Solid State Ionics 263 (2014) 152–156

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Solid State Ionics

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Deuterium diffusion in proton conductors La0.9Sr0.1ScO3-δ andBaZr0.9Y0.1O3-δ at room temperature

V.B. Vykhodets a,⁎, T.E. Kurennykh a, O.A. Nefedova b, V.P. Gorelov c, A.Yu. Stroeva c, V.B. Balakireva c,E.V. Vykhodets d, S.I. Obukhov a

a Institute of Metal Physics, Russian Academy of Sciences, Ural Division, 620990 Yekaterinburg, Russiab Institute of Engineering Science, Russian Academy of Sciences, Ural Division, 620049 Yekaterinburg, Russiac Institute of High-Temperature Electrochemistry, Russian Academy of Sciences, Ural Division, 620137 Yekaterinburg, Russiad Ural Federal University, 620002 Yekaterinburg, Russia

⁎ Corresponding author.E-mail address: vykhod@imp.uran.ru (V.B. Vykhodets

http://dx.doi.org/10.1016/j.ssi.2014.06.0030167-2738/© 2014 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 21 November 2013Received in revised form 25 March 2014Accepted 4 June 2014Available online xxxx

Keywords:Deuterium diffusion coefficientNuclear reaction analysisProton conductorsVaporDiffusion equation

Room-temperature measurements of diffusion coefficients for deuterium in proton conductors La0.9Sr0.1ScO3-δ

and BaZr0.9Y0.1O3-δ which contain dissolved H2O vapor have been performed. The concentration of oxygenstructure vacancies in oxides after treatment in vapor was close to zero. A diffusion source of deuterium wascreated by ion implantation; measurement of the concentration–distance distribution of deuterium in sampleswas performed in situ during implantation. The NRA technique and 2H(d,p)3H reaction at an energy of theincident beam of 650 keV were used. For the initial and boundary conditions of the diffusion problem whichwere realized in the work, a solution of the inhomogeneous Fick equation was obtained. Using the techniquedeveloped, measurements of the diffusion coefficients for hydrogen in proton conductors were for the firsttime performed directly. For the BaZr0.9Y0.1O3-δ oxide, the directly gained values of diffusion coefficients agreerather well with those obtained from the proton conductivity with the use of Nernst–Einstein equation.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Oxide proton conductors are characterized by high values of hydro-gen diffusion coefficients and are promising materials for solid oxidefuel cells and other electrochemical devices. Data on themobility of hy-drogen ions in thesematerials [1–3]were obtainedmainly viameasure-ments of proton conductivity. In doing so, determination of the chargediffusion coefficients, Dσ, was done with the use of Nernst–Einsteinequation. In several works [4–6], data on the diffusion coefficients forprotons in proton conductors were taken via an indirect method.When using it, the frequency of proton jumps in a crystal was deter-mined by the technique of quasielastic neutron scattering, and thevalues of diffusion coefficients Ds were found with the use of Einstein–Smoluchowski microscopic theory. In work [4], a comparison of thedata on Ds and Dσ for the BaCa(1 + x)/3Nb(2 − x)/3O3Hx oxide wasperformed, which showed up a difference in the activation energyfor Ds and Dσ approximately by 30%: Qs = 0.40 eV and Qσ = 0.55 eV.The authors of thework explain this difference by the effect of grain bound-aries on the results of measurements of proton conductivity, which is ab-sent upon measuring the frequency of proton jumps with the method ofquasielastic neutron scattering. It also can be supposed that the differencein the values of the diffusion coefficients can be conditioned by the fact

).

that theyweremeasuredbydifferentmethods: direct, indirect, and recalcu-lation from theproton conductivity. In viewof this,measurement of thedif-fusion coefficients for protons in proton conductors by direct methods, i.e.,based on Fick equations, is a topical problem.

In severalworks, (see, for example [7–9]) the hydrogen diffusion co-efficients in oxides were determined by direct methods, and the hydro-gen diffusion sourcewas created via ion implantation. However, such anapproach cannot be applied to obtaining diffusion data for systemswithhigh values of diffusion coefficients at room temperature, since in thiscase the characteristics of the diffusion source will be changing in thecourse of measuring the concentration profile, as well as when storingthe sample. Thesemanipulations commonly take place at room temper-ature. As a consequence, for proton conducting oxides, which arefeatured by high values of the hydrogen diffusion coefficients, experi-mental data on the hydrogen diffusion that are obtained by a directmethod are lacking.

