On the mechanism of the P2–Na0.70CoO2→O2–LiCoO2 exchange reaction—Part II: an in situ X-ray diffraction study

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On the mechanism of the P2–Na0.70CoO2

→O2–LiCoO2

exchange reaction-Part II: an in situ X-ray diffraction

study

Frédéric Tournadre, Laurence Croguennec, P. Willmann, Claude Delmas

To cite this version:

Frédéric Tournadre, Laurence Croguennec, P. Willmann, Claude Delmas. On the mechanism of the

P2–Na0.70CoO2

_{→O2–LiCoO2 exchange reaction-Part II: an in situ X-ray diffraction study. Journal}

of Solid State Chemistry, Elsevier, 2004, 177 (8), pp.2803-2809. �10.1016/j.jssc.2004.04.028�.

�hal-00145514�

On the mechanism of the P2-Na

0

.

70

CoO

2

→

O2-LiCoO

2

exchange reaction, Part II : an in situ x-ray diraction study

Tournadre F., Croguennec L., WillmannP.,DelmasC.

May 10,2007

Abstract

AmodelwasproposedtodescribetheexchangereactionofsodiumbylithiuminP2crystals. TheexchangecAmodelwasproposedtodescribetheexchangereactionofsodiumbylithium in P2 crystals, it was based rst on the formation of nucleation centers and then on the growth of O2 domains inP2 crystals from these nucleation centers. This studyhas shown that depending onthe ratio between the growing and nucleation speeds, O2, O6 or faulted structures are obtained andthat this modelallows agood analysis of theexchange process. XRD patterns simulation and their comparison with that of experimental O2-LiCoO

2

have shownthattherewasalmostnodefectsintheO2-LiCoO

2

structureobtainedbyion exchange in water. Therefore, this study has shown that the growth of the O2 domains in the P2-Na

0

.

70

CoO

2

crystalsisfasterthantheformationofnucleationcenters. This P2-Na

0

.

70

CoO

2

→

O2-LiCoO

2

exchange reaction was also studied in situ by X-ray diraction;simulationsofkeyXRDpatternsbyP2-O2intergrowthswerealsoachieved.Itwas shown,ingoodagreementwiththesimulations,thatthegrowthofO2domainswasfasterthan the formationof thenucleation centers and kinetically activated bya P2-Na

0

.

70

CoO

2

→

P2*-Na

∼0.50

CoO

2

phasetransition. Forthosereasons,theP2-Na

0

.

70

CoO

2

→

O2-LiCoO

2

exchange reactioninwaterleadstoanO2phase,withanalmostidealpacking.

1 Introduction

Theion exchange reactionin theNa

x

MO

2

phasesis an alternativewayto synthesize new lamel-lar lithiated phases. O2-LiCoO

2

was the rst metastable phase obtained by ion exchange from sodiumtolithiumreactioninP2-Na

0.70

CoO

2

[1]. InadditiontoLiCoO

2

,T

]

2-Li

2/3

[Ni

1/3

Mn

2/3

]O

2

[2] and recently found T

]

2-Li

2/3

[Co

2/3

Mn

1/3

]O

2

[3]are well crystallized. All other phases: O2-LiMnO

2

[4],Li

0.70

[Mg

0.30

Mn

0.70

]O

2

[5] andthosebelongingtotheLi

2/3

[Ni

1/3−x

Co

x

Mn

2/3

]O

2

and Li

2/3

[Ni

1/3−x/2

Co

x

Mn

2/3−x/2

]O

2

familiesexhibitmoreorlessstackingfaultedstructures[6]. Chow-darietal. werealsointerestedinO2-typestructuresandstudiedtheinuenceonthe electrochem-icalperformances ofthechemicalreintercalationoflithium ionsin theLi

2/3

MO

2

structures lead-ingto structuressuchasLi

(2/3+x)

[Ni

1/3

Mn

2/3

]O

2

andLi

(2/3+x)

[Co

0.15

Mn

0.85

]O

2

[7, 8]. Tobetter understand the exchange reaction mechanism we attempt to study the exchange reactionof the P2-Na

0.70

CoO

2

phase.

