10−3

0.1 mM HCO3− + 0.1 mM Cl− 0.02c 1.6 × 10−14d 0.177c 2.55d 3.5 × 10−3 4.08E−14

a Values were fitted for the first 8 h segment of the i–t curve during potentiostatically at +0.3 VSCE in 10 mM HCO3− + 10 mM Cl− .

t +0.3 VSCE in 10 mM HCO3− + 10 mM Cl− .

tically at +0.3 VSCE in 0.1 mM HCO3− + 0.1 mM Cl− .

at +0.3 VSCE in 0.1 mM HCO3− + 0.1 mM Cl− .

HdiHi

ewslgmpdbosdvascs1iowtt

b Values were fitted for the segment of the i–t curve after 8 h potentiostatically ac Values were fitted for the first 30 h segment of the i–t curve during potentiostad Values were fitted for the segment of the i–t curve after 30 h potentiostatically

CO3− + 10 mM Cl− dropped to 0.026 which indicates a significant

ecrease in the pit growth rate due to the role of n as a power termn the empirical pit growth law. After 100 h, the pit depth in 10 mMCO3

− + 10 mM SO42− solution was ca. 550 �m while the pit depth

n 10 mM HCO3− + 10 mM Cl− solution was only ca. 5 �m.

The effect of solution concentration on pit growth rate can bestimated qualitatively from the curvature of the d–t curves. Inaters of high concentration (e.g., 10 mM), the pit growth rate

lowed with time (negative curvature). In contrast, in waters ofower concentration (e.g., 0.1 mM), the pit growth rate increasedradually with time (slightly positive curvature). In waters ofedium concentration (e.g., 1 mM), the pit growth rate was inde-

endent of time (a linear curve) over the 100 h testing period. Theependence of pit growth kinetics on solution composition cane seen more clearly when comparing the value of the constant nbtained from power law fitting. Table 6 shows that in waters of theame chemistry, the value of n increased as the anion concentrationecreased. This trend indicates an interesting consequence as thealue of n determines the relationship between the pit growth ratend time as pointed out earlier. For instance, in sulfate-containingolutions (i.e. HCO3

− + SO42− and HCO3

− + SO42− + Cl−) of 10 mM

oncentration, n was less than 1 and the pit growth rate in theseolutions decreased with time. In sulfate-containing solutions of

mM, n was approximately 1 and the pit growth rate was almostndependent with time. Meanwhile in sulfate-containing solution

f 0.1 mM, n was larger than 1 and the pit growth rate increasedith time. The analysis of the pit depth vs. time curves and the fit-

ing of the empirical pit growth law to the experimental data showhat anion concentration affects the pit propagation rate such that

Fig. 12. SEM photo and EDS analysis on a cross section along a pit axis. Thepit was grown potentiostatically at +0.3 VSCE for 100 h in 10 mM NaHCO3 + 10mMNa2SO4 + 10 NaCl; (a) backscattered electron image and (b) EDS spectra. The insetin (a) is a SEM image of the pit after removal of the cap. Points 1, 2, 3,4 and 5 in (a)indicate the location where EDS analysis was performed.

H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183 6177

200 40 0 600 800 1000 1200

inte

nsity

(a.u

)

wavenumber (c m-1)

Expe rime nt Cupri te (ref ere nce ) Teno rite (reference)

200 400 600 800 100 0 120 0

inte

nsity

(a.u

)

wave number (c m-1)

Expe rime nt Mal achite (refe rence )

200 400 600 800 1000 1200

Exp erime nt Posn jakit e (r eferenc e) Brocha ntite (ref erenc e)

inte

nsity

(a.u

)

wavenum ber (c m-1)

Point 1 Point 2

Point 4

200 400 600 800 1000 1200

inte

nsity

(a.u

)

wavenum ber (c m-1)

Expe rime nt Erio cha lcite (refer enc e) Atacam ite (ref ere nce )

Point 5

(b)(a)

(d)(c)

F tenti1

pt

vf1itiavp

Ft+l

ig. 13. Raman spectroscopy on a cross section along a pit axis. The pit was grown po, 2, 4 and 5 are indicated in Fig. 12a.

its grown in more concentrated solutions tend to slow down fasterhan pits grown in more diluted solutions.

