1-s2.0-s0010938x02002123-main

Pit formation and growth of alloy 600 inCl� ion-containing thiosulphate solution at

temperatures 298–573 K using fractal geometry

Jin-Ju Park, Su-Il Pyun *

Department of Materials Science and Engineering, Korea Advanced Institute of Science

and Technology, 373-1 Guseong-Dong, Yuseong-Gu, Daejeon 305-701, South Korea

Received 25 February 2002; accepted 15 October 2002

Abstract

Pit formation and growth of alloy 600 has been investigated in aqueous 0.1 M

Na2S2O3 þ 0:1 M NaCl solution at elevated solution temperatures 298–573 K and at pressures

0.1–8 MPa in terms of fractal geometry using potentiodynamic polarisation experiment, po-

tentiostatic current transient technique, scanning electron microscopy (SEM), image analysis

method and ac-impedance spectroscopy. From SEM observation, it was realised that pit

morphology changed from cylindrical shape developed at 60 �C to highly branched shapeformed at 150 �C. Furthermore, corrosion pits formed and further grew without any mor-phological change during the whole pitting process below 200 �C. On the other hand, above200 �C, the morphology of the pits changed from highly branched shape in the early stage ofthe pitting process to widely grooved shape in the later stage. After SEM observation of the

pits, the fractal dimension of pits was determined as a function of solution temperature 60–150

�C using perimeter–area method. The value of the fractal dimension of the pits increased withincreasing solution temperature. This is caused by the increase in the ratio of perimeter to area

at higher solution temperature, indicating the formation of pits with highly branched shape.

The appearance of specific shape and fractal dimension value of the pits at each solution

temperature implies that the formation and growth of pits proceed with the typical fractal

geometry throughout the whole pitting process irrespective of pit size. In addition, constant

phase element (CPE) behaviour observed from the impedance spectra is discussed in terms of

the fractal dimension of pits.

� 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Alloy 600; Pit growth; Perimeter–area method; Fractal dimension; Solution temperature

*Corresponding author. Tel.: +82-42-869-3319; fax: +82-42-869-3310.

E-mail address: [email protected] (S.-I. Pyun).

0010-938X/03/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.

PII: S0010-938X(02 )00212-3

www.elsevier.com/locate/corsci

Corrosion Science 45 (2003) 995–1010

mail to: [email protected]

1. Introduction

Inconel alloy 600 has been widely used as the steam generator tube material in

pressurized water reactors nuclear power plants. Since the discovery of pitting in

alloy 600 steam generator tube [1,2], there has arisen a need to understand the pitting

process in the steam generator tube.Fractal geometry has been used to characterise disorderly structures in a wide

range of different fields, and the use of fractal geometry to obtain a quantitative

characterization of the morphology of corroded surfaces has been described in

several recent works [3–6]. Especially, pitting corrosion can lead to rough surfaces

because of the formation and decay of a protective layer. Considerable interest is

shown in the formation and growth of rough surfaces [7,8]. In this respect, pitting

corrosion attracted significant attention because of the challenging problem in the

development of irregular corrosion pits observed in bulk metals. Recently, manyinvestigators characterised the pitting corrosion to determine fractal roughness of

aluminium electrode using electrochemical impedance spectroscopy [9], light scat-

tering [10] and image analysis [5,11].

In general, corrosion morphologies are rarely uniform. Pits observed on corroded

surfaces may be small or large in diameter, drawing a variety of sizes and shapes.

Therefore, it is of great importance to characterise the morphology of pits quanti-

tatively in relation to fractal geometry. In addition, the role of solution tempera-

ture in morphology of pits in Cl� ion-containing solution has not been clearlyexamined.

The present work was undertaken to correlate the morphology of the pits of alloy

600 with their fractal dimension in aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl solution

as a function of solution temperature. For this purpose, first, potentiodynamic po-

larisation experiments and potentiostatic current transient technique were employed

to characterise passivity of oxide film and the formation and growth of pits by means

of anodic current flow across the specimen as a function of solution temperature.

Finally, the relationship between morphology of the pits formed at various solutiontemperatures and their fractal dimension has been established using scanning elec-

tron microscopy (SEM), image analysis method and ac-impedance spectroscopy.

