Generalized method for determining fluoroacidity by electrochemical diffusion coefficient measurement (application to HfF4)

To cite this version :

Kergoat, Mickaël

and Gibilaro, Mathieu

and

Massot, Laurent

and Chamelot, Pierre

Generalized method for

determining fluoroacidity by electrochemical diffusion coefficient

measurement (application to HfF4). (2015) Electrochimica Acta, 176.

265-269. ISSN 0013-4686

O

pen

A

rchive

T

OULOUSE

A

rchive

O

uverte (

OATAO

)

OATAO is an open access repository that collects the work of Toulouse researchers and

makes it freely available over the web where possible.

This is an author-deposited version published in :

http://oatao.univ-toulouse.fr/

Eprints ID : 20336

To link to this article: Doi :

10.1016/j.electacta.2015.06.124

URL :

http://doi.org/10.1016/j.electacta.2015.06.124

Any correspondence concerning this service should be sent to the repository

Generalized

method

for

determining

_{fluoroacidity}

by

electrochemical

diffusion

_coefficient

measurement

(application

to

HfF

4

)

M.

Kergoat,

M.

Gibilaro

*

,

L.

Massot,

P.

Chamelot

UniversitédeToulouse,UPS,CNRS,LaboratoiredeGénieChimique,118RoutedeNarbonne,F-31062Toulouse,France

Keywords: Fluoroacidity hafniumfluoride diffusioncoefficient masstransport ABSTRACT

Auniversalmethodforfluoroacidityevaluationwasdevelopedandbasedonamasstransportapproach:

itsimplyconsistsinmeasuringthediffusioncoefficientofanelectroactivespeciesinvariousmolten

media. Thereductionbehaviour ofHf(IV) ions was investigated inmolten fluoridesand diffusion

coefficientsofHf(IV)ions weremeasured. Resultsshowed thatdiffusioncoefficientsdecreasewith

fluoroacidity,due totheeffectof solventviscosity(whichis linked tobridgedfluorines). Aglobal

approachofmasstransportinsolutionwasthenproposed,takingintoaccountbothsoluteandsolvent.

TheSchmidtnumber(Sc)definedastheratiobetweensolventviscosityandsolutediffusivitywas

calculatedinordertotakeintoaccountthesetwoparameters.ResultsshowedthatScincreaseswith

fluoroacidity, in amuch more sensitive way than D. This universal method can extended to all

electroactivespeciesandtoallbathfluoroacidity.

1.Introduction

Byanalogywithaqueoussolutions,notionofacidityinmolten fluoridesolventsisdefinedby_{fluoroacidity}(pF)andbasedonthe free_fluoridesexchangeinmoltenmixturesasdescribedinEq.(1):

fluorobaseÐfluoroacid +nF" ₍₁₎

pF="log(aF") (2)

Theactivityoffreefluorides(aF"),which quantifies

fluoroa-cidity, depends on the nature of the cations constituting the solvent,thecompositionandtemperature,andinfluences solva-tion,ionstabilityandprocessesreaction.Itthereforeneedstobe studied and quantified for a better understanding of physico-chemicalpropertiesofsolventsandsolutes.

Usual molten salts solvents are mixtures of alkaline and alkaline-earth fluorides (LiF, NaF, KF, MgF2, CaF2...) and the

amountoffreeF"_{ionsdependsontheirnatureandcomposition:}

themoreamoltensaltcontainsfreefluorides(i.e.fluorodonor),the higheritsbasicityis.Asinaqueousmedia,theacidityisessentialas it influences so many parameters; however pF values are not availableyetsincetheF"_{activitycan'tbemeasured:onlyarelative}

fluoroacidityscalewasestablishedbyindirectevaluations[1–3].

Oneelectrochemicalmethodtosortmolten_fluoridesmixtures inregardoftheirfluoroaciditywasproposedinourlaboratoryby Bieberetal.[4] andKergoat etal.[5].Basedonsilicon[4] and completedwithboron[5],itconsistsinstudyingtheequilibrium betweenadissolvedspeciesandagaseouscompoundsgivenby Eq.(3)forSiandEq.(4)forB:

SiF4+xx"(bulk)ÐSiF4(g)+xF" (3)

BF3+xx"(bulk)ÐBF3(g)+xF" (4)

Thus,bydefinition,afluorobasicbath(high[F"_]

free)stabilizesa

speciesinsolution,whilea_fluoroacidbath(low[F"_]

free)promotes

thereactionofgaseousspeciesrelease.

