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Sensors2023,23,812.https://doi.org/10.3390/s23020812www.mdpi.com/journal/sensors
Review
ElectrochemicalSensorsforControllingOxygenContentand
CorrosionProcessesinLead‐BismuthEutecticCoolant—State
oftheArt
SergeyN.Orlov
1,2,3
,NikitaA.Bogachev
1
,AndreyS.Mereshchenko
1
,AlexandrA.Zmitrodan
2
andMikhailYu.Skripkin
1,
*
1
InstituteofChemistry,Saint‐PetersburgStateUniversity,7/9UniversitetskayaEmb.,
199034St.Petersburg,Russia
2
FederalStateUnitaryEnterprise“AlexandrovResearchInstituteofTechnology”,72,KoporskoeShosse,
188540SosnovyBor,Russia
3
InstituteofNuclearIndustry,PetertheGreatSt.PetersburgPolytechnicUniversity(SPbSU),29,
PolytechnicheskayaStreet,195251St.Petersburg,Russia
*Correspondence:m.skripkin@spbu.ru
Abstract:Controllingoxygencontentintheprimarycircuitofnuclearreactorsisoneofthekeytasks
neededtoensurethesafeoperationofnuclearpowerplantswherelead‐bismutheutecticalloy(LBE)
isusedasacoolant.Iftheoxygenconcentrationislow,activecorrosionofstructuralmaterialstakes
place;uponincreaseinoxygencontent,slagaccumulatesduetotheformationofleadoxide.The
generallyacceptedmethodofmeasuringtheoxygencontentinLBEiscurrentlypotentiometry.The
sensorsformeasuringoxygenactivity(electrochemicaloxygensensors)aregalvaniccellswithtwo
electrodes(lead‐bismuthcoolantservesasworkingelectrode)separatedbyasolidelectrolyte.Con‐
trolofcorrosionandslagaccumulationprocessesincircuitsexploringLBEasacoolantisalsobased
ondataobtainedbyelectrochemicaloxygensensors.Thedisadvantagesofthisapproacharethe
lowefficiencyandlowsensitivityofcontrol.Thealternative,ImpedanceSpectroscopy(EIS)Sensors,
areproposedforReal‐TimeCorrosionMonitoringinLBEsystem.Currentlytheirapplicabilityin
staticLBEattemperaturesupto600°Cisshown.
Keywords:lead‐bismutheutecticcoolant;structuralmaterials;protectivefilm;corrosion;oxygen
activitysensors;impedancespectroscopy
1.Introduction
Fastneutronreactorswithleadorlead‐bismutheutecticcoolantareoneofthesix
promisingreactortechnologiesselectedwithintheframeworkoftheGIF(GenerationIV
InternationalForum)internationalprojectasthebasisfornuclearpowerofthefuture[1].
Theadvantagesoflead‐bismutheutecticcoolantarearelativelylowmeltingpoint(125
°C),ahighboilingpoint(above1700°C),lowchemicalactivitycomparedtosodiumand
sodium‐potassiumcoolant.Allthesefactorsdetermineafairlywiderangeofnuclear
powerplantswithlead‐bismutheutecticcoolantcurrentlybeingdevelopedinRussia[2],
USA[3],China[4,5]andJapan[6].Atthesametime,thelead‐bismutheutecticcoolantis
highlycorrosion‐aggressiveinrelationtothestructuralmaterialsofthefirstcircuit[7]
becauseofthesignificantsolubilityofstructuralmaterialscomponentsinlead.
Thestructuralmaterialsoftheprimarycircuitareprotectedfromthedestructionby
oxidefilmsformedontheirsurface[8].Thestructureandprotectivepropertiesofthese
filmsdependonthechemicalcompositionofstructuralmaterials,flowrateandtemper‐
atureoftheLBEand,primarily,ontheoxygencontentinthecoolant[9].Anotherproblem
thataccompaniestheexplorationofreactorswithlead‐bismutheutecticcoolantisslag
Citation:Orlov,S.N.;
Bogachev,N.A.;
Mereshchenko,A.S.;
Zmitrodan,A.A.;Skripkin,M.Y.
ElectrochemicalSensorsfor
ControllingOxygenContentand
CorrosionProcessesin
Lead‐BismuthEutectic
Coolant—StateoftheArt.Sensors
2023,23,812.https://doi.org/10.3390/
s23020812
AcademicEditors:MatjažFinšgar
andTinkaraMastnak
Received:24November2022
Revised:7January2023
Accepted:9January2023
Published:10January2023
Copyright:©2023bytheauthors.Li‐
censeeMDPI,Basel,Switzerland.
Thisarticleisanopenaccessarticle
distributedunderthetermsandcon‐
ditionsoftheCreativeCommonsAt‐
tribution(CCBY)license(https://cre‐
ativecommons.org/licenses/by/4.0/).
