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Muon Spin Relaxation Measurements on Zirconia Samples C. Degueldre,1 A. Amato,2 and G. Bart1 1Laboratory for Materials Behavior, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland. 2Laboratory for Muon-Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland. Although of primary importance in the mechanistic understanding of Zircaloy hydriding,practi- 5 callynothingisknownonthetransport propertiesofhydrogeninzirconia. Inthisframethemuon, 0 whichcanbeconsideredasalighthydrogennuclide,canbeusedasananalogueanditsbehaviorin 0 zirconiaandZircaloycorrosionlayermayprovidemoreinsighttounderstandthebehaviorofhydro- 2 gen in these phases. Preliminary muon spin relaxation (µSR) measurements on several monoclinic n zirconia samples, including a Zircaloy corrosion layer, have been performed. From the observed a muon depolarization rate, the muon diffusivity in bulk monoclinic zirconia can be extracted and is J found comparable to that of recently reported proton diffusivity. 4 1 PACSnumbers: 66.30.Jt, 28.41.Qb,76.75.+i Keywords: zirconia,Zircaloycorrosion,muon,muonium,diffusion,hydrogen ] i c s INTRODUCTION Consequently muon diffusion in metals may be investi- - l gated and numerous studies are reported for elemental r t The study on the behavior of hydrogen in zirconia for metals (see for example Ref. [3]). Alternatively, in di- m understanding its migration mechanism in the Zircaloy electrics, part of the implanted muons can capture an t. corrosion layers is justified as stated in specific studies electron and form a muonium pseudo-atom. The Muo- a and as reported recently (see Ref. [1]): nium properties, including the nature of trapping sites m and its diffusion, can in turn be studied by µSR, as suc- - Virtually,nothingisknownabouttheformof cesfully demonstrated in a variety of studies (for a com- d n hydrogeninZrO2 orhowitmigratesthrough prehensive review on muon and muonium diffusion see o it. (...) Theargumentshavealwaysbeenover Ref. [4]). c precisely what changes are occurring in the As a complementof recentstudies using x-rayabsorp- [ oxide during this incubation time, and how tion [5, 6] to gain more insight on the influence of oxy- 1 the hydrogen migrates through the oxide. gendeficiency on electronic and localstructure of mono- v clinic zirconia,the presentµSRinvestigationaimsto ob- 3 Anatomisticpictureofinterstitialhydrogeninzirconia tain complementary information on the muon diffusion 4 involves,asitdoesforhydrogenindielectrics,determina- onmonoclinic zirconia(powder andpolycrystalline sam- 3 tionoflatticesites,configurationsadoptedandthemech- 1 ple). Moreover,preliminary data ona Zircaloycorrosion anisms of diffusion. An additional dimension is added in 0 layer are also reported. the study of muons in materials, namely the possibility 5 0 ofexaminingdifferentstatesofthedefectscenters–posi- t/ tive, neutral, negative – respectively for the diamagnetic EXPERIMENT a proton, the paramagnetic hydrogen atom and diamag- m netic hydride ion. Muon spectroscopy has been success- Muon Spectroscopy - ful in characterizing all these states, determining their d local structures, their different stabilities, mobilities and n ThemuonsusedduringµSRstudiesarebasically100% o interactions with charge carriers [2]. In addition charac- polarized and are implanted one at a time into the sam- c terization of trapping centers such as vacancies may be ple, where they thermalize within few picoseconds. Dur- v: performed. Such similar studies could therefore be em- ing his lifetime (ca. 2.2 µs), the muon can diffuse in the i ployed to get more insight on the behavior of hydrogen X in for zirconia, as the muonium (Mu=µ++e−) can be zirconia material as free (diamagnetic) muon or possibly as muonium. When the muon undergoes its weak decay r regarded as an isotopic analogue of the hydrogen atom, a a positron, among others, is produced which is prefer- with a positive muon replacing the proton. entially emitted along the direction of the muon spin at In metals, the implanted muon