Marcus P. Corrosion mechanisms in theory and practice

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measurements concluded in the formation of Cr-enriched passive films. Mechanistic

aspects of the process have been investigated in detail by Kirchheim et al.

[178,189,190] and several other groups [101,174,191].

Reaction Mechanism of the Anodic Dissolution of Fe-Cr

The anodic behavior of Fe-Cr alloys was investigated by using steady-state

polarization curves and sampling by a large number of impedance measurements

over the concentration domain (0–22% Cr) in H

-Na

media (0 < pH < 3)

[105,106]. The OH

–

and Cr contents are found to play very similar roles in the

reaction mechanism. The more salient characteristics of the role of Cr are visible

at 7% Cr in pH 0 solution, as shown in Figure 24A, which exhibits a two-peak

polarization curve and two perfectly separated passivation loops.

The passivating feature attributed to Cr at point D (capacitive loop of

characteristic frequency 4 Hz) is therefore already visible at the beginning of the

active domain (point A). Simulations of the current-voltage curves and of the

impedance diagrams were performed on the basis of a mechanistic description

derived from the reaction pattern previously elaborated for pure iron [61,62].

Therefore, coverages by five surface species were introduced in the derivation. The

whole body of data led to taking into consideration, at the same time, the three

types of interaction between Fe and Cr listed earlier namely

1. Alloying effects

2. Surface composition of the alloy distinct from the bulk one

3. Interaction of surface species with the neighbor atoms of either of the two

alloy components

The last interaction was found to be the determining one for interpreting the

impedance data and the steep onset of passivity. The mechanism is shown below. A

146 Keddam

Figure 23. Current-potential curves of iron-chromium alloys as a function of Cr

content. From ref [163].

Anodic Dissolution 147

Figure 24. Experimental (A) and calculated (B) current-potential curves and impedance

diagrams for a Fe-7Cr alloy (IRSID, France). 1M H

, 25°C. Impedance diagrams at

the corresponding polarization points on the I(E) curve. Frequency in Hertz. Simulations

according to the reaction mechanism (54). From ref [105].

specific nonlinear interaction with the chromium passivating species Cr(II)

ads

was

supposed to affect the rate of iron dissolution. Figure 24B shows the result of

simulations of the polarization curves and impedance diagrams. The sharp decay

of the iron dissolution at increasing coverage θ

Cr(III)

by Cr(II)

ads

was expressed by

introducing the factor (1 – θ

Cr(II)

) with x ≅ 0.5. A similar interaction function is

adopted in the description of poisoning effects by foreign atoms in binary alloy

catalysts. As emphasized for the first time in Ref. 106, this power law suggests that

the threshold behavior arises from surface percolation of passivated chromium sites.

According to this interpretation, passivation would occur on an incompletely

covered surface via long-range interactions between bare iron atoms and passive

chromium connected in large clusters. A computer simulation later demonstrated

the validity of this idea [184,192]. In the same paper [106], attention was also drawn

to the atomistic description of the catalytic mechanism of dissolution (see earlier)

in the case of a binary alloy. Therefore, purely macroscopic modeling of the

kinetics of dissolution is no longer possible without consideration of the alloy

microstructure, distribution of first and second nearest neighbors, and statistical

composition at the atomic level. Concepts such as the size of clusters of atoms A

and B and percolation phenomena [193] appear as determining and actually have

been extensively worked out (see later).

Analytical and Mass Balance Approaches to Dissolution

and Passivation of Fe-Cr Alloys

An important contribution is due to Japanese authors who developed rotating

double-ring and split-ring disk electrode devices [191] and introduced channel flow

arrangements [85] and data processing in the transient regime [101]. The respective

behavior of Fe and Cr in the presence of Cl

–

was investigated [191] for an Fe-30Cr

alloy. It was concluded that chloride enters the soluble ferro-complex species while

it behaves as an inhibiting species with respect to Cr. By employing time-resolved

148 Keddam

measurements on CFDE, previously introduced for iron studies [85], it was then

shown [101] that in a sulfate medium the amounts of Fe and Cr dissolving at

steady state are proportional to their concentrations in the alloy.

