Galvele05

Corrosion Science 47 (2005) 3053–3067

www.elsevier.com/locate/corsci

Tafel�s law in pitting corrosionand crevice corrosion susceptibility

J.R. Galvele *

Instituto Sabato, Universidad Nacional de San Martı́n, Av. Gral Paz 1499,

B1650KNA San Martı́n, Buenos Aires, Argentina

Available online 29 September 2005

Abstract

The critical potentials for pitting are reviewed, under the scope of their relation with thecrevice corrosion mechanism. A short review of the correlation between pitting corrosionand crevice corrosion with the Tafel�s law is made. Some problems observed in the mechanisticdescription of crevice corrosion are pointed out. The use of Tafel�s law measurements in theunderstanding of the mechanism of pitting is also mentioned.� 2005 Elsevier Ltd. All rights reserved.

Keywords: A. Aluminium, iron; stainless steel; B. Modelling studies

1. Introduction

To commemorate the centennial of Julius Tafel�s publication of his famous Tafel�sLaw, the present review recalls the particular cases where this law was applied to pit-ting corrosion and crevice corrosion studies. As for other aspects of crevice corrosionand pitting corrosion, the reader is referred to more specific reviews of the problem[1–3].

0010-938X/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.corsci.2005.05.043

* Tel.: +54 11 6772 7390; fax: +54 11 6772 7404.E-mail address: [email protected]

mailto:[email protected]

3054 J.R. Galvele / Corrosion Science 47 (2005) 3053–3067

Crevice corrosion and pitting corrosion are problems of undeniable significance inpractice and they are well documented in the literature [4–6]. Crevice corrosion couldalso be a nightmare, in the laboratory, when pitting corrosion testing is attempted onmetals or alloys susceptible to crevice corrosion. The interference of crevice corro-sion in pitting corrosion measurements explains why complex electrochemical cellshave been developed [7] in order to avoid this problem.

For certain metal-environment systems, particularly in NaCl solutions and in seawater, a strong correlation between pitting corrosion and crevice corrosion mecha-nisms has been reported by Wilde and Williams [8]. These authors have shown thiscorrelation between the critical potentials for pitting of various commercial alloys,measured in the laboratory in NaCl solutions, and the susceptibility to crevice cor-rosion, after long exposures in sea water. The present review shows that various as-pects of pitting corrosion, as well as the results reported by Wilde and Williams canbe explained by using the Tafel�s law.

2. Critical pitting potentials

Pitting corrosion is characterized by three critical potentials [9,10], the most rele-vant of them being the pitting potential, Ep (Fig. 1). The pitting potential can be de-fined, in a potentiostatic polarization curve, as the potential below which the metalsurface remains passive and above which pitting corrosion starts to grow on themetal surface. Several methods have been used to measure the pitting potential, suchas potentiostatic methods, potentiokinetic methods, galvanostatic methods, etc.Abundant literature was published, particularly in the 80s [9,10] on pitting potentialmeasurements for iron, stainless steel, nickel, manganese, zinc, cadmium, alumin-

-0.8 -0.7 -0.6 -0.5 -0.4 -0.31x10-8

1x10-7

1x10-6

1x10-5

1x10-4

1x10-3

Ep

Cur

rent

den

sity

(A

/cm

2 )

Potential (V/SHE)

Fig. 1. Typical anodic polarization curve showing the presence of a pitting potential, Ep. Curve based onmeasurements for aluminium in NaCl solutions [10].

J.R. Galvele / Corrosion Science 47 (2005) 3053–3067 3055

ium, NiSn alloy, zirconium, titanium, tantalum, etc. Most of the solutions used werehalide solutions, but references could also be found for pitting potentials in sulphatesolutions, nitrate solutions, perchlorate solutions, etc.

Since the pitting potential values measured with potentiostatic or potentiokinetictechniques, on various metals, particularly on stainless steels in chloride solutions,showed wide scattering, in 1971 Pessall and Liu [11] introduced a surface scratchingtechnique, which has been adopted by numerous authors. A comparison of the var-ious pitting potential measurement techniques could be found, for example, for zinc[12], cadmium [13] and iron [14].