Changes in morphology, the fractal dimension and constant phase element (CPE)

behaviour of pits during the whole pitting process have been discussed with respect

to solution temperature in terms of passivity of oxide film.

2. Experimental

In this work, the specimen was made from Inconel alloy 600 with a composition

(wt.%) of 15.4% Cr, 8.0% Fe, 0.3% Mn, 0.1% Si, 0.01% C and Ni bal. For elect-

rochemical experiments, the squared rod specimen was set in a block of polyimid.The upper surface of the block was ground with emery paper successively up to 2000

grit. Two kinds of electrolyte were employed in the present work: 0.5 M Na2SO4solution of 25 �C for ac-impedance measurements at open-circuit potential and a

996 J.-J. Park, S.-I. Pyun / Corrosion Science 45 (2003) 995–1010

mixed aqueous solution of 0.1 M Na2S2O3 and 0.1 M NaCl solution of 25, 60, 100,

150, 200, 250 and 300 �C for all electrochemical experiments. All electrochemicalexperiments at elevated solution temperatures and pressures were carried out using

autoclave. An external Ag/AgCl electrode and a platinum wire were used as the

reference electrode and counter electrode, respectively. Three electrodes were in-

troduced into the autoclave through a high-pressure fitting.The potentiodynamic polarisation experiments were made on the square rod

specimen with an exposed area of 2:9� 10�1 cm2 in the applied potential range of�0.5 to 1.5 V (Ag/AgCl) with a scan rate of 0.5 mV s�1 by using a Potentiostat/Galvanostat (EG&G Model 263A) interfaced with an IBM compatible computer.

The current density was recorded potentiostatically with time at an applied anodic

potential of 0.8 V (Ag/AgCl) in aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl solution at

various solution temperatures to characterise passivity of oxide film and the

pitting process of the specimen by using a Potentiostat/Galvanostat (EG&G Model263A).

The morphology of corrosion pits formed on the specimen was examined as

functions of solution temperature and pit depth using SEM. For the SEM obser-

vation, pits were made on the specimens by applying constant anodic potential of 0.8

V (Ag/AgCl) for 300 s at different solution temperatures. The pitted specimen was

rinsed with distilled water and then was cleaned with acetone immediately before

SEM observation. Thereafter, pit morphology observed by SEM was digitized and

then transferred to a computer for further image analysis. The digitized image of pitmorphology was analysed quantitatively by image analysis method. The fractal di-

mension of pits was determined as functions of solution temperature and pit depth

using perimeter–area method [8,12]. A computer program was programmed to

measure the perimeter and area of each of pits. The yardstick, which was pixel edge,

was calibrated to be 0.01 lm. The plot of perimeter against area on a logarithmicscale was linearly fitted, and twice the slope was the fractal dimension of contour

lines of pits.

AC impedance measurements were carried out with a Solartron 1255 frequencyresponse analyzer connected with the Solartron 1287 electrochemical interface. The

impedance spectra were recorded from 105 Hz down to 0.1 Hz frequency using 5 mV

amplitude perturbation. Two types of measurements were done: (A) For the deter-

mination of the oxide film resistance Rox the impedance spectra were measured asfunctions of applied potential and solution temperature in aqueous 0.1 M Na2S2O3þ0:1 M NaCl solution at various solution temperatures; Rox was determined using acomplex non-linear least squares (CNLS) fitting method [13]. (B) To correlate pit

morphology with impedance behaviour, first the corroded surfaces were preparedelectrochemically at 0.8 V (Ag/AgCl) for 300 s in aqueous 0.1 M Na2S2O3 þ 0:1 MNaCl solution at various solution temperatures; thereafter the impedance spectra

were recorded under open-circuit conditions at room temperature in 0.5 M Na2SO4solution.

For the sake of reproducible data, potentiodynamic polarisation experiment,

potentiostatic current transient experiment and ac-impedance measurement were

carried out three to five times.