Inthecompanionpaper(PartI),wehaveproposedastructuralmodelfortheP2

→

O2transition [9]. Thedrivingforceofthistransitionistheformationofoctahedralenvironmentsforlithiumions which are obtained when oneslab overtwo glidesby (2/3,1/3, 0) or by (1/3, 2/3,0) in the P2 structure. TheexchangereactionconsistsontheformationofO2-typenucleationcentersandthen on their growth into the P2 crystals. The existence of two dierent gliding vectors should lead to stackingfaulted structures that can be simulated using theDIFFaX software. Three series of simulationof stackingfaulted structures havebeenachieved, considering previoushypothesesfor thenucleation: therst onewas a simpliedcase to explainthe nucleation-growingphenomenon withonlyonetypeofslabsconcernedbythenucleation,thesecondonewasthegeneralcase(two typesofslabsaspossiblenucleationcentersandtwopossibleglidingvectors(2/3,1/3,0) or(1/3, 2/3,0))andthethird onewasthegeneralcasewithpossibilitiesofsodiumremainingin thenal structure and, therefore, of prismatic(P)-typedefects. This study has shown that dependingon theratiobetweenthegrowingandnucleationspeeds,O2,O6orfaultedstructuresareobtainedand

experimentalXRDpatterns forO2-LiCoO

2

hasnallyshownthatinthat specic casethegrowth ofO2 domainsin P2crystals isfaster thantheformation ofnucleationcenters, leadingthus to a closelyidealO2phasewithlargeO2 blocksanddefectsat theboundariesbetweentheseblocks.

We will now present the in situ X-ray diraction study of the exchange reaction of sodium by lithium in P2-Na

0.7

CoO

2

and, especially, the mechanisms proposed to explain the P2

→

O2 transition. Wewill then check if themodel proposed for the nucleation in the companionpaper (PartI)from thestudyofthenalmaterialisingoodagreementwiththewholereactionprocess.

2 Experimental

2.1 X-ray diraction

TheXRDpatternsrecordedinsituduringtheionexchangeofsodiumbylithiuminP2-Na

0.70

CoO

2

wereobtainedusinganINELCPS120curvepositionsensitivedetectorwithCoK

α

radiation. Note thatinordertofacilitatethecomparisonwithXRDdataobtainedonotherdiractometers,allthese XRDpatternswillbereportedusingtheCuK

α

radiationasreference. Ahome-madesample-holder, representedinFig. 1andpreviouslydevelopedforin situ XRD studiesof alkalinebatteries upon cycling,wasusedtoperformthisexchangein situ. Itscavitybelowthereferenceplanewasusedas atankforthesaltsolutionanditsKapton

R

windowallowedtorecordXRDpatternswithoutany contact withthe air and, therefore, to preventany carbonatation of thesalt solutionduring the experiment. Amixtureof100mgofP2-Na

0.70

CoO

2

and10mgofNipowder(usedasreferenceto correctforthesampledisplacement)waspressed(1tonduring5min)ona30

×

5mm

2

nickelfoam inanargon-lleddrybox. ThissamplewasthenplacedintheXRDsample-holder,inthereference plane,in contactwitha5Maqueous solution(Li/Na

≈

5)ofLiCl|LiOH (1:1). A totalof64 XRD patternswasrecordedduring 16h, with10minacquisitiontimeforeachXRDpattern and5min waiting time betweentwodata recording. Note that the use of acurvedetector to perform this experimentallowedto get XRD patterns with agood resolution, in short acquisition times. The accuratedetermination of thepeak positions wasdoneusing thePROFILE peak-searchprogram [10], assumingapseudo-voigtline shape. Thesize of thecrystallites(assumedto beequalto the coherencelength) wasestimated usingtheScherrerformula. Inorderto determinethe apparatus contributionto theline broadening,theverywellcrystallizedNa

2

Ca

3

Al

2

F

14

compound wasused asreference.

ThesimulationofXRDpatternswasdoneusingtheDIFFaXprogram[11],alltheexplanations weregivenin thecompanionpaper(PartI) [9].

2.2 Electrochemistry

Electrochemicalmeasurementswerecarriedoutatroomtemperature(25

◦

C)fortheLi//Li

x

CoO2, Na//Na

x

CoO

2

and Li//Na

x

CoO

2

cells. The positive electrodes consisted of a mixture of 88% byweightofactivematerial, 2%of PTFE(polytetrauorethylene) and 10%ofamixture (1:1)of graphiteandcarbonblack. Theelectrolyteusedforthelithium batterieswas1MLiPF

6

dissolved inamixtureofpropylenecarbonate(PC),ethylenecarbonate(EC)anddimethylcarbonate(DMC) (1:1:3byvolume). Theelectrolyteusedforthesodiumbatterieswas1MNaClO

4

dissolvedinPC. Thecells,assembledinanargon-lleddrybox,werecycledat400

µ

Acm

−2

(activeMASS=15mg, C/20rate).

