electrochemtcal noise signatureanalysis using...pitting corrosion is the most common form...

Paper No.

ELECTROCHEMTCALNOISE SIGNATUREANALYSIS USING

POWERAND CROSS-SPECTRALDENSITIES

AbdulmajeedAu AlawadhiMinistry ofElectricity andWater

PostBox 2, Manama,StateofBalirain

R.A. CottisCorrosionandProtectionCentre

UniversityofManchester,P.OBox 88,ManchesterM6O1QD, U.K

ABSTRACT

One of the major problems faced by desalinationplants is corrosion. Various alloys have beendeveloped,and continueto be developedto combat corrosion. Stainlesssteelsare widely used in thedesalinationindustry, due to their superior corrosion resistance.However, they are proneto localisedcorrosionin stagnantsalinewater. Thefeed water for one ofthe desalinationplants in Bahrainis highlysaline,containingreducedsulphurspecies.

The electrochemicalpotential and current fluctuations for different stainless steels in differentenvironmentalconditions prevailing in the desalinationplants in Bahrainhave beenmeasured.Digitalsignalprocessingand analysismethodsusedin otherbranchesof scienceand engineeringwere usedforthe analysisand interpretationof electrochemicalnoise signatures.By calculating the power spectraldensityat variousfrequencies,thenoisesignatureswerecompared.TheresultscalculatedusingbothFastFourier Transform and the Maximum Entropy method agreewell. The Crossspectrumbetweenthepotential andcurrentnoiserevealsthe frequenciesheld in commonin addition to improving the signal tonoiseratio. It is suggestedthat theCrossSpectralDensity,which mayberelatedto thequantity of chargein transients,maybe indicativeoflocalisedcorrosion.

INTRODUCTION

Publication RightGovernment work published by NACE International with permission of the authors. Requests for permission to publish this manuscript in anyform, in part or in whole must be made in writing to NACE International, Publications Division, P.O. Box 218340, Houston, Texas 77218-8340. Thematerial presented and the views expressed in this paper are solely those of the authors and are not necessarily endorsed by the Association.Printed in the U.S.A.

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We are all familiar with the effectsof corrosion and the measurestakento combatit. A lot ofmoney and effort is spent in developing new materialsand designsthat guaranteeagainstcorrosion.Desalinationplantsrequirecostlyalloys aswell aselaborateandexpensivetreatmentsystemsfor coolingwaterand steam,all to minimisethe effectsof corrosion. In the Arabian Gulf, desalinationplantsoftenusebrackishfeed water from bore wells contain H2S, which contributesnot only acid, H, but alsosulphideS2 bothofwhich acceleratecorrosionin the high temperatureconditionsofthewells.

Pitting corrosionis themost commonform of localisedattackon stainlesssteels. Thepassivefilmremainsstablewith respectto chemical speciespresentin the environmentandis able to regenerateitselfin caseof accidentalbreakdown. However, local areas of passive film can sometimespermanentlybreakdownelectrochemicallyor mechanically,which allows anions to attack on the exposedmetalleading to localisedcorrosion. It is difficult to measurequantitatively and comparethe extentof pittingbecauseof varying depthsand numberof pits that may occurunder identical conditions. Pitting is amicroscopicphenomenonin thesensethat high ratesof localisedpenetrationarepossiblewith avery lowoverall corrosionrate.

In the absenceof adequatecorrosion rate information, over-designis done and a conservativedesign ‘for safety sake’ approachis adopted,resultingin wastedresourcesand a higherunit cost of theproduct. This is particularlytrue in the caseof desalinationplantswherethe selectionof materialsplaysan importantrole in long, trouble-freeoperation.Eventhoughbettermaterialsarecommerciallyavailable,themain problemis to decidewhat level of cost andperformanceis acceptable.Thedesaltingprocessbyitself is expensiveandany developmentthat maydecreasethe desalinatedunit costis desired.

Variouselectrocheniicaltechniqueshavebeendevelopedto determinesusceptibilityofmaterialstocorrosion and to determinethe rate of corrosion. By carrying out electrochemicaltests on samplematerialsthe relative corrosion resistancecanbe determined,which will assistin choosing a materialwhich is a compromisebetweenperformanceand cost. However,in a large-scaleplant, the atmosphereisnot pure and sterile as in a laboratory and corrosionbehaviourcanbe unpredictable.In a desalinationplant the operatingconditionsmay changefor variousreasons.The feedwaterquality is not constantrequiringa differentset ofoperatingconditions. Theoperatingphilosophychangesasmore experienceisgathered.Theconditionsno longerremainas-designed.Thematerialsupposedto becorrosionresistantisoftenfoundto corrode.The practicenormallyadoptedin any large-scaleplant is periodic inspection,thefrequencyof inspectiondependentongatheredexperience.Inspectionnormally involvesshutdownoftheequipmentresulting in loss-of-productioncosts. On the other hand, if no periodic maintenanceis done,the equipmentmay fail without warningdueto corrosion,resultingin unplannedplant shut-down,usuallyaccompaniedby hugecosts.

Themodemtrend is to adoptpredictivemaintenancewhereinthemaintenanceis carried out basedon necessityand not just becausea certain time period has elapsed.A typical exampleis the use ofdiagnostictools for rotating machinecondition monitoring using vibration analysis. By comparingthevibration signaturesof machines,it is possibleto predict failure at as early a stageas possible,and toindicate conditions of operationwhich are detrimentalto the efficient and long term operation of thesystemunder consideration.In a large plant, a lot of money and effort could be saved if we coulddetermine,using ‘corrosion signatures’,similar to the monitoring of vibration signaturesin the caseofrotating machinery,whethera particularitem of equipmentis prone to corrosionunder the prevailingoperatingconditions.Themajorstepsrequiredfor developingsuchdiagnostictools are:

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1. Identify the appropriatephysicalparametersto be measuredwhich are representativeof theunderlyingcorrosionprocess

2. Establish techniques for measuring and recording of signaturesof the above physicalparametersapplicableto largescaleplants

3. Analysetherecordedcorrosionsignaturesandattemptto interpretthesignaturesfor differentmaterialsunderdifferentsolutionsandestablishtheunderlyingpattern

4. Identi1’ localisedcorrosion in large plants, especiallyas the signaturedataobtainedusingsmall electrodesmaynot berepresentativeofthe conditionofthetotal plant.

ElectrochemicalNoise

The conventional and well-establishedelectrochemicaltechniquessuch as linear polarisationmeasurementscontinue to be the most appropriateapproachto corrosion estimationand prediction.However, these techniquesuse an external signal, either voltage or current, to perturb the sensorelectrodesaway from thefree corrosionpotential. Moreover,thesemethodsdo not provideinformationaboutlocalisedcorrosionprocesses.Thereforeimprovedtechniquesarerequired.

