Measures for the detection of localized corrosion with electrochemical noise

www.elsevier.com/locate/electacta

Measuresforthedetectionoflocalizedcorrosionwith

electrochemicalnoise

R.A.Cottis*,M.A.A.Al-Awadhi,H.Al-Mazeedi,S.Turgoose

CorrosionandProtectionCentre,DepartmentofComputation,UMIST,P.O.Box88,ManchesterM601QD,UK

Received20June2000;receivedinrevisedform1February2001

Abstract

Asimulationofelectrochemicalnoisedatahasbeenproducedusingashotnoisemodel,andthishasbeenusedtoexaminethepropertiesofseveraloftheparametersthathavebeenproposedasindicativeofthetypeofcorrosion.Themodelproducesanelectrochemicalnoiseimpedancethatisthesameastheexpectedimpedance,despitethatfactthatthemodeldoesnotincorporateachargetransferresistanceterm,supportingtheobservedandpredictedequivalencebetweennoiseimpedanceandconventionalelectrochemicalimpedance.Ofthevariousparametersthathavebeenexamined,thecharacteristicchargeandcharacteristicfrequencyareproposedasusefulgeneralindicatorsofthenatureofthecorrosionprocess.Skewandkurtosisstatisticsmaybeindicativeofthelocalizedcorrosion,buttheresultswillbesystemdependent,particularlywithrespecttowhetheruni-orbidirectionaltransientsareobserved,andwhetherthecurrentmeasuringelectrodesaresymmetricalorasymmetrical.©2001ElsevierScienceLtd.Allrightsreserved.

Keywords:Electrochemicalnoise;Simulation;Shotnoise;Coefficientofvariation;Localizationindex;Characteristiccharge;Characteristicfrequency;Roll-offslope;Skew;Skewness;Kurtosis;Crosscorrelation;Crossspectra

1.Introduction

Itisclearthatelectrochemicalnoise(EN)measure-mentsareinfluencedbythenatureofthecorrosionprocess,andseveralparametershavebeensuggestedasindicatorsoflocalizedcorrosion.However,ourunder-standingoftheapplicabilityofthevariousparametersremainslimited.Thereareseveralreasonsforthis:󰀁Itisoftendifficulttodeterminewhatthe‘right’answeris.Inordertoknowwhatthetypeofcorro-sionisduringthecollectionofaparticulartimerecord,weideallyneedanindependenttechniquetoidentifythecorrosion,butfewin-situtechniquesare

*Correspondingauthor.Tel.:+44-161-236-3311;fax:+44-161-228-7040.

E-mailaddress:bob.cottis@umist.ac.uk(R.A.Cottis).

available,withmicroscopicobservationprobablybe-ingthemostreliable[1].

󰀁Thenormalmethodofvalidatinganalyticalmethodsforscientificdatareliesontestingthemethodonasmanyavailabledatasetsaspossible.However,thisisdifficultinENstudies,becauseitisveryrareforrawENdatatobepublished.Consequently,analysismethodsareusuallyonlytestedonalimiteddatasetthathasbeencollectedinasinglelaboratory.

󰀁ENmeasurementsintroduceinstrumentationre-quirementsthatareunfamiliartomanycorrosionscientists.Consequentlymanymeasurementssufferfromexperimentalartefacts,notablyaliasing,quan-tizationandinstrumentnoise,andtheirreliabilityisoftenquestionable.

Theobjectiveoftheworkpresentedhereistocon-structanartificialdatasetofknowncharacter,andtouseittotestsomeofthemeasuresthathavebeen

0013-4686/01/$-seefrontmatter©2001ElsevierScienceLtd.Allrightsreserved.PII:S0013-4686(01)00645-4

3666R.A.Cottisetal./ElectrochimicaActa46(2001)3665–3674proposedfortheidentificationoflocalizedcorrosion.Inadditiontheprogramwillbepublished[2],sothatitwillbeavailableforotherstoapplytootheranalyticalmethods.

2.Themodel

Thephysicalmodelassumestheconventionalthreeelectrodemeasurement,wherebythecurrentnoiseismeasuredasthecurrentbetweentwonominallyidenti-calworkingelectrodes,whilethepotentialofthecou-pledworkingelectrodepairismeasuredagainstanideal,noise-freereferenceelectrode.

