Electrochemical kinetics of hydrogen intercalation in gadolinium switchable mirrors

JOURNAL OF APPLIED PHYSICS VOLUME 94, NUMBER 7 1 OCTOBER 2003

Electrochemical kinetics of hydrogen intercalation in gadoliniumswitchable mirrors

M. Di Vece,a) I. Swart, and J. J. KellyDebye Institute, Physics and Chemistry of Condensed Matter, Utrecht University, P.O. Box 80 000,3508 TA Utrecht, The Netherlands

~Received 3 March 2003; accepted 18 July 2003!

Potential-step experiments on gadolinium thin-film electrodes provide current and opticaltransmission transients, whose time constants are related to effective hydrogen diffusion coefficientsaccording to a standard diffusion model. The diffusion coefficients and switching kinetics depend ontemperature, hydrogen concentration, potential, and film thickness. A thickness dependence of thekinetics is observed in which the diffusion coefficient and optical switching time are linearlydependent. ©2003 American Institute of Physics.@DOI: 10.1063/1.1606863#

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I. INTRODUCTION

Electrochromic material research was extended in 1to a class of smart optical materials: the metal hydride swchable mirror.1 The switchable mirrors consisted of thin ytrium and rare-earth metal films, that showed a reversoptical change on going from the dihydride to the trihydristate. However, the films were yellow in transmission, whled to a search for color-neutral switchable mirrors. Coneutrality was achieved by alloying the rare earths wmagnesium.2,3 More recent research showed that thin filmcontaining magnesium alloyed with other metals also exhan optical transition upon hydrogen intercalation.4,5 A solid-state device based on the gadolinium magnesium alloybeen shown to switch with speeds in the minute range.6

The switching time, which is technologically very important, is typically of the order of seconds in gas-phaexperiments.1,7 Van der Molenet al.7 determined mobilitycoefficients from lateral hydrogen diffusion underneathoxide layer of an yttrium thin film by optical inspection. Thlateral mobility coefficients were compared to switchitimes in thickness-dependent experiments on yttrium masamples. The interpretation of these results was complicby the fact that the morphology of the film depends onfilm thickness. A difference between the layer structure nmal and parallel to the sample surface therefore raisesquestion as to how the switching time and the diffusionefficient normal to the sample surface are related.

Experiments on the rare-earth switchable mirrorsusually performed with a cap layer of palladium which aas a catalyst for hydrogenation and protects the film froxidation. Hydrogen can be introduced from the gas pha1

chemically with NaBH4,8 and electrochemically9 accordingto the reactions10

H2O1e2→Had1OH2, ~1a!

MHx1Had→MHx11 . ~1b!

a!Author to whom correspondence should be addressed; [email protected]

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Electrochemical loading has the advantage that the contration of hydrogen in the film can be controlled accurateThe adsorbed hydrogen diffuses into the material;hydrogen/metal atomic ratio in the film,x, is proportional tothe charge transferred in reaction~1a!.11

In the present work electrochemical potential-stepperiments provide information about the kinetics of tswitching process. The transmission and current were stuas a function of time after a potential step. It is shown thboth transients are directly related to hydrogen diffusionormal to the sample surface. These kinetic experimeperformed as a function of temperature, hydrogen concention, film thickness, and applied potential, provide insiginto the nature of optical switching.

II. EXPERIMENT

The active layers were 57, 100, 200, 300, and 400thick, polycrystalline gadolinium films top-coated with a thpalladium layer~nominal thickness 10 nm!, deposited on anindium–tin–oxide~ITO! coated glass substrate. The actifilm covered only part of the ITO surface to allow a bacontact to the film via the ITO.12 To ensure good adhesion othe gadolinium, a 0.5 nm thick magnesium layer was evarated onto the ITO. The layers were deposited by evaporaat 1027 mbar base pressure. A platinum lead was fixed wsilver glue~2400 Circuit Works Conductive Epoxy, Agar Scentific! on the free ITO, and both the lead and the ITO weprotected from the solution by Apiezon wax. The active sface area was 1.2 cm2.