3 Results

3.1 General description

Fig. 2 shows the XRD patterns obtained during the exchange reaction: it clearly appears that twodierentstepsoccurduringthereaction. Intherststep,duringtherst4h, theamountof O2phaseis almost negligible,then at thebeginningof thesecond stepit increasessuddenlyand simultaneouslytheinterslabdistanceoftheremainingP2phaseincreases. This eectisevidenced ontheenlargementoftheXRDpatterns(14.5-19

◦

XRD patterns,andonthecontraryto whatisobservedontheexsituXRD pattern,all the(00l) lines aremore intense thanexpecteddue to theimportantpreferentialorientation caused by the samplepreparation(powderpressedonthenickelfoam). TheXRD patternsrecordedjust before andjustaftertheP2

→

P2*phasetransitionarepresentedinFig.3;after5hallthediractionlines oftheO2phasearepresent,butwithaverysmallintensity. TheP2*phasecanbeindexedas P2-Na

0.70

CoO

2

intheP6

3

/mmcspacegroupwitha

hex.

andc

hex.

cellparameters,respectively,smaller and larger than those observed for the starting P2-Na

0.70

CoO

2

phase (Table 1). This evolution suggeststhat there is an oxidationof P2-Na

0.70

CoO

2

. Indeed, the removalof sodium ions from the structure induces increasing electrostatic repulsions between adjacent oxygen layers through the interslab space and thus an increase of c

hex.

. Furthermore, the oxidationof the cobalt ions induces adecrease of themetal?metal distance and, therefore, of a

hex.

. By comparison with the resultsobtainedelectrochemicallybyBraconnieretal. fortheNa//P2-Na

x

CoO

2

system,itcanbe assumedthat P2*correspondsto Na

0.5

CoO

2

[12]. Note that the residualP2 phaseobservedby Carlieretal. after exsituexchangereactionsin water,hexanolandmethanol,correspondsalsoto theP2*phase(seeFig. 3inRef. [13]). Attheendoftheinsituexperiment,theP2*phaseremains inalargeramountthanattheend oftheexchangemadeexsitu,suggestingthatthereactionwas nottotallyachieved. Thisbehaviorcanresultfrom thesmallerexcessofLiCl|LiOHused inthein situexperimentversustheclassicalexchange one.

TheevolutionoftheFWHMof(002)diractionlines,ofthevariousphasesversusthereaction timeisgiveninFig. 4. NotethatthoseFWHMsgivedirectlythecoherencelengthperpendicularly to the slabs. Fig. 5 shows thus the evolution of the average size of the O2 domains (given in numberofslabs)during theexchangereaction. The slopeof theline representedin each domain (beforeandaftertheP2

→

P2*phasetransition)isrelatedtothegrowthrateoftheO2domains. At thebeginningoftheexchangereaction,theFWHMofthe(002)P2diractionlineremainsalmost constant, the coherence length is equal to 1400 Å which corresponds to about 250 slabs. This value must be compared to the coherence length of the starting P2 phase before the exchange. Inthis case, theScherrer formulagivesacoherence lengthof 4400 Å (around800slabs) in good agreementwith theScanning Electron Microscopystudy, which showsthat theaveragethickness ofNa

0.7

CoO

2

crystalliteswithoutapparentdefectsiscloseto5000Å(correspondingto 900slabs). The accuracy of this coherence length value is verysmall because the involved FWHM value is close to the limit one to use the Scherrer formula. Nevertheless, the comparison of the values before and afterexchange showsthat theP2domain thicknessdecreasesveryquicklyat thevery beginningoftheexchangereaction,thenitremainsalmostconstantduringthefollowing4h. The rstXRD pattern hasbeen recorded1hafter thebeginningof theexchangereaction. Thishour correspondstothetimerequiredtoassemblethecellandtostarttheexperimentaftertheexchange solutionintroduction. OntherstXRDpattern,the(002)diractionlineoftheO2phaseappears clearly. It is verybroadand it corresponds to 10slabs. Then, this (002) diractionline narrows continuouslyin an almost linearprocess. After 5h, it corresponds to O2domains with 30slabs. Allthese resultsgiveonlyatendency,becauseitiswellknownthat theScherrerformulaisavery crudemodel. TheP2

→

P2*phasetransitionoccursjustafter5hofreactiontimeandisassociated toasuddenincrease,immediately followedbyadecrease,oftheFWHM ofthe(002)