J.-J. Park, S.-I. Pyun / Corrosion Science 45 (2003) 995–1010 997

3. Results

Fig. 1 presents potentiodynamic polarisation curves for alloy 600 with a scan rate

of 0.5 mV s�1 in aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl solution at various solution

temperatures. As solution temperature increased, corrosion rate rose and at the same

time the value of current density increased at any given anodic potential. Here,corrosion rate is defined as the open-circuit current density. The increase in the value

of current density in chloride solution is known to arise from the increase in the

passive current density below the pitting potential, whilst it is indeed due mainly to

the formation and growth of a stable pit on the surface above the pitting potential.

This implies that the increasing solution temperature is destructive to passivity of

oxide film formed on the specimen, leading to an occurrence of pitting corrosion [14–

16].

Fig. 2(a) and (b) depicts typical impedance spectra in Nyquist presentation ob-tained from alloy 600 at various applied anodic potentials in aqueous 0.1 M

Na2S2O3 þ 0:1 M NaCl solution at various solution temperatures of 25 and 100 �C.It can be seen that the value of total impedance at 100 �C is much lower than that at25 �C. This means that oxide film formed at higher solution temperature has lowerdegree of passivity compared with that formed at room temperature. In order to

compare the degree of passivity of oxide film quantitatively as a function of solution

temperature, real and imaginary components of measured impedance were analysed

by using CNLS fitting method suggested by Macdonald [17] and modified in thislaboratory [13] on the basis of the equivalent circuit which is given in Fig. 2(c) below

the pitting potential. The equivalent circuit consists of charge transfer resistance Rctin parallel to the double layer capacitance Cdl and the oxide film resistance Rox and

Fig. 1. Potentiodynamic polarization curves of alloy 600 with a scan rate of 0.5 mV s�1 in aqueous 0.1 M

Na2S2O3 þ 0:1 M NaCl solution at various solution temperatures 25–300 �C.


(a)

(b)

(c)

Fig. 2. Impedance spectra in Nyquist presentation obtained from alloy 600 at various applied anodic

potentials in aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl solution at various solution temperatures of (a) 25 �Cand (b) 100 �C. (c) Equivalent circuit used for the analysis of impedance spectra. Rs solution resistance, Rctcharge transfer resistance, Cdl, double layer capacitance, Rox oxide film resistance, CPEox CPE of oxidefilm.


the CPE of oxide film CPEox in parallel to Rox. Charge transfer resistance Rct isneglected because it is so small. Thus Rox is considered to correspond to the measuredtotal resistance.

Fig. 3 gives changes in the value of Rox with applied anodic potential on a semi-logarithmic scale obtained from alloy 600 in aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl

solution at various solution temperatures. The value of Rox decreased with appliedanodic potential, irrespective of solution temperature. It is generally agreed [18,19]

that the presence of chloride ion on the metal surface hinders the oxide film for-

mation. In this work, it is conceivable that the concentration of adsorbed chlorideions on the metal surface increased with increasing applied potential due to their

higher electronegativity. Consequently, the increase in the adsorbed chloride ion

concentration on the metal surface hindered the oxide film formation by competitive

adsorption between oxygen containing species and chloride ions [20], resulting in the

decrease of the oxide film resistance Rox. In addition, the value of Rox decreased withincreasing solution temperature over the whole applied anodic potential, suggesting

the formation of a more non-protective oxide film at higher solution temperature.

Fig. 4 exhibits potentiostatic current transients of alloy 600 subjected to a con-stant anodic potential of 0.8 V (Ag/AgCl) in aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl

solution at various solution temperatures. In this figure, it can be seen that the

pitting process is categorized into the three stages, i.e. the first passivation stage, the

second pit formation and growth stage and the final steady-state stage. The anodic

current density of the first stage descended abruptly with time and then reached

current minimum at time t1. The fall of current density indicates the thickening of

Fig. 3. Changes in the oxide film resistance Rox with applied anodic potential on a semi-logarithmic scaleobtained from alloy 600 in aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl solution at various temperatures 25–

300 �C.


oxide film on the surface. In the second stage, the value of current density ascended

from the moment just after t1 to t2, which is attributed to film breakdown caused bythe formation and growth of pits. In the presence of thiosulphate ions in chloridecontaining solution, after pit initiation, pitting corrosion product such as black

sulphide would be precipitated inside the pits. The corrosion product blocks up the

pits and hence hinders the current flow through the pits. Thus, a steady-state was

attained between the metal dissolution and oxide film formation including a

blockade by pitting corrosion product in the third stage of current transient after t2.In the third stage, the increment in current density caused due to the metal disso-

lution just equals the sum of the decrement in current density due to oxide film

formation and the decrement of current density due to the blockade by pittingcorrosion product, leading to nearly constant current density.

