Marcus P. Corrosion mechanisms in theory and practice

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for Fe in 0.01 M KCl + 0.1 M KSO

(Fig. 15) [53]. Apparently the potential-

independent plateau values of i

c,p

are related to the formation of a salt layer that

provides electropolishing conditions at the pit surface (Fig. 13a). If, however, the

current becomes still smaller such as for Ni below 1.0 V, the growth of the pit

becomes unstable and irregular shapes are observed as shown in Figure 14.

A special geometry for localized corrosion studies has been applied by

Frankel and co-workers [59,60]. They subjected vapor-deposited thin Ni-20% Fe and

Al films on an inert substrate as working electrodes of a potentiostatic circuit to the

local attack of chlorides, which causes fast perforation of the film and subsequent

growth of two-dimensional pits with actively corroding cylindrical side walls. With

this method the authors avoid the usual deepening of three-dimensional pits on bulk

materials with the related increasing diffusion length for the transport of corrosion

products and ohmic drops. Thus, the geometry for metal dissolution and transport of

corrosion products was kept constant with time of growth of the two-dimensional

pits. For this simpler and constant geometry, the local current density and the

potential of repassivation of pits could be measured more accurately. The local

current densities i

c,p

could be directly deduced from the growth of the radius of the

two-dimensional pits applying Faraday’s law without any assumptions for the

geometry of the actively corroding surface. Usually, i

c,p

increases linearly with the

electrode potential up to 100 A/cm

, where it is controlled by mass transport and

ohmic resistance. It finally gets to a diffusion-controlled potential-independent

limiting value. There exist a critical local current density i

and a repassivation

potential E

that are closely related to each other. The accumulation of corrosion

Mechanisms of Pitting Corrosion 269

Figure 15 Local pit current density i

c,p

, as a function of potential E deduced from pit

growth on polycrystalline nickel and Fe electrodes in 0.05 M phthalate buffer, pH 5.0. Ni:

() 0.1 M KCl + 0.1 M K

, (c) 0.1 M KCl; Fe: () 0.01 M KCl + 0.1 M K

, (z)

0.01 M KCl. (From Ref. 58.)

products is interpreted by the authors as a stabilizing factor for pit growth. If the

local current density goes below a critical value i

, localized corrosion will stop due

to a less aggressive environment corresponding to a smaller local concentration of the

corrosion products that may be maintained. Apparently, a sufficiently high concen-

tration of chloride is required to prevent repassivation. Estimates have shown that

~ 50% of the concentration of saturation is required to prevent repassivation [59]. As will

be shown later for a hemispherical pit, the locally increased concentration of corrosion

products and thus chlorides is proportional to the product of the local current density

and the pit radius i

c,p

r [Eq. (18)]. For a two-dimensional circular pit this relation

simplifies to a proportionality to i

c,p

which yields critical conditions that are inde-

pendent of the radius of the two-dimensional pit [59]. In this sense, these studies may

give valuable information on the stabilty of polygonal and hemispherical pits. With

increasing metal film thickness and consequently larger side walls of the actively

corroding cylinder surface, i

decreases due to a larger corroding surface and hence

to an increased ohmic resistance and higher accumulation of corrosion products. For

similar reasons, di/dE decreases with increasing film thickness.

As already discussed in relation to the adsorption mechanism of pit nucleation,

the halides cause catalytically enhanced dissolution of the passivating oxide. Any

attempt of the bare metal surface of a pit to passivate by oxide formation will fail in

the presence of high concentrations of aggressive anions, similar to the galvanostatic

transient behavior of preactivated specimens. Thus, there is a close correspondence

of small iron and nickel electrodes in solutions of high Cl

–

content (>1 M) and an

intensively corroding pit surface that will be discussed in the next section. In both

cases, the formation of a passive layer is suppressed. In the case of Al a sufficiently

low pH by hydrolysis of the corrosion products will stabilize pitting additionally.