Any form of corrosioninvolvesanelectrochemicalcell with a pair of electrodesimmersedin anelectrolyte,in which electronsareliberatedfrom oneelectrodeandaretakenup at the other.Therefore,acontinuousmonitoringofthebasicelectricalparameters,potential andcurrent,should give an insight intotheunderlyingcorrosionprocess.Noiseis a generalterm usedto describethe fluctuatingbehaviourof aphysical variable with time,and the electrochemical potential fluctuations are referred to aselectrochemicalpotentialnoise.For an electrochemicalprocesseithertheelectrochemicalpotentialnoisethe fluctuation in the electrochemicalpotential with time or the electrochemicalcurrent noise thefluctuation of galvanic current flowing betweentwo specimensmay be measured.The potentialfluctuations have been measured since 1968 by many researchers.However, the current noisemeasurementshavenot beensopopulardueto thenon-availabilityofcurrentmeasuringinstrumentswithsufficient sensitivity. Theanalysisofelectrochemicalnoise is now consideredby manyresearchersin thefield to give usefulinformation aboutthe rateand natureof the electrochemicalprocesstaking placeatthe electrode,although the theoreticalbasis for much of the interpretationis somewhatlimited seereference2 for asummary.

Electrochemicalnoisehasvariousorigins, including:

1. Chargeflow in diffi.ision andelectrochemicalreactions

2. film deterioration,destructionandrecoveryat metal-solutioninterface,and

3. gasevolutionduringcorrosionreactions.

Oftheabove,thenoise intensityarising from surfacefilm deterioration,destructionandrecoveryisfar higher than the thermalintensity, so such noise is mucheasierto detectand is our areaof interesthere.Even thoughthesourceof noiseis somewhatlessclear, it tendsto beattributedto the breakdownand repairof the passivefilm on the metal surface.The fluctuationsarising from electrochemicalnoiserepresenta randomor stochasticprocessand henceare describedin terms of probability statementsand

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statisticalaveragesratherthan by explicit equations.In somecasesthe classificationof electrochemicalnoiseasrandommaybedebatableasafurther knowledgeofthe mechanismand sourceofthenoisemayenableexactmathematicaldescriptionsofthephenomenawhichwould thenbecomedeterministic.

In this paperwehaveattemptedto addresssomeof the aboveissues.Studieswere conductedtodeterminethe most suitable physical parameterwhose signatureis representativeof the corrosionprocess.The corrosion signaturesfrom different stainlesssteels of known corrosion resistanceinsolutionsofdifferent corrosivitywere analysed.

EXPERIMENTALPROCEDURE

Materials

Variousgradesof stainlesssteelswidely usedin the desalinationindustry were usedin our tests.The resistanceof stainlesssteels to localised corrosion is enhancedby increasingthe contentsofchromium,molybdenumand nitrogen.A roughestimateoftheresistanceofa steelto localisedcorrosioncanbe obtainedby assigningdifferentweightingfactorsto thesethreemost importantalloying elements.Theso calledPitting ResistanceEquivalentPRE factorhasbeendefinedas

PRE=%Cr+3.3x%Mo+30x%N

Thecompositionofthe commercialstainlesssteelsusedin ourstudyandtheirPR.Evalueusingtheaboveformulaareshownin Table 1.

TABLE 1CHEMECAL COMPOSITIONOF MATERIALS USED-%TYPICAL

SS grade C max Cr Ni Mo N PRE304 0.08 18 9 18

316L 0.03 17 12 2.5 0.06 26904 L 0.02 20 25 4.5 0.06 37

254 SMO 0.02 20 18 6.1 0.2 46

Solutions

The solutionswere chosento closely reproducethe Rus-UmmEr Radhmaaquiferwater and theseawateraround Babrain. SulphatesSO4 are normally presentin seawater- 3600 mg/i in BalirainseawatersampleandH2S presentin theaquiferwatercouldalso get oxidisedto sulphatein thepresenceofoxygen. Thesesulphatesare reducedto thiosuiphatesin thepresenceof sulphurreducingbacteria.Tostudy the effect of different feedwaterconditionsin the desalinationplantsin Bahrainvarious solutionswereused.Analargradereagentswereusedin the preparationofthe corrodent.In a majority ofthetestssolutionscontaining1.5 % NaCI, 1.5 % Na2S2O3and 1.5 % NaCl + 1.5 % Na2S2O3exposedto airwereused,representingthe prevailingandworstcaseconditionsoftheaquifer.

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ElectrochemicalPotentialandCurrentNoiseMeasurement

Dataanalysisis relatively complex andfor transformationof the datainto the frequencydomain,thereasonsfor which will becomeclearlater it is convenientthat thedatabe in digital form. Digital datacollection requiresthe transferof information betweenthe measuringdevice, suchasvoltmeter,and aprocessorand the subsequentstorageof datafor analysis.As a resultofthe finite time requiredfor datatransfer, a processcan only be sampledat intervals and this sampling interpolatedto be an accuraterealisationof the particularprocess.A time record collected in this way is known asa discretetimerecord.A sampledrepresentationofa processcanbeascloseto theprocessby placingthe samplepointsclosetogether,i.e. samplingat a fasterrate, althoughthis will obviously be limited by the speedof datatransferofthehardwareinvolved.

In this work two computer-controlledHAMEG 1 multimetersand a Zero ResistanceAmmeterZRA wereusedto samplethe potential and currentnoise data. TheZRA wasusedto couplethe twoelectrodestogetherandforce themto the samepotentialandalsoto transformthecoupling currentinto aproportionalvoltage,enablingit to be readby avoltageprocessor.Thecommandsto themultimetersanddatasampledby them were communicatedto the computerthrough an IEEE 488 bus by a computerprogram developed for the personalcomputer. By triggering the voltmeters simultaneously,it waspossible to obtain potential and current samplessimultaneously.This makesit possible to reveal therelationshipbetweenthe two parametersin the frequencydomain. The samplingratewas 1 point persecondand2048 datapointswerecollected.Theexperimentalset-upusedis shownin Figure 1.

InstrumentNoiseMeasurement

Although the many unwantedcontributionsto the noisewhich occursin a systemmay, at leastinprinciple, be eliminated, the noise due to the fundamentalnatureof matter cannotbe reduced. Theoutstandingpropertyof manmadenoise is the fact that it exhibits a certainperiodicity and thereforeitsremoval is theoreticallypossible.However,the secondcategoryof noise sourcesare thosewhich arefundamentalto the corpuscularnatureof matterand which in any given deviceunder given operatingconditionscauseafixed knownoutput.Themain sourcesofsuchnoisesarethermalnoise,shot noiseandflicker noise.As they arerandomin nature,all we canever saywith confidenceis the probability ofsucheventsoccurringandtheirprobablemagnitude.