The current transient revealed that there is a growing tendency that the rate of

passivation dominates over the rate of oxide dissolution as solution temperature

decreased, resulting in the increase in t1. From the experimental findings that the

slope of current transient in the range from t1 to t2 is drastically increased with in-creasing solution temperature, it is deduced that the rate of growth of pits increased

with solution temperature [20–22]. Moreover, since the amount of charge consumed

Fig. 4. Potentiostatic current transients of alloy 600 subjected to a constant anodic potential of 0.8 V (Ag/

AgCl) in aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl solution from 60 to 150 �C.


during the whole pitting process at higher solution temperature is much larger than

that at lower solution temperature, it can be said that the pit area density increased

with solution temperature. Increasing tendency of the pit area density with solution

temperature was validated by SEM micrographs of Fig. 5. Fig. 5(a) and (b) illus-

trates SEM micrographs of pit morphology of the surface of alloy 600 subjected to

a constant anodic potential of 0.8 V (Ag/AgCl) for 300 s in aqueous 0.1 MNa2S2O3 þ 0:1 M NaCl solution at 60 and 150 �C, respectively. In this figure, it waseasily found that the ratio of pitted area to total surface area increased with in-

creasing solution temperature.

Fig. 6(a)–(g) shows typical SEM micrographs of pit morphology of the surface of

alloy 600 subjected to a constant anodic potential of 0.8 V (Ag/AgCl) for 300 s in

aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl solution at 25, 60, 100, 150, 200, 250 and 300

�C, respectively. It was observed that no stable pitting phenomena occurred on thespecimen exposed to room temperature solution. On the contrary, there was an

Fig. 5. SEM micrographs of pit morphology on the surface of alloy 600 subjected to a constant anodic

potential of 0.8 V (Ag/AgCl) for 300 s in aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl solution at (a) 60 �C and(b) 150 �C.


Fig. 6. Typical SEM micrographs of pit morphology on the surface of alloy 600 subjected to a constant

anodic potential of 0.8 V (Ag/AgCl) for 300 s in aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl solution at (a) 25,

(b) 60, (c) 100, (d) 150, (e) 200, (f) 250 and (g) 300 �C.


occurrence of intense pitting corrosion on the specimen exposed to elevated tem-

perature solutions 60–300 �C. Moreover, it was also found that pit morphologychanged from cylindrical shape made at 60 �C to highly branched shape formed at150 �C [23,24] and finally it changed from highly branched shape in the early stage ofthe pitting process to widely grooved shape in the later stage above 200 �C.Fig. 7 illustrates logarithmic plots of pit perimeter vs. area for pit morphology of

alloy 600 subjected to a constant anodic potential of 0.8 V (Ag/AgCl) for 300 s in

(a)

(b)

Fig. 7. (a) Logarithmic plots of pit perimeter vs. area for the pit morphology of alloy 600 subjected to a

constant anodic potential of 0.8 V (Ag/AgCl) for 300 s in aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl solution

from 60 to 150 �C. (b) Logarithmic plots of pit perimeter vs. area for the pit morphology of alloy formed at150 �C by sectioning the plane with pit depth of 5 and 10 lm.


aqueous 0.1 M Na2S2O3 þ 0:1 M NaCl solution as functions of solution temperature

and pit depth. In particular, in the case of 150 �C, image analysed data obtainedfrom the pits by sectioning the plane with pit depth of 5 and 10 lm in the downwarddirection are plotted in Fig. 7(b). In this figure, it was found that the linear rela-

tionship between pit area and pit perimeter given in Fig. 7(b) is the nearly same as

that linear relationship shown in Fig. 7(a). It is generally known [8,12] that twice theslope of the plot of perimeter against area on a logarithmic scale is the fractal di-

mension Df of contour lines of pits. In this figure, solution temperature raised thefractal dimension as follows: Df ð60 �CÞ ¼ 1:04� 0:04, Df ð100 �CÞ ¼ 1:24� 0:06and Df ð150 �CÞ ¼ 1:40� 0:1. Higher value of the fractal dimension at 150 �C is dueto the increase in ratio of perimeter to area, indicating the formation of pits with

highly branched shape as shown by SEM observation.