As implied by the surface scratching technique, the main characteristic of the pit-ting potential is that the exposure of bare metal to the aggressive solution, below thepitting potential, leads to repassivation, and that it is only above the pitting potentialthat pitting corrosion begins to grow. This fact was confirmed on aluminium samplesstrained in chloride solutions and in nitrate solutions at various potentials [15,16].

The second characteristic potential for pitting corrosion was described by Pour-baix [17]. Pourbaix found that pits that start to grow at the pitting potential, willkeep growing even when the potential is lowered below the pitting potential. Accord-ing to Pourbaix, the pits will stop growing only when the potential of the metal islower than a certain potential called repassivation potential, or protection potential,Er (Fig. 2). The existence of a repassivation potential was reported by several authorsin a wide variety of metal-environment systems [9,10]. It was found that the repass-ivation potential varied with the amount of pit propagation that had taken place[8,18]. The deeper the pit the lower the Er.

The third characteristic potential for pitting corrosion, present only in certainmetal-environment systems, was described by Schwenk [19] and is usually called pittinginhibition potential, Ei (Fig. 3). Schwenk reported that, for 18/10 chromium–nickel

0.0 0.2 0.4 0.6 0.8 1.01x10-6

1x10-5

1x10-4

1x10-3

1x10-2

EpEr

Cur

rent

den

sity

(A

/cm

2 )

Potential (V)

Fig. 2. Typical anodic polarization curve showing the presence of a pitting potential, Ep, and arepassivation potential, Er. Arbitrary values used, examples of curves could be found in Ref. [8].

0.0 0.5 1.0 1.51x10-6

1x10-5

1x10-4

1x10-3

1x10-2

EiEpCur

rent

den

sity

(A

/cm

2 )

Potential (V/SHE)

Fig. 3. Typical anodic polarization curve showing the presence of a pitting potential, Ep, and an inhibitionpotential, Ei. Curve based on measurements for stainless steel in NaNO3 + NaCl solutions [20].


stainless steel in chloride solutions containing nitrates, above the pitting potential therewas a pitting inhibition potential, above which the steel became passive. This observa-tion was later confirmed by Leckie and Uhlig [20].

The existence of a pitting inhibition potential was described [9,10] in systems suchas iron in sulphate solutions, iron in perchlorate solutions, iron and nickel in mix-tures of chloride plus nitrate solutions, in bromide plus perchlorate solutions, etc.

While both the pitting potential, Ep and the pitting repassivation potential, Er,have important practical applications, this does not seem to be the case with the pit-ting inhibition potential, Ei. Keitelman and Galvele [21] studied the anodic behaviourof high purity iron in a 0.5 M sodium sulphate solution. They measured the pittingpotential of iron in pH 9.0 and pH 10.0 solutions. The pitting potential was foundto be very close to the corrosion potential measured in a Na2SO4, pH 2.7, pit-likesolution. On the other hand, the pitting inhibition potential measured in a 0.5 MNa2SO4 solution, pH 10.0, was very close to the passivation potential found for themetal in the pit-like solution. The practical use of the pitting inhibition potentialwas limited, because susceptibility to crevice corrosion was observed at potentialsabove the pitting inhibition potential. Keitelman and Galvele [21] concluded thatthe pitting inhibition potential could not be used to stop pitting corrosion, becausein those areas where a high potential drop could be found, like in a crevice, the pittinginhibition potential was not reached and crevice corrosion developed.

3. Origin of the critical potentials for pitting corrosion

As early as 1951, Edeleanu and Evans [22] showed that in the case of aluminiumthe pH in the solution inside the pits, was lower than the pH in the bulk solution.


This observation was later confirmed by various authors, not only for aluminium butalso for a wide variety of metals and alloys [8,23–27]. It was on the basis of theseobservations that Van Muylder et al. [24] advanced the first explanation for the pit-ting potential. Their work was centred on pitting corrosion of copper and they sug-gested that the pitting potential of copper, in neutral or alkaline solutions, was equalto the equilibrium potential of Cu/Cu++ in the acid solution inside the pit. They as-sumed that the same explanation applied to other metals.