Sensors2023,23,8122of14
accumulationduetooxidationofthecoolantifoxygencontentinthecircuitistoohigh.
Insufficientattentionthatwaspaidtothisissueattheearlystageofoperationledtoa
seriousradiationaccidentwiththemeltingofthecoreontheK‐27nuclearsubmarineof
Project645[10].
Thus,anadequatechoiceofoperatingrangesandeffectivecontroloftheoxygencon‐
tentintheprimarycircuitisthebasisfortrouble‐freeoperationofnuclearreactorswhere
lead‐bismutheutecticcoolantisexplored.Inaddition,animportantissuerelatedtothe
aggressivenessofLBEinrelationtostructuralmaterialsistheorganizationofcorrosion
monitoring.
Theaimofthisreviewistoanalyzeexistingapproachestothemeasurementofoxy‐
gencontentandcontrolofcorrosionandslagaccumulationprocessesinLBE.Specialat‐
tentionispaidtotheuseofoxygenactivitysensorsandalternativeelectrochemicalmeth‐
odsformonitoringcorrosionprocessesandslagaccumulationincircuitswithLBE.An
additionaltaskofthereviewistofamiliarizetheinternationalscientificcommunitywith
theresultsoftheworkofRussianscientists,currentlypublishedmainlyinRussian.
2.Discussion
2.1.TheOperatingRangeofOxygenConcentrations
Aswasmentionedabove,theprotectivepropertiesoffilmsformeduponoxygenin‐
hibitionofcorrosionaredeterminedbytheconditionsoftheirformation—thetempera‐
tureandflowrateoftheLBE,thetemperaturegradientinthecircuitandtheconcentration
ofoxygeninthecoolant.Dependingontheoxygencontentinthecoolant,theconditions
inthecircuitcanbedividedintothreegroups[9]:
(1) Highoxygencontent:from1×10−6%to1×10−3%byweight;
(2) Averageoxygencontent:from1×10−6%–1×10−7%byweight;
(3) Lowoxygencontent:≤1×10−7%.
Iftheoxygencontentinthecircuitislow,thestructuralmaterialsareactivelydis‐
solved.Asimilarsituationisalsoobservedattemperaturessohighthattheresultingox‐
idelayercannotpreventthedissolutionofstructuralmaterials[11].Atanaverageoxygen
concentration,anoxidefilmformsonthesurfaceofstructuralmaterials.Atthesametime,
oxygenreactswiththedissolvedcomponentsofsteel.Theresultinginsolubleoxidesof
corrosionproductsaredepositedonthesurfaceofthesteel,asaresultofwhichasingle‐
layeroxidefilmofferro‐chromiumspinel(Fe2‐xCrx)2O4isformedonthesurface[11].
Atahighoxygenconcentration,theoxidationofironatomsdiffusedoutwardfrom
structuralmaterialtakesplaceontheoxidefilm/LBEinterface,resultingintheformation
ofanexternaloxidelayerofmagnetite.Asnotalloxygenisboundinthisreaction,the
remainingmoleculesmigratethroughtheoxidelayerandreactwithbothironandchro‐
miumunderthefilm,increasingthethicknessoftheferro‐chromiumspinellayer.Asa
result,atwo‐layeroxidefilmisformedonthesurfaceofthestructuralmaterial,inwhich
onlytheinnerlayerhasprotectivefunctions[12,13].
Theprocessesofcorrosionandoxidationofstructuralmaterialsintheflowofliquid
metalcoolantdifferfromthecaseofstaticLBE.Klok[14]hasshownthatthecorrosion
rateisproportionaltov0.6−0.8,wherevisthelinearvelocityofLBE.Theincreaseinthe
corrosionratewithanincreaseintheflowrateofthecoolantisexplained,firstly,bydam‐
ageoftheoxidelayerduetoerosionand,secondly,byacceleratingthediffusionofcorro‐
sionproductsfromthesurfaceofthestructuralmaterialintothevolumeofthecoolant.