The study of these equilibria, moved by the free fluorides concentration, is then an indicator of _{fluoroacidity.} Indeed the releaseofSiF4(g)orBF3(g)leadstoadecreaseofSi(IV)andB(III)ions

concentrationsrespectively,controlledbyin-situelectrochemical titrations.

Bycalculatingkineticconstantsofsilicon(kSi)andboron(kB)

releases, ranking of various eutectic mixtures was established (Fig.1a) and a _{fluoroacidity} scale of _fluoride compounds was proposed(Fig.1b)[5].

Howeverseverallimitationswerepointedout:

- thechoiceofthesoluteiscriticalasithastoformagaseous speciesandbeinequilibriumwithit,

- thesolutemustnotreactwiththesolvent, * correspondingauthor:GibilaroMathieuTel.:+33561557219fax:+3356155

6139

- hastobemoreacidthanthesolventtocapturefreefluorides, - forthemostacidicbaths,thegaseousspeciesreleaseistoofast

todeterminethekineticconstants.

To avoid these drastic conditions, a universal method for fluoroacidity evaluation was developed and based on a mass transportapproach:itsimplyconsistsinmeasuringthediffusion coefficientofaspeciesinvariousmoltenmedia[5].However,small differenceswereobservedbetweenthediffusioncoefficientsand thediscriminationwascomplicatedbyalackofselectivity.Aglobal approachofmasstransportinsolutionwasthenproposed,taking intoaccountbothsoluteandsolvent.

Severalauthorsalreadyshowedthatanincreaseoffluoroacidity directlyimpactsthechemical structureofthemoltensalt[6–8] and leads to a decrease of the free F" _{which are involved in}

coordinationofonecomplex.Forthemostacidicbaths,complexes shares fluorinesbyforming bridges leading toa structure asa network-likeliquid[9–11].Thischemicalbehaviour(coordination and bridging) affects physico-chemical parameters as solute solubility,vaporpressureandviscosity[12].

BymeasuringthediffusioncoefficientsofSi(IV)andB(III)ions and calculating theSchmidt number(Sc),defined asthe ration between solvent kinematic viscosity

y

(in m2s"1) and solute

diffusivityD(inm2_s"1_{)invariousmolten}

fluoridesmixtures,itwas shown thatDdecreasesandSc (Sc=

y

/D)increaseswithacidity

validatingthepreviousscaleobtained.

This novel approach is easier to set up than kinetic rates determination,asanaccuratemeasurementcouldbeperformed by electrochemical techniques; moreover, it could be certainly extendedtoallelectroactivespeciesandtoallbathfluoroacidity. Inordertoconfirmthisassumption,hafniumtetrafluorideHfF4

solutewas selected:itis stablein solution,inerttothesolvent constitutants,anddonotformgaseousspeciesinourexperimental conditions.

OnlyfewstudiesoftheelectrochemicalbehaviourofHf(IV)ions are presented in the bibliography. The available results were mainlyacquiredinmoltenchloridesorchloro-fluoridesmedia.In moltenchlorides,Poinsoetal.[13,14]andAdhoumetal.[15]did notagreeontheonHf(IV)ionreductionmechanisminNaCl-KCl mixture.Spinketal.[16]inCsCl,showedthatHf(IV)ionsreduction is a one step process exchanging 4 electrons leading to the formationofHfmetal.Quitethecontrary,Guang-Senetal.[17]and Serrano [18] demonstrated inNaCl-KClthat reduction ofHf(IV) ionstakesplaceinatwostagesprocess,Hf(IV)toHf(II)toHf(0). However, all theseauthors agree that fluorideions addition in moltenchloridesstabilizes Hf(IV)ionstoformhafniumfluoride complexHfF62"(Eq.(5))inmoltenchloro-fluoridesmedia,asthe

reductionofHf(IV)ionstoHf(0)isperformedinasingle4electrons reversiblestepunderdiffusioncontrol(Eq.(6)):

HfCl62"+6F"ÐHfF62"+6Cl" (5)

HfF62"+4e"ÐHf+ 6F" (6)

Inthefirstpartofthispaper,thereductionbehaviourofHf(IV) ionswasinvestigatedinmolteneutecticLiF-NaF(61–39mol.%)at 750#_{C by cyclic voltammetry, square wave voltammetry and}

chronopotentiometricmethods.Then,diffusioncoefficientsofHf (IV) ionsweredeterminedindifferentconditionsvalidatingthe previousobtainedfluoroacidityscale.