P 2

line. This behaviorsuggeststheformationofanintermediateP2phasewithadistributionofdistancesalong thec-axis. Atthistransition,theFWHMofthe(002)

O2

peakdecreasessuddenlyandthendecrease slowlyuntiltheendoftheexchangereaction. Asshownbythestrongincreaseofthelineintensity, asignicantpartoftheO2-LiCoO

2

phaseisthusformed after 5h, onlytheproportionoftheO2 and P2* phases changes afterwards. As shown in Fig. 5by the comparison of the slopesof the twolines, after theP2

→

P2* phasetransition the growth rateis highly increased (i.e. four times higherthantheinitialone). Itshould benotedthat aftertheformationoftheO2-LiCoO

2

phase, theFWHMofthe(002)

P 2

*lineincreasescontinuously. Asexplainedjust before, thisevolutionis certainlyrelatedto thesize oftheresidualsmallP2*domainsin O2-LiCoO

2

crystals.

Duringthisionexchangereaction,onlyslabglidingsareattheoriginoftheP2-Na

0.70

CoO2

→

O2-LiCoO

2

phasetransition.Therefore,insuchacase,aP2-O2intergrowthwithacontinuouschange intheratiobetweenthetwophasescouldexplaintheevolutionoftheFWHMs. Notethattheoverall numberofslabsremainsalmostconstant(not,vert,similar300slabs)aftertheinitialnucleationof thereaction.

3.2 Simulation of P2

→

O2 intergrowths during reaction

Inorder to determineifsmall domains ofO2 in P2-Na

0.70

CoO

2

crystalsare largeenoughfor the coherence length to induce diraction and thus observation of the (002)

O2

diraction line, XRD patterns associated to P2-O2 intergrowths were simulated using the DIFFaX software. In the companionpaper(PartI), wehaveshownthat thesmall amount ofdefects foundin the O2nal phaseresultedfrom ahighgrowthspeedversusthenucleation one. Therefore, thesimulationsof P2-O2intergrowthsweredoneassumingtheexistenceofidealO2domainswithintheP2structure. StartingfromaP2crystalwith about250slabs,thenumberofslabsinvolvedintheO2structure wasgradually increased. In thepreviouspaper,wehavereported in detailthe way todescribea givenpackingto simulate its XRD pattern using the DiFFaXsoftware. Fig. 6presents thus the idealP2phasepackingandanexampleofP2-O2intergrowth,withtheassociatedstackingvectors (

R

ij

) and probabilities (

α

ij

). Tobuilt up the P2-O2 intergrowth using DIFFaX, three AB-type slabsandthreeBA-typeslabswereused: oneofeachfortheP2description(slabs(1)and(2))and theothersforthetwoO2descriptions(growthfrom aBA-typeslab(slabs(3) and(4))andfrom AB-typeslab(slabs(5)and(6))). Inordertotakeintoaccountthedierenceininterslabdistances betweenP2andO2,thestackingvectorsare(

α

,

β

,c

hex.(P 2)

/2)and(

α

',

β

0

,c

hex.(O2)

/2)inP2and O2domains, respectively. As shownin Fig. 6,theprobabilityassociatedtothe(1)

→

(6)and the (2)

→

(3) transitions xes the average size of the P2 and O2 domains, because these transitions initiatethegrowthofanO2domainintheP2crystals. Withaprobabilityof0.4%(1/250),thereis onechanceevery250P2-typeslabstobegintheformationofanewO2domain,ingoodagreement withan average sizeof 250slabsfor theP2domains (Fig. 4). Forthe O2domains, oneoverthe twotransitions is associated to aprobabilityequal to one ((6)

→

(5) or (3)

→

(4))and the other ((5)

→

(6)or(4)

→

(3))toaprobabilityequalto(1-1/(n/2)),withntheaveragenumberofslabs in O2 domains. Theend of the O2 domainis reached whenthe (5)

→

(2)or (4)

→

(1) transition occurswithaprobabilityequalto1/(n/2). TheatomicpositionswithintheAB-andBA-typeslabs aregiveninTable2,whereastheprobabilitiesoftransitionandthestackingvectorsassociatedare giveninTable3. Fig. 7showstheXRDpatternscalculatedforP2-O2intergrowthswithanaverage sizeof250slabsforP2andanincreasingnumberof O2slabs(between0and40). Thediraction lines associated to O2-LiCoO

2

(noted with *) clearly appear when the average size of the O2 domainsbecomeslargerthansixsuccessiveslabswithin aninitial P2crystal.