Theeffectoftheflowvelocityonthestructureoftheoxidefilmisdemonstratedbythe
resultsofWiesenburgandhiscoauthors[15].Thecorrosionresistanceofmartensiticsteel
T91wasanalyzed.Itwasshownthat,atanoxygencontentof10−8–10−10%,acoolanttem‐
peratureof450°C,aflowrateof1m/sfor2000hoftheexperimentandthepenetration
ofLBEintothesteeltoadepthof10micronsoccurred.Atanoxygencontentof10−8%,a
coolanttemperatureof300°Candaflowrateof1m/sfor10,000hoftheexperiment,
neithertheformationofanoxidefilmnorthedissolutionofsteelwasobserved.Whenthe
Sensors2023,23,8123of14
temperatureofthecoolantroseto450°Cundersimilarconditions,athinlayerofoxide
filmwasformedonT91steel,preventingitscorrosion.Atanoxygencontentof10−6%,a
coolanttemperatureof480°C,aflowvelocityof1.3m/sandtwo‐layer(magnetiteand
ferro‐chromiumspinel)filmwithathicknessof28micronswasformedonsteelduring
6600hoftheexperiment.Anincreaseintemperatureupto550°Cundersimilarcondi‐
tionsledtoanincreaseinthefilmthicknessupto45microns.Withanincreaseintheflow
rateupto2m/s(oxygencontent10−6%,coolanttemperature550°C)for15,000hofthe
experiment,asingle‐layerspinelfilmwithathicknessof45micronswasformedonT91
steel.Additionally,oneoftheexperimentsconductedintheLBEstream(1m/s),atan
oxygenconcentrationof10−8%ontheLINCEloop(Madrid),shouldbenoted[16]—when
thesamplewasheldfor5000h,thedissolutionofT91steel(upto300microns)wasob‐
served,althoughneitherforsampleswithanexposureof2000h,norforsampleswithan
exposureof10,000,suchapatternwasnotobserved.Theincreasedcorrosiondamagein
theconsideredexperimentwasexplainedbytheturbulentflowofLBE,whichconfirmed
theinfluenceofthecharacteristicsofthecoolantflowonthestateofstructuralmaterials.
Theareasofleadoxidesandprotectivefilmsformationdependingonthetempera‐
tureandoxygenconcentrationintheLBE[17,18]areshowninFigure1.
Figure1.ConditionsofleadoxideandprotectivefilmsformationaccordingtoMartynov[17]and
Müller[18].Theredlineindicatesthemaximumcoretemperatureforcurrentlydesigned
reactorswithLBE.
Sensors2023,23,8124of14
AsonecanseefromthedatapresentedinFigure1,ifthetemperatureoflead‐bismuth
eutecticcoolantwasabove350°Candoxygenconcentrationwasabove(7–8)×10−6wt%,
leadmonooxidewasformedinthecircuit.Theoptimaloxygenconcentrationvalues,
whichensuredtheformationofstrongprotectivefilmsandatthesametimeprevented
theformationofslag,areinanarrowrangewith(1–4)×10−6wt%width[19].Currently,
attemptsarebeingmadetoexpandthisrangebymodifyingthecompositionofstructural
materialsandapplyingthincoatingsenrichedwithelementswithahighaffinityforoxy‐
gentotheirsurface.ItwasshownbyDingetal.[20]thattheenergiesoftheelement‐
oxygenbondintheLBEmediumforthepairsFe–O,Cr–O,Ni–O,Al–OandSi–Ohadthe
followingvalues:−0.93;−1.26;−0.56;−1.45and−1.75eV,respectively.Thus,silicon,chro‐
miumandaluminumformedmorestableprotectiveoxidefilmscomparedtoirononthe
surfaceofstructuralmaterials.Aluminumiscurrentlythemostwidelyusedmaterial
whenapplyingprotectivecoatings.
Alltheprincipalindustrialmethodsofsurfacefilmsformationwereusedforcoating
structuralmaterials.Amongthemwerechemicalandphysicaldepositionfromthegas
phase(batchcementing,pulsedlaserspraying,vacuumarctechnology,thermalspray‐
ing),mechanicalmillingandsoon[21–28].Themainproblemoftheapplicationofthese
coatingstoinhibitcorrosionofstructuralmaterialsintheLBEenvironmentwasensuring
theirsufficientmechanicalstrengthandadhesiononthesurfaceofthemainalloy[27].
Themethodofhigh‐currentpulsedelectronbeamsofmicrosecondrange[29–31]isa
promisingapproachtocreateprotectivecoatingsonthesurfaceofstructuralmaterialsin
nuclearreactorswithLBE.Whentheelectronbeamactedonthepreliminarylayerofalu‐
minum,itsmeltingwiththestructuralmaterialtookplace.Asaresult,anintermetallic
phaseoftheAlxFeycompositionwithadepthof20–30micronsformedonthesurface.The
mixingprocesshadavortexcharacter.Becauseoftheoxidationoftheintermetallicphase
inLBE,anextremelydenseultrathinAl2O3oxidefilmformedonthesurfaceofthemate‐
rial,whichpersistedduringthetestingprocess.Thisfilmcompletelypreventedliquid
metalcorrosionatanoxygencontentof10−8–10−7wt%andallowedtheexpansionofthe
oxygenrangeofnormaloperationofreactorswithheavyliquidmetalcoolants[32].