Van Muylder�s [24] model was able to explain the pitting of copper, but failed toexplain the pitting potential of metals such as iron, aluminium, zinc, etc., or whenreducible anions were present, such as it was the case with aluminium in nitrate solu-tions. Neither could this model explain the fact that buffer solutions acted as pittinginhibitors, increasing the pitting potential of numerous metals in corrosive solutions.

An alternative model [12,13,15,28–35] was developed to explain the pitting poten-tial of metals such as zinc, cadmium, aluminium or iron, and the pitting potentialsfound in the presence of reducible anions or pitting inhibitors. Contrary to the ther-modynamic approach used by Van Muylder et al. [24], the authors of this alternativemodel assumed that the pitting potential was the resultant of the kinetic reactionsinside the pit.

The model was based on the assumption that the aggressive ions were anions ofstrong acids, the only requirement being that they would not produce insoluble prod-ucts when in contact with the metal and that the metal, while corroding in aqueoussolutions, would react with water, producing localized acidification. While the finalresult was the same, perhaps from a mechanistic point of view it would have beenmore appropriate to emphasize that, instead of a localized acidification, a depletionof HO�, ions was being produced.

The localized acidification was the result of the two following reactions: first, thedissolution of the metal at the bottom of the pit

Me ¼ Mezþ þ ze ð1Þfollowed by the hydrolysis equilibrium of the metal ions inside the pit:

Mezþ þ zH2O $ MeðOHÞz þ zHþ ð2ÞReactions (1) plus reaction (2) gave the rate of production of protons. Simulta-neously, there was a series of reactions leading to the consumption of protons.Numerous authors reported the evolution of hydrogen from active pits [10]. Thisobservation indicated that the reaction of hydrogen evolution was taking place

2Hþ þ 2e ¼ H2 ð3ÞIf reducible anions were present, they could consume protons by reactions such as

NO�3 þ 10Hþ þ 8e ¼ 3H2OþNHþ

4 ð4ÞAnother factor that will limit the localized accumulation of protons is the presence ofweak acid anions (L�). The presence of soluble salts of weak acids will reduce thepresence of protons inside the pit, by the following equilibrium:

Hþ þ L� $ HL ð5Þ


If the diffusion of protons from the acidic solution inside the pit to the bulk solutionis also taken into account, the conclusion is that, in order to keep a localized acidi-fication, the pitting potential, Ep, must be equal to or higher than the corrosion po-tential of the metal in the pit-like solution, E�

c .This model of pitting allowed to explain numerous experimental observations re-

lated to pitting corrosion. In the particular case of pitting of aluminium it explainedwhy the pitting potential of aluminium in nitrate solutions was so high (+1.70 V(SHE)) while in NaCl solutions it was only �0.53 V (SHE). Wexler and Galvele[15] reported the evolution of gaseous nitrogen from the pits of aluminium in nitratesolutions. This observation was confirmed by Bargeron and Benson [36]. The evolu-tion of nitrogen indicated that the following reaction was taking place inside the pit:

2NO�3 þ 12Hþ þ 10e ¼ N2 þ 6H2O ð6Þ

Pitting of aluminium in nitrate solutions could only take place at potentials at whichthe nitrate ion was thermodynamically stable. According to Pourbaix�s diagrams thethermodynamic stability of nitrate ions was reached at potentials above +1.2 V(SHE).

The model of localized acidification for pitting received serious criticisms, themost important of them being that the changes in composition expected in small pitswere insignificant and could not explain pitting initiation [29].

As a result of those criticisms, a series of publications was made studying thetransport phenomenon inside a pit [28,29,33,34]. The most important conclusionof these studies was that there was a critical x Æ i value (Figs. 4 and 5), above whichimportant changes in the ion composition inside the pit took place. x being the depthof the pit, in cm and i the current density circulating in the pit, in A/cm2. For all the

1x10-8 1x10-7 1x10-6 1x10-5 1x10-4 1x10-30

20

40

60

80

100

Fe[

II] (

%)

x . i (A/cm)

Fe(OH)2(aq)

Fe2+

Fe(OH)+

Fe(OH)2(s)

Fig. 4. Distribution of iron corrosion species as a function of the product of the depth x and the currentdensity i in a unidirectional pit, for iron in a pH 10 solution [33].