ThecomparisonoftheexperimentalandsimulatedXRDpatternshasthenbeenachieved, espe-ciallybytakingintoaccounttherst(00l)diractionline ofeachphase,that allowstodetermine the numberof slabs involved. Fig. 8shows in the [14

◦

-20

◦

] (2

θ

Cu

) range comparison between theexperimental pattern recordedafter 4h of reaction time and thepatterns calculated for P2-O2 intergrowth with O2 domains with an average size of 18, 20 and 22 consecutive slabs. The best agreementisobtainedwithanaveragesizeof 20consecutiveslabs,in rathergood agreement withthecoherencelengthcalculatedfrom theexperimentalFWHMfortheO2domainsusing the Scherrerformula. Indeed,theexperimentalFWHMof the(002)

O2

diractionline, despiteasmall accuracyduetolowintensity,leadsto 150Ådomains,i.e. to30slabs(Fig. 4).

4 Discussion

StartingfromaP2-Na

0.70

CoO

2

crystalwithanaveragesizecorrespondingto800slabs,itappears thatafter1hofexchangereaction,there areonlyafewnucleationcenters(oneevery250slabsin average). Then during the rst step of the exchange process (5 h), there is only aslowgrowing oftheO2 domain withoutothernucleation (in rstapproximation). Aswehavediscussed in the conclusionofthecompanionpaper(PartI),thedierenceinCo-Cointerslabdistancesbetweenthe O2-LiCoO

2

andP2-Na

0.70

CoO

2

domainsleadstoadestabilizationoftheinterslabspacesadjacent totheO2-LiCoO

2

domains. Therefore,thegrowingofanO2domainiseasierinthatcasethanthe nucleationofanewone.

After 5h of reactiontime, thesize oftheO2 domainsis stillsmall (30slabs),but within 1h, associatedtotheP2

→

P2*phasetransition,itraisesquicklyto100slabswhereasthesizeoftheP2* domainsdecreasesto 200slabs. Thenduring thefollowing10h theexchangecontinuesbut more slowly. Sincetheprocess involvedwhen theP2*phaseappearsis obviouslyrelatedto redox reac-tions,wehavecomparedtheelectrochemicalbehaviorofP2-Na

x

CoO

2

andO2-Li

x

CoO

2

insodium

tainedforLi//Li

x

CoO

2

andNa//Na

x

CoO

2

cells. NotethatanLi/NaClO

4

/Na

x

CoO

2

cellwasmade inorder tocomparethepotentialoftheNa

x

CoO

2

phasein asodiumcellandin alithiumcell. It appears that there is an0.3 V dierence in potential due to the dierence in negative electrode materials. As illustrated schematically in Fig. 9, the formation of O2-Li

x

CoO

2

domains in P2-Na

0.70

CoO

2

crystalsinduces,therefore,locallyahigh3.8VpotentialversusLi. Inordertobalance thepotentialalloverthecrystal,thereareprobablysimultaneouslytheoxidationofP2-Na

0.70

CoO

2

toP2*-Na

0.50

CoO

2

andthereductionofO2-Li

x

CoO

2

toO2-Li

x≈1

CoO

2

. Thefurtherreductionof Li

x

CoO

2

occursthroughtheoxidationofwater(fromthesaltssolution)asshownbytheequation:

2Co

4+

+H

2

O

→

2Co

3+

+2H

+

+

1

2

O

2

.

Note that agas releasewas observedduring thein situ experiment throughthe formationof bubbles.

AftertheP2

→

P2*transition,twofactorshavetobetakenintoaccountinorderto discussthe exchangemechanism:

4

TheCo-CodistancesintheP2oxidizedP2*phasearenowveryclosetotheO2-LiCoO

2

ones (2.808and 2.804 Å, respectively), therefore thedriving force due to the distance mismatch isno moreinvolved. This thusleadstoamoredicultgrowthoftheO2domains.

4

Thedecreasing of sodium in the P2* structure induces an enlargement of the P2 interslab spacewhichleadstoanincreaseofthelithiumdiusionthroughthestructureandthereforewhich shouldinducealargeincreaseofthekineticoftheexchangereaction.

AsshownbytheincreaseoftherateoftheexchangereactionaftertheP2

→

P2*transition, the increaseofthelithiumdiusion inthecrystallitesplaysthemostimportantrole.

Acknowledgements : Theauthors wish to thank CNES and Région Aquitaine for nancial support.

References

[1] C.Delmas, J.J.BraconnierandP.Hagenmuller.Mater.Res.Bull.17(1982),p.117.