As the instrumentnoiseis affectedby the sourceimpedanceofthe systemwe aremeasuring,theinstrumentnoisewasmeasuredfor sourceresistanceof 100, 1k, 10k ohms connectedacrosstheinputsofZRA Thenoiseintroducedby thereferenceelectrodesaturatedcalomelelectrodeandthemeasurementchannelwasmeasuredaspotentialfluctuationsbetweena platinumcounterelectrodeassumednoiselessand the referenceelectrodein the 3 different solutionsusedin our testsand also in distilled water forcomparison.The resultsare shown in Figure 2 in which Plot a showsthe instrumentnoise from thepotentialmeasurementchannelfor the variousinput resistancesand doesnot include the noise from thereferenceelectrode.Plot b showsthe instrumentnoise from the potentialnoise measurementchannelwith the referenceelectrodein varioustestsolutions.Plot c showsthe instrumentnoisefrom thecurrentmeasurementchannelfor variousinputresistances.

1 HAMEG GmbH,Frankfurt,Germany.

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DIGITAL SIGNAL PROCESSING

In thefield ofdigital signal processingaknowledgeofrandomfunctionsis centralto understandingboth the information content of digital signals and the propertiesof digital noise. The principles ofprobability and statisticsareusedto defineuseful averagemeasuresof randomsamplesequences.It isimportantto notethat in principlea randomsequencecanrepresenteithera digital signal or digital noise,dependingon one’sviewpoint. If thesequencecontainsuseful information,it is a ‘signal’; if it representsunwantedinterference,it is ‘noise’. The statisticalmeasuresusedto describethemarevery similar in thetwo cases.A majordifficulty ariseswhenthe signalandnoiseareofcomparablemagnitudeandwhenwearenot certainof the natureof signal we hopeto extract from the digital sequence.Though variousimprovementsin themeasurementtechniqueshavebeenreported,it appearsthat thereis still muchto bedone in the interpretation of measured data. Digital signal analysis techniques developed incommunicationengineeringand relatedareascanalsobeusedin corrosionsystems.

Analysis could be carried out in the time domain or the frequencydomain. The advantageoftransformingsignalsfrom thetime domaininto the frequencydomainbecomesevidentwhenwe havetoextractthe signal contaminatedwith randomnoise.Therandomnoise,also called white noise,is directlyproportionalto the bandwidth,resultingin equalnoisepowerat all frequencies.A commonexampleofwhite noiseis thermalnoise,generatedby electricalconductors,causedby the random,thermallyexcitedvibration of the chargecarriers. Breakinga digital signal down into its spectralcomponentsis a veryvaluabletechniquein the sensethat suchanalysisis likely to reveal informationnot apparentin the timedomain signal. Analysis of data in the frequencydomain is generally the preferredtechniqueas thefrequencyspectrumbrings out featuresnot readily seenin thetime domain. Yet anotheradvantageofanalysisin the frequencydomain is readily seenwhen the signal is buried in noise. As the individualchargetransfereventsmaking up thesourceofthe randomfluctuationsin potential/currentareburied inthebackgroundnoiseofthe instrumentationused,it is preferredto analysethe electrochemicalnoisedatain thefrequencydomain.

TheessenceoftheFourier seriesis that any waveformcanbedecomposedor separatedinto a sumof sinusoidsof different frequencies.If thesesinusoidssum to the original waveform, thenwe havedeterminedtheFouriertransformofthe waveform.Fourier analysisis essentiallyspectrumanalysis.Theoriginal waveform is split up into sinusoidshaving specific frequencieswith specific amplitudesandphases.The spectrumis also referredto as discreteor line spectra,becauseeachspectralcomponentisdiscretelylocatedon a frequencyaxis - eachcomponentis representedby a singleline or impulse.Thelength of eachspectralline indicateseither magnitudeor phase,dependingon which quantity is beingconsidered.

DiscreteFourierTransform

The DiscreteFourier TransformDFT and Fast Fourier transformFFT are the necessarytoolsfor quick and easyapplicationof Fouriertheory. TheDFT and FFT operateon finite sequences- setsofdatawith eachpoint discretelyand evenly spacedin time. Waveformsin real life are analogin naturewithout any ready-mademathematicalequationto describethem and they are continuous in time.Therefore,real life analogwaveformsmust be sampledat discretepoints beforethe DFT or the FFTalgorithm is applied. In most casesthe samplevaluesare convertedinto digital dataand stored inmemory,to bemanipulatedby the computerlater. Thetwo basicconceptsofanalogto digital conversionare windowing and sampling. The concept of windowing is necessarybecausewe cannot sampletheprocessfor an indefinite duration. Our view of the processis limited for a fixed duration or in other

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wordsthe analysisand further interpretationall pertain to the windowedwaveformofdefinite duration.After windowing, sampling is representedby a train of unity amplitude impulses.Each impulse in thistrain rises from zero, and returnsto zero, all instantaneously.Thus, eachimpulse is nonzeroat only asingle, discrete time. When this impulse train, or sampling train, is multiplied with the windowedwaveform, the product is a windowedand sampledwave. And since eachimpulse exists at a singlediscretetime point, eachsampleexistsat a single discretetime point. In termsof physicalprocesses,theeffectsofwindowing andsamplingareobtainedusinga analogto digital converter.This doesnot actuallyinvolve physical generationand multiplication of waveforms, but the conversionis analogousandproducesthe sameend result.

In 1965 Cooley and Tukey ‘ presenteda methodfor machinecalculationofthe complexFourierseries, basedon existing algorithms, but significantly faster than traditional methodsby eliminatingredundantcalculations.This techniquehasbecomeknownasthe Fast FourierTransformPET methodalthough its mathematicalpropertiesare identical to the traditional DiscreteFourier Transform. Thisadvancein decreasedcomputationtime hasallowedthe Fourier transformationof many points to becompletedin seconds,ratherthanminutesearlier.

PowerSpectralDensity

Every time domain function has a counterpart in the frequency domain. In the caseof anautocorrelationfunction ACE, which is a functionof thetime shift variablem, the counterpartis calledthe Power SpectralDensity PSD. A plot of PSD againstfrequencyis called the Power spectrum.Itindicateshowthesequence’spoweror energyis distributedin thefrequencydomain,andis awidely usedmeasureof randomsequences.Formally, the ACE and powerspectrumof a digital sequencearerelatedasaFouriertransformpair.

When thepowercontainedin thefrequencyintervalbetweenf and f+6f is calculated,one doesnotdistinguishbetweenpositive and negativef, but ratherregardsf asvarying from 0 to +. In suchcases,we definethe onesidedPSDas

IHf12+ IH-O2 for 0fx. 1

PSDis a real function of frequency,with no information aboutthe relative phasesofthe variousfrequencycomponentspresent.HencePSDrelatesto power,ratherthanamplitudeor phase.

Two major problemsassociatedwith spectral estimation techniquesare abasingand leakage.Aliasing is an error introduceddueto the samplingratebeingtoo slow. It resultsin the representationofa high frequencycomponentby a lower frequencycomponent.The rule governingproper sampling,referredto as the Nyquist sampling theorem,statesthat the sampling rate must be at least twice thefrequencyof the highest frequencycomponentin the waveform being sampled.In otherwords, theremustbe at least2 samplesper cycle for any frequencycomponentwewish to define.If therearefewer-ifthe samplingrate is less than twice the highest frequencycomponent-thenabasingoccurs. For the 1sampleper secondsamplingratetheNyquist frequencyis 0.5 Hz.