Theanodicprocessisconsideredtogeneratepulsesofcharge(as,forexample,inthecaseofmetastablepittingofstainlesssteels),whilethecathodicprocessisatafixed,noise-free,limitingcurrentdensity(as,forexample,mightapplyforoxygenreductionintheab-senceofturbulenceinthesolution).Theanodicpulsesareassumedtobeindependent,andthetimetothenexteventisthereforeasamplefromanexponentialdistri-bution.Thechargegeneratedineachpulseiseitherconstant,orhasanexponentialdistribution(thelatterisusedforallresultspresentedhere).Thepulsesareassumedtooccurinstantaneously.Theuseofinstanta-neouspulsesandacathodiclimitingcurrenthelptosimplifythemodellingprocess.Theeffectsthattheselimitationsintroducearediscussedfurtherbelow.Thetimetothegenerationofthenextanodicpulseisassumedtobeafunctionoftheelectrochemicalpoten-tialaccordingtoaTafelrelationship.Aconsequenceofthisdependenceisthattheprobabilitythatapulsewillbeemittedvariesovertimeasthepotentialchanges,andinsomecircumstancesthiscouldleadtoverylargeerrors.Thusanunusuallylargeanodicpulsewillreducethepotentialsufficientlythatthenextpulsewilltypi-callybealongtimeinthefuture.However,thelongtimewithoutapulseleadstoasignificantincreaseinthepotentialduetochargingofthedoublelayercapac-itancebytheconstantcathodiccurrent(possiblyhun-dredsofmV),suchthatapulseshould,onaverage,beemittedfarsooner.Itisdifficulttocorrectanalyticallyforthechangeinpulseemissionprobabilityasthepotentialchangesbetweenpulses.Anapproximatecor-rectionhasbeenmadebyregeneratingthetimetothenextpulseattheendofeverysampleinterval(thisisvalidbecausetheprobabilityofapulsebeingemittedisindependentofthepriorhistoryoftheelectrode).How-ever,forlowsamplingfrequenciesandlargecathodiclimitingcurrentsthismaystillresultinasignificantchangeinpotentialbeforetheprobabilitiesarecorrected.

Themodelissusceptibletoaliasingasaresultoftheproductionofsampleddatafromthecontinuouspoten-tialandcurrenttimerecords(thefactthatthesampling

isachievedmathematicallyratherthaninstrumentallydoesnotchangethefundamentalproblem),andtoaformofquantization,ifthetimingoftransientsrelativetothesamplingtimeisfixed.Tominimizetheseeffectstransientsaregeneratedonthebasisofthetimetothenexttransient,drawnasasamplefromanexponentialdistribution.Themeasuredpotentialandcurrentarethendeterminedbyanalyticalintegrationofthepoten-tialandcurrentoverthesampleinterval.Thislargelyremovesaliasingbyactingasalow-passfilterthatremovesfrequenciesabovetheNyquistfrequency.Theparametersusedinthemodelare:1.CathodiclimitingcurrentIc(A).2.Doublelayercapacitance,Cdl(F).3.Solutionresistance,Rsol(V).4.Meanpulsefrequency,fn(s−1).5.Chargeineachpulse,q(C).

6.AnodicTafelslope,ia(VforunitchangeinlnI;notethatthisisbasedonnaturallogs,sincethisslightlysimplifiesthecomputation).

7.Relativeprobabilityofapulseoccurringonworkingelectrode1,p1.

NotethatIc,fnandqarecoupled(sincethesystemwillautomaticallyfindapotentialsuchthatfnq=Ic).Consequently,fortheresultsdiscussed,fnqissettogiveIcatE=0,andfnistreatedastheindependentvari-able.Whereqhasadistributionofvalues,themeanisgivenbytheaboveequality.

Notealsothatthemodelisnotnormalizedforspecimenarea(i.e.itreferstocurrentratherthancurrentdensity).However,forthisworktheparametersselectedarechosentobereasonableforanelectrodeareaof1cm2.