Passivity of this metal requires a dissolution equilibrium of the anodic oxide with the

electrolyte that requires weakly acidic to alkaline solutions. Localized acidification is

therefore a good additional stabilizing factor for corrosion pits on Al. This special

situation, however, does not contradict the necessary active chemical role of halides,

i.e., their complexing properties.

Precipitation of Salt Films

After a sufficiently long time of high dissolution current densities, the accumulation

of corrosion products will lead to the precipitation of a salt film. This precipitation is

expected in an early stage of pit growth if sufficiently large potentials and as a

consequence large current densities are applied. Galvanostatic transients of

preactivated small electrodes in solutions of high chloride content are not subject

to passivation, and the dissolution at potentials within the passive range leads to a

related steep increase of the measured electrode potential after the transition time τ

(Fig. 16). For the linear diffusion problem of the completely dissolving electrode

surface it was found that Sand’s equation is valid; this relates the current density i

c,p

and time t of corrosion to the difference Δc = c

– c

m,b

of the metal ion concentration

with c

at the electrode surface and its bulk value c

m,b

, their charge z

, and diffusion

constant D of the metal ions [56].

270 Strehblow

In the absence of supporting electrolyte, i.e., in a solution containing the salt

of the dissolving metal, a diffusion constant D

eff

= D(1 + z

/ | z

|), which includes

the contribution of migration to the transport, has to be used instead D. Here z

and z

are the valences of the metal ions and anions. Figure 17 presents the

accumulation of metal ions Δc according to Eq. (17) during dissolution of a small

nickel electrode in solutions of high chloride content as a function of i√t

–

. When

reaches its value of saturation c

m,s

for t = τ, precipitation of a salt film will

occur. This salt film has been examined further with galvanostatic pulses

superimposed on the main transient to determine ohmic drops (Fig. 16). The

results lead to a model for the forming salt film with a spongy, porous outer part

and a barrier-type inner part [56]. Besides experimental examinations [56], numerical

calculations [61] have shown that Eq. (17) may also be applied for concentrated

electrolytes. Different solutions with and without aggressive anions have been

tested using galvanostatic transients with small Fe and Ni electrodes, such as 0.5

M H

, 1 M HClO

, 1 M NaClO

, and 1M HNO

. Figure 18 gives an example

for Fe. In the absence of aggressive anions, no potential plateau but only a small

shoulder was found for galvanostatic transients; i.e., only passivation with no

large free metal dissolution was observed. The product i√

—

starts at small values

and decreases with increasing current density i. Only in the presence of > 1 M Cl

–

(or possibly other halides) were much larger values independent of i found for

i√

—

. These studies also prove that the presence of aggressive anions is necessary

to prevent passivation of Fe and Ni surfaces.

For a hemispherical pit the diffusion-limited local current density i

c,p

changes

according to Eq. (18), which is a simple combination of Fick’s first diffusion law and

Mechanisms of Pitting Corrosion 271

Figure 16 Galvanostatic transient of Ni in saturated NiCl

solution with i = 1.5 A/cm

and the related voltage drop ΔE + ΔU

across the total salt layer and ohmic drop ΔU

across the porous film. (From Ref. 56.)

272 Strehblow

Figure 17 Concentration of NiCl

at a corroding Ni surface c

as a function of the product

i√t for linear and spherical transport (including nonstationary conditions) calculated with

Eqs. (17) and (20). (From Ref. 30.)

Figure 18 Plot of i – i√

—

, τ = transition time, for galvanostatic transients of small Fe

electrodes in different solutions without and with 1 M Cl

–

depending on the applied current

density. (From Ref. 58.)

Faraday’s law for the hemispherical electrode geometry with the same varibles as

used for Eq. (17):

Mechanisms of Pitting Corrosion 273

This equation contains a constant a that takes into account the change from the

convex to the concave pit geometry. For the simple analytical solution of the convex

hemispherical transport problem a = 1 will hold. For a concave hemispherical pit

a has been estimated to be 3 [6,30,31]. Computer-assisted numerical calculations

yield a result that is very close to this value for the pit bottom [62,63]. With the

simple stoichiometric relation between the local current density i

c,p

of a

hemispherical pit and its growth rate of the radius dr/dt and Faraday’s law [Eq.