In the current work, to perform such measurements, a new tech-nique has been developed that allows simultaneously conducting ionimplantation of deuterium into a sample, diffusion annealing of thesample, and measurement of the deuterium concentration profile.Such an approach was originally aimed at gaining experimental datafor systemswith high diffusion coefficients. Within this approach, mea-surement of the concentration profile was carried out by the nuclear re-action analysis technique (NRA), the 2H(d,p)3H reaction was employed.In this case the deuteron beam was used for both implantation of the

153V.B. Vykhodets et al. / Solid State Ionics 263 (2014) 152–156

deuterium ions into the sample and formeasurements of the deuteriumconcentration in the sample. The idea of such an experimentwas for thefirst time suggested in work [10]. However, it was not realized to thestage of measuring diffusion coefficients. Taking account of the devel-oped version of the method, it was called “nuclear reaction analysison-line” (NRAOL).

2. Principles of NRAOL technique

The NRAOL technique requires oxide sample under study to be posi-tioned in the vacuum chamber of the accelerator setup under continu-ous deuteron irradiation. The source of diffusion in this method isdeuterium ions implanted, which lose their kinetic energy when beingstopped in the sample bulk. During irradiation, diffusion of deuteriumions takes place and their concentration–distance distribution isformed. The mathematical problem of calculation of the diffusion coef-ficients D is significantly simplified if experiments are conducted withdeuteron beams having a diameter of no less than 1 mm and energyof particles of no less than several hundred keV. An analysis performedusing the SRIM program [11,12] showed that in this case, to a great ac-curacy, conditions can be provided that will lead to one-dimensionaldiffusion of deuterium atoms from a very thin layer (let it be called“instantaneous” plane source) in two directions. One of the directionswill coincide with the motion of accelerated particles in the beam (i.e.,there will be diffusion into the sample bulk) and the other will be oppo-site (i.e., diffusion toward the irradiatedflat surface of the sample). Fig. 1illustrates the experimental scheme above described. The characteristicdepth xo at which there is located the instantaneous diffusion sourcemakes up a fewmicrons, and the diffusion processeswill proceedmain-ly inside a cylinder having a diameter close to the diameter of the beam.The NRAOL method also suggests a detector-assisted registration of theproton spectrum resulting from the 2H(d,p)3H nuclear reaction. Thesespectra will be a source of information on the distribution of deuteriumions c(x,t), where x is the depth into the sample, and t is the time ofirradiation. When using the NRAOL technique, experimental dataon c(x,t) can be obtained only for values x b xo. In a general case, thec(x,t) distribution will depend on the radiation intensity and thedeuterium diffusion coefficient.

When choosing initial and boundary conditions for solving the diffu-sion problem, the results of preliminary experiments on the stability of

Fig. 1. Scheme of the NRAOL technique: 1 — sample; 2 — detector; light circles are thedeuterium ions in the plane diffusion source; xo is the depth in the sample at which thediffusion source is located; dark circles are the diffusing deuterium ions; broken linesare examples of diffusion trajectories for deuterium ions.

the oxides under study have been taken into account, which showedthat the concentration of deuterium in the samples had not decreasedafter one week of storing them in air or in vacuum. This fact served asa ground to neglect in the mathematical problem the escape of thedeuterium atoms from inside of the samples during irradiation.

In accordance with the above considerations, a one-dimensionalboundary value diffusion problem was solved for a semi-infinitemedia, with a constantly acting internal “instantaneous” plane sourcelocated at a depth x = xo. An inhomogeneous diffusion equation forthis case has the form:

∂c x; tð Þ∂t ¼ D

∂2c x; tð Þ∂x2

þ f x; tð Þ; ð1Þ

where function f(x,t) characterizes the source performance. Approxima-tion of the internal “instantaneous” plane source is given by the follow-ing expression for f(x,t)

f x; tð Þ ¼ wδ x−xoð Þ; ð2Þ

wherew= I/(Sqo) is the deuteron flux incident onto the sample, I is thecurrent of the deuteron beamand S is its cross section, qo is the deuteroncharge, δ(x − xo) is the Dirac delta-function. When solving Eq. (1), thefollowing initial and boundary conditions were used:

c x;0ð Þ ¼ 0; ð3Þ

∂c 0; tð Þ∂x ¼ 0 and ð4Þ

c ∞; tð Þ ¼ 0: ð5Þ

Eq. (3) corresponds to the absence of deuterium in the sample at theinitial time instant (prior to irradiation); Eq. (4) is the mathematicalcondition for the zero flow of deuterium atoms through a boundary ofthe sample. The application of the boundary condition in Eq. (5) corre-sponds to approximation of an infinite sample thickness, which actuallymeans that the sample thickness is much larger than xo.