Fig. 8(a) envisages impedance spectra in Nyquist presentation obtained from alloy

600 at open-circuit potential in aqueous 0.5 M Na2SO4 solution at room temperatureafter anodic polarisation of 0.8 V (Ag/AgCl) for 300 s in aqueous 0.1 M Na2S2O3þ0:1 M NaCl solution from 60 to 150 �C. Constant phase element (CPE) was observedin the frequency range of 103–1 Hz. For the better understanding of CPE behaviour,

the total impedance was reduced to the values of tan�1½dð�Z 00Þ=dZ 0 and CPE ex-ponent as a function of frequency. Fig. 8(b) plots the changes in the values of

tan�1½dð�Z 00Þ=dZ 0 and CPE exponent with frequency obtained from alloy 600 at

open-circuit potential in aqueous 0.5 M Na2SO4 solution at room temperature after

anodic polarisation of 0.8 V (Ag/AgCl) for 300 s in aqueous 0.1 M Na2S2O3 þ 0:1 MNaCl solution from 60 to 150 �C. The values of tan�1[dð�Z 00Þ=dZ 0] and CPE expo-

nent showed nearly constant in the frequency ranges from 102 to 10 Hz and from 10

to 1 Hz, irrespective of solution temperature as indicated as dashed arrow in Fig.

8(b).

4. Discussion

4.1. Effect of passivity of oxide film on change in pit morphology with solution

temperature during the whole pitting process

In Fig. 6(b) and (d), it was found that pit morphology changed from cylindricalshape at 60 �C to highly branched shape at 150 �C. This morphological change isunder the control of degree of passivity of oxide film formed on the specimen as a

function of solution temperature. From the experimental results of Figs. 1, 3 and 4, it

is recognised that degree of passivity of oxide film was diminished with increasing

solution temperature.

Since no obvious inclusion was revealed on the surface of the specimen by using

high resolution SEM, it is assumed that pit formation and growth sites covered with

less protective oxide film are uniformly distributed over the specimen surface. It istherefore expected that once corrosion pit embryos are generated at 60 �C at suchsites covered with less protective oxide film, the pit embryos would be then sur-

rounded on all sides immediately with the region covered mainly with more


protective oxide layer owing to higher degree of passivity of oxide film at 60 �C.Thus, the viable pit embryos have the same tendency to grow further in all radialdirection and hence the grown pits finally form cylindrical shape. In contrast, cor-

rosion pit embryos generated at 150 �C would be plausibly surrounded on all sides

(a)

(b)

Fig. 8. (a) Impedance spectra in Nyquist presentation and (b) plots of tan�1[dð�Z 00Þ=dZ 0] and CPE ex-

ponent vs. frequency obtained from alloy 600 at open-circuit potential in aqueous 0.5 M Na2SO4 solution

at room temperature after anodic polarization of 0.8 V (Ag/AgCl) for 300 s in aqueous 0.1 M

Na2S2O3 þ 0:1 M NaCl solution from 60 to 150 �C.


directly with the region covered predominantly with less protective oxide film due to

lower degree of passivity of oxide film at 150 �C. The coverage by less protectiveoxide layer of the region immediately adjacent to pit embryos may limit pit growth in

all radial direction. Thus, the viable pit embryos have a preferred tendency to grow

further in specific direction and hence the grown pits finally form highly branched

shape. With higher solution temperature the effect would be much greater.Above 200 �C, the morphology of the pits changed from highly branched shape in

the early stage of the pitting process to widely grooved shape in the later stage. This

is due to the fact that since the passivity of oxide film was lowered above 200 �C, allthe pit embryos would be surrounded on all sides with the region covered with non-

protective oxide layer. Thus, they grow further in all directions, resulting in the

transition in pit morphology from highly branched shape to widely grooved shape.