Leakageresults from the basic assumptionof the Fourier transformthat a finite time record isassumedto beperiodic. If, for example,a sinusoidalprocessis sampledand a whole numberof cyclesare

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recordedthen the Fouriertransformwill infer correctly that, the processis an infinitely long sinewaveandwill resolveits characteristicfrequencyin thefrequencydomain. However,if a wholenumberof sinewavesare not recorded,thentheFouriertransformassumesawaveformdistortedfrom theoriginal.

The above methods of spectral estimation do not always give acceptablespectral resolution.Variousmoremodernapproacheshavebeendeveloped,in which therandomsequenceis modelledastheoutputof a processordriven by noise.By making reasonableassumptionsaboutthe structureand orderofthe systemit is oftenclaimedthat it is possibleto extrapolatetheACF outsidethe observationinterval.Such model-basedmethodsinclude the so-calledmoving average,auto regressivemoving averageandmaximumentropytechniques.

Spectraldensityestimationis a secondorder statisticalmanipulationand the availabletechniquescouldbebroadlyclassifiedinto two categories:linear or non-adaptivemethodsandnon-linearor adaptivemethods.Techniquesusing Fourierbasedtransformationofthe ACF are classified as linear methodsasthey only involve theuseoflinear operationson the availabletime series.TheMaximum EntropyMethodMEM and a similar techniquecalled the Maximum likelihood method, are non-linearor adaptivetechniquesastheirdesignis dataindependent.

TheMaximum EntropyMethod

The MEM was originally developedby Burg and has since beenthe subjectof further work byBurg and others. Whereasthe Fourier Transformcomputesthe coefficientsof a seriesof sine wavesthat sum to the observedtime record,theMEM effectively computesthecoefficientsof aparticularclassof digital filter that would give the observedtime record when applied to a white noise input signal.Briefly, the MEM mathematicallyensuresthat the fewest possible assumptionsare made aboutunmeasureddataby choosingthespectrumthat is the mostrandomor hasthe maximumentropyfor theprocessunderinvestigation,andis consistentwith all knowndata.

The unique advantageof the MEM is that it neitherassumesthe time recordto be periodic norassumesall data outside the time record to be zero. The technique, as describedby Burg, is acombinationof informationtheoryandthepropertiesofpredictionerror filters. Theentropyfunctionhasbeenusedin the past for solving probability distributions by maximising the entropy subjectto knownconstraints.This principlecanbe appliedto spectralanalysis.For a detailedtreatiseonMEM, thereaderis referredto theoriginal work ofBurg andtheothersreferredabove.

CrossSpectrum6

Thefrequencydomaincounterpartof a CrossCorrelationFunctionCCF relatingtwo sequencesx[n] and y[n] is known asCross SpectralDensity CSD or simply as Crossspectrum.It givesvaluableinformation about frequenciesheld in commonbetweenx[n] and y[n]. Thus if x[n] hasa componentAisinn1+O and y[n] hasa componentA2sinn1+, their crossspectrumwill have magnitudeofA1A2/2 andphaseO-w at frequencyQ. A sharedcomponentis representedin proportionto theproductofthe individual amplitudes,andwith a phaseequalto the differencebetweentheindividual phases.Sincea crossspectrumholds phaseinformation, it is generallya complexfunction of , whereasthe powerspectrumof an individual sequenceis always real. If two sequenceshave no sharedfrequencies,orfrequencyranges,theircrossspectrumis zero andtheyare saidto be linearly independentor orthogonal.

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TimeDomain

EXPERIMENTAL RESULTS

Averagenoise behaviouris typically describedby the averagenoise power, also describedasthevarianceofthepotential or currentand describedasa poweron the basisthat the powerdissipatedin a

resistoris proportionalto thesquareofthevoltageappliedacrossthe resistorE2IR. It is also common

to measurethe squareroot of the noise power, also known as the standarddeviation of the

potentialnoise.

The averagenoise power varianceof potential noise and currentnoise for the collected timerecordfor variousstainlesssteelsof specimenarea1 cm2 in differentsolutionsareshownin Table2 andTable3.

NoiseResistanceRe

TABLE 2AVERAGE NOISEPOWER OF POTENTIAL NOISEV2

TheNoiseResistanceis definedasthe ratio of the standarddeviationsof thepotential noise andcurrentnoise measuredovera fixed period of time betweentwo identicalworking electrodeswhich arelinked by aZRA. Thenoiseresistancethuscalculatedis shownin Table4.

R = a- [Vt] / a- [1t] wherecr is therespectivestandarddeviation 2

304 316 904 2541.5% NaCl 9.26E-10 4.18E-09 7.73E-09 5.74E-08

1.5%Na2S2O3 1.44E-07 2.20E-07 2.61E-07 4.77E-071.5%NaCl+1.5%Na2S2O3 1.57E-08 9.14E-08 7.56E-08 5.16E-07

TABLE 3AVERAGE NOISEPOWEROF CURRENTNOISEA2

304 316 904 254l.5%NaCI 9.88E-16 1.76E-17 744E-l8 3.52E-19

1.5%Na2S2O3 1.14E-17 5.24E-18 6.74E-18 1.81E-191.5%NaCl+1.5%Na2S2O3 l.31E-15 1.87E-17 7.88E-18 1.70E-19

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TABLE 4NOISERESISTANCE FOR A SPECIMENAREA OF I SQ.CM

304 316 904 2541.5%NaCI 9.68E+02 1.54E+04 3.22E+04 4.04E+05

1.5%Na2S2O31.5%NaC1+1.5%Na2S2O3

1.12E+05 2.05E+05 1.97E+05 1.62E+063.46E+03 6.99E+04 9.80E+04 1.74E+06

EstimationofCharge

It hasbeensuggestedby Coins that the electrochemicalnoise producedby randomlyoccurringtransientsis analogousto shot noise and that suchelectrochemicalreactionscanbe treatedwith a shotnoiseanalysis.This is a purelystatisticalphenomenonwith noise resultingfrom the discretenatureofthecharge pulses and the random emission of thesepulses. On the basis of present knowledge, thefluctuationsobservedin electrochemicalsystems,often are due to currentburstsat levels much higherthana single charge,taking place at the electrodes.Essentiallythis assumesthat the noise arisesas aresultoftherandomvariationin the numberof pulsesarriving in a given interval oftime, and hencecanbeanalysedusingthe shot model.