Thus,maintainingtheoxygencontentatagivenlevelintheLBEensuredthecorro‐
sionresistanceofstructuralmaterialsthatdeterminestheactualityofthemonitoringof
theoxygenconcentrationinthecoolant.
2.2.MeasurementofOxygeninaLead‐BismuthEutecticCoolant
Oneofthemostcommonwaystomeasureoxygenconcentrationinliquidsisthe
electrochemicalone[33].Theconventionalelectrochemicalsensorstomeasureoxygenac‐
tivityinalead‐bismuthcoolantareagalvaniccellwithtwoelectrodesseparatedbyasolid
electrolyte.InsensorsutilizedatnuclearplantsinRussia,thereferenceelectrodeisasat‐
uratedoxygensolution(withaconstantoxygenactivityequalto1)inmetalswithalow
meltingpoint.Usually[34–39],Bi‐Bi2O3system(meltingpoint544K)isusedfortherefer‐
enceelectrode.Theoperatingtemperaturerangeoftheoxygensensorcanbeexpanded
bysubstitutionofthissystemonIn‐In2O3[40,41](meltingpoint433K)eitherSn‐SnO2
[42,43](meltingpoint505K)systems.
Alternativeoptionsforreferenceelectrodesare:
Air/metal(Pt)[43,44]orperovskiteoxidee.g.,LanthanumStrontiumManganite
(LSM)andLanthanumStrontiumManganite‐GadoliniumDopedCeria(LSM‐GDC)
[45,46];
Solidmetal/metaloxidemixturese.g.,Fe/Fe3O4[47–50],Cu/Cu2O[51].
ThemaindisadvantageofthePt‐airreferenceelectrodeisthehighminimumtem‐
peratureofthereadings—about400°C.Atlowertemperatures,especiallyintheareaof
lowoxygenconcentrations,asignificantmeasurementerrorispossible[52,53].
Sensors2023,23,8125of14
Todate,thepossibilityofusingperovskitesforhigh‐temperaturesensorshasbeen
proven[54].Atthesametime,asignificantdisadvantageofallairelectrodesisthepossi‐
bilityofcontactofthecoolantwiththeexternalatmospherewhentheinsulatinglayerof
theelectrodeisdamaged[44].
Liquidmetal/metaloxidereferenceelectrodesmightcausethemechanicalfailureof
thesolidelectrolyteoncethemeltingpointofthemetalphaseiscrossede.g.,indiummelts
at157°CandLBEmeltsat125°C[44].Atthesametime,animportantadvantageofthe
liquidbismuth/bismuthoxidereferenceelectrodeistherefinementofitstechnologyand
extensiveexperienceinapplicationofthesensorsbasedonitbothinreactorswithstatic
andwithcirculatedcoolantatnumerousnuclearindustryenterprisesinRussia(JSC“NI‐
KIET”,Moscow.CRISM“Prometey”,Saint‐Petersburg,OKB“Giropress”JSC,Podolsk
etc.)andabroad(e.g.,ENEAcenteratBrazimone,Italy)[49].
Asaworkingelectrode,alead‐bismutheutecticcoolantacts,theoxygenactivityin
whichislessthanorequalto1.Solidelectrolytesseparatingtheworkingandreference
electrodeinthesensorsaresolidsolutionsofthecompositionMeOx*Me’Oy.Thesolutions
arebasedonrefractoryoxidesZrO2,HfO2,ThO2,stabilizedbytheadditionofCaO,Y2O3
andSc2O3[50,55].Theseoxideadditivesprovideionicconductivityandmechanical
strengthofelectrolytesduetostabilizationofthecubiccrystallatticesimilartofluorite.
Thehighestionicconductivityofelectrolytesisachievedatconcentrationsofstabilizing
additivesof7–15mol%[50].
Theseoxidesdemonstraten‐typeconductivity,whichispreservedinsolidsolutions.
Asaresult,solidelectrolytesinoxygensensorshavemixedion‐electronconductivity.To
accountforthisfact,theaveragetransfernumberswereused—iontiandelectronte[50].
Thesenumbersareequaltothefractionsofionicandelectronicconductivity,respectively.
𝑡𝑡 =1(1)
Theionictransfernumbersoftheoxygensensorelectrolyteweredeterminedexper‐
imentally.Itisconsideredtobeaconditionedsensoriftiisintherange0.95–1.
Whenthesensorwasoperating,theionizationreactionofoxygenatomsproceeded
onthereferenceelectrode,followedbythetransferofanionsthroughtheelectrolyteto
theworkingelectrode,wheretheanionsweredischarged[56].Itwasassumedthatoxy‐
gendissolvedinaliquidmetalandinareference,electrodewasinatomicform[57]and
wassubjecttotheSievertslawthatallowsthepredictionofitssolubilityinmetals.