To solve Eq. (1), the approach [13] was used upon which the diffu-sion source is considered as an ensemble of “instantaneous” sources,and the distribution c(x,t) after the diffusion annealing was sought asa superposition of solutions corresponding to the “instantaneous”sources. For the case of one-dimensional diffusion in an infinite mediasuch an approach results in a solution in the form of integral

c x; tð Þ ¼Zt0

Zþ∞

−∞

f ξ; τð ÞG x; ξ; t−τð Þdξdτ; ð6Þ

where function G x; ξ; tð Þ ¼ 12ffiffiffiffiffiffiπDt

p exp − x−ξð Þ24Dt

� �is the solution of the

second Fick equation for an “instantaneous” plane source. For a semi-infinite media such an approach gives the following solution

c x; tð Þ ¼ 12ffiffiffiffiffiffiffiπD

pZt0

Z∞0

f ξ; τð Þffiffiffiffiffiffiffiffiffiffit−τ

p exp − x−ξð Þ24D t−τð Þ

!þ exp − xþ ξð Þ2

4D t−τð Þ

!" #dξdτ:

ð7Þ

Here, it is taken into account in the explicit form that the formationof the diffusion source proceeds continuously during the whole time ofirradiation. As a consequence, deuterons coming into the sample withthe accelerator's beam at later stages of irradiation will take part inthe formation of c(x,t) less time than those coming earlier. Functionf(ξ, τ) in Eq. (7) has the same form as in Eq. (2). In integrating over τand ξ, the form of f(ξ, τ) was taken into account as well as the filtering

Fig. 3.Dependences of deuterium concentration c(t) calculated using Eq. (8) for the depthinto sample x=3 μm. Parameters I, R, and xo are the same as in Fig. 2. Curves 1, 2, 3, and 4correspond to the diffusion coefficients D =10−12, 10−13, 10−14, and 10−15 m2/s,respectively.

154 V.B. Vykhodets et al. / Solid State Ionics 263 (2014) 152–156

property of the delta-function. Finally, the expression for c(x,t) takes theform

c x; tð Þ ¼ w2D

sgn x0−xð Þ x−x0ð Þ− xþ x0ð Þ þ x−x0ð Þerf x−x0

2ffiffiffiffiffiffiDt

p� �

þ xþ x0ð Þerf xþ x02Dt

� ��

þw

ffiffiffiffiffiffiffitDπ

rexp

xx0Dt

� �þ 1

� �exp − xþ x0ð Þ2

4Dt

!;

ð8Þ

where sgn x0−xð Þ ¼ 1; x0Nx−1; x0bx

�.

From the results of simulation calculations performed with the useof Eq. (8) and shown in Fig. 2 it is seen that the calculated dependencesof the deuterium concentration on the depth in the sample c(x) for thegiven time instants are characterized by the presence of maxima at adepth equal to the depth at which the diffusion source is localized.Upon growing time of irradiation of the sample t, at all depths there isalso observed an increase in the deuterium concentration. Calculations

show also that the normalization condition ∫∞

0

c x; tð Þdx ¼ wt is valid for

the concentration–distance distributions of the deuterium atoms.The calculated data shown in Fig. 3 demonstrate a high sensitivity of

the NRAOL technique to the values of the deuterium diffusion coeffi-cients in the range from 10−12 to 10−15 m2/s. It is seen that in thisrange, upon decreasing the diffusion coefficient, the deuterium concen-tration in the zone under analysis monotonously increases at all irradi-ation durations. Moreover, the curves c(t) are characterized by adecrease of derivative ∂c(t)/∂t with increasing the time of irradiation.At D N 10−12 m2/s and D b 10−15 m2/s, the sensitivity of the NRAOLtechnique to the values of the deuterium diffusion coefficients will belower than in the range from 10−12 to 10−15 m2/c because of low con-centrations c(t) in the zone under analysis. Note that at very low valuesof the diffusion coefficients (the case is not shown in Fig. 3), the calcula-tion curves c(t) are characterized by growth of the derivative ∂c(t)/∂twith increasing the time t. According to the data of [2], in the rangefrom room temperature to 300–400 °С, the values of the diffusion coef-ficients for protons in proton conductors fall predominantly in the range

Fig. 2.Dependences of deuterium concentration on depth into the sample, c(x), calculatedby Eq. (8). Parameters of calculations: deuterium diffusion coefficient D =10−14 m2/s;current of the deuteron beam I = 180 nA; radius of the deuteron beam R =1 mm;depth of localization of the internal source xo =3.71 μm. Curves 1, 2, 3, and 4 correspondto the irradiation time t: 1 — 1800 s, 2 — 3600 s, 3 — 7200 s, 4 — 10,800 s.

from 10−12 to 10−15 m2/s. The results of simulations presented testifythus to the high potentiality of the NRAOL technique for studying thehydrogen diffusion in these materials.