1x10-8 1x10-7 1x10-6 1x10-5 1x10-4 1x10-30

20

40

60

80

100

Al[I

II] (

%)

x . i (A/cm)

Al(OH)3(s)

Al3+

Al(OH)++

Al(OH)2

+

Al(OH)3(aq)

Fig. 5. Distribution of aluminium corrosion species as a function of the product of the depth x and thecurrent density i in a unidirectional pit, for aluminium in a pH 8 solution [33].


metals studied, the critical x Æ i value was of the order or x Æ i = 10�6 A/cm. Since itwas known [29] that at pit initiation the current density could reach values of theorder of 1–9 A/cm2, it was clear that a flaw in the surface oxide film could giveenough length for the diffusion path to reach the critical x Æ i value. Since the modeldid not restrict the nature of x, Figs. 4 and 5 could be applied without distinction topitting corrosion as well as to crevice corrosion.

The initiation of pits in surface flaws, as well as the relation between pitting andcrevice corrosion was supported by Wood et al. [37]. These authors have shown thatpitting, on both aluminium and stainless steels starts from flaws in the oxide film andpropagates by the ion transport mechanism described above. The existence of flaws,as precursors of pitting was also shown, by electrochemical methods, for zirconiumin various environments [38,39].

Wood et al. [37] also studied the evolution of crevice corrosion of AISI type 304austenitic stainless steel under a 13 mm diameter · 0.3 mm glass microscope coverslide, at constant potential, in an air saturated 5% NaCl solution, pH 8.0. The devel-opment of crevice corrosion was followed with an appropriate optical system. Theyobserved that, while at 600 mV (SCE) pits nucleated on all the metal surface, at400 mV (SCE) pits nucleated only under the glass cover and spread laterally to takethe shape of crevice corrosion. According to these authors, their study confirmed theclose link between pitting and crevice corrosion in the case of stainless steels, and itstrongly suggested that crevice corrosion is really no more than ‘‘lateral pitting’’occurring within an occluded area. From their study it is concluded that the onlyfunction of IR drops was to favour the nucleation of pits near the border of the glasscover, and that they made it difficult to nucleate in the centre.

Another conclusion from the transport process studies [28,29,33,34] was the nat-ure of the pitting potential. It was concluded that the pitting potential had no


relation with thermodynamic equilibrium, as suggested by Van Muylder et al. [24],but it was given by the following equation:

Ep ¼ E�c þ g þ / ð7Þ

Ep being the pitting potential, E�c the corrosion potential in the pit-like solution, g the

polarization needed to reach the critical x Æ i value, and / the electrical potential in-duced by the migration of the aggressive anions to the bottom of the pit. The validityof Eq. (7) was tested in numerous publications [9,10,35] and it was confirmed also inan independent work by Newman et al. [40].

4. Critical x � i values and Tafel’s law

Studies as shown in Fig. 4 were made for Fe, Ni, Co, Zn and Cd. In all these cases,the metal dissolved from pits as a divalent cation. As shown in Fig. 4, for iron in apH 10 solution, for low x Æ i values the main, and practically the only corrosion spe-cies was insoluble Fe(OH)2,S. The proportion of soluble species is practically nil.Nevertheless, there is an x Æ i value above which there is an abrupt change in the rela-tion of the corroded species. At a value of x Æ i close to 10�6 A/cm, the proportion ofinsoluble species, Fe(OH)2,S drops sharply, and it is replaced by soluble Fe2+.

From Fig. 4 it is evident that this is a critical x Æ i value above which the solid cor-rosion species are replaced by soluble corrosion species. This is a necessary, and fre-quently sufficient, condition for pitting to start to grow. The low value for the criticalx Æ i indicates that pitting could start to grow in any small defect in the oxide film.