comes at rest at an decay time. For a µSR experiment, the direction along intersticial position and is in a diamagnetic state. Af- whichthedecaypositronisemittedandtheelapsedtime ter implantation, it may diffuse between interstitial sites interval between the muon implantation and the decay and/or towards trapping spaces (defects, vacancies, for- are determined. After 107 muons have been observed, eign atoms). By µSR technique, information about the ∼ theobtainedtimehistogramofthecollectedintervalshas local magnetic field distribution at the muon site can be the form: obtained. Such distribution will be sensitive to the dy- namics of the local moments and/or of the muon itself. N(t)=N0exp( t/τµ)[1+AG(t)]+Bg , (1) − 2 whereBg isatime-independentbackground,N0 isanor- Particle Mass (amu) malization constant, τ is the muon lifetime and the ex- µ ponential accounts for the muon decay. AG(t) is often 60.1 1 10 called the µSR signal. A is the asymmetry parameter, which will depend on the experimental setup. G(t) re- flects the normalized muon-spin S autocorrelation func- ) m tion G(t) = S(t) S(0) /S(0)2, which depends on the n average valueh, dist·ributiion, and time evolution of the h ( pt internal fields sensed by the muons, and therefore con- e D tains all the physics of the magnetic interactions of the n muon inside the sample [7]. The present µSR measure- o ments were obtained with the so-called transverse-field rati 105 et technique where a weak magnetic field is applied trans- n e versetothe initialspindirection. Theformandwidthof P the fielddistributionsensedby the muonis therefore de- e g tected by monitoringthe decay ofthe muonpolarization ra e (i.e. reflected by the envelope g(t) of the G(t) function). v A The µSR experiments were performed at the Swiss Muon Source (SµS) of the PaulScherrerInstitute (PSI), 4 Villigen (Switzerland). The GPS instrument [8] located 10 9 onthesurfacemuonπM3.2beam-linewasused. Thetyp- 10 icalrangeinmatterofthemuonsavailableonthisbeam- line is about 150 mgcm−2. Samples were cryo-cooled 108 ) inliquid heliumandµSRwasperformedasa functionof m n 7 temperaturebetween5and300K.Duetothesmalldepo- h ( 10 larizationratesobserved,theso-calledMuon-On-Request pt (MORE)setup [9] wasused. This setupdramaticallyre- De 106 ducesthevalueofBgandallowsonetoextendtheusable n o µSRtime windowupto20µsandthereforedetectdepo- ati 105 r larization rates as low as 0.001 µs. et n e 4 P 10 e Samples ag 3 r 10 e v A Different monoclinic zirconia samples were investi- 2 10 gated: i) a very pure powder sample; ii) a solid pellet sample; iii) a sample of natural monoclinic zirconia 1 10 1 2 3 4 5 formed by a mosaic of single crystals. The zirconia pow- 10 10 10 10 10 der was produced by Fluka (pro-analysis) and was com- Incident Energy (keV) posed by particles in the size range of 1 to 10 µ. The FIG. 1: Upper panel: Calculated penetration depth for lep- zirconia solid pellet was a sample of nanoparticles of tons and hadrons with a 4 MeV incident energy (see text). pure zirconia pelletised and sintered at low temperature Lowerpanel: Comparisonbetweenthecalculatedpenetration (kindly offeredby the PennState University)as reported depthsof µ+ (squares), H+ (triangles) and 3H+ (circles). earlierbyRaghavanetal. [10]. Naturalzirconiawaspart of a brown rolled pebble comprising baddeleyite (ZrO2) and zirconfrom Poçosde Caldas, Minas Gerais (Brazil). The baddeleyite part was 22.5 22 mm2 with a thick- × nessof1.5to3mm. Thissamplewaskindlyprovidedby x-ray diffraction and were found to assume the mono- theMineralogicalDepartmentoftheGeologicalMuseum clinic structure of zirconia. of the University of Lausanne (Switzerland). The main impurities were Fe and Hf both at the percent level. In addition, a Zircaloy(Zry4)sample wasalso investigated. DuringµSRmeasurements,thesamplesweremounted This sample (40 10 mm2), corroded in autoclave, was either on special containers (powder sample) or on fork- × coveredbyalayerofZrO2. Thismonocliniczirconiacor- likeholders. Inbothcases,thefractionofmuonsmissing rosionlayer had a thickness of 100 µm as determined by the sample and creating a time-dependent background gravimetry (1692 mgdm−2). All samples were tested by signal can safely be neglected. 