OxygenactivityinLBEcanbedeterminedfromtheNernstequation:
𝐸 𝑅𝑇
2𝐹ln 𝑎
𝑎(2)
whereETisthecalculatedEMFofthegalvaniccell,V;Ristheuniversalgasconstantequal
to8.31J/(mol×K);FistheFaradaynumberequalto96,500C/mol;Tisthetemperatureof
thecoolantinthesensorarea,K;aref—thermodynamicactivityofoxygeninthereference
electrode;aLBE—thermodynamicactivityofoxygeninLBE.
ThecalculatedEMFofagalvaniccellcorrelateswiththemeasuredoneasfollows:
Eo=ti∙ET(3)
ForasensorwithabismuthreferenceelectrodeinLBE,therelationshipbetweenthe
valueofthemeasuredEMFandactivityofoxygencanbeexpressedintheform[58]:
Eo=ti∙(0.088−9.91∙10−5T(0.18+lgaLBE)),(4)
wherethermodynamicactivityofoxygeninLBEcanberelatedtoitsconcentrationbythe
simpleequation:
aLBE=CLBE/Cs(5)
whereCLBEistheoxygenconcentrationinLBE,mass%;Csisthesolubilityofoxygenin
LBE,mass%.ThesolubilityofoxygeninLBEcanbecalculatedaccordingtotheequation:
Sensors2023,23,8126of14
Cs=A−B/T(6)
whereAandBareempiricalcoefficients.ThevaluesofparametersAandBobtainedby
variousauthorsweresummarizedbyAskhadullin[49].TheyarelistedbelowinTable1.
Table1.ParametersforcalculatingthelimitsolubilityofoxygeninLBE[49].
AuthorYearTemperatureRange,°CAB
Martynov1998400–7001.203400
Ghetta2004300–5003.274852
Muller2003200–6002.524803
Gouruouau2004350–5003.344962
Ganesan2006540–7402.424287
Pityk[56]hasmentionedthattheuseoftheabovementionedequationtocalculate
thelimitsolubilityofoxygeninLBEisnotmetrologicallyjustified,and,therefore,the
oxygenconcentrationvaluesobtainedusingthisequationcanonlybeusedasillustrative
andhavenomeaningasphysicalquantities.
AnotherproblemarisinguponuseofthermodynamicactivitysensorsinLBEwasthe
polarizationoftheelectrodes.Thefollowingpolarizationfactorsthatchangedtheelec‐
trodepotentialcanbeimplementedontheworkingelectrodeofthesensor[50]:
Oxidesdepositiononthesurfaceofthesolidelectrolyte;
adsorptionofmetallicimpuritiesontheelectrolytesurface;
formationofmicrocracks;
reductionoftheresistanceoftheinterelectrodeinsulator;
thepresenceofopenmicroporesonthesurfaceoftheelectrolyte.
Polarizingfactorsincreasedtheioniccurrentinthesensorcircuitandtheoxygen
activityontheelectrolytesurface,whichledtoanincreaseintheelectrodepotentialby
thepolarizationvalueη.Therefore,themeasuredEMFoftheoxygensensorwasreduced
bythesamevalue:
E=E0−η.(7)
ToaccountforthemagnitudeofpolarizationMusikhin[50]calculatedthecorre‐
spondingfunctionsthatallowedthemodelingandpredictingofthepolarizationpro‐
cessesontheworkingelectrode.
Oxygenactivitysensorsaredesignedtoworkinacorrosiveenvironmentwithaddi‐
tionalexposuretoradiationandneutronflux,whichcancauseadditionaldamagetosen‐
sormaterials[59].Okuboandco‐authors[60,61]havestudiedeffectoftheirradiationofa
solidelectrolyte—zirconiumdioxidestabilizedbytheadditionofyttriumoxide—by
gammaradiationandelectronswithanenergyof100keV.Theyshowedthatbend
strengthwasnotaffectedbytheirradiationevenathighdoseof10mGy.Atthesame
time,forpartiallystabilizedzirconiawithyttriacontentof3%byweight,apartialtransi‐
tionofthemonoclinicphasetothetetragonalphasewasobserved.
Despitetheharshoperatingconditions,thelifetime(servicelife)ofsensorsinLBEis
4000hormore[62].Tocontrolpossiblesensorfailures,itwasproposedtoinstallatleast
threeDACsinthecircuit[63].Inthiscase,beforemeasuringtheoxygenactivityinthe
coolant,itwaspossibletochecktheoperabilityofthesensors.Thistestconsistedinmeas‐
uringthepotentialdifferencebetweenthereferenceelectrodesofapairofsolid‐electrolyte
sensors.Ifthisdifferencewasconstantwithintheabsolutemeasurementerror,thesesen‐
sorswereoperational.Ifthisconditionwasnotmet,thenbysequentiallysortingthrough
pairsofsensors,aninoperablesensorwasdetectedandexcludedfromfurtherconsidera‐
tion.