The charge,q, can be estimatedfor the assumedshot noisemodel at the low frequencylimit fromtherelationderivedby Cottis:

q=fEXI

32Bb

The Stern-Gearyproportionalityconstantcalculatedfrom the Tafel constantsis given as:

B /Ja/3c /2.30313a + flu 4

We have selectedTafel constants,13 = = 118 mV. Even if the actual Tafel constantsareunknown,anapproximatevalueof 100 mV give a constanterror in the calculatedcorrosionrateofonly afactor of two maximum. Such an error is often within experimental scatter in plant corrosionmeasurements.Moreover,relativecorrosionratesareusuallymore significantthanabsolutevalues.Withthevaluechosenthe Stem-Gearyconstant,B, is 26 mV. Thebandwidth,b, is 0.5 Hz in ourcase.

Thecalculatedvaluesofq for thevarioustestconditionsareshownin Table5.

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TABLE 5CHARGECOULOMB CALCULATED BASED ON AVERAGE NOISE POWER

304 316 904 254

FrequencyDomain

1.5%NaC1 3.68E-I1 1.04E-11 9.22E-12 5.46E-121.5%Na2S2O3 4.93E-1I 4.13E-11 5.IOE-Il 1.13E-11

1.5%NaCl+1.5%Na2S2O31.75E-10 5.03E-11 2.97E-lI 1.14E-11

Each time record was processedby calculating the PSD by the FFT method after detrending,windowing and by the MEM method. The PSD calculatedfrom the first half of the time record1024datapointsfor the stainlesssteels304, 316, 904 and 254 in 1.5%NaC1+ 1.5% Na2S2O3using both the

techniques is shown in Figures 3 to 6. The ElectrochemicalNoise Impedancecalculated using

/I, is also shown. We have usedthe unit V2/Hz to plot PSD, as it relates to the power

distribution of the sequenceand the ‘amplitude-squared’measurehas the dimensionsof power. Some

workersplot v/1i ratherthan V2/Hz. Note that the variancemeasuredby a samplingprocedureisequivalent to the integral of the noise power spectral density over the measurementbandwidth. Theterminology usedfor currentnoise is essentiallythat for potential noise. The currentpower spectraldensityis reportedwith unitsof A2/Hz.

The instrumentnoise dataare superimposedon the MEM plots to differentiate the backgroundnoise.From theinstrumentnoiseplot Figure2 it is seenthat thereferenceelectrodeby itself introducessignificant noiseespeciallyat low frequenciestill 0.01 Hz andvariesbetweenthe different solutions.Theinstrumentcurrent noise is superimposedfor a sourceresistanceof 10 k and the instrumentpotentialnoiseat the respectivesolution. It was found that in all the teststhe spectraldensityof the currentnoiseto be many ordersat least 1000 higher than the instrumentnoise. However, the instrumentpotentialnoise was found to be comparable,and in certain caseseven higher than the potential noise at lowfrequenciestill 0.005 Hz. Such casesare shown shadedin Table 6 to indicate that their interpretationrequirescaution and the shadingis applicableto all the tables. The intensity of shadingdenotestheseverityof instrumentnoiseat low frequencies.

It is seen from the plots that both the techniquesF-FT and MEM generally give the sameinformation,otherthanthelargeamountof scatterseenin thePET method.TheMEM hastheadvantageof producinga smoothspectrum,whereasthePET necessarilyhasa largescatter.On the otherhandF-FThasa more direct relationshipwith the time record,in the sensethat thetime recordcanbe reconstructedby meansofinversetransformation.In practiceit is reportedthat bothmethodsgive thesameinformationandthis is confirmedby our result also. Theinstrumentnoisedataare shownonly in the MEM plots, forbetterreadability.

ElectrochemicalNoiseImpedanceR

The squareroot ofthePSDEto thePSDI alsohasthe dimensionofresistanceand is a functionof frequency. Therefore, it has some analogy with the modulus of the electrode impedance.The

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ElectrochemicalNoiseImpedancecalculatedusing /I from thePSD calculatedby MEM at a

frequencyvery closeto zerois shownin Table 6.

TABLE 6ELECTROCHEMICALNOISE IMPEDANCE AT ZERO FREQUENCY fl

I 1.5%NaC1

________

1.5%Na2S2O3

__________

[_1.5% Naçl+1.5%Na2S2O3

Note:ni-ni InstrumentNoiseexceedsPotentialNoise

InstrumentNoisecomparableto PotentialNoiseat lowfrequencies.Theintensity ofshadingindicatesthe closenessofthe instrumentnoiseto the observednoise.

CrossSpectralDensity

The Cross Spectrumgives valuableinformation about frequenciesheld in common betweentwosequences.If we assumethat the potential noise is a secondaryeffect of the currentnoise, wherebytheelectrodepotentialis modified by thechargingofthedoublelayercapacitance,we expectthetransientsinboth current and potential noise to occur at the sameinstant. If the CSD is calculatedbetweenthecorrespondinghalvesofpotentialand currentnoise,wemight be ableto pick out suchoccurrences.

In orderto developa statisticalbasisfor the analysisofthe noise potential and current,we havemadeassumptionsaboutthe statisticalpropertiesofthesequenceofpulsesconsideredto be the sourceofnoise.For simplicity, we haveassumedthat the pulsesare statistically independentandthe timing of theemissionof the pulse is not affectedby the previous history of the electrode. In order to test ourassumption,thetime recordwasdivided into four quartersandthe CSD was calculatedindependentlyforeachquarter.The CSD was extractedfrom the PSDs of the two sequencescalculatedusing Welch’saverageperiodogrammethod 8 whereinthe time record is divided into overlappingsections,eachofwhich is detrended,thenwindowedusing a Hanningwindow. MATLAB 2 softwarewas usedfor thecalculationofthe CSD.TheCSDfor thecorrespondingsectionsofthe potentialand currentnoisefor the4 stainlesssteelsin the solution 1.5%NaCl + 1.5%Na2S2O3areshownin Figures7 to 10.

TheCSD was averagedfrom arangeoflow frequencies,zeroto 0.01 Hz, ratherthantaking at onepoint to improvenoiserejection.TheMeanvalueof CSD at low frequenciesis shownfor all the casesinTable7.

NumericComputationSoftwarefrom The MathWorksInc.

304 3161 904 I 254

1.3_ 53.7.2 2.32E+05 9. __+-05

7.67E+05

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PotentialNoise

TABLE 7CROSSSPECTRALDENSITY V2.12/HZAT LOW FREQUENCIES UPTO 0.01 HZ

ANALYSIS AND DISCUSSION OF RESULTS

For the electrochemicalmodel basedon shot noise, the meansquaredpotential noiseaveragepotentialnoisepowerandi arerelatedby the equation:

T = 2B2qb/I0,. 5

Thustheaveragepotentialnoisepoweris expectedto beinverselyproportionalto i at thelowfrequencylimit directly proportionalto R from the Stem-Gearyequation.

Therelative ratio ofpotentialnoisepowersagainstSS 304 is shownin Table 8.

