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,0I,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=1x[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=1x[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]thattheexpectedcoefficientofvariationforperfectlysymmetricalelectrodesisoftheorderofN,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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