Active and Active-Passive Transition; Impedance and Frequency-Resolved

RRDE Measurements The association of impedance and frequency-resolved

RRDE techniques initially introduced for iron [38,117,197] has been extensively

applied to the prepassive and passivation ranges of Fe-Cr alloys with and without

chloride added [174,194,195]. Of course, the interpretation is more intricate than

for pure metals (even with multiple dissolution valences). For kinetic reasons, Cr

species are not detectable on the ring. In order to draw unambiguous conclusions,

reasonable assumptions had to be made concerning simultaneous alloy dissolution

at steady state (see thermodynamics and rate constant approach earlier) and

dissolution valences of Cr.

Completely different behaviors were found depending on whether or not

chloride is present. The salient features are

Emission efficiency for Fe(II) greater than 1 (for Fe-12Cr), an apparent paradox for

a pure metal because that violates the principle of electrical charge conservation

A positive imaginary part of N

(passivating charge) in the absence of Cl

–

A negative imaginary part of N

(dissolution intermediate) in the presence of Cl

–

A model depicting the surface processes in terms of reaction paths and topographic

interaction has been elaborated. It incorporates the key points previously introduced

in the model based on impedances [37]. In particular:

Modification of the iron rate constants by chromium

Sharp passivation of the alloy represented by a nonlinear dependence of the

blocking on the Cr species coverage

The reaction model and the corresponding surface picture are shown in

Figure 25. It accounts for the nature and position of the first-order nearest neighbor

for making explicit the interaction and mass balance of the surface species. This

kind of approach was introduced in pioneering work [107] and then worked out in

the framework of percolation models of passivation [180,192]. In view of the process

complexity, an accurate fit is hopeless, but the main features could be semi-

quantitatively simulated, including the amazing N

> 1. A comparison of the

experimental and computed N

relative to Fe(II) is displayed in Figure 26.

According to the model, this extra emission of Fe(II) with respect to the

electrical current across the electrode can be understood in terms of the contribution

of chemical dissolution of an Fe(II) species by a step such as K

Later on, the same model was considered for interpreting the results in

chloride-containing media. The main modification was to enhance considerably

the rate of dissolution (catalytic) via the Fe(III)

ads

, whereas in Cl

–

-free media most

of the iron dissolves from the Fe(II)

ads

(step K

). The resulting change in the sign

of N

arises from the role of the dissolution intermediate of Fe(II)

ads

. These results

supported to some extent those of Ref. 191.

Dissolution in the Passive State In a series of papers by Kirchheim et al.

[173,189,190], the dissolution rates of Fe and Cr in Fe-Cr alloys were investigated

Anodic Dissolution 149

within their passive range in H

solution. Time-resolved chemical analysis of

the solution was performed by atomic absorption spectroscopy of samples of

electrolyte. Selective dissolution of iron during the transient passivation stages

was exploited in terms of Cr enrichment in the passive layer, and once the steady

state was reached, simultaneous dissolution was accurately verified.

Figure 27 is an illustration of the time-resolved monitoring of the percentage

of Cr in the dissolution products during a phase of film growth triggered by a

galvanostatic square pulse [173]. In-depth concentration profiles of Fe and Cr in

the film were concomitantly measured by XPS, and the significant enrichment in

Cr for corrosion in the passive state was attributed to the outer first layer of the

film. Equation (53) expressing simultaneous dissolution is applied to both the

alloy phases (a) and the film outer layer (e):

i = i

+ i

150 Keddam

Figure 25. Schematic representation of the reaction mechanism and of the topographical

interaction of reaction step and surface coverages. From ref [195].

Figure 26. Emission efficiency of Fe(II) for Fe-l2Cr alloy in 0.5 M H

. In the active

dissolution (“a”: E = 0.07V/SSE) and passivation (“b”: E = 0.l8V/SSE) ranges. From [195].

and for the same dissolution valences of both components (3+).