3 comparison between penetration depths of µ+, 1H+ and 3H+ at various energies. Figure 1 (lower panel) shows a comparison between the three particles as a function of their energy. µSR Results Forallsamples,transverse-field(TF)µSRstudieswere first performed in an applied magnetic field of 7 G. This low field value was choosen in order to differentiate the diamagnetic muon fraction from the muonium one (i.e. representing the formation of muonium in the sample). For all samples, a reduced fraction (typically 25% of the total signal) of diamagnetic muons was observed at all investigatedtemperatures. The spin ofthese muons pre- cesses according to the gyromagnetic ratio of the free muon [γ /(2π) = 13.55 kHzG−1 – the muons in a muo- µ niumstateexhibitaprecessionwhichistypicallytwoor- ders of magnitude faster]. The remaining fraction of the µSR signal was related to the occurrence of muonium. However, a muonium signal could only be detected at very low temperature (below 6–7 K) where it is charac- terizedby anextremely fastdepolarizationratepointing to muoniumdelayedformation. Figure2 exhibits atypi- cal µSR spectra recorded at 4 K on monoclinic zirconia. Whereas diamagnetic muons are detected over the en- FIG.2: TFµSRspectra,recordedinanexternalfieldof7G tire time window, neutral muonium is detected only at overthefull available timewindow (8 µs– top) and overthe very early times (bottom panel of Fig. 2). The popu- first 0.5 µs (bottom), in monoclinic zirconia at low temper- lation of prompt muonium is, however, rather low and ature (4 K). The signal surviving at long time is associated reaches about 10% at this temperature, A slight tem- to diamagnetic muons, whereas the rapidly damped signal is perature increase has a devastating effect on the prompt ascribed to a muonium fraction (see text). muonium population and already at 6 K the population basically disappears (<1%), most probably in reason of delayed muonium formation It is consequently impossi- RESULTS AND DISCUSSION ble already at low temperature to study the diffusion of muonium, even in a semi-quantitative way. Therefore, Modelling the Muon Implantation diffusion studies have been restrictedto the diamagnetic muon fraction. For such TF µSR measurements with an Penetration and implantation of leptons nx+ and external magnetic field of 50 G were performed. This hadronsnX+ inzirconia(density 5.9gcm−3)weremod- method was preferred to the zero-field µSR technique eled using the software SRIM2000 (Ref. [11]). First cal- sinceitallowsthedeterminationofthe temperatureevo- culations were carried out for energy of 4 MeV corre- lution of very weak muon depolarization rates quite ac- sponding to the muon energy available for the real mea- curately. surements. The average penetration depth for the µ+ For all samples, the diamagnetic part of the µSR sig- amounts to 344 µm with a straggle of 23 µm. For the nal could satisfactory be fitted utilising the so-called same energya protonpenetration depth is 74 µm with a Abragam formula, which describes the muon diffusion straggleof2.3µm. Inthisenergyrange,thedeceleration in transverse field (see for example Ref. [12]): mpeecctheadn,itshmeohcecauvrisestthrpoaurgtihcleelsechtarvoeniacisnhtoerrtaecrtipoennse.tArastieoxn- G(t)=exp[−M2τc2exp(−t/τc)−1+t/τc]cos(ωt+φ) (2) depth. Figure 1 illustrates this behavior for particles of whereM2 isconnectedtothe secondmomentofthefield vpaorsisoibulsempaarstsiecslensafmoreslya:mµp+le,ir1rHa+di,a2tHio+n,a3nHd+1.,2Hτ++,,π1.+5Ha+s idnissitdriebuthtieonlaattticteheanmduτonisstothpepinhgopspitineg(Mtim2e=(wγµh2hicBh2iis) c and5H+forhypotheticalirradiation. Itisstrikingtofind related to the hopping rate Γ = 1/τ ). The oscillatory c alinearrelationshiponthelog-logplotofthepenetration term,ontheright-handsideofEq.