Inasecondpart,measurementsofdiffusioncoefficientsofHf (IV) ionswereperformedintwoothersmoltenmedia:LiF-NaF-KF andLiF-CaF2selectedinregardsoftheirfluoroacidity(thefirstone

is more basic and thesecond one more acid than LiF-NaF:cf. Fig.1a),inthe800–900#_{Ctemperaturerange. Resultsobtained}

werecorrelatedtosolventviscositythankstotheSchmidtnumber previouslydefined.RelationshipsbetweenD,Scandfluoroacidity previouslydemonstratedwereconfirmedwiththis electrochemi-calspecies.

Thisglobalmasstransportapproachisvalidatedwithasimple determinationofadiffusioncoefficient,andisapowerfultoolin ordertodetermine_{fluoroacidity.}

2. Experimental

The cell consisted in a vitreous carbon crucible placed in a cylindricalvesselmadeofrefractorysteelandclosedbyastainless steellidcooleddownbycirculatingwater.Theinnerpartofthewall wasprotectedagainstfluoridevapoursbyagraphiteliner.Thiscell hasalreadybeendescribedinpreviouswork[19].Theexperiments wereperformed underaninert argonatmosphere. Thecellwas heatedusingaprogrammablefurnaceandthetemperatureswere measuredusingachromel-alumelthermocouple.

Threeeutecticmixtures(CarloErbaReagents99.99%)wereused as electrolyteand selectedaccording totheir _{fluoroacidity}and relativeeasyhandling:

- a basic bath: LiF-NaF-KF (46.5-11.5-42 mol%, melting point 452#_C),

- anacidbath:LiF-CaF2(79.2-20.8mol%,meltingpoint767#C),

- an intermediate bath: LiF-NaF (61-39 mol%, melting point 652#_C).

Allthe solvents were initially dehydrated by heating under vacuum from ambient temperature up to their melting point during4days.Hafniumionswereintroducedintothebathinthe formofhafniumtetrafluorideHfF4powder(SigmaAldrich99.9%).

Silverwires(1mmdiameter,Goodfellow)wereusedasworking electrode.Thesurfaceareaoftheworkingelectrodewasdetermined aftereachexperimentbymeasuringtheimmersiondepthinthe bath.Theauxiliaryelectrodewasavitreouscarbonrod(V25,3mm diameter)withalargesurfacearea(2.5cm2_{).Thepotentialswere}

referredtoaplatinumwire(0.5mmdiameter,Goodfellow)actingas aquasi-referenceelectrodePt/PtOx/O2"[20].

AlltheelectrochemicalstudieswereperformedwithanAutolab PGSTAT30potentiostat/galvanostatcontrolledbyacomputerusing theresearchsoftwareGPES4.9.

3. Resultsanddiscussion 3.1.Hf(IV)reductionmechanism 3.1.1.Cyclicvoltammetry

Hf(IV)ionsreductionbehaviourwasinvestigatedinmolten LiF-NaFinthe750-900#_{Ctemperaturerange.Ashafniumandsilver}

Fig.1.Fluoroacidity scaleof various eutectic mixtures. Fluoroacidity scaleof fluoridecompounds.

arenotmiscibleatoperatingtemperature,silverwasselectedasan inertworkingelectrode[21].