A two-compartment electrochemical glass cell was usfor the measurements. The working electrode was positiotogether with a Hg/HgO reference electrode in one compment and a platinum counter electrode was placed inother compartment. All potentials are given with respectHg/HgO. Argon gas was bubbled through both chambeThe glass cell had windows on both sides through whichcould illuminate the sample and measure transmission widiode laser~Vector, 670 nm! and a standard photodiode. Aelectrochemical experiments were performed in a 1 M KOHsolution at room temperature, unless otherwise statedil:

9 © 2003 American Institute of Physics

license or copyright, see http://jap.aip.org/jap/copyright.jsp

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4660 J. Appl. Phys., Vol. 94, No. 7, 1 October 2003 Di Vece, Swart, and Kelly

potentiostat/galvanostat@EG&G Princeton Applied Researc~PAR 273A!# was computer controlled by in-house program~LabView!.

III. RESULTS AND DISCUSSION

The gadolinium samples were first galvanostatica‘‘loaded’’ to the trihydride state. Unloading of the samplea metal/hydrogen ratio close to two is possible at positpotential. The current and transmission transients werecorded simultaneously after a step from 0.2 V to a negapotential. At 0.2 V the sample is in the unloaded st(GdH1.8). In Fig. 1 typical transients in the long-time domaare shown. In the first seconds a fast decay of the curreclear. The slight initial decrease of the transmission is cauby an optical window9,11 at aroundx52, which is the start-ing point for the transients. Van Goghet al.13 explain thisfeature by a screening of the plasma energy and a low inband absorption coefficient, leading to lower absorptionmuch slower decay in the current transient is accompanby the main optical change, as can be seen from the trmission in Fig. 1. The transmission increases until the hydgen concentration is uniformly distributed within the filand the electrochemical potential corresponds to the apppotential. The current reaches a low steady-state value wcorresponds to the hydrogen evolution reaction. The curtransients can be fitted with a double exponential functiusing five parameters; pre-exponential termsA1 and A2 ,time constantst1 andt2 and I 0 , the steady-state current

I ~ t !5I 01A1 expF2t

t1G1A2 expF2

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This exponential current decay suggests an analogyresults obtained previously by Wenet al.14 In this studylithium was intercalated in a lithium–aluminum alloy ascharge-storage material. A relation between the fit paramefor the current decay and a diffusion coefficient was derivwith a simple model. The system is considered to consistwo parallel plates; one side~the substrate! is not permeableto the intercalating species while the concentration atother side~the film/solution interface! is constant. Before thepotential step, the lithium concentration in the film is un

FIG. 1. Transient of the current~solid line! with fit ~dashed-dotted line! andthe transmission~dashed line! of a gadolinium thin film after a potential stefrom 0.2 to20.95 V.


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form and constant. Solving Fick’s diffusion equations15 andtaking first order terms, Wenet al.14 have shown that thetime dependence of the current is given by

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pt G1/2

t, l2/D, ~3a!

I ~ t !52FSDDC

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whereD is the diffusion coefficient,L the film thickness,Fthe Faraday constant,S the active surface area, andDC thedifference between the concentration before and after thetential step. The exponential decay of the current foundt.L2/D, corresponds to the time at which the intercalatispecies has reached the impermeable side of the film.model enables us to relate the decay times from our resula hydrogen diffusion coefficient.

The double-exponential decay can be explained bytwo structural phases involved in the reversible dihydridetrihydride transition. In the hydrogen concentration rangex51.8– 2.3 theb phase exists.16 From x52.3 to x52.9 abandg phase coexist~miscibility gap!. Forx.2.9 the singlegphase remains.16 The dihydrideb-phase has an fcc structurewhile the trihydrideg phase has a hcp structure.17 Duringswitching the hydrogen concentration passes throughrange corresponding to theb phase and thebg coexistencerange in which the diffusion coefficients are expected todifferent. The concentration range corresponding to thebphase fills up first; theb–g transition is subsequently completed to give a singleg phase. The total charge of the faexponential decay is typically 37% of the total deloadicharge. Comparing this result with theb phase concentrationrange of about 40% in the phase diagram of the gadolinhydride, we therefore conclude that the fast decay very likcorresponds to the concentration range of theb phase with ahigher diffusion coefficient. The slow decay is then relatedthe b to g transformation in thebg coexistence range.