The critical x Æ i values found for iron [33] were

pH ¼ 10; x � i ¼ 5:0 10�7 A=cm

pH ¼ 11; x � i ¼ 5:0 10�6 A=cm

pH ¼ 12; x � i ¼ 5:0 10�5 A=cm

The critical x Æ i value increases one order of magnitude each time the pH increasesone unit. If the x value, e.g. thickness of the oxide film, is constant, the current den-sity to start pitting will also increase one order of magnitude every time the pH in-creases one unit. If the current density, in the pit-like solution, follows a logarithmicrelation to the potential, we can conclude that the relation between pH and pittingpotential would be of the type:

Ep ¼ Aþ B � pH ð8Þwhere A and B are constants. According to this result B should be close to the Tafelslope for iron in the pit-like solution. Such results were confirmed for iron in a NaClsolution [10,14], for cadmium in NaCl solution [41] and for cadmium in a Na2SO4

solution [41].In the case of trivalent metals, like Al3+, the presence of a further step of hydro-

lysis slows down the effect of the external pH on the x Æ i value. As shown in Fig. 5,the transition from passivity to pitting is not as sharp as for divalent metal ions,


Fig. 4. Consequently, for comparison reasons, the critical x Æ i value chosen was thepoint where the concentrations of solid Al(OH)3 and soluble Al3+ were equal, i.e. theintersection point of both concentration curves. The results found were [33]

pH ¼ 5; x � i ¼ 1:4 10�6 A=cm

pH ¼ 8; x � i ¼ 2:0 10�6 A=cm

pH ¼ 10; x � i ¼ 3:1 10�6 A=cm

While for divalent metal ions an increase of only one unit in the pH of the bulk solu-tion produced an increase as big as one order of magnitude in the x Æ i value; for alu-minium an increase of 5 pH units produced just a twofold increase in the x Æ i value.It can be concluded that the critical x Æ i value, for aluminium, is practically indepen-dent of the external pH. This conclusion is in agreement with the observation madeby Kaesche [42], who found that the pitting potential of aluminium was not affectedby the solution pH.

The critical x Æ i value can also be changed by the presence of weak acid salts in thebulk solution. As shown by ion transport analysis [29] an increase of one order ofmagnitude in the concentration of the weak acid salt, produced also an increase ofone order of magnitude in the x Æ i value. If the current density, in the pit-like solu-tion, follows a logarithmic relation to the potential, we can conclude that the relationbetween weak acid salt concentration, Cb, and pitting potential would be of the type

Ep ¼ Aþ B � logCb ð9Þwhere A and B are constants. According to this result B should be close to the Tafelslope for the metal in the pit-like solution. Such results were reported for iron in bo-rate containing NaCl solutions [14], and also for zinc in borate containing NaClsolutions and in borate containing NaClO4 solutions [43]. In the case of zinc itwas found that when the borate concentration exceeded that of the aggressive salt,the values of the pitting potential exceeded those predicted by Eq. (9), but it wasshown that Eq. (7) was still valid [34,35].

5. Flaws, passivity breakdown and metastable pitting

If flaws, as suggested by Wood [37], really exist, and if to start pitting a critical x Æ ivalue has to be reached, it is reasonable to expect that, below the pitting potential,incipient processes of pit initiation should exist. Galvele et al. [38] studied the repass-ivation rate of various metals and alloys. The current decay, when measuring repass-ivation rates, could be described by a relation of the type

i ¼ A � tb

where i is the current density, t is the time and A and b are constants. A value ofb = �1 is typical of a high field film formation reaction, and it is usually relatedto the formation of a compact highly protective passive film.

Galvele et al. [38] studied the repassivation rate for zirconium in various halidesolutions, as well as for brass in pH 12, 1 M NaNO2 solution. They observed that


at low potentials the value of b was �1. Then there was a region of potentials wherean initial value of b = �0.5, typical of a diffusion controlled process, was followed bya repassivation rate of b = �1. The authors identified this potential region as the re-gion where passivity breakdown took place. They also concluded that the repassiva-tion rate technique was very convenient for detecting the passivity breakdown. Noother references were found in the literature where this line of work was followed.

Using different techniques, abundant work is found on the subject of formation ofmetastable pitting, which should be closely related to the phenomenon of passivitybreakdown mentioned above. In the particular case of stainless steels, Pistoriusand Burstein published an extensive work [44–46]. Metastable pitting was also stud-ied for other metals, and a full description of the subject could be found in the reviewpublished by Frankel [2]. An analysis of metastable pitting or of passivity breakdownwould fall outside the scope of the present work.