TABLE 8RATIO OF POTENTIAL NOISEPOWERRELATIVE TO 304

The potential noisepower is lowest for SS 304 followed by 316, 904 and 254 increasingin thatorder as expectedfrom the shot noise model confinning the superior corrosion resistanceof 254comparedto 304. Thepotentialnoise powerfrom 254 in 1.5 % NaCl is 62 times that from SS 304 andabout33 times in 1.5%NaC1+1.5%Na2S2O3comparedto ratiosof lessthan 10 for SS 316 and904. Thisshowsthat, eventhoughSS 316 and 904 aresuperiorcomparedto 304, the protectionofferedby 254 ismanytimeshigher.Whereasin a solutioncontaining1.5%Na2S2O3,knownto be passive,theratio is onlyabout 3.3 indicating that there is no appreciabledifference in the corrosionbehaviourbetweenthestainlesssteelsin 1.5%Na2S2O3.

304 316 904 2541.5%NaCI 6.25E-06 3.11E-05 3.47E-06 1.68E-05

1.5%Na2S2O3 2.05E-04 2.93E-05 1.54E-04 9.51E-061.5%NaC1+1.5%Na2S2O3 9.74E-05 4.91E-04 1.74E-05 4.82E-06

304 316 9041.5%NaCl

1.5%Na2S2O31.5%NaCl+1.5%Na25203

1.0 4.5 8.3 62.01.0 1.5 1.8 3.31.0 5.8 4.8 32.8

254

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207

CurrentNoise

Theproposedshot noise model suggeststhat the averagecurrent noisepower is expectedto bedirectlyproportionalto i.

I = 2 q, ‘corr" 6

Table9 showstherelativecurrentnoisepowersagainstSS 304.

TABLE 9RATIO OF CURRENTNOISEPOWERRELATIVE TO 304

304 316 904 2541.5%NaCl

1.5%Na2S2O31.5%NaCl+1.5%Na2S2O3

1.0 0.02 0.0075 0.00041.0 0.46 0.5895 0.01591.0 0.01 0.0060 0.0001

NoiseResistance

From the knowncorrosionbehaviourofthe stainlesssteelstested,theaveragecurrentnoisepoweris expectedto be the lowest for 254 and increasingin the order of 904, 316 and 304. The superiorcorrosionresistanceof 254 is clearly demonstratedby the lower currentnoise power comparedto theother stainlesssteelstested. The current noise power of 254 in 1.5% NaC1 and 1.5% NaCl+ 1.5%Na2S2O3is considerablylower -.2500timescomparedto SS 304. Eventhoughthecurrentnoisepowerfrom SS 316 and 904 are lower relativeto SS 304, the relativeratio is only about 166, indicating thesuperior corrosion resistanceoffered by 254. In a solution containing 1.5% Na2S2O3, known to bepassive,thereis no appreciabledifferencebetweenthe currentnoisepowerratiosbetween316 and 904comparedto SS 304 ratio -2 suggestingthat the corrosionbehaviouris expectedto be moreor lesssimilar. Evenfor 254 theratiois only 62.

The noiseresistancehasthe dimensionofresistance.It hasbeenusedconsiderablyin the researchof corrosionphenomenaand is oftenfound to be analogouswith linear polarisationresistance.Uniformcorrosionmight be expectedto be free ofnoise,with atomsleavingthe metal surfaceat a uniform rate.However, even a perfectlyhomogenousprocesswill give somefluctuations in rate, akin to Brownianmotion. Furthermore,thereare a numberof mechanismsby which it might be expectedthat even auniform dissolutionprocesswould occurasa seriesof bursts.Even thoughan inverserelationbetweenthe valueofR1, and corrosionratehasbeenpointed out in the past,thenoiseresistancehasbeenusedinmost part to study the onsetof localisedcorrosion,ratherthangeneralcorrosion. Whereas,the linearpolarisation resistancedoes not contain information about localised corrosion. The pitting initiationprocessis often found to result in metastablepit nucleationand propagation,giving rise to currenttransientslasting for a time of the order of 1 second,and involving a chargeof the order of l0 Ccorrespondingto around 1012 atoms. Thus the noise associatedwith pitting corrosionis much largerthanthat observedfor generalcorrosion.

14

207

It hasbeensuggestedthat the electrochemicalnoise resistancemethod, after accountingfor areaeffects, will measurethe resistancein the low frequencylimit much the same way as the linearpolarisationresistancetechnique.Attemptshave also beenmadeto justi1y a relationshipbetweenR andthepolarisationresistanceR zerofrequencylimit of impedance‘.

If weassumethat thepotentialnoise is a secondaryeffect of currentnoise,thepotentialnoisewillresultfrom the anodicreactionacting on the electrochemicalimpedanceof the electrode.At first sight,therefore,we may computethe electrodeimpedanceand calculatethe potential noise spectrumas theproductof the currentnoise spectrumand the squareof the amplitude of the impedance.However,amass transportlimited cathodicreaction will have an infinite impedance,and will not appearin theimpedancespectrum.

From the known corrosion behaviour of the different stainless steels tested R increasesprogressivelyfrom SS 304 and is the highest for 254. From the Table 4 it is seenthat R for differentstainlesssteelsfollows a similar patternand increasesfrom -968 for SS 304 in 1.5 NaC1 to --400 kTfor 254. Theratioofnoiseresistancerelativeto SS304 is shownin Table 10

TABLE 10RATIO OF NOISERESISTANCERELATIVE TO SS 304

304 316 904 2541.5%NaCl 1 16 33 417

1.5%Na2S2O3 1 2 2 141.5%NaC1+1.5%Na2S2O3 1 20 28 503

The noiseresistanceis 503 times higherfor 254 in 1.5 NaC1+ 1.5%Na2S2O3comparedto SS 304.However,in a solutioncontaining1.5%Na2S2O3theincreaseis only about 14 times,indicatingthat thereis not much differencein the behaviourof thetestedstainlesssteelsin a passivesolution suchas 1.5%Na2S2O3.

EstimationofCharge

If we considerthe fundamentalprocessesunderlying the generationof electrochemicalnoise, aparameterthat may bemoreappropriateis the amountof chargein eachtransient.We cancomputethisfrom the shot noise equation.Based on the shot noise model of electrochemicalnoise, it has beensuggestedby Cottis and others that a largevalue of q is indicative of localisedcorrosion.Table 11showstherelativequantity ofchargerelative to SS 304.

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207

TABLE 11RATIO OF CHARGERELATIVE TO SS304

304 316 904 2541.5%NaCl 1.000 0.284 0.251 0.148

1.5%Na2S2O3 1.000 0.838 1.034 0.2291.5%NaC1+1.5%Na2S2O3 1.000 0.288 0.170 0.065

The resultsshownin Table 11 agreewell with the proposedmodel. The chargecalculatedis thelowest for 254 and increasesprogressivelyin the order of 904,316 and 304. The superior corrosionresistancebehaviourof 254 is clearly demonstrated.In a solution containing 1.5% Na2S2O3thereis nosignificantdifferencein the chargesinvolved in SS 304, 316 and904 andreduces4-Stimes in the caseof254 indicatingthat all thestainlesssteelsbehavesimilarly in apassivesolution.