Each phase should show both the square root andexponential dependence of the current on time. With tphases there are consequently four time domains. The forincludes a square root and exponential current decay. Tfast square root current decay corresponds to time domawhich are not detectable with the current setup. The fexponential decay overlaps with the ‘‘square root decay’’the slow process, and is probably masked by it; this comcates the interpretation of the first current decay proceTherefore the analysis in this article will be focused mainon the exponential current decay of the slow process, whdetermines optical switching.

On the basis of the experimentally determined diffusicoefficients, we can conclude that the conditiont.L2/D isnot valid for the entire time range of the transient. HowevMontella18 has shown that fort>0.23•L2/D the error madewill be <1%.

The diffusion coefficients for the slow process canobtained from the fit of Fig. 1; the values range from 10212

to 10210cm2 s21 depending on film temperature, concentrtion, potential, and thickness. The corresponding valuethe fast process is 1 order of magnitude larger. Hydrog


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4661J. Appl. Phys., Vol. 94, No. 7, 1 October 2003 Di Vece, Swart, and Kelly

diffusion coefficients have not been reported for theb andgphases of gadolinium hydride. The values for the related mterial yttrium, also measured on a switchable mirror, are othe same order of magnitude. From the yttrium hydride diffusion coefficient parameters provided by Majeret al.19 frompowder nuclear magnetic resonance~NMR! experiments inthe b phase we calculate a diffusion coefficient of10211cm2 s21 which is close to our values for the gado-linium thin film.

A. Temperature dependence

In Fig. 2, the logarithm of the diffusion coefficient forthe slow process, derived from the exponent@Eq. ~4!#, isshown as a function of the reciprocal temperature. Thstraight line clearly indicates an Arrhenius dependence. Thdiffusion coefficient for the slow process ranges from 4.5310212 to 2.0310211cm2 s21 in a temperature intervalfrom 25 to 65 °C; the corresponding activation energy is 0.3eV. The fast decay gives a activation energy of approxmately 0.29 eV. Our values are similar to those reported foyttrium thin films; these gas-phase experiments on filmsloaded by lateral hydrogen transport, provide an activatioenergy of 0.37 eV for thebg transition.20

Assuming free diffusion through the entire film, a certainminimum charge must be passed~e.g., a % of the chargeneeded to fully load the sample! before the film becomestransparent. It can be shown that the expected switching timtD is related to the diffusion coefficient according to

tD}L2

D. ~4!

We define the measured switching timets as the maximum ofthe derivative of the transmission with respect to time. Threlation betweentD and ts is an unknown function but as-sumed to be independent of external parameters. Therefots5htD , in which h is a constant. In Fig. 2 the reciprocalswitching time is plotted as a function of the reciprocal temperature. From the slope we calculate an activation energy0.29 eV. The markedly good agreement between the activtion energies independently determined from the current an

FIG. 2. Arrhenius plots of the diffusion coefficient and the reciprocaswitching time for the slow process in a 200 nm film determined from thexponent in the exponential current decay fit.


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transmission transients and the good agreement of thevation energies with literature values for hydrogen diffusiin yttrium thin films, is strong evidence for diffusion-limitekinetics.

B. Concentration dependence

In practical systems the effective diffusion coefficiecan in principle depend on the concentration of the diffusspecies.15 After a large potential step this concentration mchange considerably. Crank and Park21 have shown that aconcentration dependent diffusion coefficient can betained by averaging over the concentration range; thisproach is independent of the nature of the concentrationpendence. If in our case the diffusion coefficient dependsthe hydrogen content of the film, then this should be cleaexperiments in which the film is first preloaded~abovex52) before the potential step experiment is performed. Ptial loading of the sample prior to the potential step wprovide a diffusion coefficient which is averaged overshorter concentration range, thus corresponding to higconcentrations. Current transients measured after additioa fraction of the possible loadable hydrogen concentratare shown in Fig. 3. The first exponential decay clearly dappears. After introduction ofDx>0.2 the transient can befitted with a single exponential function. Subsequent additof hydrogen before the potential step leads to a furthercrease of the current density in the transients. The cosponding diffusion coefficients for the slow decay are shoin Fig. 4. The diffusion coefficient increases from 3310212 to 6.9310212cm2 s21 with increasing hydrogenconcentration. Since this concentration-dependent diffuscoefficient is determined by the average diffusion coefficietaken over a decreasing concentration domain, we canclude that the diffusion coefficient must be increasing wincreasing hydrogen content. The diffusion coefficient ually decreases at higher concentrations of the diffusing scies due to blocking.22 However, a change in electronistructure at higher hydrogen concentrations, as is appafrom the optical change, could give rise to a lower diffusibarrier.23 The optical switching time also decreases aftertroduction of hydrogen in the film before the potential ste