= ix

Fe,a

= ix

Cr,a

where the x’s refer to the molar fractions in the alloy. At the outer side of the film,

the same partial currents are supported by the molar fractions of cations x

Fe,e

and

Cr,e

. The ratio of the individual dissolution rates of each of the elements from the

metal (a) and the first layer of the passive film (e) is reflected in the dissolution

currents of the pure metal components in the same passive conditions, i

co,Fe

and

co,Cr

, so that

Anodic Dissolution 151

Figure 27. Galvanostatic transients for the dissolution (bars in a), the Cr fraction in the

dissolution products (b) and the potential (c) for two different alloys (left: 1 at.%Cr, right:

14 at.%Cr) after attainment of steady-state. From ref [173].

Chromium enrichment in the film, according to Eq. (53), is directly correlated

with the lower dissolution rate of pure Cr with respect to pure iron. This is consistent

with a lower diffusivity of this element in the film and tentatively explained by the

high-field migration model. However, this is done at the expense of introducing,

nonclassically, the diffusivity in the preexponential factor of Eq. (42) [188]. After

simple transformation, Eq. (55) can be written as a reciprocal dependence of the

passive current of the alloy with respect to its Cr content.

Figure 28 shows an example of the good agreement reported in Ref. 179 and

considered as supporting the model. The model validity has been also discussed in

the case of Fe-Mo and Fe-Al alloys [189]. Subsequently [190], precipitation from

supersatured anolyte in the initial stage of active dissolution was proposed as a

determining step of the passive film growth on alloys with a low Cr content at low

pH. This hypothesis can be traced back to the 1930s [11].

Selective Dissolution

Conditions for simultaneous dissolution generally involve the formation of a 2D

or 3D surface layer in which the relative dissolution rates of the elements are equal

to their alloy fraction. Even in cases where simultaneous dissolution is obeyed, the

process must begin by an initial period of selective dissolution at least at a 2D

level [191]. As briefly mentioned earlier, many mechanisms have been invoked to

explain how, for a nonpassive alloy, the dissolution of the more reactive element

can continue across the dealloyed structure [32,1194]. Surface changes have been

attributed to surface diffusion and recrystallization, redeposition, short-range atomic

rearrangement, and a roughening transition by capillary effects.

Electrochemical measurements coupled with solution analysis were progres-

sively backed up by analysis of the surface and in-depth profiling of the alloy

composition in the dealloyed layer [198]. Current-voltage, current-time, and

potential-time relationships, as a function of the alloy composition and of the degree

of selective dissolution, are the techniques employed extensively. Contributions to

the field using this kind of approach can be found in Ref. 173, 196, 199.

152 Keddam

Figure 28. Relation between the passive current densities, i

, and the concentration of

chromium in Fe-Cr alloy, x

Cr.a

according to the model relating the dissolution of the alloy

to the Cr/Fe proportion at the outer side of the film. From ref [179].

Anodic Dissolution of Binary Alloys Studied by Electrochemistry,

Solution, and Surface Analysis Techniques

These investigations have dealt with alloys such as AgPd, CuPd, NiPd, and AgAu

under conditions of no passivation. Alloy-electrolyte (LiCl) combinations offer the

possibility of observing both selective and simultaneous dissolution behaviors

depending on the concentration of the noble metal. Two quantities are defined for

describing the amount and in-depth property of the dealloyed surface:

= surface excess of the more noble metal B:

Anodic Dissolution 153

where X

(z) is the mole fraction of B at distance z from the surface (z) and X

B,b

the bulk alloy.

= selectivity coefficient (dimensionless):

where Q

is the charge corresponding to the amount of B dissolved (from solution

analysis) and Q

B,th

its amount calculated for simultaneous dissolution by the

same charge (S

= 1 corresponds to complete selective dissolution of A, S

= 0

to simultaneous dissolution).

The value of e

can be estimated from potential-time transients or AES analysis,

and the value of S

is determined by weight loss and solution analysis. The potential

increases with the dissolving charge passed at the interface in the selective

dissolution stage, then reaches a critical value E

and exhibits a plateau where

either both components dissolve in stoichiometric proportion or only one keeps

dissolving with formation of surface roughness. On Ag-Pd alloys the e

values at

the critical potential, estimated by electrochemistry and AES, are in reasonably good

agreement; they show a steady decay when the Pd content in the alloy is increased

and become negligible above 50%. Figure 29 shows an example of this dependence

for three alloys [199]. A threshold of Pd concentration is observed around

0.2, beyond which no Pd enrichment takes place. This can be understood in the

framework of percolation theory (see the next section).