(19)] one obtains Eq. (20), which is the equivalent relation for the transport from

a hemispherical pit to the linear transport from a small electrode dissolving totally

at its surface [Eq. (17)]. V

is the molar volume of the metal under study. Figure 17

compares the calculated results for NiCl

for both electrode geometries.

Precipitation of corrosion products is expected for the transition times t = τ when

saturation is achieved at the pit surface with c

m,s

= 4.8 M and 4.2 M for NiCl

and

FeCl

, respectively. This condition is achieved first at the pit bottom for a = 3. The

calculated data agree well with the experimentally observed precipitation within

pits [30]. For Ni

i√

—

= 14.8 A cm

–2

1/2

is obtained. With the assumption of

nonstationary transport conditions one yields almost identical results (Fig. 17).

Some deviation is obtained only for values i√t

–

> 12 A cm

–2

1/2

[30].

The precipitation of a salt film is closely related to a change in the growth of

a corrosion pit. When the salt film is formed, the growth rate slows down and the

pit morphology changes from a polygonal to a hemispherical structure. This change

starts at the pit bottom, where it is expected first, and often is combined with an

electropolishing effect [55]. Direct microscopic in situ and ex situ examinations of

growing pits for potentiostatic conditions show a decrease of the growth of the

radius when a salt film precipitates (Fig. 19) [58]. The time of change of the growth

rate coincides with the electropolishing effect at the pit bottom [55]. Heimgartner

and Böhni [64] discussed the growth of corrosion pits for longer times under

diffusion-limited conditions in more detail. If the local current density i

c,p

in a pit

is not constant and decreases inversely with the pit depth r according to Eq. (18a),

one deduces with Eq. (19) a reciprocal relation of its growth rate dr/dt with its

depth r [Eq. (21)]. Integration leads to a parabolic dependence of the pit radius on

time t [Eq. (22)] and combination with Eq. (18a) to Eq. (23) with an inverse change

of the local pit current density i

c,p

with √t

–

. This discussion assumes a saturated

solution with a change of the metal ion concentration Δc = c

m,s

, i.e., a salt film at

the actively corroding pit surface and a vanishing bulk concentration c

m,b

Therefore a later stage of pit growth is discussed and not the initial situation of free

metal dissolution as for the beginning of pit growth of Figure 15. Equations (22)

and (23) assume a minimum pit radius r

where a saturated solution at its surface

is achieved. Equation (23) is simply the combination of Eqs. (18a) and (22).

Enhanced convection may lead to a situation where ohmic resistance instead of

diffusion is rate determining. Convection by an increasing flow rate of the electrolyte

or the evolution of gas bubbles in corrosion pits will increase the local dissolution

and finally cause ohmic current control. Like diffusion control, ohmic control will

lead to a parabolic dependence of the pit radius or pit depth on time.

Potential Drops

There exist detailed studies for the potential drop ΔU, the composition of the pit

electrolyte, and related changes of the pH. All these factors have been used to

explain the stability of a corroding pit. The potential drop within the electrolyte

for an open hemispherical pit can be estimated by the simple equation:

274 Strehblow

Figure 19 Deviation from linear pit growth with time when precipitation of a salt layer

occurs, Ni, E = 1.00 and 1.30 V phthalate buffer, pH 5.0 + 0.1 M KCl with inserted diagram

of applied potential pulses. (From Ref. 58.)

with specific conductivity κ, local current density i

c,p

radius r, and geometric factor

a = 3 [6]. It depends on the specific situation whether ΔU is large enough to shift

the potential below the Flade potential, i.e., in the active range of the polarization

curve (Fig. 20). For 0.5 M H

with κ = 0.22 cm

and i

c,h

= 0.3 A/cm

, which

is a reasonable value for moderately high pit current densities for Fe, one obtains