Tosummarizetheresults,themeasurementofoxygencontentinthecoolantwas
currentlycarriedoutbythepotentiometricmethod;thehardwareaspectsofthemethod
Sensors2023,23,8127of14
werewelldeveloped.Atthesametime,questionswereraisedabouttherelationshipbe‐
tweenthevaluesobtainedbymeansofsensorsandtheactualoxygenconcentrationinthe
coolant,aswellasconfirmationoftheoperabilityofsensorsinstalledintheflowcircuits
withLBE.
2.3.ControlofCorrosionandSlagFormationProcessesinLBEUsingOxygenActivitySensors
Diagnosticsofthestateofstructuralmaterialsandprotectivecoatingsontheirsur‐
facesduringtheoperationofnuclearpowerplantswithLBEinRussiawascarriedout
duringtheejectionofgasmixturesinisothermalmodeat300–330°C[64].Twovariants
oftheintroducedgasmixtureswereprovided:He+O2andHe+H2O(g)+N2+H2.
Whenthefirstcompositionwasused,achangeinthethermodynamicactivityofox‐
ygenwasconsideredanindicator.Inthecaseofsignificantamountsofnon‐oxidizedcor‐
rosionproductsofstructuralmaterialspresentinthecoolant(liquidmetalcorrosion)or
violationofprotectivecoatingsonthesurfaceofthecircuittakesplace,therateofdeoxi‐
dationofthecoolantincreased.Onthecontrary,inthepresenceofsignificantamountsof
slags(oxidecompounds)inthecircuit,therateofdeoxidationdecreased.Ifareducinggas
mixturewasusedindiagnosticmode,therateofincreaseintheconcentrationofhydrogen
intheprotectivegaswasmonitored.Inthepresenceofoxideslagsinthecoolant,therate
ofhydrogenincomingdecreased,inthepresenceofnon‐oxidizedcorrosionproducts,it
increased.Infact,whenthisapproachwasused,thecontrolwasratherqualitativeand
didnotprovidearelationshipwiththequantitativevaluesofthecontentofcorrosion
productsandslaginthecoolant.
Diagnosticsofthestateofthesurfacesofstructuralmaterialsofpromisingnuclear
powerplantswithLBEwasproposedtobecarriedoutonthebasisofmonitoringthe
amountofdissolvedoxygensuppliedfromthemasstransferapparatus[65].Anincrease
inthisindicatorreflectedtheintensificationofcorrosionprocesses,adecreaseistheevi‐
denceoftheaccumulationofslagsortheappearanceofanadditionalsourceofoxygen.
Establishingtherelationshipofthesechangeswiththeratesofcorrosionprocessesand,
moreover,thelocalizationofcorrosionsites,thedeterminationofcorrodingequipment
waspracticallyimpossible.
Toincreasetheinformativenessofthecontrolofcorrosionandslagaccumulation
processesbasedonthedataoftheoxygenactivitysensors,IvanovandSalaevhaveana‐
lyzedtherelationshipbetweenthekindoftemperaturedependencesofoxygenactivity
andthecontentofchemicallyactiveimpuritiesinthecoolant[66,67].Thedeviationfrom
thelinearformofthedependenceofthereadingsoftheoxygenactivitysensoronthe
temperatureofthecoolanttakesplaceasaresultofachangeinthephysico‐chemicalstate
ofthecoolantassociatedwiththeappearanceofimpuritiesinit.Theresearcherssupposed
that,inthefuture,arelationshipwillbedevelopedthatquantitativelylinkstheoxygen
activitysensorreadingsobtainedinthemodesofthermalcyclingofthecoolantwiththe
contentofimpuritiesinthecoolant,butatthemomentthisworkhasnotbeencompleted.
Tosummarizetheresults,thedevelopmentofaquantitativerelationshipbetween
theindicationsofoxygenactivitysensorsandcorrosionprocessesinthecircuitwithLBE
isacomplexandnon‐trivialproblem,thesolutionofwhichhasnotyetbeenobtained.
2.4.ImpedanceSpectroscopyApplicationtoMonitorCorrosionProcessesinLBE
Atthemoment,theElectrochemicalImpedanceSpectroscopymethodiswidelyused
tomonitorthecorrosionprocessesinvariousenvironments[68–72].Thismethodisused
tostudythestructureofcorrosiondepositsandthemechanismoftheirformation[73],the
resistanceofcoatingsonthesurfaceofmaterials[74]andtheeffectivenessofcorrosion
inhibitors[75].TheadvantageoftheImpedanceSpectroscopymethodisitsabilitytotrack
changesinthestateofthemetal/liquidmetalinterface,whichisextremelyimportantin
thecaseofusingoxidefilmstoinhibitcorrosionprocessesinLBE.