Fortheresultspresentedhere,thefollowingparame-tershavefixedvalues:1.Cdl=50mF2.Rsol=1000V3.ia=0.052V

3.Analysismethods

Anumberofanalysisprocedureshavebeeninvesti-gatedinthiswork:

3.1.Coefficientof6ariationofcurrent

Thecoefficientofvariationofthecurrent(thestan-darddeviationofcurrentdividedbythemeancurrent)wasoneofthefirstparametersproposedfortheiden-tificationoflocalizedcorrosion[3].Itsuffersfromthetheoretical(ifnotpractical)limitationthattheexpectedvalueofthemeancurrentiszero,leadingtoalargeexpectedvalueofthecoefficientofvariationwhatevertheactualpropertiesofthesystemunderinvestigation.Itisalsoverysensitivetoelectrodeasymmetryandthe

R.A.Cottisetal./ElectrochimicaActa46(2001)3665–36743667

actualvalueofthemeancurrent,ashasbeendemon-stratedbySunandMansfeld[4]fortheLocalizationIndex(seeSection3.2).

Itcanbearguedthattherealproblemwiththeuseofthecoefficientofvariationisthatitusesthemeanmeasuredcurrent,whereasitshouldusethemeancorrosioncurrent.IfitisassumedthatthelattercanbedeterminedusingtheENresistance,thenitcanbeshownthatthe‘truecoefficientofvariation’canbeestimatedfromtheelectrochemicalpotentialnoise[5].Theresultantparameteriscloselyrelatedtothecharac-teristicfrequency,butsuffersfromitsdependenceonthemeasurementbandwidth,soitwillnotbeconsid-eredfurtherhere.

3.2.Localizationindex

Thishasbeenproposedasanalternativetothecoefficientofvariation,andisdefinedasthestandarddeviationofcurrentdividedbythermscurrent.How-ever,itcanbeshownthatitisasimplemathematicaltransformationofthecoefficientofvariation[6],andconsequentlyitsuffersfromthesamelimitations.Whileitmayhavesomeadvantages,particularlyinrespecttotheavoidanceofverylargevaluesthattendtomakeplottingdifficult,itislessamenabletotheoreticalinter-pretation,anditisnotconsideredfurtherhere.

3.3.Characteristiccharge

Itcanbeshownthattheamplitudeofthechargeinindividualtransients,q,canbeestimatedusingashotnoiseanalysis[6]:q=

󰀁󰀂E,0󰀁󰀂I,0B

whereqisthechargeintransient,󰀂E,0isthelowfrequencylimitofpowerspectraldensityofpotential,󰀂I,0isthelowfrequencylimitofpowerspectraldensityofcurrent,andBistheStern–Gearycoefficient.

ThechargemayalsobeestimatedusingthevariancedividedbythebandwidthinplaceofthePSD,althoughthisintroducesthepossibilityoferrorsassociatedwiththerangeoffrequenciesincludedinthemeasurement.Thisisdemonstratedinsomeoftheresultsobtainedbelow.

Itisreasonabletoequatelargetransientswithlocal-izedcorrosion,soalargevalueofthisparametermaybeexpectedtobeindicativeoflocalizedcorrosion.Theterm‘characteristiccharge’isproposedtoaccommo-datethosesystemswhereashotnoiseanalysismaynotbeapplicable(andwherethesignificanceoftheparameteriscurrentlylessclear).

3.4.Characteristicfrequency

Thetransientfrequencyforashotnoiseprocess,fn,canbeestimatedasthecorrosioncurrentdividedbythechargeinthetransient:IcorrB2fn=q=

󰀂E,0wherefnisthefrequencyoftransients,andIcorristhecorrosioncurrent(=Ic).

NotethatthisisinverselyproportionaltothePSDofpotential,andindependentofthecurrentnoise.Theconverseisnottrue,andthecurrentnoiseisinfluencedbyfn,butthisiscounteredbythenecessaryconcomi-tantincreaseinIcorrordecreaseinq.Localizedcorro-sionmaybeassociatedwithalowtransientfrequency,andhenceahighpotentialnoiseamplitude.Thisisthemostdirectmeasurethatmaybeexpectedtocontaininformationaboutlocalizedcorrosion.