ΔU > 1 V for a pit radius r > 2.4 mm, but only ΔU = 0.41 mV for r = 1 μm. This

short calculation demonstrates that it is absolutely necessary to define well which state

of the growth of a pit is discussed. Potential drops may stabilize localized corrosion

for large pits but never for small ones, i.e., for initial stages. The conductivity of

the electrolyte is, of course, another factor that has to be taken into account. The

accumulation of ions within a corroding pit may increase

and thereby reduce ΔU

compared with the value obtained with the bulk conductivity. Evidence for potential

control of pit growth is given for studies on Al by Hunkeler and Böhni [65]. They

found a linear dependence of the product i

c,p

r on the voltage drop ΔU.

Composition of Pit Electrolyte

The accumulation of electrochemically nonactive electrolyte components is closely

related to the potential drop ΔU within the electrolyte, similar to a Boltzmann

dependence of the concentration c

of these species on the electrical energy ΔU zF

[6,30]. Together with the electroneutrality equation, one obtains a dependence of

the concentration of the corroding metal ions c

at the metal surface on ΔU with

– c

= c

for a vanishingly small bulk concentration c

[6,30]. The

corresponding bulk values are c

j,b

and c

m,b

Mechanisms of Pitting Corrosion 275

Figure 20 (a) Typical current density potential curve of a passive metal; (b) hemispherical

pit with potentials E

inside and E

outside the pit according to the rejected theory

frequently used for small pits. (From Ref. 31.)

Equation (25) requires that only one electrochemical process occurs with no

subsequent reactions within the bulk electrolyte. The concentration of the metal

cations c

may also be calculated from Eq. (18) or (18a). For vanishingly small

bulk concentration of the cations, Δc equals the surface concentration c

. The

accumulation of cations is proportional to the local pit current density and the pit

radius [Eq. (18)]. One may therefore take i

r as a measure of the cation

concentration at the pit surface, which depends on the age of the pit. Therefore this

scale is included in Figures 21 and 22.

276 Strehblow

The concentrations c

at the pit surface of species that are not involved in the

electrode process and the cation concentration have been calculated according to

Eq. (25) for some bulk electrolytes frequently used for pitting studies (Fig. 21).

Metal ion concentrations c

go up to saturation of a few moles per liter when the

potential drop increases to several tens of millivolts, which is usually the case for

a pit radius of several micrometers. Equation (26) was applied for the calculation

of the concentrations c

at the pit surface as given in Figure 22.

pH shifts have often served to explain the stability of a corroding pit. Equation

(25) permits the calculation for buffered solutions when the pH is not affected by

hydrolysis of the corrosion products [30]. Buffer ions change in concentration

in agreement with the pH shift as given for the phthalate buffer in Figure 21. An

Figure 21 Ionic concentration at the metal surface depending on the ohmic drop ΔU

within the electrolyte according to Eqs. (25) and (26). (From Ref. 30.)

accumulation of dissolving metal ions leads to accumulation of the (buffer) anions

and to depletion of the other cations and consequently to a positive pH shift

according to Eq. (27).

Mechanisms of Pitting Corrosion 277

Figure 22 Concentration of metal ions at the dissolving metal surface depending on the

ohmic drop ΔU

and the parameter i

c,p

r according to Eq. (26). (From Ref. 30.)

In nonbuffered solutions the usual hydrolysis equilibrium of the metal ions leads

to acidification according to

+ H

O ↔ MeOH

(z–1)+

+ H

With [MeOH

(z–1)+

] = [H

] for nonbuffered electrolytes one obtains:

With hydrolysis constants of K

= 10

–10

and 10

–7

one obtains for the saturation

concentrations 4.8 and 4.2 M, pH values of 4.3 and 2.4 for saturated NiCl

and FeCl

solutions, respectively. These calculations show that the precipitation of hydroxide

within a corrosion pit may be prevented for these metals by acidification. However,

as discussed before, passivation should nevertheless be possible for many technically

important metals. For Fe, Ni, and other metals, especially in acidic media, passivity

cannot be explained on the basis of thermodynamic equilibria and Pourbaix

diagrams. In these cases passivity is a kinetic phenomenon. Otherwise these metals

should not show passivity in a strongly acidic environment. Thus, different

explanations are required for the stability of a corrosion pit.