Electrochemicalimpedancespectroscopyisbasedonmonitoringtheresponseofan
electrochemicalsystemtoasinusoidaldisturbanceofsmallamplitude(severalmV)ina
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widefrequencyrange(10
7
to10
−4
Hz).Quantitativeanalysisofthefrequencydependence
oftheimpedanceonthebasisoftheselectedequivalentcircuitmakesitpossibletointer‐
pretitselementsinaccordancewiththephysicochemicalnatureoftheprocessesoccurring
ontheelectrodes[76,77].
Initially,theapplicationofthismethodtothestudyofoxidefilmsinLBEwaspro‐
posedbyLillardandStubbinsin2004–2008[78–80].Asmallsinusoidalvoltageexcitation
wasmeasuredbetweenthesampleandreferenceelectrodeinathree‐electrodeconfigura‐
tion,wherethecurrentfromtheworkingelectrodepassedthroughacounterelectrode
andtheimpedancewasmeasuredasafunctionoffrequency.Inthefirstsetoftheexper‐
iments,theworkingelectroderepresentedametalrodinaceramictube[81]andimped‐
ancespectroscopyprobewasformedbypushingastainless‐steelweldingroddownthe
centerofaceramictube,untilthetipoftherodpenetratedveryslightlyfromtheendof
thetube.AsteelreferenceelectrodewasalsoplacedintheLBE.Thedifferencebetween
theimpedancesmeasuredfromthesteelwithandwithouttheoxidelayersindicatedthe
existenceoftheoxidelayersinthefirstcase,andthemagnitudeand/orkindofdifference
yieldedinformationaboutprocessesoccurringontheelectrodes[77].Thisdevicepro‐
ducedreasonableresultsonlyattemperaturesupto200°Cor300°C,whichwasnot
enoughtoorganizereal‐timecorrosionmonitoringinthecircuitsofnuclearreactorswith
LBE.
Tosolvethisproblemthemodificationofworkingelectrodewassuggested[81,82].
Themodifiedelectrodeconsistedofa410stainless‐steeldisk,completelycoatedwithalu‐
minaexceptfortwosmallareasonthebackside,forelectricalconnections,andonesmall
areaonthefrontside,actingastheactiveareatobeexposedtotheLBE.Thisactivearea
wasacircleof0.25‐inchdiameter.Thisdiskwasthenpushedontothemostlyclosedbot‐
tomofastainless‐steelcylinder;thebottomhada0.375‐inch‐diameterholedrilled
throughittoallowtheactiveareaofthedisktocommunicatewiththeoutsideofthe
cylinder.
Thisimprovementofworkingelectrodemadeitpossibletoraisetheoperatingrange
oftheimpedancespectroscopymethodinSVTtoatemperatureof600°C.Kondo[83,84]
hasshownthattheapplicationofthismethodinaleadcoolantispossibleuptoatemper‐
atureof500°C.
AsimplifiedRandleselectricalequivalentcircuit(EEC),withouttheWarburgdiffu‐
sionelement[84],wasusedforequivalentcircuitfittinginliquidmetal,asshowninFig‐
ure2.Forequivalent‐circuitfitting,aparallelcombinationofaresistorandconstant‐phase
element(CPE)wasused.TheresistorandCPEinthiscircuithavebeenassignedtothe
resistanceandcapacitanceoftheoxidelayer.
Figure2.Electricalequivalentcircuitusedtofitimpedancedata.
CPEImpedanceZ
CPE
[78]isequalto:
𝑍
1
𝐴
𝑖𝑤(8)
wherew—frequency,Hz;A—frequencydependentparameter;n—mathematicalconstant
withoutobviousphysicalsense.
Theequivalentcapacitanceofthesurfaceoxidefilmcanbecalculatedas
Sensors2023,23,8129of14
𝐶𝑅
𝐴
(9)
whereRoxide—polarizationresistanceofthesurfaceoxidefilmformedonsample,Ohm.
AlltheparameterscouldbeacquiredfromthefittingoftheNyquistplot,basedon
theexperimentaldata.TheNyquistplotisacomplexohmicplane,impedancerealcom‐
ponentZ′wasdepositedalongthexaxis,andtheimaginarycomponentofresistanceZ′′
wasdepositedalongtheyaxis
𝑍𝑍
𝑖𝑍(10)
𝑍 𝑍cos 𝜑(11)
Z′′ 𝑍sin 𝜑(12)
whereZ0isvoluminousimpedanceofthesampleandφisphaseangle.