(2)reflectsthemuon- vs. mass. Additional modeling effort was focused to the spin precession with ω = γ B (where B is the internal µ i i 4 assumption that the muon diffuses to equivalent sites. The parameter M2 was found to equal 0.0256 MHz2, 0.040 MHz2 and 0.23 MHz2 for the pellet, powder and 100 natural sample, respectively. Such values are unexpect- edlyhighincomparisontocalculatedfielddistributionat the possible muon site. Assuming the monoclinic structure and a perfect crystal, the field distribution at the muonsiteisproducedbythenuclearmagneticmoments, i.e. principally by the ion 91Zr4+. This ion has a spin 10 I = 5/2 with a moment µ = 1.298 µN and a relatively − low abundance of 11.2%. For the most likely interstitial sites, and in particular for the site (0.5,0.5,0.5), theoret- s) (c i0c.a0l05caMlcuHlaz2ti.onTshpirsohvuidgeeadpisacrraempaentecryMsu2gcaglecsotsf tthheatortdheisr specificmaterialhasinherentlyalargedensityofdefects, 1 impurities and/or vacancies. Consequently, the samples may contain important local distortions, not reflected in theoretical calculations. The major role played by defects on the magnetic field distribution at the muon site is illustrated by the rather high value of M2 observed in the natural sample. In this sample, it is believed that 0.1 a large contribution to the enhanced M2 is provided by 0 5 10 15 20 25 iron-rich clusters as FeO or Fe2O3. 1000/T (K-1) Figure 3 exhibits the parameter τc obtained on the powder, pellet and natural samples by fitting Eq. (2) to the data. Clearly, the temperature evolution of the τ FIG.3: Arrheniusplotsoftheparameterτc measureddiffer- c entmonoclinic samples of ZrO2: in thepowder sample(solid assumes an Arrhenius behaviour of the form: symbols), in the low-temperature sintered nanoparticle sam- 1 ple (pellet sample – open squared) and in a natural sample =ν0exp( E0/kBT) , (3) (opendisks). Notetheincreased errorsbarsforthenanopar- τc − ticlesample duetotheunavailabilityof theMOREsetupfor those measurements. where E0 is an activation energy and kB is the Boltz- mann constant. Best fits of Eq. (3) on the data provides activation energies of 3.6 0.3 meV, 4.7 0.2 meV and ± ± 16.2 0.9 meV respectively for the powder, the natural fieldatthemuonsiteandoftheorderoftheexternalfield ± and the pellet sample (see also table I). Eventhough the of 50 G) and φ is a phase essentially given by the geom- errorsbarsareratherhigher,note thatthehopping time etry of the instrument. The Abragamfunction describes τ extracted from the data obtained in the nanoparti- the time-dependence, introduced by the muon diffusion, c cle sample is rather longer than that of the other sam- oftheinteractionbetweenthenuclearspinsandthemuon ples, corresponding therefore to a reduced hopping rate spin. If the muon motion is fast enough, the muon spin Γ. Such observation may be related to the presence of will sense an average nuclear field distribution, that is, latticestrainsleadingtoareductionofthehoppingprob- the observed muon depolarization rate will decrease. In ability through tunnelling. NMR the similar effect is known as motional narrowing. From the value of τ , and taking into account the TheAbragamfunctionreduces,asexpected,tothestatic c nearly cubic symmetry of the zirconia system, the dif- depolarization function (Gaussian) in the limit of slow fusion parameter D can in principle be extracted by the muon motion. On the other hand, for fast motion, the expression[12]: limit is correctlygivenby the exponentialdepolarization function and an overalldecrease depolarization rate. 1 d2 D = . (4) In the Eq. (2), the parameter M2 was experimentally τ 6 c determined at low temperature, i.e. below about 20 K. Inthistemperatureregion,thedepolarizationofthedia- Equation (4) assumes a perfect crystal, where the muon magneticµSRsignalisfoundtobetemperatureindepen- diffusion occurs between adjacent and identical intersti- dent and is interpreted as a regime with a slow hopping tial stopping sites. Considering the most probable muon rate(i.e. Γ=1/τ 1/τ ), i.e. withamuonessentially stoppingsite(0.5,0.5,0.5)mentionedabove,thejumpdis- c µ ≪ static. On a second step M2 was kept constant during