Fig. 2 shows typical cyclic voltammogram of LiF-NaF-HfF4

(0.69molkg"1_{) on silver at 750}#_{C and 100mVs}"1_{. Only one}

reduction peak and its corresponding reoxidation peak are observed at -1.43 and -1.25V vs. Pt respectively. The signal crossingbetweenforwardand backwardscansis typicalofthe formationofasolidphaseattheelectrode(crossover).Inaddition, theasymmetricalshapeofthereoxidationpeakischaracteristicsof ametaldepositeddissolutioninthecathodicrun(strippingpeak). AspresentedintheinsetofFig.2,novariationsofpeakpotentialat differentscan rateprovedthatHf(IV)electrochemicalreduction processisreversible[22].Thus,accordingtoequationsofcyclic voltammetryforareversiblesoluble/insolublesystem,thenumber of exchanged electrons can be calculated by measuring the differencebetweenthepotentialpeakandthehalfpeakpotential [22]: jEp" Ep 2j¼ 0:77 RT nF (7)

whereEpisthepeakpotential(V)andEp/2isthehalfpeakpotential

(V),Rtheidealgasconstant(8.314Jmol"1_K"1_{),Tastheabsolute}

temperature(K),nthenumberofexchangedelectronsandFthe Faradayconstant(Cmol"1_).

In this study, the difference was found to be 18&2mV, correspondingtoavalueof3.8&0.3exchangedelectrons.

ThelinearrelationshipbetweenHf(IV)reductionpeakcurrent density at -1.43V vs. Pt and the square root of the scan rate presented in the inset of Fig. 2, proved that electrochemical reductionprocessiscontrolledbyHf(IV)diffusion[22].Diffusion coefficients were determined using Berzins-Delahay equation (Eq.(8))forareversiblesoluble/insolublesystem[23]:

J_p¼0:61nFCðnFDv RT Þ

1=2 ₍₈₎

where Jp is the peak current density (Am"2), C the solute

concentration (mol m"3_{), D the diffusion}

coefficient (m2 _s"1₎

and

y

thepotentialscanrate(Vs"1).

At750#_{C,avalueof(3.5&0.3)x10}"9_m2_s"1_{forDwasfound.}

Serrano [18] and Poinso [13] found a Hf(IV) ions diffusion coefficientinNaCl-KCl-NaFat750#_{Cequalto2.2and4.9)10}"9

m2_s"1_{respectively.}

DiffusioncoefficientsweredeterminedinLiF-NaFinthe800– 900#_{C temperaturerangeand are presentedinTable 1. Results}

showedthatDandTfollowanArrheniuslawtype,therelationship isexpressedasfollows:

InD¼"EA

RTþInDo¼" 7863:4

T "11:8 (9)

FromEq.(9),theactivationenergyisfoundtobe65.4&0.7kJ mol"1_{.Thisvalueisbythesameorderofmagnitudewithprevious}

studies,asforinstance213kJmol"1_{forSi(IV)ions[4]or48.9kJ}

mol"1_{forNd(III)ions[24].}

3.1.2.Squarewavevoltammetry

The square wave voltammetry was used to confirm more accuratelythenumberofexchangedelectronsofHf(IV)reduction thancyclicvoltammetry.

Fig.3showsasquarewavevoltammogramoftheLiF-NaF-HfF4

(0.69molkg"1_{)systemonsilverelectrode at750}#_{C and9Hz.A}

singlepeakaround-1.40Vvs.Ptisobserved,inagreementwith cyclicvoltammetryandpresentinganasymmetricGaussianshape characteristicofasoluble/insolublesystem[25].

Theasymmetryofthepeakisduetothecurrentlessnucleation overvoltage needed for the formation of the first crystals of metallichafniumattheelectrodesurface.Thisphenomenondelays theappearanceofthefaradiccurrent,leadingtoasignaldistortion [26]. The nucleation overvoltage

h

(V) can be determined by

measuringthewidthatmid-height ofthetwohalfpeaksusing Eq.(10):

h

=2(10)(W2-W1) (10)

The obtained value,

h

=32&2mV, is in agreement with previous overvoltage values for metals deposition available in theliterature[27].

After checking in the frequency domain that the reduction reactionofHf(IV)hasareversiblebehavior(linearvariationofthe peakdifferentialcurrentdensitywiththesquarerootoffrequency (cf. inset Fig. 3)), the number of exchanged electrons was determinedfrom themeasurement of thewidthat mid-height W1/2(V)carriedoutonanisolatedpeak.

However,togetridofthenucleationprocess,thewidthat mid-heightW1/2measurementhasbeendeterminedbydoublingthe

half-widthatmid-heightW2(V)oftheGaussiancurve(Eq.(11)).

Thismethodologyhasalreadybeenvalidatedinmoltenfluorides fordifferentmetalsstudies[24].