Eventhoughit is possibleto calculatethe diameterofthe pit assuminghemi-sphericalbasedonthevolumeof metalgoing into dissolution,it may bedifficult to seesucha pit. This is becausethechargecalculatedcorrespondsto the metastablepitting phaseand consideringthat our specimenare stainlesssteel,it is unlikely that any of the metastablepit will continue to grow during the test. However,thechargecalculatedgives an indication ofthe materialsresistanceto localisedcorrosionon arelativescale.It must also be emphasisedthat the shot noise model is applicableonly for frequenciesthat are lowenough that individual transientscan be regardedas instantaneouspulses. The detrendingprocess,necessaryto satisfy the ‘stationarity’ criterion, doesto a certain extent removesthe low frequenciesdependinguponthe orderofthepolynomialusedto determinethetrendcurve.

ElectrochemicalNoiseImpedance

Table 12 showstheElectrochemicalNoiseImpedancerelativeto SS304.

TABLE 12RATIO OF ELECTROCHEMTCALNOISE IMPEDANCE RELATIVE TO SS304

304 316 904 2541.5%NaCl 1.000 4.068 1.991 31.458

1.5%Na2S2O3 1.000 0.304 6.956 4.7641.5%NaCl+1.5%Na2S2O3 1.000 3.219 13.152 36.930

Thesuperiorcorrosionresistanceof 254 is evident from the highest valuesin 1.5% NaC1and1.5% NaCl+1.5%Na252O3solutions. The R valuesof the testedstainlesssteelswith the exceptionof316 and 254 arehigher in 1.5% Na2S2O3 solutioncomparedto the othersolutions. This is expectedbecause1.5% Na2S2O3 is a passivemedium with the highest resistivity. The stainlesssteels exhibitincreasingR, with the exceptionof 316 in 1.5% NaCl basedon their known corrosionbehaviour.However,suchan increasingtrendcould not be clearly seenin 1.5%Na2S2O3probablybecausethereisnot much differencein thebehaviourofthe testedstainlesssteelsin 1.5%Na2S2O3.ThevaluesofR arehighercomparedto K1 in thecaseof 304. However,thedifferenceis not significantfor 254.

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CrossSpectralDensity

We haveseenearlierthat a sharedfrequencycomponentis representedin proportionto the productof the individual amplitudes,and with a phaseequalto the differencebetweenthe individual phases.Iftwo sequenceshaveno sharedfrequencies,or frequencyranges,their crossspectrumis zero. The crossspectrum,in our case,will have a magnitudeproportionalto the productofthe powerspectraldensities

of potentialand currentnoiseE2 x J2 It was shownearlierthat thequantityof chargein the charge

transfereventsis relatedto theaveragenoisepowerby theequation:

7

The CSD, calculatedasthe crossspectrumof thepowerspectraldensitiesofpotential and currentnoise,appearsto havea similarity to theparameterusedto calculateq, andit is reasonableto expecttheCSD to be relatedto the squareof q. Table 13 shows the CSD of the testedstainlesssteels at lowfrequenciesrelativeto q2.

TABLE 13RATIO OF CSD AT LOW FREQUENCIES UPTO 0.01 HZ TO q2 NORMALISED

=

___

q2Bb

l.5 NaC11.5%Na2S2O3

1.5%NaCl+l .5%Na2S2O3

I 304 I 316 I 904

0.03 I I 0.17

Thecorrelationcoefficientbetweenthemeanof CSD at low frequenciesand q2 was calculatedtobeabout0.11. Correlationcoefficientsrangein valuefrom -1.0 to 1.0. A correlationcoefficient of zeromeansthat two variables are not correlated. A variable correlatedwith itself returns a correlationcoefficient of 1.0. Our assumptionthat the potential and current noisesto have similar frequencyresponseis valid only at zero frequency,as at any other frequencywe haveto takeinto accounttheelectrodeimpedanceand not just R. However,asthe instrumentnoise is significant at low frequenciesand is comparablewith potential noise in some cases,it becomesdifficult to establisha correlationbetweenthe quantity of chargeand the CSD. If the caseswheretheinstrumentnoiseeitherexceededorwere comparableto the observednoise were excluded,the correlationcoefficient improvesto 0.72.Therefore,by using a low noise referenceelectrode,low noiseZR.A and measuringinstruments,it isbelievedthat the chargeand CSD may be more suitablethanotherparametersas indicatorsof localisedcorrosion.

CONCLUSIONS

Metastablepitting consistsof randomly-occurring,brief pulse of charge,with the occurrenceofeachevent being independentof any other event Poissonprocess. Therefore, currentnoise is the

254

0.514.89

0.65

17

207

fundamentaloutputof the corrosionreaction,while potentialnoise is an indirectoutputthat resultsfromthe effect of currentnoiseon the metal-solutioninterfacial impedance.If we assumethat the pulsesofchargeare statisticallyindependent,thenelectrochemicalnoisecanbeanalysedwith a shotnoisemodel.

With theassumptionsmade,the currentnoisepower is directly proportionalto thecorrosionrate,while thepotentialnoisepoweris inverselyproportional.

Using the shot noise model and assumingthat the noise resistanceis the same as polarisationresistance,at the low frequencylimit, the quantityof chargein eachpulse canbe calculated.Our resultshave shownthat a largevalue of q is indicative of localisedcorrosion,and it may be more useful thanalternativeparametersthat havebeenproposed.

The Noise resistanceand the ElectrochemicalNoise Impedanceagreewell with the expectedlocalisedcorrosionbehaviourofthestainlesssteelstested.

It is believed that the Cross SpectralDensity will be closely correlatedwith the squareof thequantityof chargeat low frequencies.Thelow correlationobservedwasdueto the significant instrumentnoiseespeciallyat low frequencies.The correlationimprovedwhenthe caseswith significant instrumentnoisewereexcluded.

REFERENCES

1. AbdulmajeedAli Alawadhi,Ph.D. thesissubmittedto UniversityofManchester1998

2. S. TurgooseandR.A. Cottis, CorrosiontestingMadeEasy:ElectrochemicalImpedanceand

ElectrochemicalNoise,NACE, 1999.

3. Mats Liljas, AvestaSheffield,ACOM, 2-1995,Internationalconferenceon weldingofstainlesssteels,

June12-13,1995, Stockholm,Sweden.

4. Cooley,J.W,Tukey,Math. Comput.,19, 297-3011965.

5. Burg, J.P,ModernSpectralAnalysis, 42-48, IEEE, NewYork, 1978.

6. Lynn, PA, Digital signals,processorsandnoise,Macmillan,London,1 Edition, 1992.

7. R.A Cottis and S.Turgoose,‘Electrochemicalnoise measurements-Atheoreticalbasis’, EMCR’94,

Sesimbra,Portugal,1994.