WhenconstructingtheimpedancespectruminNyquistcoordinates,toobtaineach
pointofthecurve,thevaluesZ′andZ″arecalculatedfromthedataarray(ω,Z0,φ)orthe
vectorZ0isplacedontheplaneatanangleφtothexaxisandthepositionofitsendpoint
isfixed(thecoordinategridmustbesquare).
TheexampleofNyquistplotfortheneatironinLBEandtheresultsoffittingtheEIS
datausingtheZviewsoftware[85]areshownatFigure3below.Measuredandfitted
impedanceagreeoneanotherfairlywell.
Figure3.NiquistplotforironinLBE:experimentaldataaremarkedwithsquares,solidlinerepre‐
sentsfittinone.Fittingparametersare:n=0.964,Q0=8.67∙10−10S∙sn/cm2,RLBE=3.02∙10−4Ω/cm2,Roxide
=2.71∙104Ω/cm2.
Fromequivalentcapacitancethethicknessofoxidefilmcanbecalculatedasfollows:
𝑑𝜀𝜀𝑠
𝐶(13)
wheredisoxidelayerthickness,μm;ε—absolutepermittivity,(F/m);ε0—vacuumpermit‐
tivity,(F/m);s—theelectrodearea(surfaceexposureareaofthespecimeninLBE),cm2.
Qiuetal.[86]consideredtheimpedancepropertiesofironoxidefilmsinLBE.They
showedthattheimpedancevaluewasproportionaltothethicknessofthefilm.Whenthe
thicknessoftheironoxidefilmwaslessthan50nm,theimpedancevaluewasinsignifi‐
cant.Withanincreaseinthethicknessoftheoxidefilmto200nm,theimpedancevalue
increasedto1kΩcm2.Disruptionoftheoxideviascratchingledtoanimmediatelossof
Sensors2023,23,81210of14
impedanceduetoshortcircuiting.Thisfacttestifiestothepossibilityofimpedancespec‐
troscopysensorsapplicationtodetectdamagetotheoxidefilmonstructuralmaterialsin
LBEinrealtime.
Thenextsteptowardstheintroductionofimpedancespectroscopyintothecorrosion
monitoringsystemofstructuralmaterialsofthefirstcircuitofthenuclearreactorswith
LBEcoolantisthetestingofthismethodinLBEstreamsatcirculationstandsthatallow
ustodrawthefinalconclusionabouttheapplicabilityofthiskindofsensors.
3.Conclusions
Theelementsthatmakeupausteniticandmartensiticsteelswereeffectivelydis‐
solvedinlead‐bismuthcoolant.Oxidefilmsprotectedthestructuralmaterialsofthe
primarycircuitfromdestruction.
Topreservetheprotectivefunctionsofoxidefilms,astableoxygenconcentrationwas
maintainedintheprimarycoolantinanarrowrangefrom1×10−6%to4×10−6%or
upto1×10−8–1×10−7%whenusingprotectivecoatingsmadeofaluminumoxide.
MeasurementoftheoxygencontentintheLBEwascarriedoutbythemethodof
potentiometry.Atthemoment,thismethodisfullydeveloped,butdoesnotexclude
anumberofmetrologicaldifficultiesininterpretationandensuringthereliabilityof
measurementresults.
Theuseofoxygenactivitysensorstomonitortheprocessesofcorrosionandslag
formationinLBEwashamperedbythelackofaquantitativerelationshipbetween
thesensorreadingsandthecontentofimpuritiesinthecoolant.
Toobtaindataonthestateofprotectiveoxidefilms(includingthicknessandme‐
chanicaldamage)onstructuralmaterialsinstaticLBEattemperaturesupto600°C,
impedancespectroscopysensorscanbeused.
Thenextstagefortheintroductionofimpedancespectroscopysensorsintothecor‐
rosionmonitoringsystemofthefirstcircuitofpromisingnuclearreactorswithLBE
istoconfirmtheiroperabilityinflowingLBEloops.
AuthorContributions:Conceptualization:S.N.O.andM.Y.S.;methodology:A.A.Z.;software:
N.A.B.;validation:A.S.M.;formalanalysis:A.S.M.;investigation:S.N.O.;resources:A.A.Z.;data
curation:M.Y.S.;writing—originaldraftpreparation:S.N.O.;writing—reviewandediting:M.Y.S.;
visualization:N.A.B.;supervision:A.S.M.;projectadministration:N.A.B.;findingacquisition:
M.Y.S.Allauthorshavereadandagreedtothepublishedversionofthemanuscript.
Funding:Thisresearchreceivednoexternalfunding.
InstitutionalReviewBoardStatement:Notapplicable.
InformedConsentStatement:Notapplicable.
DataAvailabilityStatement:Notapplicable.
ConflictsofInterest:Theauthorsdeclarenoconflictofinterests.
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