Theterm‘characteristicfrequency’isproposedtoaccommodatethosesystemswhereashotnoiseanalysismaynotbeapplicable.Thecharacteristicfrequencyisexpectedtobeproportionaltospecimenarea(atleastforashotnoiseprocess),anditmaybeappropriatetoreportitasfrequencyperunitarea.

3.5.Corrosionrate,noiseresistanceandnoiseimpedance

Itisreasonablywell-establishedthatthecorrosionratecanbeestimatedfromtheENresistance(or,probablymoreaccurately,fromthelowfrequencylimitoftheENimpedance).Thisprovidessupportinginfor-mationfortheinterpretationofENdata,butdoesnotgivedirectinformationonthetypeofcorrosion.

3.6.Roll-offslope

Ithasbeensuggestedthatroll-offslopemaybecharacteristicofthetypeofcorrosion.Thismeasurecannotreallybetestedwiththissimulation,asthecurrentnoisespectrumisdeterminedbythetransientshapethatisassumed,modifiedonlyslightlybytheeffectofthesolutionresistance.Theroll-offslopeofthepotentialisalittlemoreinterestinginthecontextoftheENimpedance,astheanalysisdoesnotincorporateaconventionalRctterm,anditisinterestingtoseewhethertheconventionalequivalentcircuitisrecreatedbythemodel.

3.7.Skeworskewness

Theskewofadistributionisameasureofitssymme-try,andisdefinedas:

3668

Nx[k]−x¯31

%

N−1k=1󰀁x[k]2Skewisnormalizedrelativetoanormaldistribution,suchthatthevalueindicatespurelytheshapeofthedistribution,andisindependentofthemeanandstan-darddeviation.AnENsignalcomprisedofuni-direc-tionaltransientsmaybeexpectedtohaveaskeweddistribution,andthishasbeenusedinapracticalsituationwheretheelectrodesaredeliberatelymadeasymmetrical[7].Thissimulationprobablyprovidesasomewhatbiasedviewofthismeasureasappliedtoelectrochemicalpotentialnoise,asthelimitingcathodiccurrentproducesa‘sawtooth’potentialtimerecord,ratherthantransientsfallingfromamoreconsistentbaseline.Amorerealisticmodelinthiscontextwouldassumeactivationcontrolledcathodickinetics;thiswouldresultinareasonablyconstantpotentialwithnegative-goingtransients,whichwouldgiveasignifi-cantnegativeskew.

Skew=

󰀃

n

R.A.Cottisetal./ElectrochimicaActa46(2001)3665–3674caldetectionoflocalizedcorrosion[8].Aswiththeanalysisofskew,themodelthathasbeenusedforthisworkhassomelimitationsintermsofmodellingthedistributionrealistically.Notethatinthisworkthenormalizedkurtosishasbeenused,suchthatavalueofzerowouldbeobtainedforanormaldistribution:

3.9.Crosscorrelationandcrossspectra

ThecorrelationbetweeneventsinthecurrentandpotentialnoisetimerecordsisanimportantfeatureofENdata.Atransienteventincurrentthatisnotaccompaniedbyacorrespondingeventinpotentialwouldgenerallyberegardedassuspect.Therelation-shipbetweenthepotentialandcurrenttimerecordscanbedeterminedbythecrosscorrelationor(equivalently)bythecrossspectrum.Onelimitationofcrosscorrela-tionisthatitcanbeexpectedtobeconfusedifuni-di-rectionaltransientsinonetimerecord(i.e.potentialnoise)translatetobidirectionaltransientsintheother(i.e.currentnoise).Inprinciplethiscanbeovercomebytakingtheabsolutevalueofthebidirectionalprocess,althoughthisisonlyreliableifthebidirectionalsignalhascleardistincttransientsandastablebaseline.Ifthetimerecordissampledatalowfrequencycomparedtothefrequencyoftransientevents,suchthateachsamplecorrespondstomanyevents,thenthecrosscorrelationmaybeexpectedtobelost.

Owingtocomputationaldifficultiesthecross-correla-tionanalysishasnotyetbeencompleted;resultsforrealdatamaybeseeninRef.[9].