W1=2¼2W2¼3:52 RT nF (11) -0.2 -0.1 0.0 0.1 0.2 0.3 -1.5 -1 -0.5 0 0.5 1 1.5

J/

A

cm

-2

E vs. Pt/V

-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0 0.2 0.4 0.6 0.8 Jp /A cm -2 υ1/2_/V1/2_s-1/2 -1.45 -1.44 -1.43 -1.42 -1.41 -1.4 -1.5 -1 -0.5 0 Ep v s. P t/ V log υ/V s-1

Fig.2.CyclicvoltammogramofLiF-NaF-HfF4(0.69molkg"1)at100mVs"1and T=750#_{CWorkingEl.:Ag;AuxiliaryEl.:vitreouscarbon;ReferenceEl.:PtInsets:} LinearrelationshipofHf(IV)reductionpeakcurrentdensityversusthesquareroot ofthescanningpotentialrate.Hf(IV)reductionpeakpotentialversusthelogarithm ofthescanningpotentialrate.

Table1

Diffusioncoefficient(D),kinematicviscosity(y)andSchmidtnumber(Sc)ofHf(IV) ionsfordifferentfluoridemediaatdifferenttemperature.

T(#_{C) LiF-NaF-KF LiF-NaF LiF-CaF} 2 Molarcomp. 46.5–11.5–42 61–39 79.2–20.8 109_D(m2_s"1₎ 800 5.34 4.96 1.49 850 9.25 6.80 1.94 900 16.66 9.46 2.48 107_y(m2_s"1₎ 800 7.8 12.1 30.2 850 6.5 10.8 29.6 900 5.6 9.7 29.2 Sc=y/D 800 145 245 2028 850 71 158 1528 900 34 102 1178

82&4mVwasfoundforW1/2,correspondingtoanumberof

exchangedelectronsof3.8&0.2.

Theresultsobtainedbycyclicandsquarewavevoltammetries allowconcludingthatHf(IV)ionsreductioninmoltenfluoridesisa one-stepprocessexchanging4electronsunderdiffusioncontrol. 3.1.3.Chronopotentiometry

To confirm the diffusion-controlled process of the Hf(IV) electrochemicalreduction,chronopotentiogramswereperformed. Fig.4showsthevariationofthechronopotentiogramsofHfF4with

theappliedcurrentonsilverelectrodeat750#_{C inLiF-NaF-HfF}

4

(0.05mol kg"1_{). These curves exhibit a single wave, obviously}

associatedtothereductionofhafniumionsinthepotentialrange (+-1.4Vvs.Pt)alreadyobservedonvoltammograms.

According to the data plotted in the inset of Fig. 4, Sand's equation(Eq.(12))wasverified[22]:

I

t

1=2

C ¼ nFSD1=2

p

1=2

2 ¼constant

¼0:160&0:004Acm3_s"1=2_mol"1 ₍₁₂₎

whereIistheappliedcurrent(A),

t

thetransitiontime(s),andS

theimmergedelectrodesurfacearea(m2_).

Thushafniumreductionprocesswasconfirmedtobelimitedby the diffusionof Hf(IV) ionsin solution. Its diffusioncoefficient calculated using Eq. (12) and assumingthat n=4 is:(3.3&0.2)

x10"9_m2_s"1_at750#_{C,inaccordancewithourpreviousresultby}

cyclicvoltammetry((3.5&0.3)x10"9_m2

s"1_).

The reversal chronopotentiogram presentedin Fig. 5 proves thataninsolublecompoundisformedonsilverelectrodeduring thecathodicrun,asthetransitiontimeofthereductionwaveis veryclosetotheoxidationtime(

t

red+

t

ox+0.6s)[28].Thisresult

confirmsonemoretimethatthereactionleadstoHfmetalonthe workingelectrode.

Allthese electrochemical techniques allow to concludethat reductionofHf(IV)ionsaddedasHfF4inmoltenfluorides:

- isaone-stepprocessexchanging4electrons, - iscontrolledbydiffusionofHf(IV)ions, - andleadstotheformationofmetallichafnium.