The pH shift of the passivation potential E

may not give an explanation either.

Its change usually by –0.059 V/pH is much too small to cause a shift above the

potentiostatically applied value E well within the passive range, so that the metal

surface might reach the active range of the polarization curve. In 0.5 M H

the

passivation potential for Fe or Ni is E

= 0.58 or 0.35 V, respectively, with a shift of

–0.059 V per pH unit. If the potential is set in the passive range up to 1.5 V one has

to explain a shift of the passivation potential by 0.9 to 1.15 V, which is absolutely out

of range of any reasonable explanation. If, however, the potential E is set to values

close to E

, as often realized in technical corrosion situations with open-circuit con-

ditions, acidification may cause its shift above E with E

> E, which especially in

weakly acidic and alkaline unbuffered solutions may fulfill these requirements. In

addition, the much more negative passivation potential of Fe for neutral and alkaline

solutions, such as E

= –0.1-0.059 pH for Fe, will not be effective as a consequence

of acidification by hydrolysis. The passivation potential becomes more negative

because of the insolubility of lower valent Fe oxides such as Fe

or Fe(OH)

neutral and alkaline solutions. However, these oxides dissolve very quickly in acidic

electrolytes, so they do not provide passivity for these conditions. In conclusion, one

may say that local negative pH shifts due to hydrolysis of corrosion products may

support and stabilize pitting at negative electrode potentials for neutral and weakly

acidic and alkaline bulk electrolytes. This will hold especially for metals that cannot

be passivated at low pH, e.g., Cu and Al, because of their fast dissolution or high

solubility in this environment. However, this interpretation does not hold for Fe, Ni,

and steels in strongly acidic electrolytes at sufficiently positive electrode potentials.

Thus, pitting needs another, more general explanation. Furthermore, anions of other

strong acids such as perchlorates and sulfates should act as aggressive anions as well

if hydrolysis and pH shifts are the essential causes of localized corrosion. However,

ClO

–

may even act as an inhibitor if the potenital is not too positive and most

metals may be passivated in sulfuric and perchloric acid, which demonstrates that

the specific chemical properties of the aggressive anions have to be taken into

account in the explanation of pitting corrosion.

An attempt has been made to explain the requirement for a minimum

concentration of aggressive anions to maintain stable pit growth [30,31]. With the

assumption that a salt film of thickness δ has to be maintained at the growing pit

surface, one obtains:

278 Strehblow

With this assumption the experimentally found value of c

min

= 3 × 10

–4

M has been

confirmed with a local current density i

c,p

= 1 A/cm

, a salt layer thickness δ = 5 nm,

geometric factor a = 3, molar volume V

= 3.55 cm

/val for the equivalent volume

for Fe metal and V

= 21.25 cm

/val for FeCl

, and diffusion constant

D =10

–5

/s for Cl

–

ions.

The accumulation of aggressive anions has been found at the surface even of

small polygnal pits of some few μm diameter when their change to a hemisphere by

the precipitation of a salt film was not already achieved. A special preparation

technique of pulling the electrode with actively corroding pits into a benzene layer

above the electrolyte preserved the special situation at the corroding pit surface even

after rinsing with acetone and dry storage in air [66]. These pits remained active and

continued their growth immediately when reintroduced into the electrolyte at the

same potential; however, they became inactive on rinsing with water or stepping

the potential below the critical value. With electron microprobe analysis, chloride

could be found that corresponded to layer of ~ 5 nm FeCl

when the pit remained

active but was lost completely on rinsing with water or repassivation [66]. These

studies show clearly that the formation of a thin layer of aggressive anions even in

pits of some few μm is responsible for stable pit growth. The later precipitation