As solution temperature increased, the transition in pit morphology appeared more

markedly.

4.2. Relationship between morphology and the fractal dimension of the pits as a

function of solution temperature during the whole pitting process

Now, let us establish the relationship between morphology and the fractal di-

mension of pits. SEM micrographs of Fig. 5 revealed that specific one pit among

many small pits with cylindrical shape at 60 �C grew with merging the neighbouringsmall pits and then finally grew into a large one without any morphological change

during the whole pitting process. In the case of highly branched pits formed at

150 �C solution, it is noted that each of small pits with many branches grew indi-vidually and then finally coalesced into a large branched one. Similarly, pit morp-

hology is unchangeable during the whole pitting process at 150 �C.From the fractal dimension theoretically derived from fractal surface, it is ac-

cepted [7,8] that adherence to the same pit morphology is a sufficient condition for

keeping constant fractal dimension of pits during the whole pitting process. From

the fractal dimension determined (Fig. 7), based upon pit morphology in Fig. 6 using

perimeter–area method, it is noted that the fractal dimension of the pits maintains

nearly constant in value during the whole pitting process, irrespective of pit size.

Consequently, it has been experimentally born out that keeping constant fractal

dimension is a necessary condition for the development of the same pit morphologyduring the whole pitting process of alloy 600 specimen.

The unchanged fractal dimension of the pits in value during the whole pitting

process can be explained in terms of the relation between the diffusivity of defects

and solution temperature. In general, defects in oxide film play an essential role as

active sites in pit formation and growth [25,26]. Moreover, the distribution of defects

across oxide film is determined by the value of their diffusivity, and at the same time

the value of the diffusivity of defects is also determined by solution temperature.

Therefore, when a solution temperature remained unchanged, the distribution ofdefects in oxide film was then also remained constant, which leads to the fixed pit

morphology during the whole pitting process. Thus, the fractal dimension of the pits

maintains nearly constant in value during the whole pitting process.


It is widely known [12,27] when pit morphologies are derived from initial surfaces

with the fractal dimension Df , the value of the fractal dimension of their perimeters isfixed for Df � 1. This relation involves implicitly that the unity ‘‘1’’ indicates that thevalue of the fractal dimension in the downward direction is constant irrespective of

pit depth. From the result of Fig. 7, it was recognised that the image data analysed

from pit morphology under various pit depths at 150 �C gave the nearly same linearrelationship between pit area and pit perimeter, regardless of pit depth. This implies

that the pits form and grow with the same fractal dimension in the downward

direction.

At this point, in order to justify the fractal dimension determined from pit mor-

phology, it should be mentioned about cutoff range, i.e. inner cutoff and outer cutoff.

In the present work, it is very difficult to determine the cutoff range by means of

perimeter–area method. However, one would determine roughly the cutoff range by

considering the length of yardstick and the diameter of the largest pit. Firstly, whenthe length of yardstick is smaller than that of inner cutoff, the fractal dimension of

Df ¼ 1 was observed by perimeter–area relation. Because the region of fractal di-mension Df ¼ 1 was not observed from Fig. 7, it can be deduced that the value ofinner cutoff is at least smaller than the length of yardstick of 0.01 lm. Furthermore, itis reported [7,28] that outer cutoff might be the diameter of the largest circle en-

compassing an island for slit-island method. It is therefore reasonable to consider that

the diameter of the largest circle encompassing a pit is just the value of outer cutoff.

Consequently, the value of outer cutoff may be considered to be atleast 170 lm.

4.3. Effect of the fractal dimension on impedance behaviour of the pits formed on the

electrode surface at various solution temperatures during the whole pitting process

In Fig. 8, constant value of tan�1½dð�Z 00Þ=dZ 0 was observed in the frequencyranges from 102 to 10 Hz and from 10 to 1 Hz. One of the most possible causes of the

constant value of tan�1½dð�Z 00Þ=dZ 0 is known to be of geometric origin: an irregularand porous electrode geometry causes current density inhomogeneities and thusyields deviations from ideal behaviour. The impedance of a real electrode is fre-

quently represented by an equivalent circuit containing CPE showing power law

frequency dependence as follows [17]:

ZðxÞ ¼ ð1=rÞðjxÞ�a ð1Þ

where r and a mean the CPE coefficient and the CPE exponent, respectively, and xrepresents the angular frequency. In recent years, it has been demonstrated by many

researchers [29–32] that the deviation from ideal capacitive behaviour observed on a

real electrode, i.e. CPE exponent a is intimately related to surface roughness. SuchCPE behaviour has often been found in the porous, rough and irregular electrode.