As it is stated in thelitterature that cations coordinancyis stronglyinfluenced byfluoroacidity,reductionmechanismofHf (IV) ionsinmoltenfluoridescanbewrittenasinEq.(13): HfF4+xx"+4e"ÐHf+(4+x)F" (13)

3.2.Diffusioncoefficientsandmasstransportapproach

The effect of _{fluoroacidity} on Si(IV) and B(III) ions mass transportswaspreviouslydemonstrated[5].Resultsshowedthat anincrease ofthefluoroacidityleadstoa decreaseof diffusion coefficientsduetocoordinancyandbridgingsolventphenomena. Thesephysico-chemicalsparametersleadtoanincreaseofsolvent viscosity with fluoroacidity. As a consequence solutes mass transportbecomemoredifficult.

In order to confirm these resultson a simple electroactive species,investigationonhafniumsolutewasperformedinthree moltensystemswithdifferentfluoroacidities:

- abasicbath:LiF-NaF-KF, - anacidbath:LiF-CaF2,

- andanintermediatebath:LiF-NaF.

Diffusion coefficients of Hf(IV) ions were determined by calculating the average of cyclic voltammetry (Eq. (8)) and chronopotentiommetry (Eq. (11))values. Results are presented inTable1wheresolventsaresortedfromthemorebasictotheleft tothemoreacidtotheright.

ResultsonHf(IV)ionsshowthatdiffusioncoefficientsdecrease with fluoroacidity whatever the temperature.However for the lowesttemperature,theminordifferencesbetweenvaluesandthe -0.18 -0.16 -0.14 -0.12 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0

δ

j/

A

cm

-2

E vs. Pt/V

W

2

W

1 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0 2 4 6 8 10 δ j/ A cm -² f1/2_/Hz1/2

Fig.3.SquarewavevoltammogramofLiF-NaF-HfF4(0.69molkg"1)atfrequency= 9HzandT=750#_{CWorkingEl.:Ag;AuxiliaryEl.:vitreouscarbon;ReferenceEl.:Pt} Inset:LinearrelationshipofHf(IV)reductionpeakcurrentdensityversusthesquare rootofthefrequency.

Fig.4.TypicalchronopotentiogramswiththeintensityofthesystemLiF-NaF-HfF4 (0.05molkg"1_{) at T=750}#_{C Working El.: Ag; Auxiliary El.: vitreous carbon;} ReferenceEl.:Pt. -1.75 -1.5 -1.25 -1 -0.75 -0.5 0 0.5 1 1.5 2

E

v

s.

P

t/

V

Time/s

τred= 0,591s τox= 0,610s

Fig.5.ReversalchronopotentiogramofHfF4(0.083molkg"1)inLiF-NaF,J=&207

mAcm"2_atT=750#_{CWorkingEl.:Ag;AuxiliaryEl.:vitreouscarbon;ReferenceEl.:}

uncertaintyofmeasurement(&3)10"10_m2_s"1_{)donotallowthe}

discriminationofsolventsfluoroacidity.

Itisobviousthattheionicradiusoftheelementinsolutionand itscoordinancyaffecttheabilityofthespeciestomovethroughthe solution(representedbyD).Inhighlyacidbaths,wherethecontent offreeF"_{islow,hafniumcomplexeshavetoshareoneormore}

fluorinebybridging,andthenform,bypolymerization,largersizes species,whichslowsdownthemasstransportinsolution.

AsthehaniumHfF4+xx"coordinancyisafunctionof

fluoroa-cidityand cannot bedeterminebyelectrochemistry, thesolute transportresultshavetotakeinaccountthesolventcontribution throughitsviscosity:aviscosityincreaseleadstoamoredifficult solutemasstransport.

Kinematicviscosities

y

(inm2s"1)definedastheratiobetween

dynamicviscosity

m

(inkgm"1s"1)anddensity

r

(inkgm"3)were

calculatedfromtheMoltenSaltsHandbookvalues[29].Notethat data for LiF-CaF2 viscosity at operating temperatures are not

availableinliterature.Then,viscositywasextrapolatedfromthe work of Robelin et al. as thesum of the _fluoridescompounds viscosities balanced by their molar fractions in the eutectic mixture[30].ThesevaluesaregatheredinTable1.

It shows that molten _fluorides viscosity increase with fluoroacidity, and could be correlated to a bridging phenomen by sharing available free fluorides, modifying the molten salt structure and forming a network-like liquid. This behaviour is particularlyimportantwiththepresenceofcalcium,which was demonstratedasoneofthemoreacidcompounds(Fig.1a).