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FIG. 3. Current transients measured after addition to a 100 nm filmdifferent amounts of hydrogenDx. Dx is indicated in the inset.


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as shown in Fig. 4. A linear dependence of the reciproswitching time on added charge is apparent for the first fpoints. AfterDx50.8 the switching time could not be estalished accurately, since the transparency is almost compbefore the potential step is applied.

C. Potential dependence

In Fig. 5 the effective diffusion coefficient related to thslow process is plotted as a function of the applied potenof the potential-step experiments. The diffusion coefficieincreases from 1.4310211 to 1.3310210cm2 s21 in the po-tential range from20.91 to 21.2 V. The switching timedecreases from a 100 to 10 s with decreasing potential.reciprocal switching time as shown in Fig. 5 is also clealinearly dependent on the potential. The linear dependencboth the reciprocal switching time and the diffusion coecient on the potential are an indication that the switchingdetermined by diffusion.

The potential at the sample corresponds, via the Neequation, to an equivalent hydrogen pressurepH2

24

FIG. 4. Diffusion coefficients calculated from the current transients shoin Fig. 3 ~squares!, and the reciprocal switching time~triangles, right axis!of the film as a function of the added hydrogenDx, intercalated before thepotential step.

FIG. 5. The potential dependence of the diffusion coefficient and the rerocal switching time~calculated from the maximum of the derivative of thtransmission with respect to time! of a 400 nm film.


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Here,F is the Faraday constant,R the universal gas constanT the temperature, andn the number of electrons involved ithe hydrogen evolution reaction (n52). The hydrogen pressure is expressed in bar. Equation~5! is only valid for equi-librium. During a potential step experiment an overpotencomponent will influence this direct relation between the ptential and pressure. A dependence of the switching timethe hydrogen pressure in epitaxial yttrium thin films has bereported by Remhofet al.25 in gas phase experiments. Assuming that the production of adsorbed hydrogen accordto Eq. 1~a! is not limited by the applied potential, it is therefore likely that the electrochemically applied equivalent hdrogen pressure also influences the effective hydrogen dsion coefficient. From the isotherm of gadolinium26 we knowthat the pressure and concentration are directly related.therefore also possible that the potential dependence isrectly a concentration dependence.

D. Thickness dependence

In Fig. 6 the diffusion coefficient is shown as a functioof film thickness for two potentials. For the potential step21.0 V the diffusion coefficient increases from 3.2310212

to 2.1310211cm2 s21 as the thickness is increased from 5to 400 nm. The diffusion coefficient for the potential step21.1 V is higher, as expected from the potential-dependmeasurements, but shows the same trend with increathickness. It is known that for thin metal films hydrogediffusion coefficients can depend on the film thickness.27 Theupward trend in our results is in agreement with the increof the mobility coefficient for lateral hydrogen diffusion witincreasing thickness as reported for yttrium films by Van dMolen et al.7 In the same study the morphology was showto depend on the film thickness. This is confirmed byAFM study on our gadolinium films. In Fig. 7 the increasingrain size of films with increasing thickness is apparent. Itherefore likely that the diffusion coefficient is determinedthe morphology of the film. The effect of morphology ma

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FIG. 6. Diffusion coefficients as a function of film thickness for two applipotentials: 1.0 V~squares! and21.1 V ~triangles!.


4663J. Appl. Phys., Vol. 94, No. 7, 1 October 2003 Di Vece, Swart, and Kelly

FIG. 7. The surface morphology as recorded by AFM for a 100 nm~A! and a 300 nm~B! gadolinium film.