In a similar way, in this work, the CPE exponent becomes the measure of surface

irregularity, i.e., the fractal dimension. For example, for a perfectly smooth surfaceat all scales, the value of CPE exponent is unity. In other words, if there is such

surface inhomogeneity as pore and roughness, the value of CPE exponent is lower

than unity. In Fig. 8(b), it was found that the value of CPE exponent at 60–150 �C is


lower than unity. Therefore, it can be deduced that lowered value of CPE exponent

at 60–150 �C is due to the increase in the surface roughness of the specimen by theformation and growth of pits with a certain value of fractal dimension.

In addition, from the result of Fig. 8(b), it was noted that the values of CPE

exponent in the frequency range from 102 to 10 Hz and that frequency range from 10

to 1 Hz were found to be about the same irrespective of solution temperature, re-spectively. At the same time, it was found that impedance spectra in the Nyquist plot

of Fig. 8(a) measured from the pitted specimen exposed to elevated temperature

solutions of 60–150 �C were similar to one another in value and shape. At this point,it should be stressed that impedance spectra experimentally measured at different

solution temperatures were similar to one another even though the value of fractal

dimension of the pits increased with increasing solution temperature. This is prob-

ably because the impedance of the large sized pits mostly contributed to the total

impedance of the pits as compared with the impedance of the small and mediumsized pits [33]. As a result, impedance spectra experimentally measured from the

pitted specimens as a function of solution temperature were similar to one another in

value and shape, resulting in the nearly same value of CPE exponent irrespective of

solution temperature.

5. Conclusions

1. From SEM observation, it was found that pit morphology changed from cy-

lindrical shape at 60 �C to highly branched shape at 150 �C. In as much as theirregion immediately surrounding pit embryos generated at 60 �C is likely coveredmainly with more protective oxide film, the viable pit embryos have the same ten-dency to grow further in all radial direction and hence the grown pits finally form

cylindrical shape. By contrast, since their region immediately neighbouring pit em-

bryos generated at 150 �C is plausibly covered predominantly with less protectiveoxide film, the viable pit embryos have a preferred tendency to grow further in

specific direction and hence the grown pits finally form highly branched shape.

2. Below 200 �C, SEM micrographs showed that pits formed and further grew

throughout without any morphological change. From the fractal dimension deter-

mined based upon pit morphology observed by SEM using perimeter–area method,it is concluded that the fractal dimension of the pits maintains nearly constant in

value during the whole pitting process at each solution temperature.

3. Above 200 �C, SEM micrographs showed that the morphology of the pits

changed from highly branched shape in the early stage of the pitting process to

widely grooved shape in the later stage. Because the passivity of oxide film was

lowered above 200 �C, all the pit embryos would be surrounded on all sides with theregion covered with non-protective oxide layer. It follows therefore they grow fur-

ther in all directions, leading to the transition in pit morphology from highlybranched shape to widely grooved shape.

4. From the measured impedance spectra, the occurrence of CPE was observed in

a certain frequency range 102–1 Hz at the pitted specimen exposed to the corrosive


electrolytic solution at 60–150 �C. This CPE behaviour is caused by the rougheningof the electrode surface resulting due to the formation and growth of the pits

characterised with a certain value of fractal dimension at each solution temperature.

Acknowledgements

The authors are gratefully indebted to Dr. H.-C. Shin working as a postdoctoral

research fellow at Corrosion and Interfacial Electrochemistry Research Laboratory

in Korea Advanced Institute of Science and Technology for his help with the image

analysis procedure. This work was partly supported by the Brain Korea 21 project

and the nano programme 2002/2003 of MOST, Korea.

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