3.8.Kurtosis

Thekurtosisofadistributionisameasureofitsflatnessorpeakiness.Itisdefinedas:

N1x[k]−x¯4Kurtosis=%

N−1k=1󰀁x[k]2Asthekurtosisforanormaldistributionis3,itiscommontousethe(kurtosis-3)suchthatanormaldistributionwillgiveakurtosisofzero.Thisisoftensimplycalledthekurtosis,whichcanbeconfusing,anditissuggestedthatthelatterformisreferredtoasthenormalizedkurtosistoemphasizethatthe3hasbeensubtracted.

Whetheruni-orbidirectionaltransientsareobserved,relativelyinfrequentfasttransientsareexpectedtopro-duceahighkurtosis,andthishasbeenusedforpracti-

󰀃

n

4.Results

TypicaltimerecordsproducedwithlargeandsmallvaluesoffnareshowninFigs.1and2.

Fig.1.Typicaltimerecordproducedbythesimulation;lowtransientfrequency.

R.A.Cottisetal./ElectrochimicaActa46(2001)3665–36743669

Fig.2.Typicaltimerecordproducedbythesimulation;hightransientfrequency.

Foralowvalueoffntheindividualtransientscanbeseen.Fortheparametersusedhere,theseconsistofasharpcurrentspikethatlastsforlessthan1s(sincetheRsolCdltimeconstantisshortandthechargeisdis-tributedbetweenthetwoworkingelectrodesrapidly).Thepotentialrisessteadilywithtimeduetothecharg-ingofCdlbytheconstantcathodiccurrent,anddropssharplyasaresultofeachcurrentspike.Thisisslightlyunnaturalbehaviour,andariseinpotentialwithanexponentialcharacter(suchasmightbeobtainedforanactivation-controlledcathodicreaction)mightbemorenatural.However,therearesignificantcomputationaladvantagesforthemodelusedhere[2];alternativemodelsmaybedevelopedinfuture.

ThemodelcomputesrelativelyquicklyonamodernPC,exceptforthecaseofahightransientfrequencyanalysedatalowsamplingfrequency.Thusareason-ablylargenumberof‘experiments’havebeenper-formedforthedeterminationofthesimplerstatisticalparameters.ThesearesummarizedintermsofthedependenceofthevariousparametersonelectrodeasymmetryinFigs.3–5.Whenthevaluesarecalculatedfromthestandarddeviation,theresultsobtainedarestronglydependentonthebandwidthofthemeasure-ment,ashasbeenindicatedbyHuetetal.[10].How-ever,consistentresultsareobtainedusingthelowfrequencylimitoftheMEMpowerspectrum(whereappropriate).

Itcanbeseenthatthecoefficientofvariationislargeforsymmetricalelectrodes(correspondingtoapropor-tionofpulsesonWE1of0.5),butfallsquiterapidlyto1orlessfortheparametersusedinthesimulationofFig.3.Itcanbeshown[5]thattheexpectedcoefficientofvariationforperfectlysymmetricalelectrodesisoftheorderof󰀁N,whereNisthenumberofpointsinthetimerecord(i.e.64forthe4096pointtimerecordusedhere),andtheresultsobtainedareconsistentwiththisprediction.Incontrasttheestimatedvaluesofqandfnarerelativelyaccurateandindependentoftheasymmetry.Whenestimatedfromthestandarddevia-tionthebandwidthofthemeasurementissomewhattoohigh,andthemeasuredvalueoffnisaboutafactorofthreetoohigh.Theestimatedvalueofqisclosertothecorrectvalue,becauseitislessstronglydependentonthepotentialnoise.TheestimatesfromthelowfrequencylimitoftheMEM(atapproximately2.5×10−5Hz)arealsosomewhatinerror,inthiscasethisisprobablybecauseofthelossofpoweratverylowfrequenciesduetotrendremoval.

Theskewofpotentialisessentiallyindependentofasymmetry(asmightbeexpected,asthepotentialnoiseisaresultoftheresponseofthepairofelectrodes),andsignificantlygreaterthanzero.Theskewofcurrentisstronglydependentonasymmetry(againthisisasexpected,inthecurrentpulseswillbepredominantlyinonedirectionwhentheelectrodesareasymmetrical).Thekurtosisofbothpotentialandcurrentisrela-tivelyindependentofelectrodesymmetry.TheresultsofFig.5wereobtainedusing4096pointsinthetimerecords,sothestandarderroris0.077,thusthecurrentkurtosisisclearlypositive,thoughwitharelativelylowsignificance,whilethepotentialkurtosisisnotsignifi-cantlydifferentfromzero(forthesimulationparame-tersusedhere).