InordertotakeintoaccounttheeffectoftheviscosityonHf(IV) diffusioncoefficients,theadimensionalSchmidtnumber(Sc=

y

/D)

wascalculated tocharacterizethe soluteglobalmass transport throughitsenvironment.ThecalculatedScnumberaregatheredin Table1.Atagiventemperature,theresultsshowedthatScforHf (IV) ionsincreaseswithfluoroacidity, allowing tosort melts in regardoftheirfluoroacidity.

Thus relationships between _{fluoroacidity,} bridging _fluorines andviscositydirectlyimpactmasstransportofasimplespeciesin solution.Thedeterminationofdiffusioncoefficientsofaspecies, whichisdirectlyaffectedbyacumulativeeffectofviscosityand ionicradiusofthesolute,allowstodiscriminatemoltenfluorides mediaasa function of fluoroacidity.However, ifthe difference betweenD values is very low, the Schmidt number by taking accountviscosityincreasethisdifference,asforinstancebetween LiF-NaF-KFandLiF-NaFat800#_{Cwherethedifferenceisaround7%}

onDand69%onScinthesameconditions. 4. Conclusion

TheHfF4electrochemicalbehaviourwasinvestigatedinmolten

fluorides. By cyclic voltammetry, square wave voltammetry, chronopotentiometry and reversal choronpotentiometry, Hf(IV) ionsreduction mechanism was demonstrated tobe a one step processexchanging4electronsunderHf(IV)ionsdiffusioncontrol leadingtotheformationofhafniummetal:HfF4+xx"+4e"ÐHf+

xF".

Diffusion coefficients of Hf(IV) were determinated in three moltenfluoridessolvents,withdifferentfluoroacidities,between 800 and 900#_{C. Hf(IV) diffusion coefficients decrease with}

fluoroacidity:thisphenomenumisduetoacumulativeeffectof solventviscosity(whichislinkedtobridgedfluorines)andionic radiusofthesolutewithfluoroacidity. Asviscosityreferstothe solventanddiffusioncoefficienttothesolute,theSchmidtnumber wascalculatedinordertotakeintoaccountthesetwoparameters. Resultsshowed that Sc increases withfluoroacidity, in a much moresensitivewaythanD.

Thismasstransportapproachconsistinginthedetermination of thediffusion coefficient and the calculation of the Schmidt number is easier to set up than kinetic rates determination. Moreover,thisuniversalmethodcanextendedtoallelectroactive speciesandtoallbathfluoroacidity.

References

[1]D.Elwell,Electrowinningofsiliconfromsolutionsofsilicainalkalimetal fluoride/alkalineearthfluorideeutectics,Sol.Energ.Mater.5(1981)205. [2]E.W.Dewing,Theeffectsofadditivesonactivitiesincryolitemelts,Metall.

Trans.B20B(1989)657.

[3]B. Gilbert, E. Robert, E. Tixhon, J.E. Olsen, T. Østvold, Structure and ThermodynamicsofNaF-AlF3MeltswithAdditionofCaF2andMgF2,Inorg. Chem.35(1996)4198.

[4]A.L. Bieber, L. Massot, M. Gibilaro, L. Cassayre, P. Chamelot, P. Taxil, Fluoroacidityevaluationinmoltensalts,Electrochim.Acta56(2011)5022. [5]M.Kergoat,L.Massot,M.Gibilaro,P.Chamelot,Investigationonfluoroacidity

ofmoltenfluoridessolutionsinrelationwithmasstransport,Electrochim. Acta120(2014).

[6]C.Bessada,A.-L.Rollet,A.Rakhmatullin,I.Nuta,P.Florian,D.Massiot,Insitu NMRapproachofthelocalstructureofmoltenmaterialsathightemperature, C. R.Chim9(2006)374.

[7]A.-L.Rollet,S.Godier,C.Bessada,HightemperatureNMRstudyofthelocal structureofmoltenLaF3-AF(A=LiNa,KandRb)mixtures,PCCP10(2008) 3222.

[8]C.Bessada,A.Rakhmatullin,A.-L.Rollet,D.Zanghi,HightemperatureNMR approachofmixturesofrareearthandalkalifluorides:Aninsightintothelocal structure,J.FluorineChem.130(2009)45.