6. Crevice corrosion

The way crevice corrosion mechanisms are treated in the literature causes certainconcern to the present author. To reduce the number of possibilities, the presentconsideration will be restricted to those systems where a passivating species is de-pleted from the crevice. After such a depletion, corrosion inside the crevice will start.But the way corrosion will proceed, for example if the potential is changed, will de-pend on the nature of the aggressive species present inside the crevice. For certainanions, like chloride ion, the corrosion of the metal generally increases monotoni-cally with the potential. On the other hand, with anions like sulphate ion, and metalslike iron, an active to passive transition is found when the potential is increased.Nevertheless, when considering the mechanisms involved, it seems to the presentauthor that both the nature of the anions, and their role, are not sufficientlyemphasized.

The author has taken into account two recent papers. One by Wang and Newman[47], and the other by Al-Zahrani and Pickering [48]. The first paper studies crevicecorrosion of Type 316L stainless steel in alkaline solutions. The second studies cre-vice corrosion of spontaneously passive iron in 0.2 M Na2SO4 + 0.025 M K2CrO4

(pH 9) solution. In the first system, when the passivating species, OH� ions, are con-sumed, the metal is exposed to a chloride solution where pitting could occur. In thesecond one, when the chromate is reduced, iron is exposed to a sulphate solutionwhich, as described above, shows a pitting potential and a pitting inhibition poten-tial. The present author finds it difficult to accept that these differences are irrelevant.

The discussion of this problem, though significant as it might be, falls outside thescope of the present work. The only reason to mention it here is to use it as an intro-duction to the next section. In the next section a classical work by Wilde and Wil-liams [8] will be analysed from the point of view of Tafel�s law. In this case crevicecorrosion in NaCl solutions is considered. No evaluation is made of the validityof Wilde and Williams� technique as a general tool for detecting crevice corrosionsusceptibility.


7. Correlation between repassivation potential and crevice corrosion

The existence of a critical x Æ i parameter, described in Section 4, has anotherimportant implication. It explains the existence of a pitting repassivation potential,Er, lower than the pitting potential, Ep. As mentioned above, Er is lower the deeperthe pits are allowed to grow, and this was easily explained by the use of the criticalx Æ i value [29]. Once the critical x Æ i value is reached, at a certain potential, the pitwill start to grow. If, after allowing the growth of the pit, the potential is reduced,the current density, i, will decrease, and pitting will stop once the critical x Æ i valueis reached again. Nevertheless, the final x value will be larger than the initial one, andconsequently the current density value required to stop pitting will be lower. The cur-rent density is directly related to the electrode potential, and the difference betweenthe i value reached at Ep and the new i value required at Er will depend on theE = f(i) relation, which in many cases is the Tafel�s Law.

Wilde and Williams compared the value of the difference Ep � Er with the suscep-tibility to crevice corrosion for a series of alloys. Since the value of Er was function ofthe size of the pit, Wilde and Williams [8] used a standardised method to measure theEp � Er difference. They worked in a 3.5% NaCl solution, and determined the valueof Ep with a potential scanning rate of 0.600 V/h. The value of Er was determinedafter reversing the sweep at 0.2 A/cm2. Crevice corrosion was measured as weightloss on samples exposed for 4.25 years in sea water. Fig. 6 schematically showsthe results found by these authors. Wilde and Williams found that the larger theEp � Er difference the more susceptible the alloy was to crevice corrosion.

0 5 10 15 20 25 300

50

100

150

200

250

300

410

USS 100430

446304

316

Hastelloy C

Ep

- E

r (m

V)

Weight loss (mg/cm2)

Fig. 6. Comparison between the difference Ep � Er, measured potentiokinetically in a NaCl solution, andcrevice corrosion measured after long exposures in sea water. Schematic representation based on Wildeand Williams [8].

0.0 0.5 1.0 1.5 2.01x10-4

1x10-3

1x10-2

1x10-1

1x100

1x101

(b)(a)

aprox. 0.800 V

aprox. 0.050 V

Cur

rent

den

sity

(A

/cm

2 )

Potential (V)

Fig. 7. Susceptibility to crevice corrosion in NaCl solutions based on the Tafel slope, inside the pit, foriron (a) [14], and the pseudo-Tafel slope for stainless steel (b) [49]. The potential scale is arbitrary, and waschosen for illustrative purposes. In this example the following assumptions are made: critical valuex Æ i = 10�6 A/cm, pit size x = 10�6 cm, crevice size x = 10�4 cm. In case (a) the difference in potentialrequired to start pitting corrosion from that to start crevice corrosion will be of only 50 mV. In case (b)crevice corrosion will start at a potential 800 mV lower than that required to start pitting.