In HCO32− + SO4

2− and HCO32− + SO4

2− + Cl− solutions, while naries in a small range around 1, do changes in a much larger rangerom 10−5 (in 0.1 mM solutions) to 10−3 (in 1 mM solutions) to0−2 (in 10 mM solutions). The magnitude of the pit growth rate

n HCO32− + SO4

2− and HCO32− + SO4

2− + Cl− solutions also followshe order that the lowest is in 0.1 mM solutions, the medium is

n 1 mM solutions and the highest is in 10 mM solutions, with thectual magnitude depending on the growth time. Therefore, thealue of do reflects the aggressiveness of solutions that causes cop-er pitting.

ig. 14. SEM photo and EDS analysis on a cross section along a pit axis. (a) backscat-ered electron image and (b) EDS spectra. The pit was grown potentiostatically at0.3 VSCE for 100 h in 10 mM NaHCO3 + 10 NaCl. Points 1 and 2 in (a) indicate theocation where EDS analysis was performed.

ostatically at +0.3 VSCE for 100 h in 10 mM NaHCO3 + 10mM Na2SO4 + 10 NaCl. Points

The effect of anion concentration on the dependence of pitgrowth rate with growth time poses a question that whether ornot the bulk solution conductivity directly affects the pit growthrate or something else involves in the process of slowing downthe pit propagation. If the pit growth rate is controlled by solu-tion conductivity, one would expect that the pitting current wouldbe proportional to the solution concentration, i.e. current densityin 10 mM solutions would have been 10 times higher than that in1 mM and 100 times higher than in 0.1 mM based on differencesin bulk ionic conductivity. However, the i–t curves in Figs. 1 and 2did not follow that trend. Therefore, the solution conductivity doesnot directly control the pit growth rate during pit propagation oncopper. This conclusion points to the role of a resistive cap whichis a large factor in controlling pit growth. It makes sense that theamount of corrosion product available would be proportional to thetotal pit growth charge. The other important factor is the effect ofwater chemistry on polarization resistance which is lower in sulfatesolutions (Fig. 7e).

5.2. Effect of water composition on pit cap Ohmic resistance

The total Ohmic resistance of pit during potentiostatic polariza-tion at +0.3 VSCE were extracted from the intermediate frequency

region in EIS spectra and was shown in Fig. 8. This total Ohmic resis-tance, R�pit, includes the Ohmic resistance inside the pit, Rinside, theOhmic resistance of corrosion product, Rcap, and the Ohmic resis-tance of the bulk solution, Rbulk. The magnitude of Rinside and Rbulk

6178 H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183

200 40 0 600 80 0 10 00 120 0

inte

nsity

(a.u

)

wavenu mber (cm-1)

Exper imen t Cup rite (r eference) Teno rite (referen ce)

200 40 0 60 0 80 0 100 0 120 0

inte

nsity

(a.u

)

waven umbe r (cm-1)

Exper iment Malach ite (r eference)

Cross sec� onTop surfa ce (b)(a)

F e pit wl icrog

coHsR

ml

R

wt

FSCnct

ig. 15. Raman spectroscopy on top layer and on a cross section along a pit axis. Thaser beam on cross section covered both point 1 and point 2 as shown in the SEM m

an be estimated based on the knowledge of the conductivitiesf the solution inside pits and of the bulk solutions, respectively.ence, the value of Rcap can be obtained as a function of time by

ubtracting Rinside and Rbulk from the effective Ohmic resistance

�pit measured by EIS.Considering a pit with corrosion product cap as a hemispherical

icroelectrode, the resistance of the bulk solutions can be calcu-ated:

1

bulk =

2�bulk�rcap(21)

here �bulk is the conductivity of bulk solution (S/cm) and rcap ishe radius of cap (cm). The bulk solution conductivity of the test

ig. 16. Prediction of morphology and porosity of corrosion products inside and outsidO4

2− , (b) 10 mM HCO3− + 10 M SO4

2− + 10 mM Cl− and (c) 10 M HCO3− + 10 mM Cl− . Th

u(I) and Cu(II) solid corrosion product formation govern by equilibrium thermodynamicantokite, cuprite, brochantite and atacamite corrosion product formation were consideompact corrosion product and deep red color means no solid (For interpretation of the rhis article.).

as grown potentiostatically at +0.3 VSCE for 100 h in 10 mM NaHCO3 + 10 NaCl. Theraph in Fig. 14(a) The chemical species detected are shown in Fig. 14(b).

solutions is listed in Table 3. The radius of cap in HCO3− + SO4

2− andHCO3

− + SO42− + Cl− solutions is taken as 500 �m and the radius of

the cap in HCO3− + Cl− solution is taken as 125 �m, approximately

the actual cap size observed by SEM.The resistance inside the pits is calculated as follows:

Rinside = d

�inside�r2(22)

where d is the pit depth (cm), �inside is the conductivity of solutioninside pit (S/cm) and r is the radius of pit (cm). The pit depth is cal-culated from Equation 3. The conductivity of the solutions insidepits is assumed to be about 10 times greater than the conductiv-

e pits grown potentiostatically at +0.3 VSCE for 75 h in (a) 10 mM HCO3− + 10 mM

e model included copper oxidation kinetics, transport by migration and diffusion,s and a saturation index, as well as pit current and depth of penetration. Malachite,red. The model was developed for cylindrical pit geometry. Deep blue color meanseferences to color in this figure legend, the reader is referred to the web version of

H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183 6179

-1 0 1 2 3 4

0

10

20

30

40

Con

cent

ratio

n of

sol

id (m

ol/L

)

Distance ( m)

Cuprite Mala chit e Atachamite Nantokite

-40 -30 -20 -10 0 10 20

0

10

20

30

Con

cent

ratio

n of

sol

id (m

ol/L

)

Dis tance ( m)

Cuprite Ma lach ite Brochan tit e

-30 -20 -1 0 0 10 20

0

10

20

30

40

Con

cent

ratio

n of

sol

id (m

ol/L

)

Dis tance ( m)

Cuprite Ma lach ite Brochan tit e Ata chami te Nantokite

(a) (b )

(c)

Fig. 17. Prediction of corrosion product concentration at locations inside and outside of the pits grown potentiostatically at +0.3 VSCE for 75 h in (a) 10 mM HCO3− + 10 mM

SO42− (b) 10 mM HCO3

− + 10 mM SO42− + 10 mM Cl− and (c) 10 mM HCO3

− + 10 mM Cl− . Distance at zero is at the pit mouth. Positive distances are outside of the pit andn

i�

t1(atitctlirp

5

Ofiscd

egative distances are inside of the pit.

ty of the 10 mM HCO3− + 10 mM SO4

2− + 10 mM Cl− solution, i.e.inside = 0.05 S/cm.

The calculated values of Rcap for different waters are plotted onhe same graph with R�pit at different period of times of 1, 3, 5,0, 20, 50 and 100 h during potentiostatic polarization at 0.3 VSCEFig. 19). In all cases, the Ohmic resistance of corrosion productccounts for more than 90% of the total effective Ohmic resis-ance of pit. The Ohmic resistances of bulk solution and of solutionnside pit are negligible in comparison to the total Ohmic resis-ance of the growing pit. It has been shown in Fig. 6 that the pittingurrent is inversely proportional to the sum of the total Ohmic resis-ance of pit and the interfacial resistance. In many solutions R�pit isarger than the interfacial resistance. Therefore, the pitting currents shown by this analysis to be inversely proportional to the Ohmicesistance of corrosion product associated with the cap over theits as shown in Fig. 18.

.3. Effect of HCO3− + SO4

2− vs. HCO3− + Cl−

Water chemistry affects the polarization resistance and thehmic resistance. The polarization resistance in pits is lower in sul-

ate solutions. Ohmic resistance of corrosion products deposited

nside and outside pit depends on various physical parametersuch as geometry, size and porosity of the layer as well as thehemical nature of the corrosion products. All of these factorsetermine the apparent resistivity of the layer. No information

is available on the ionic resistance of a given corrosion productvs. its aggregate behavior including porous pathways for ionicconduction in the electrolyte phase. Characterization of corro-sion products inside and outside pits was performed with SEM,EDS and Raman spectroscopy which indicated a relationshipbetween the composition and concentration of the waters and themorphology, structure, and chemical identity of corrosion prod-ucts.

Fig. 20 is a sketch summarizing the morphology, structureand chemical identity of corrosion products formed potentiostat-ically at +0.3 VSCE for 100 h in HCO3

− + SO42−, HCO3

− + SO42− + Cl−

and HCO3− + Cl− solutions. This schematic can be summarized

based on all of the information presented above. The composi-tion of solution, particularly the anion species, determines thechemical identity and the morphology of corrosion products. Thecaps in 10 mM concentration solutions of HCO3

− + SO42− and

HCO3− + SO4

2− + Cl− are similar and are characterized by a volu-minous and porous outer layer of malachite and a sublayer ofbrochantite + malachite (Figs. 10–13). A thin layer of malachitewas found experimentally at the pit mouth in both solutions(Figs. 10 and 12). Inside the pit, cuprite (in HCO3

− + SO42−)

or cuprite + atacamite/eriochalcite (in HCO3− + SO4

2− + Cl−) form

porous deposits (Figs. 10 and 12). In more diluted solutions, i.e.1 mM or 0.1 mM, the cap loses the outer malachite layer (Fig. 8).Overall, the corrosion products deposited inside and outside pitsgrown in HCO3