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be different for lateral or normal diffusion; in both cases tswitching time does not show theL2 dependence expectefrom Eq. ~4! ~see Fig. 8!.

A surface-limited process, either at the palladium surfaor the palladium–gadolinium interface, should result inswitching time which is independent of the film morphologonly the surface process should affect the kinetics. Sincegeometric area and properties of the surface are unlikelbe influenced much by the internal structure of the filmdo not expect a dependence of a surface limited procesthe morphology. The switching time should then be lineadependent on the film thickness, since only the size of‘‘reservoir’’ matters. From the clear nonlinear dependencethe switching time we conclude that switching limited bysurface process can be excluded.

In a diffusion-controlled process, an indication of thswitching time can be obtained from Eq.~4!. In Fig. 9 thediffusion coefficient is shown as a function of the reciprocswitching time. A linear relation between ofL2/ts and D isfound, which is not dependent on the film thickness;

FIG. 8. The reciprocal switching time as a function of film thickness for tapplied potentials:21.0 V ~squares! and21.1 V ~triangles!.


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slope of this linear plot, or prefactor, is determined byhwhich relates the optical absorption coefficient to the cocentration profile within the film. If the optical switching icompletely diffusion limited, the prefactor should have tsame value for all thickness-dependent experiments. Fthis information we conclude that a dependence of the dision coefficient on the morphology directly influences toptical switching time, but the diffusion process and tswitching time remain strongly correlated.

In Fig. 10 the logarithm of the diffusion coefficient iplotted as a function of the logarithm of the reciprocswitching time, for the results obtained at various tempetures, concentrations and potentials. It is clear that the dpoints lie about a straight line, like the results of Fig. 9. Tdifferent relative positions of the data points from differeexperiments are the result of the different film thickness uin these experiments. A difference of the prefactor for theexperiments would translate in a upward or downward sof the points. The results of Fig. 10 show that the strocorrelation between current decay and optical switching ti

FIG. 9. The diffusion coefficient as a function ofL2/tswitch for the films ofdifferent thickness.


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is independent of temperature and potential. The firstpoints of the concentration dependent results~filled squares!lie on the straight line. The deviation of the remaining poinis explained by a dependence on concentration of the fution that relates the transmission and concentration.

E. Comparison with literature

In the experiments of Den Broederet al.20 involving lat-eral diffusion, thebg phase boundary is visible as a tranmission discontinuity, which moves with at1/2 dependenceSince the film is very thin, formation of a phase boundaduring loading normal to the surface is unlikely due to tlimited time. For much thicker films a phase boundary mocould relate the diffusion coefficient to the switching time

Typical electrochemical switching times are in the ordof 10 s for a potential stepped to around21.1 V. More nega-tive potentials will only result in hydrogen gas developmeGas phase experiments on yttrium switchable mirrors abar hydrogen pressure show similar switching times. VanMolen et al.7 reported a switching time of 3 s for a 200 nmyttrium film. Huibertset al.1 measured a switching time o70 s for a 500 nm yttrium film. Therefore a fundamendifference in switching kinetics for gas phase and elecchemical loading seems unlikely.

IV. CONCLUSIONS

We show that a simple diffusion model describes contently the switching kinetics of a gadolinium thin film upohydrogenation. The time constants of the current and tramission transients are directly related to the diffusion coecient, pertaining to the reversible loading of the gadoliniufilm. Two time domains are attributed to the different strutural phases involved in the transition from the dihydridethe trihydride state. There is a clear dependence ofswitching time and diffusion coefficient on temperature, ptential, concentration, and film thickness. The measuredtivation energies correspond well with literature values

FIG. 10. The diffusion coefficient determined from the current transientfunction of the reciprocal switching time. The experimental results for dferent temperatures~triangles!, concentrations~squares! and potentials~dots! are shown.


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similar materials. A significant increase of the diffusion cefficient with increasing hydrogen concentration and dcreasing applied potential is found. A thickness dependeof the switching time and diffusion coefficient is also cleaThe nonlinear dependence of the switching time on the fithickness indicates the role of diffusion limited kineticsoptical switching.