[2] J.M.Paulsen,C.L.ThomasandJ.R. Dahn.J.Electrochem.Soc.147(2000),pp.2862-2867.

[3] Z.H.Lu,R.A. Donaberger,C.L. ThomasandJ.R.Dahn.J.Electrochem.Soc.149(2002),pp. A1083-A1091.

[4] J.M.Paulsen,C.L.ThomasandJ.R. Dahn.J.Electrochem.Soc.146(1999),p.3560.

[5] J.M.Paulsen,R.A.DonabergerandJ.R.Dahn.Chem.Mater.12(2000),pp.2257-2267.

[6] Z.H.LuandJ.R.Dahn.Chem. Mater.13(2001),p.2078.

[7] K.M.Shaju,G.V.S.RaoandB.V.R.Chowdari.Electrochem.Commun.4(2002),pp.633-638.

[8] K.M. Shaju, G.V. Subba Rao and B.V.R. Chowdari. Solid State Ionics 152?153 (2002), pp. 69-81.

[9] F.Tournadre,L.Croguennec,I.Saadoune,D.Carlier,Y.Shao-Horn,P.Willmann,C.Delmas, J.Solid StateChem.,acceptedforpublication.

[10] Dirac-At,Siemens andSocabim,1993.

[11] R.D.Shannonand C.T.Prewitt. ActaCrystallogr.B25(1969),p. 925.

[12] J.J.Braconnier,C.Delmas,C.FouassierandP. Hagenmuller.Mater.Res.Bull.15(1980),p. 1797.

[13] D. Carlier, I.Saadoune,E. Suard, L.Croguennec, M.Ménétrier andC. Delmas. Solid State Ionics144(2001),pp.263-276.

Figure 2: XRD patterns recorded in situ during the exchange of sodium by lithium in P2-Na

0.70

CoO

2

. A total of 64 XRD patterns was recorded during 16 h, with 10 min acquisition timeforeachpatternand 5minwaiting timebetweentwopatterns.

Figure3: ComparisonoftheXRDpatternsrecordedjust beforeand justaftertheP2

→

P2*phase transition.

Figure 4: Evolution of the FWHM of the (002) diraction lines for the P2-Na

0.70

CoO

2

, P2*-Na

0.50

CoO

2

and O2-LiCoO

2

phases, during the ion-exchange reaction. The coherence lengths, calculatedfrom experimental FWHMsusingtheScherrerformula,arealsogiven.

reaction.

Figure 6: Scheme of the structural models used by DIFFaX software in order to simulate the XRD patternforpure P2phase(a)andfor P2-O2intergrowth(b). Thestackingvectorsand the associatedprobabilitiesarealsogiven.

Figure7: XRD patterns calculatedforP2-O2intergrowths. *indicates theO2-LiCoO

2

peak posi-tions. Theaveragesize oftheO2domains variesfrom0to 40slabs.

Figure 8: Comparison betweenthe experimental XRD pattern recorded just before the P2

→

P2* phasetransitionandthepatterncalculatedforanaveragesizeof20slabsfortheO2domainsinthe P2-Na

0.70

CoO

2

crystals. Enlargementofthe(002)

O2

diraction linewith thepatterns calculated foran average size of 18, 20 and 22 slabsfor the O2 domains and thecorrespondingFWHMs is alsoreported.

Figure 9: The VOLTAGE=f(x) electrochemical curves obtained for the Li//Li

x

CoO

2

and Na//Na

x

CoO

2

systems. Note that fora givenphase, an0.3 V dierencein potentialis observed betweenasodiumandalithium cell.

Table1: CellparametersofP2-Na

0.70

CoO

2

andP2*-Na

0.50

CoO

2

phases

Table 2: Description of the AB-type slabs (slab no. 1, slab no. 3,

. . .

, slab no. 5) and of the BA-typeslabs(slabno. 2,slabno. 4,

. . .

,slabno. 6)

Thecellparametersusedarea

hex.

=b

hex.

=2.8035Åandc

hex.

=9.540Å.

Table3: StructuralmodelusedforthecalculationoftheXRDpatternsforP2-O2intergrowths

Translation probabilities (

α

ij

) and translation vectors (R

ij

: R

xij

,

R

yij

,

R

zij

) associated to the stackingof theslabsno. j abovetheslabsno. i. Theprobabilityof creatingO2domainsis 0.4% (whichgivesanaveragesizeof250slabsfortheP2domains). Then variablerepresentstheaverage numberofslabsnecessarytodescribetheO2domains.