Some mechanistic data on surface enrichment can be inferred. Surface

enrichment is essentially constant after a minimal amount of dissolution (5 mC cm

–2

independent of the dissolution rate. Redeposition and surface diffusion are ruled out

in favor of short-range rearrangements of surface atoms. A reciprocal shift of binding

energy between Ag and Pd atoms is assumed to participate to some degree in

simultaneous dissolution of Pd at potentials lower than from the pure metal [156].

Quite identical conclusions are reached for Cu-Pd, Ni-Pd, and Ag-Au alloys [180].

Investigation of the anodic dissolution below the critical potential is likely to

provide more relevant information on the mechanism of selective dissolution [178].

The emphasis is generally put on the current-time relationships, which are supposed

to reflect the mechanism of transport within the surface layer. Dynamic polarization

curves and current-time decays have been investigated for Cu-Au and Ag-Pd in LiCl

and acidic sulfate solutions. In all cases, current-voltage profiles display a plateau

followed by a steep increase at the same critical potential E

evidenced on the

potential-time transient. The shape of these curve is shown schematically in Figure 30.

154 Keddam

Figure 29. Measured charge corresponding to Pd enrichment as a function of Pd bulk

mole fraction. From ref [199].

Figure 30. Schematic illustration of the anodic polarization curves for a binary A-B

alloy with respect to the curves for the individual elements A and B. From ref [32].

In agreement with previous work, the current-time transients recorded at

various potentials below the critical potential are correctly represented by a

reciprocal power law:

Anodic Dissolution 155

regardless of the alloy composition. The interpretation suggested in Ref. 196 is

derived from the model of divacancy diffusion [182]. Diffusivity of the vacancies

is supposed to depend on concentration and potential. The resulting nonlinear

diffusion is most probably responsible for a t

–m

current dependence, as indicated

by numerical simulations.

Actually, even the sophisticated studies combining electrochemistry and surface

analysis seem unable to yield any further decisive information on the detailed

mechanism of selective dissolution. Atomic arrangements in which dissolution of

atoms A can proceed throughout a rough electrode structure enriched in B type

have been recognized as amenable to percolation theory [193]. The same theory

was also applied to the passivation of binary Fe-Cr alloys in which, as suggested

in Ref. 105, 106, passivation of the more soluble element, Fe, is enhanced by a

connected surface lattice of passive Cr atoms. The main power of percolation theory

is to provide diagnostic criteria for computer simulations in terms of concentration

thresholds.

Atomistic Modeling of Selective Dissolution and Related Passivation

by Percolation Theory

The now popular concept of percolation has proved quite successful in many

fields in which a macroscopic property depends on the existence of a connected

path within a two-phase discrete medium, most often a regular 2D or 3D arrangement

of sites (site lattice percolation). Typical features related to percolation are the

existence of a critical phenomenon, for instance, a threshold concentration of

conducting sites when conduction is considered, and of a power law dependence

with respect to the critical quantity in the close vicinity of the critical point. Both

the site percolation thresholds and the power exponents have well-established

theoretical values for any given lattice geometry and connection rules [193].

In spite of its extensive use in the description of heterogeneous systems,

including electrolytic crystal growth, it seems that the percolation concept was

considered relatively recently in the field of electrode processes for explaining

sharply varying properties of alloys. The characteristic feature of a critical concentration

of Zn in α-brass and Al in Al-Cu alloy was correlated with the percolation threshold

on an fcc lattice [175].

Computer Simulations of Selective Dissolution An extensive contribution

was reported [32] addressing the problems raised by experimental dealloying

thresholds p* at variance with theoretical site percolation thresholds p

Possible interpretations are listed:

1. Dissolution from low-coordination sites (kinks and ledges) faster than from

terraces

2. Not randomly distributed atoms in the alloy

3. Surface diffusion of B (noble atoms)