ACKNOWLEDGMENTS

The authors would like to thank E. M. H. Evens andM. Kerkhof from Philips Research~Eindhoven! for prepara-tion of the samples. We also thank F. H. Reincke for AFassistance. The work described here was supported byCouncil for Chemical Sciences~CW!, with financial aid fromthe Netherlands Organization for Scientific Research~NWO!and the Netherlands Foundation for Technical Resea~STW!.

1J. N. Huiberts, R. Griessen, J. H. Rector, R. J. Wijngaarden, J. P. DekD. G. de Groot, and N. J. Koeman, Nature~London! 380, 231 ~1996!.

2P. van der Sluis, M. Ouwerkerk, and P. A. Duine, Appl. Phys. Lett.70,3356 ~1997!.

3D. G. Nagengast, A. T. M. van Gogh, E. S. Kooij, B. Dam, and R. Grisen, Appl. Phys. Lett.75, 2050~1999!.

4T. J. Richardson, J. L. Slack, R. D. Armitage, R. Kostecki, B. Faranand M. D. Rubin, Appl. Phys. Lett.78, 3047~2001!.

5T. J. Richardson, J. L. Slack, B. Farangis, and M. D. Rubin, Appl. PhLett. 80, 1349~2002!.

6P. van der Sluis and V. M. M. Mercier, Electrochim. Acta46, 2167~2001!.7S. J. van der Molen, J. W. J. Kerssemakers, J. H. Rector, N. J. KoemaDam, and R. Griessen, J. Appl. Phys.86, 6107~1999!.

8P. van der Sluis, Electrochim. Acta44, 3063~1999!.9P. H. L. Notten, M. Kremers, and R. Griessen, J. Electrochem. Soc.143,3348 ~1996!.

10J. O’M. Bockris, J. McBreen, and L. Nanis, J. Electrochem. Soc.112,1025 ~1965!.

11E. S. Kooij, A. T. M. van Gogh, and R. Griessen, J. Electrochem. S146, 2990~1999!.

12M. Di Vece, P. van der Sluis, A.-M. Janner, and J. J. Kelly, J. ElectrochSoc.148, G576~2001!.

13A. T. M. van Gogh, D. G. Nagengast, E. S. Kooij, N. J. Koeman, J.Rector, and R. Griessen, Phys. Rev. B63, 195105~2001!.

14C. J. Wen, B. A. Boukamp, and R. A. Huggins, J. Electrochem. Soc.126,2258 ~1979!.

15J. Crank,The Mathematics of Diffusion, 2nd ed.~Oxford University Press,New York, 1999!.

16W. M. Mueller, J. P. Blackledge, and G. G. Libowitz,Metal Hydrides~Academic, New York, 1968!, Chap. 10.

17Handbook on the Physics and Chemistry of Rare Earths, edited by K. A.Gscheidner, Jr. and L. Eyring~North Holland, Amsterdam, 1979!, Vol. 20,Chap. 20.

18C. Montella, J. Electroanal. Chem.518, 61 ~2002!.19G. Majer, U. Kaess, and R. G. Barnes, Phys. Rev. Lett.83, 340 ~1999!.20F. J. A. den Broederet al., Nature~London! 394, 656 ~1998!.21J. Crank and G. S. Park, Trans. Faraday Soc.45, 240 ~1949!.22H. C. Bauer, J. Volkl, J. Tretkowski, and G. Alefeld, Z. Phys. B29, 17

~1978!.23G. Majer, J. Gottwald, D. T. Peterson, and R. G. Barnes, J. Alloys Com

330–332, 438 ~2002!.24M. Kremers, N. J. Koeman, R. Griessen, P. H. L. Notten, R. Tolboom

J. Kelly, and P. A. Duine, Phys. Rev. B57, 4943~1998!.25A. Remhof, G. Song, K. Theis-Brohl, and H. Zabel, Phys. Rev. B56,

R2897~1997!.26M. Di Vece, S. J. M. Zevenhuizen, and J. J. Kelly, Appl. Phys. Lett.81,

1213 ~2002!.27Y. Li and Y. T. Cheng, Int. J. Hydrogen Energy21, 281 ~1996!.

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Electrochemical kinetics of hydrogen intercalation in gadolinium switchable mirrors

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Transcript of Electrochemical kinetics of hydrogen intercalation in gadolinium switchable mirrors