tancedcanbeshowntobed=a/√2,wherearepresents all the remaining fitting procedure,correspondingto the the lattice parameter. However, and as observed above, 5 TABLEI: Comparison ofthediffusioncoefficient (estimated at 500 K) for various species in zirconia. The activation en- 0.30 ergy and species radius are also reported. ZrO2 Exponential Fit radius (pm) D (m2s−1) E0 (eV) Ref. z) 0.25 H Zr4+ 80 10−20 – [13] M O2− 136 10−12 3.2 [13] e ( 0.20 Cs+ 167 10−20 0.5–1.0 [13] rat n H 78 ∼10−16 – [14] o H+ – 1.5×10−12 – [15] zati 0.15 µ+ – 0.5–1.0×10−13 3–16×10−3 thiswork olari p 0.10 e D 0.05 the picture of a clean and perfect crystalhas to be ques- tioned in view of the quite strong depolarization rate of the muon at low temperature (i.e. when the muon is es- 0.00 10 100 sentially static). An alternative view is to consider that afterthermalisationthemuoncomesatrestatatrapping T (K) site,whichprovidesadeeper potentialthana regularin- FIG. 4: Comparison between the temperature evolution of terstitial site. Such a scenario appears conceivable if the the depolarization rate measured in different ZrO2 samples. concentrationof trapping sites is very high and/orif the For sake of comparison, thedata were here analysed with an exponential decay of the polarization (see also text). A nat- ‘free’ diffusion is extremely fast, meaning that all muons ural sample (open circles), an ultra-pure powder (solid sym- would be likely to have reached a trap during the first bols) and a layer sample obtained from a corroded Zircaloy few nanoseconds. Equation (2) would still be valid, but plate (open triangles). (Note that the error bars are smaller nowτc wouldrepresentthestepsindiffusionbetweenthe than the data points and that the layer sample data were trapping sites and M2 wouldbe connected to the second performedduring4differentcoolingandwarmingprocedures moment of the field distribution at a trapping site. As with perfect reproducibility). observed, such field distribution can be safely expected to strongly deviates (i.e. be wider) than the calculated one for normal interstitial sites in a perfect crystal. In Finally, preliminary µSR studies have been performed this‘dirtylimit’,andbyassumingthattheconcentration on a monoclinic sample present as zirconia layer from a oftrappingsitesislessthanonesiteperunitcell,thede- corroded Zircaloy sample. In view of the reduced thick- termination of the diffusion parameter [see Eq. (4)] can ness of the layer (100 µm) and of the available muon be considered as a lower limit. energy (about 4 MeV), a series of test runs have been Table I presents a comparison of the diffusion coef- performedtodefinetheoptimumdegrader(460µm). For ficient D obtained for various species in zirconia. The the degrader, ultra-pure Al was utilized. The obtained valuesareestimatedaround500Kusing,ifnecessary,an thickness corresponds closely to the one calculated from Arrhenius law. The diffusion coefficients of ions such as the muon range (see above). As the temperature depen- O2− and Cs+ in zirconia are reported in the literature dence of the µSR signal is strongly non-monotonic com- [13]. At room temperature typical diffusion coefficients pared to the former samples, an analysis based on the arefoundintherange10−12to10−22 m2s−1 forO2− and Abragam formula [Eq. (2)] is not possible and a simple Cs+, respectively. The diffusion coefficient of hydrogen exponential depolarization (reflecting satisfactorily the in zirconia (10−16 m2s−1) was measured by Aufore [14]. overalltemperature dependence) was assumed. Figure 4 Thisstudysuggestsasignificantmobilityinzirconia. On shows the T-dependence of the exponential depolariza- the other hand, Lim et al. [15] studied by electrochem- tion rate of the corrosion layer sample compared to the istry the mobility of proton in zirconia scales and found formersamples. The differentmaxima observedpointto largerdiffusioncoefficientthanforhydrogen. As already a number of trapping-detrappingeffects occurring in the discussed, from the present study no information can be layer. Clearly, this suggests a variety of