Whenthecharacteristicchargeisestimatedusingthestandarddeviationformulawitharelativelyhighsam-plingfrequency,theresultsexhibitapoorfitwiththeactualmeanchargeusedinthesimulation.However,

3670R.A.Cottisetal./ElectrochimicaActa46(2001)3665–3674Fig.3.Effectofelectrodeasymmetryoncoefficientofvariation,qandfn.Actualfnwas1Hz,q100nC,4096samplesatafrequencyof0.1Hz.

whenthelowfrequencypowerspectraldensityisused(or,equivalently,whenthestandarddeviationismea-suredatalowsamplingfrequency),thefitisgood(Fig.6).Thisresultisnotunexpected,asthenumericalmodelisbasedonexactlythesamemodelasthatusedintheestimationofq.Theslightunder-estimationofthefrequencyandover-estimationofthechargebytheMEManalysisisprobablyaresultofaslightreductioninthelowfrequencypowerspectraldensitiesasaresultofthetrendremovalprocess.

Thecomputationofthevariousspectralmeasuresissomewhatmoretimeconsuming,andsomewhatfewerexperimentshavebeenperformed.Figs.7and8presenttypicalpotentialandcurrentpowerspectra.

Fig.4.Dependenceofskewofcurrentandpotentialonelectrodeasymmetry.fnwas1Hz,q100nC,4096samplesatafrequencyof0.1Hz.

R.A.Cottisetal./ElectrochimicaActa46(2001)3665–36743671

Fig.5.Dependenceofkurtosisofcurrentandpotentialonelectrodeasymmetry;fnwas1Hz,q100nC,4096samplesatafrequencyof0.1Hz.

NotethatthecouplingofqandfnasaresultofthefixedvalueofIchasasignificantinfluenceontheresults.Thus,Fig.7showsanincreaseinpowerspec-traldensityasfnfalls;thisisaresultoftheincreaseinqoutweighingthedecreaseinfn(sincePSD8q2fn).Fig.9presentsthecomputationofthenoiseimpedance.ThepredictedimpedancewillconsistofalowfrequencylimitofRsol+Rct,whereRctcanbeestimatedusingtheTafelslopeofthepulseemissionfrequencyandthecorrosioncurrent(asthecathodicreactionismass-transportlimited,itscontributiontoRctisnegligible).AthigherfrequenciestheimpedancewillbedominatedbyCdlandthenRsol.Thesecompo-nentsareplottedindividuallyonFig.13(Rsolis100Vandisthereforecoincidentwiththex-axis),anditcanbeseenthatthereisnoeffectofthetransientfrequencyontheimpedance(foraconstantcorrosioncurrent),andthattheobservedandpredictedimpedancesmatch.

Fig.6.Variationofestimatedchargeandfnwithmeanpulsefrequency;4096points,sampledat1Hz,Ic=10−7A.

3672R.A.Cottisetal./ElectrochimicaActa46(2001)3665–36745.Discussionandconclusions

Oftheassumptionsmadeintheconstructionofthismodel,theassumptionofinstantaneouspulsesofchargeisrelativelyinsignificant,astheeffectoftreatingcurrenttransientsoffinitedurationwillsimplybetoconvertthewhitecurrentnoisespectrumtoaspectrumthatmatchestheunderlyingtransients.Whilethiswillmodifytheshapeofthehigherfrequencyendofthepowerandimpedancespectra,itwillnotaffectthelowfrequencylimitbehaviour.

Theassumptionofaconstantcathodiclimitingcur-rent,whileplausible,leadstoaslightlyunnaturaltran-sientappearance.Italsoimpliesthattheeffectivechargetransferresistancedependsonlyonthepotentialdependenceofthepulseprocess(sincetheresistanceoftheparallelcathodicprocessisinfinite).Inthattheobservednoiseimpedancespectrumisconsistentwith

Fig.7.Examplecurrentpowerspectraforhighandlowtransientfrequency(computedusingMEMwithorder50,averageofsixspectra).