8. MATLAB softwarereferencemanual-TheMathworksInc, 1981

18

GPIB

FIGURE 1 Electrochemical Noise-Simultaneous sampling ofPotential and Current Noise -

Schematic Diagram of Experimental Set-up

Multimeter-1CurrentNoise

Multimeter-2PotentialNoise

0N0

Potential Channel Noise MEM Potential Channel Noise MEMwithout Reference electrode o. with Referenceelectrode

>.o.ooi1E-O4‘1 E-04 I E-05

1E05 ôlE-061E:06 1E-071E-O7 .1E-08

1 E-08 1 E-09 - - - -

8.1E-09 olE-lO01 E-1 0lE-1l

1E-ll i0.001 0.01 0.1

0.001 0.01 0.1 1 Frequency HzFrequency Hz

_________________

H20 --1.5%NaCI 1I-v-100 1k 10k [--- 1.5% Na2S2O3 1.5% NaCI+1.5% Na2S2O3

Na Instrument Noise without Reference Electrode b Instrument Noise with Reference Electrode 00

Current Channel Noise MEM

.1E-12.1E-131E-14a 1 E-15 -= - - -1E-16

IE-171E-18

01E-19L.IE_20 I ‘i I liii I

0.001 0.01 0.1 1Frequency Hz

I --- 100 ---- 1k - 10k Ic Instrument Noise with ZRA

FIGURE 2: Instrument Noise of Potential & Current Measurement Channels by MEM

Potential-Time record Current-Time record

N0-.1

N

FIGURE 3: SS 304 in 1.5 % NaCI + 1.5% Na2S2O3

Potential-Time record Current-Time record

.

0.01

1h1i81IEIO

111El1

Potential Noise MEM1E-12

IIJI1E19lE20

Current Noise MEMlEG::41E30.0001

Noise Impedance- MEM

1

..

"------

.Y""N

0.001 0.01 0.1FrequencyHz

0.0001 0.001 0.01 0.1FrequencyHz

1 0.0001n.

0.001 0.01 0.1FreqjencyHz

I

-InsfrumentNo4sel I- Insfreni

NN

N0

FIGURE 4: SS 316 in 1.5 % NaCI + 1.5 % Na2S2O3

800 1000

Potential-Time record.0.17

-0.18

-0.19

-0.2

0.23i I I I I0 200 400 600 800 1000

TimeSecs

Current-Time record

200 400 600Timesecs

Potential Noise FFT0.01 -

......H0.0001 0.001 001 0.1 1

FrequencyHz

Current Noise FFT1E.14

0.0001 0.001 0.01 0.1 1FrequencyHz

Noise Impedance- FFT1E8

I

..-

0.0001 0,001 0.01 0.1 IFrequencyHz

0.01FrequencyHz 0.01

FrequencyHz

I - Insfrijnent Nolsel

FIGURE 5: SS 904 in 1.5% NaCI + 1.5% Na2S2O3

N-;w

N0

FIGURE 6: 254 SMO in 1.5 % NaCI + 1.5 % Na2S2O3

Potential-Time record-0.175

018

-0.185

> .0.19

-0.195

-0.2

Current-Time record

N

0.01FrequencyHz

HJ!1ntnen1NseI

N0

0.01FrequencyHz

- Insent

0.01FrequencyHz

0.001 -

I E.041E-05

1 E-06

N1 E-07.1 E-08

I E-09

1E-lO1 E-1 1IE-12 -

0.001

Cross Spectral DensityPotential against Current Noise

0.01 0.1Frequency Hz

0.0011 E-04I E-05

J1 E06çl E-07

I E-091E-lO1 E-l 1IE-12

0.001

First Quarter Second QuarterCross Spectral DensityPotential against Current Noise

0.001

E-051E-06

1E04

ç IE-07

1 E.08

1E-091E-lO1E-il

. Cross Spectral DensityPotential against Current Noise

0.001

1E-05I E-06

1E04

j I E.07

1E-08O1E-091E-10

IE-li1E-12 - I I

0.001 0.01 0.1 1Frequency Hz

IE.12 I I0.001 0.01 0.1

Frequency Hz1

Third Quarter

FIGURE 7:

Fourth Quarter

Cross Spectral Density of Potential & Current Noise


NU,

0.01Frequency Hz

0.1 1

N0-4

SS 304 in 1.5 % NaCI + 1.5 % Na2S2O3

Third Quarter

FIGURE 8

Fourth Quarter


SS 316 in 1.5 % NaCI + 1.5 % Na2S2O3

N0--4


0.001 -

1 E.041E.05J IE-06

N 1E-07.1 E.08

1E.09IE.101 E-I I1E-12 -

0.001


0.01

0.001 -

1 E-041E.05

I E-06ç4 I E-07IE08

I E-091E.1OIEli1E-12 -

0.001Frequency Hz

0.1

N.J

First QuarterCross Spectral DensityPotential against Current Noise

001

0.001 -.

1 E-041E-05

? IE-06ç-,j 1E-07..lE-08

1E-091E-lO1E-IlIE-12 -

0.001

Frequency Hz0.1

Second QuarterCross Spectral DensityPotential against Current Noise

0.01 0.1

0.001 -

1 E-04lE-05

I E.06çj I E-07.lE.08

1 E-09IE-lOI E.1 11E.12 -

0.001Frequency Hz

0.01Frequency Hz

0.1

0.001


IE-04lE-05

1 E-06I E-07

IE-081 E-09

1E-loIE-1IIE.12 . -

0.001


0.01

0.001 -

1E-04’1 E-051 E-06

1 E-07.lE-0801 E-09

IE-lO1 E-l 11E.12 -

0.001Frequency Hz

0.1


0.01Frequency Hz

0.1

0.001 -

1 E-041 E-0S

1 E-06

ç, 1 E.07lE-08

1E-09IE-lOIE-I I1E.I2 - I

0.001 0.01

Second QuarterCross Spectral DensityPotential against Current Noise

0.0011E-04

IE-051 E-06

ç.j 1 E-07alE-08OIE.09’

IE-lO1E-11

Frequency Hz0.1

N0--4

0.001

Third Quarter

FIGURE 9:


Fourth Quarter


SS 904 in 1.5 % NaCI + 1.5 % Na2S2O3

Third Quarter Fourth Quarter

FIGURE 10: Cross Spectral Density of Potential & Current Noise

254 SMO in 1.5 % NaCI + 1.5% Na2S2O3


0.0011 E-04I E-05I E.06

ç.j I E-07.1E-0801 E-09

1E-lO1 E.1 IIE-12

0.001


Frequency Hz0.01 0.1 1

0.001 -

I E-041 E-05IE-06

.j IE-07.1E-0831 E-09

1E-lO1E-liIE.12 -

0.001

N



0.0011 E-04IE-05

J 1E-06,j 1E-07-1 E.08

1E-091E-lO1E-lIIE.12

0.001

Second QuarterCross Spectral Density

Potential against Current Noise


0.0011E-041 E-051 E.06

ç..j 1 E-07IE.08

I E-091E-lO1E-li1E-12

0.001

N0-‘I


electrochemtcal noise signatureanalysis using...pitting corrosion is the most common form...

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