− + SO42− and HCO3

− + SO42− + Cl− solutions are

6180 H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183

0 20 40 60 80 100-10

0

10

20

30

40

50 C+S (e xperi ment)C+S+Cl (experi ment)C+Cl (experi ment)C+S (fitt ing)C+S+Cl (fi ttin g)C+Cl (fit tin g)

Pit d

epth

(m

)

Time (hrs )

0 20 40 60 80 100

0

100

200

300 C+S (experi ment)C+S+Cl (e xperi ment)C+Cl (experiment)C+S (fit tin g)C+S+Cl (fi ttin g)C+Cl (fi ttin g)

Pit d

epth

(m

)

Time (hrs )0 20 40 60 80 100

0

100

200

300

400

500

600Pi

t dep

th (

m)

Time (hrs )

C+S (experiment )C+S+Cl (experiment)C+Cl (experiment)C+S (fi ttin g)C+S+Cl (f itti ng)C+Cl (f itti ng)

(a) (b )

(c)

10 mM 1 mM

0.1 mM

F s of poH . The c

pcai

F1d

ig. 18. Experimental pit depth vs. time curves plotted together with the fitting curveCO3

− + SO42− + Cl− and HCO3

− + Cl− solutions (a) 10 mM, (b) 1 mM and (c) 0.1 mM

orous. In HCO3− + Cl− solutions of all tested concentrations, the

ap is thin and compacted with an outer malachite layer and mixture of atacamite/eriochalcite/nantokite and cuprite form-ng a thin and dense sublayer at the pit bottom. It is reasonable

)a(0 20 40 60 80 100

100

101

102

103

104

105

RΩ

pit ,

Rca

p(kΩ

)

t (hou rs)

ig. 19. Dependence of Rcap and R�pit with time during 100 h potentiostatic polarization mM. The value of R�pit was obtained from EIS measurement. The value of Rcap was calculenote the concentration of 10 and 1 mM of the test solutions, respectively. The characte

wer function for pit grown potentiostatically at +0.3 VSCE for 100 h in HCO3− + SO4

2− ,haracters C, S and Cl in the legends indicate HCO3

− , SO42− and Cl− , respectively.

to propose that a porous cap provides better ionic conduc-tion path for ionic species transport into and out of the pit incomparison to a dense compacted cap. It is assumed that themorphology and pores of the corrosion product controls this

)b(0 20 40 60 80 10 0

101

102

103

104

RΩ

pit ,

Rca

p (kΩ

)

t (ho urs)

at +0.3 VSCE in different water chemistries and concentrations (a) 10 mM and (b)ated by subtracting Rinside and Rbulk from R�pit. The numbers 10 and 1 in the legendsrs C, S and Cl in the legends indicate HCO3

− , SO42− and Cl− , respectively.

H. Ha et al. / Electrochimica Acta 56 (2011) 6165– 6183 6181

F of corw

ina

ctoHotctc

rcistMsFTsc1eSg(o

auarilw

ig. 20. Schematic representation of morphology, structure and chemical identity

ater chemistries at +0.3 VSCE for 100 h.

onic conductivity in comparison to the intrinsic semiconductorative of the product. However, further insight is not avail-ble.

The effect of water composition on the Ohmic resistance oforrosion product can be seen from Fig. 19. The Ohmic resis-ance of corrosion product in HCO3

− + Cl− solution is at leastne order of magnitude higher than that in HCO3

− + SO42− and

CO3− + SO4

2− + Cl− solutions. This effect of water compositionn the corrosion product Ohmic resistance is closely related tohe effect of water composition on the morphology, structure andhemical identity of corrosion products as discussed earlier and nothe electrolyte conductivity which are similar at the same solutiononcentrations.

Through the Ohmic resistance effect brought about by the cor-osion product cap, the water composition also affects the pittingurrent and the pit growth rate. Both experimental and model-ng data showed that the pitting current densities in HCO3

− + Cl−

olutions were much lower than those in sulfate-containing solu-ions (i.e. HCO3

− + SO42− and HCO3

− + SO42− + Cl−) (Figs. 3 and 4).

oreover, one remarkable feature of the i–t curves in HCO3− + Cl−

olutions is the sudden current drop (marked by arrows inigs. 3 and 4) observed in experiments and predicted by the model.hese current drops indicate rapid stifling of the pit in HCO3

− + Cl−

olutions. In contrast, in sulfate-containing solutions, the pittingurrent densities were still on the order of 10−3 to 10−2 A/cm2 after00 h potentiostatic polarization at +0.3 VSCE. The difference in theffect of SO4

2− and Cl− on pit propagation is visually shown byEM micrographs of pits morphology (Figs. 8, 9, 10, 12 and 14). Pitsrown in sulfate-containing solutions often developed to deep pits∼1000 �m depth) while those grown in HCO3

− + Cl− solutions wasnly a few dozen micrometers in depth.