At this point it is important to notice that the technique developed by Wilde andWilliams contains an implicit assumption. It assumes that the depth of the pits is thesame in all the samples under comparison, and that this condition is achieved whenthe current density reaches 0.2 A/cm2. Nevertheless, this condition will be true onlywhen the number of pits in all the samples tested is similar.

The reason for Wilde and Williams correlation could be found more clearly inFig. 7. We will assume that the current density, when pitting starts, is of the orderof 1 A/cm2. We will also assume that curve (a) shows the Tafel curve for iron in apit-like solution in NaCl, and curve (b) is a pseudo-Tafel curve for stainless steel; thislast value being based on [49]. If the critical x Æ i value is of the order ofx Æ i = 10�6 A/cm, pitting could start on any flaw of 10�6 cm. If the pit is allowedto grow up to 10�4 cm, to reach again the critical x Æ i value the current density willhave to drop to 10�2 A/cm2. In the case of curve (a) the difference Ep � Er will be ofonly 50 mV. On the other hand, the difference Ep � Er, for the curve (b) will be of800 mV. If, instead of a pit of 10�4 cm, we have a crevice of the same size, in case(a) the difference between pitting and crevice corrosion will be of only 50 mV, a valueusually obscured by the corrosion potential oscillations in practical cases, and itcould be concluded that the metal (a) is not susceptible to crevice corrosion. Onthe other hand, for the metal (b), crevice corrosion will start at a potential800 mV lower than that required for pitting, and this metal will be more susceptibleto crevice corrosion than to pitting.


8. Recent Tafel’s law measurements

The present review described a limited number of cases where Tafel�s law was ap-plied to localized corrosion, most of them published some time ago. The pit propa-gation process being electrochemical in nature, one would expect to find morefrequently relations of the type: i / expE (Tafel�s law) between the current densityand the potential. But, as pointed out by Frankel [2], the nonsteady state natureof the deepening of pits complicates the clear identification of the i–E relationship.

One remarkable exception is the work by Laycock and Newman [50]. The authorsused artificial pit electrodes prepared with AISI 302 and 316 stainless steel wires. Thewires used were of 10, 50 and 500 lm diameters, and the measurements were carriedout in 1, 0.3, 0.1 and 0.01 M NaCl solutions.

Laycock and Newman measured the Tafel slopes inside the pits, and were able toidentify two regimes of pit growth. At low potentials they found a mixed activation/ohmic control, and at higher potentials they observed that the growth was under dif-fusion control with a metal salt film present on the electrode surface. They were alsoable to explain, based on their measurements, the variation of the pitting potentialwith chloride concentration. As for the beneficial effect of molybdenum alloyingon the pitting resistance of stainless steel, they concluded that it was completely ac-counted by its effect on the anodic kinetics within the pit. Besides the results just de-scribed, Laycock and Newman�s paper [50] contains a very thorough review onpitting research techniques and pitting mechanism theories.

9. Conclusions

As shown in the present review, there are cases, both for pitting corrosion and forcrevice corrosion where the use of Tafel�s Law allows us to explain:

(a) The effect of pH on the pitting potential of divalent metals.(b) The effect of weak acid salts on the pitting potential of metals, when the con-

centration of the weak acid is low, and the aggressive solution acts as a sup-porting electrolyte.

(c) The susceptibility to crevice corrosion of metals and alloys in NaCl solutionsand in sea water, under conditions where those metals show a pitting potential.

(d) The salt film formation, and the electrochemical kinetics involved in pitpropagation.

(e) The mechanism by which molybdenum improves the pitting corrosion resis-tance of stainless steels.

Acknowledgement

The financial support of the FONCYT, Secretarı́a de Ciencia y Tecnologı́a, fromArgentina, is acknowledged.


References

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