[9]C.F.BaesJr.,ApolymermodelforBeF2andSiO2melts,J.SolidStateChem.1 (1970)159.

[10]V.Dracopoulos,J.Vagelatos,G.N.Papatheodorou,Ramanspectroscopicstudies ofmoltenZrF4-KFmixturesandofA2ZrF6A3ZrF7(A=LiKorCs)compounds,J. Chem.Soc.DaltonTrans.(2001)1117.

[11]M.Salanne,C.Simon,P.Turq,P.A.Madden,Conductivity-Viscosity-Structure: UnpickingtheRelationshipinanIonicLiquidy,J.Phys.Chem.B111(2007) 4678.

[12]D.Williams,L.Toth,K.Clarno,AssessmentofCandidateMoltenSaltCoolants for the Advanced High-Temperature Reactor (AHTR), ORNL/TM-2006/12 (2006).

[13] J.Y.Poinso,Ph.DThesis,(1993).

[14]J.Y. Poinso, S.Bouvet, P. Ozil, J.C. Poignet, J. Bouteillon, Electrochemical ReductionofHafniumTetrachlorideinMoltenNaCl-KCl,J.Electrochem.Soc. 140(1993).

[15]N.Adhoum,L.Arurault,J.Bouteillon,A.Cotarta,J.C.Gabriel,J.C.Poignet, ElectrochemistryofRefractoryMetals:Hf,Mo,Cr,in:D.Kerridge,E.Polyakov (Eds.),RefractoryMetalsinMoltenSalts,vol.53,Springer,Netherlands,1998, pp.61–72.

[16]D.R.Spink,C.P.Vijayan,HafniumElectrowinningStudies,J.Electrochem.Soc. 121(1974).

[17]C.Guang-Sen,M.Okido,T.Oki,Electrochemicalstudiesofzirconiumand hafniuminalkalichlorideandalkalifluoride-chloridemoltensalts,J.Appl. Electrochem.20(1990).

[18] K.Serrano,Ph.DThesis,UniversitéToulouseIII-PaulSabatier,(1998). [19]L.Massot,P.Chamelot,F.Bouyer,P.Taxil,Electrodepositionofcarbonfilms

frommoltenalkalinefluoridemedia,Electrochim.Acta47(2002)1949. [20]A.D.Graves,D.Inman,Adsorptionandthedifferencialcapacitanceofthe

electricaldouble-layeratplatinum/halidemetalinterface,Nature208(1965) 481.

[21]H.Okamoto,Ag-Hf(silver-hafnium),J.PhaseEquilib17(1996).

[22]A.J. Bard, L.R. Faulkner, Electrochemical Methods: Fundamentals and Applications,2ed.,JohnWiley&Sons,NewYork,2001.

[23]T.Berzins,P.Delahay,OscillographicPolarographicWavesfortheReversible DepositionofMetalsonSolidElectrodes,J.Am.Chem.Soc.75(1953). [24]C.Hamel,P.Chamelot,P.Taxil,Neodymium(III)cathodicprocessesinmolten

fluorides,Electrochim.Acta49(2004).

[25]L.Ramaley,M.S.Krause,Theoryofsquarewavevoltammetry,Anal.Chem.41 (1969).

[26]G.J.Hills,D.J.Schiffrin,J.Thompson,Electrochemicalnucleationfrommolten salts—I.Diffusioncontrolledelectrodepositionofsilverfromalkalimolten nitrates,Electrochim.Acta19(1974).

[27]C.Nourry,L.Massot,P.Chamelot,P.Taxil,Dataacquisitioninthermodynamic andelectrochemicalreductioninaGd(III)/Gdsystem inLiF–CaF2media, Electrochim.Acta53(2008).

[28]H.B. Herman, A.J. Bard, CyclicChronopotentiometry.Diffusion Controlled ElectrodeReactionofaSingleComponentSystem,Anal.Chem35(1963). [29]G.J.Janz,MoltenSaltsHandbook,ElsevierScience, 2013.

[30]C.Robelin,P.Chartrand,Aviscositymodelforthe(NaF+AlF3+CaF2+Al2O3) electrolyte,TheJournalofChemicalThermodynamics43(2011).