defects in the extractedfor the muoniumdiffusion. However,anevalu- corrosion layer material. This variety impeeds a more ation of the muon diffusion coefficient can be performed quantitative analysis of the data obtained. Hence, each with the restrictionsreportedaboveconcerningtrapping trappingsitetypeicanbecharacterizedbya‘meantime effects. Forsakeofcomparison,the coefficientτ wasex- ofstay’τi andtheaveragetimeneededforamuonescap- c 0 trapolated at 500 K using Eq. (3) and subsequently the ing from this kind of trap to reach the next trap variety lower bound of the diffusion coefficient D was estimated τi. The depopulation and repopulation processes lead 1 using Eq. (4). to the characteristichumps observedin the temperature 6 evolution of the muon depolarization rate. To compli- their interest in their work. cateevenmorethe picture, eachtype oftraphasagiven concentration c and a given local field distribution Mi. i 2 By adding also the fact that the diffusion out of traps processes assume their own Arrhenius law (i.e. with different activation energy for the τi), it is obvious that [1] IAEAWatersidecorrosionofzirconiumalloysinnuclear 0 power plants, IAEA-TECDOC-996 (1998) 102-104. quantitative information is, at least, extremely complex [2] E.B. Karlsson, Solid state phenomena (Clarendon press, to extract. The present measurements should be basi- Oxford, 1995). cally taken as a strong hint for different trapping site [3] M.Borghini, T.O.Niinikoski,J.C. Soulié,O.Hartmann, types in the layer sample. E. Karlsson, L.O. Norlin, K.Pernest˚al, K.W. Kehr, D. Richter, E. Walker, Phys.Rev.Lett. 40 (1978) 1723. [4] V.G.StorchakandN.V.Prokofev,Rev.Mod.Phys.70 CONCLUSION (1998) 929. [5] P.Villela,S.Conradson,F.Espinosa-Faller,S.R.Foltyn, K.E. Sickafus, J.A. Valdez, C.A. Degueldre, Phys. Rev. The first goal of this muon spectroscopy study was to B 64 (2001) 104101. provide more insight on the hydrogen and proton dif- [6] S.Conradson,C.A.Degueldre,F.J.Espinosa-Faller,S.R. fusion in zirconium oxide. The work was achieved by Foltyn, K.E. Sickafus, J.A. Valdez, P.M. Villella Prog. analysingmuon behaviorin zirconiasamples. The muon Nucl. Energy 38 (2001) 221. interactions in monoclinic polycrystalline zirconia sam- [7] S.J. Blundell, Contemporary Physics 40 (1999) 175. ples were investigated, with the aim of applying later [8] http://lmu.web.psi.ch/facilities/gps.html [9] R.Abela,A.Amato,C.Baines,X.Donath,R.Erne,D.C. the study onthincorrosionlayersontoZircaloy. Prompt George, D. Herlach, G. Irminger, I.D. Reid, D. Renker, muonium was not identified in zirconia above 6 K. The G. Solt, D. Suhi, M. Werner and U. Zimmermann, Hy- diffusioncoefficientofmuoninzirconiawasestimated to perfine Interactions 120-121 (1999) 575. be about 10−13 m2s−1 at around 500 K. In a prospec- [10] S. Raghavan, H. Wang, R. Dinwiddie, W. Porter, M. tive way the work has been completed by studying the Mayo, Script.Materialia 39 (1998) 1119. properties of muon in a Zircaloy corrosionlayer. [11] http://www.srim.org This work was performed at the Swiss Muon Source [12] A. Schenck, Muon Spin Rotation Spectroscopy (Adam Hilger, Bristol, 1985). (SµS) of the Paul Scherrer Institute (PSI), Villigen, [13] C. Degueldre, M. Pouchon, M. Döbeli, K. Sikafus, K. Switzerland. Acknowledgements are due to Swiss Nu- Hojou, G. Ledergerber, S. AbolhassaniDadras, J. Nucl. clear for its financial support of the LWV, to N. Meisser Mater. 289 (2001) 115. Curatorofthe mineralogicaldepartmentGeologicalMu- [14] L. Aufore, Etude du transport de l’hydrogène produit seumofLausanneforprovidingthenaturalzirconiasam- lors de la corrosion des gaines d’élément combustibles ple and to S. Raghavan from University Penn state for des réacteurs à eau sous pression dans la zircone et le providing the piece of pure monocline zirconia ceramic. Zircaloy-4, CEA report TH-656 (1997). [15] B.H. Lim, H.S. Hong, K.S. Lee, J. Nucl. Mater. 312 The corrodedZircaloysample was kindly providedby P. (2003) 134. Barberis from CEZUS, Framatome-ANP, Ugine, France. The authors thank W. Hoffelner and U. Zimmerman for