Fig.8.Examplepotentialpowerspectraforhighandlowtransientfrequency(calculatedusingMEMwithorder50,averageofsixspectra).

R.A.Cottisetal./ElectrochimicaActa46(2001)3665–36743673

Fig.9.Effectoftransientfrequencyonnoiseimpedanceforfn=1kHzandfn=0.1HzforconstantIc(henceqisinverselyproportionaltofn);spectraareessentiallycoincident;dashedlinescorrespondtopredictedBodeplot;seetext).

thatexpected,itisreasonabletosupposethatamorecomplexcathodicprocesswouldalsoconformtotheexpectedbehaviour,butthisneedstobetestedfurther.ItisapparentfromFig.9thatthemodelgivestheimpedancespectrumexpectedonthebasisofaconven-tionalequivalentcircuitmodelofthecorrosionprocess,withRctbeingasexpected.ItcouldbearguedthattheseresultsprovideevidencethatENimpedancemeasuresthesamethingasaconventionalimpedancemeasure-ment,withoutmakingthenormalassumptionthattheimpedancecanbeusedtotreattherelationshipbetweencurrentandpotential(andhenceassumingtheresulttobeproved).However,theresultiseffectivelynotmuchmorethanapracticaldemonstrationofthetheoreticalresultobtainedbyTyagai[11]in1971,andlargelyignoredbythecorrosioncommunity.ItisprobablyalsoimportantthataTafelrelationshiphasbeenas-sumedforthepulseemissionprobability,asthisleadstothevalidityoftheStern–Gearyrelationshiponthebasisofmeancurrentversuspotential.

ItisapparentfromFig.9thatthemeasurednoiseimpedanceisessentiallyunaffectedbythefrequencyandamplitudeofthetransientsmakingupthesignal(otherthanthroughtheircombinedeffectonEcorr).Ingeneralthecoefficientofvariationissensitivetothelocalizationofcorrosion,asindicatedbytheampli-tude/frequencyoftransients,butitisevenmoresensi-tivetotheasymmetrybetweentheelectrodes,andhencetothemeancurrent,andconsequentlyitisanunreliableindicatorofthetypeofcorrosion.

Skewandkurtosisarenottestedverythoroughlybythissimulation.The‘saw-tooth’natureofthepotentialtimerecordleadstoalowerpotentialskewthanmightotherwisebeexpected,andalsointerfereswiththekurtosis.Theseparametersdoappeartobesensitivetolocalizedcorrosioninsomesituations.Whiletheyalsoexhibitasensitivitytoelectrodeasymmetry,ittendstoberatherlessseverethanforthecoefficientofvariation.

Thecharacteristicsofthepotentialandcurrentpowerspectraare‘pre-ordained’bytheassumptionsmadeinthesimulation,anddonot,therefore,testtheabilityoffeaturesofthepowerspectratoprovideinformationaboutthelocalizationofthecorrosionprocess.However,thefacttheshape(asopposedtotheamplitude)ofthepowerspectracanbeexactlythesameformanysmalleventsasitisforafewlargeeventsdoesleadtoquestionsaboutitsreliabilityfortheidentifica-tionofthecorrosiontype.

Thecharacteristicchargeandfrequencyappeartoprovideinformationaboutthenatureofthecorrosionprocessinawaythatcanreadilybeunderstood.Thechargeessentiallyprovidesanindicationoftheamountofmetallostineachoftheeventsthatconstitutethecorrosionprocess,whilethefrequencyindicatestherateatwhichtheseeventsareoccurring.Thusintenseactivecorrosionmayhavebothalargechargeandahighfrequency,pittingcorrosionwillhavealargecharge,butalowerfrequencyandpassivesystemswillhaveasmallchargeandahighorlowfrequency(dependingontheprocessesoccurringonthepassivefilm).Astheseparametersareeffectivelyusedtoconstructthemodelthathasbeenusedinthesimulationwork,thefitsobtainedareinherentlybiasedtowardstheseparame-

3674R.A.Cottisetal./ElectrochimicaActa46(2001)3665–3674ters.However,theyhavealsoprovidedasensibleinter-pretationofrealENdata[12],anditissuggestedthattheymeritfurtherinvestigation.

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