Although the effects of sulfate on pitting propagation of copperre well know [8,9,16,17,19–21], analysis of pit corrosion prod-ct Ohmic resistance, pit morphology, corrosion product identitynd pit growth rate indicates for the first time an interdependent

elationship between these parameters. Corrosion products hav-ng high Ohmic resistance are characterized with thin and compactayers of malachite, atacamite/eriochalcite/nantokite and cuprite

hich produced low pitting currents and shallow pits. Meanwhile,

rosion products inside and outside of artificial Cu pits (C11000) grown in different

corrosion products having low resistance are characterized bybulky and porous layers of malachite and brochantite/posnjakitewhich are related to high pitting current and deep pits. These rela-tionships reflect the effect of water composition, specifically theeffect of SO4

2− and Cl−, on pit propagation process. Sulfate hasa detrimental effect of promoting the formation of low Ohmicresistance copper salt layers such as malachite, brochantite andposnjakite. In contrast, chloride promotes the formation of highOhmic resistance copper salt layers such as atacamite, eriochalciteand nantokite. It is not clear at the present time what the conduc-tion mechanism through these layers is, i.e. whether this effect iscontrolled by porosity and morphology or intrinsic semiconductionor ionic conduction in each form of mineral scale.

Increasing the concentration of anions (HCO3−, SO4

2− and Cl−)in solution facilitates the rapid formation of corrosion product lay-ers, therefore a higher Ohmic resistance corrosion product layercan be obtained in a shorter time and hence the pitting currentdensity decreases at a faster rate. In 0.1 mM solutions, thick corro-sion product layers could not form while the solutions inside thepit became more aggressive due to hydrolysis reactions during longterm potentiostatic polarization. This explains the increasing pit-ting current densities observed in the 0.1 mM solutions. Increasingthe growth time increases the local solution ionic strength. Thiseventually leads to the formation of a thicker and denser corrosionproduct layer (i.e., higher Ohmic resistance) and hence graduallyreducing the pitting current density.

6. Summary

The effects of water composition on the kinetics of pit propa-gation were separated from pit initiation and stabilization usingthe artificial pit method. The kinetics of long term pit propaga-tion on copper was studied systematically using a range of diluteHCO3

−, SO42− and Cl−-containing waters. Water chemistry vari-

ables affected both the polarization resistance and the Ohmic

resistance of pits. The effective polarization resistance in pits islower in sulfate solutions and greater in Cl− containing solutions.Interdependent relationships between the solution compositionand the resulting, corrosion product identity and morphology

6 ica Ac

wrs

1

2

3

4

5

A

ta

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

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[

182 H. Ha et al. / Electrochim

ere found. These, in turn controlled the corrosion product Ohmicesistance and subsequently the pit growth rate. The findings areummarized as follows:

. The highest pit propagation rates and deepest pits arefound in sulfate-containing waters (i.e. HCO3

− + SO42− and

HCO3− + SO4

2 + Cl−) while lowest pit propagation rates and mostshallow pits are found in HCO3

− + Cl− waters.. Pits in sulfate-containing waters display slower growth rates

over long time periods but do not repassivate. In HCO3− + Cl−

solutions, repassivation occurs more readily as indicated by cur-rent density decreases below 10−6 A/cm2.

. The pit propagation rate is mediated by the morphology, chemi-cal nature and the amount of corrosion products deposited insideand over the pits through the influence of these factors on theeffective Ohmic resistance of the pit. The Ohmic resistance is, inturn, a significant factor that controls of pit growth.

. Dense copper chloride (atacamite and eriochalcite) corrosionproduct layers with high Ohmic resistance decrease pit growthrates to the point where repassivation is possible in HCO3

− + Cl−

solutions. Porous copper sulfate (brochantite and posnjakite)and copper carbonate (malachite) corrosion product layers thathave low Ohmic resistance were formed in HCO3

− + SO42− and

HCO3− + SO4

2− + Cl− solutions. Pit growth can be stifled overtime at very slow rate controlled by a slowly increasing Ohmicresistance. The current density never increases in cylindrical pitsof constant pit area.

. More concentrated waters cause faster initial growth rates buttended to reduce pit propagation rate faster than more dilutedwaters. This effect was traced to the formation of thicker anddenser corrosion product layers in waters with greater sulfate,chloride or bicarbonate concentrations.

cknowledgements

The financial support from the Copper Development Associa-ion, Inc. and the International Copper Association, Ltd. is gratefullycknowledged.

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