A serious shortcoming of the NRAOL technique can be influence ofirradiation on the deuterium diffusion coefficients. On the one hand,the experiments are worth doing at a high current density of thebeam, since its increasewill result in the enhancement of the deuteriumconcentration in the sample and, consequently, increase in the accuracyofmeasurements of concentration profiles and diffusion coefficients. Onthe other hand, this increase in the current density can cause negativeaftereffects: uncontrolled change of the deuterium diffusion coefficientbecause of increase in the sample temperature and formation of radia-tion defects. Accounting for this, in this work, the current density valuesat which no remarkable influence of irradiation on the diffusion coeffi-cients for deuterium is observed were found from experiments.

3. Samples and methods

Experiments were performed on micropowders of the proton-conducting oxides La0.9Sr0.1ScO3-δ and BaZr0.9Y0.1O3-δ. The oxides weresynthesized by the standard high-temperature ceramic technologyfrom highly pure oxides and carbonates La2O3, SrCO3, Sc2O3, BaСО3,ZrO2, and Y2O3. The micropowders of the initial materials were mixedin the required proportions in a zirconia mortar in the medium ofethyl alcohol. Then, after pressing, the samples were annealed in air at1400 °С. After annealing, the pressed samples were ground again inthe zirconia mortar in the medium of ethyl alcohol. Such annealing–grinding treatments were run several times. After several annealingswith subsequent grinding, the final sintering was performed at1600 °С in air for 5 h. Then, sintered samples were ground dry in asapphire mortar. The specific area of the micropowders was 2–3 m2/g.X-ray analysis showed that the samples were single-phase. In the caseof the BaZr0.9Y0.1O3-δ they possessed a cubic perovskite structure,while samples of La0.9Sr0.1ScO3-δ, possessed orthorhombic perovskitestructure. The X-ray analysis was carried out on a Rigaku DMAX 2200diffractometer in CuКα radiation with a monochromator.

In this study, the NRAOL technique was used to measure diffusioncoefficients for deuterium in oxides containing dissolved vapors. In

200 250 300 350 400 450 500 550 6000

4

8

12

16

20

24

x 0.2

12C(d,p)13C

16O(d,p0)17O

2H(d,p)3H

yiel

d

channel number

Fig. 4. Spectra of nuclear reaction products obtained upon irradiation of the La0.9Sr0.1ScO3

H0.1 oxide for the current of the deuteron beam I = 180 nA: dark circles — time of irradi-ation t = 764 s, light circles — t = 2407 s, and stars — t = 6488 s.

155V.B. Vykhodets et al. / Solid State Ionics 263 (2014) 152–156

doing so, a homogeneous distribution of water molecules in the initialsample must be provided. This condition is difficult to achieve formassive samples; that is why our diffusion measurements were carriedout on micropowders. To produce samples containing water vapor, theoxide powders were treated in an air atmosphere that containedsaturated vapor of H2O or D2O. In the hydrogen subsystem, the heavywater contained 99.8% of deuterium. The temperature of water was25 °С. At the final stage, the temperature of annealing in wet air was300 °С for the BaZr0.9Y0.1O3-δ oxide and 400 °С for La0.9Sr0.1ScO3-δ. Theduration of annealing was about 150 h. The concentration of deuteriumin the samples treated in the D2O vapor was determined by the NRAtechnique using the 2H(d,p)3H reaction with the energy of particles inthe incident beam of 650 keV. The deuterium concentration in theoxide samples corresponded to the formulae La0.9Sr0.1ScO3D0.1 andBaZr0.9Y0.1O3D0.1. One can suppose that in the oxides of such composi-tion the concentration of structure oxygen vacancies is close to zero.Such conclusion follows from the condition for electrical neutralityand assumption on the ionic type of bonding in oxides. In this case,the following charge states were employed: La3+, Sr 2+, Sc3+, Ba2+,Zr4+, Y 3+, D+, andO2−. Aswas already noted, the sampleswere stable,and the concentration of deuterium in them did not decrease duringstorage in air or in vacuum. The concentration of protium in the pow-ders treated in the H2O vapor was not measured. In what follows,upon discussion of the experimental data on diffusion it was taken forgranted that the oxides treated in the H2O vapor had a composition ofLa0.9Sr0.1ScO3H0.1 and BaZr0.9Y0.1O3H0.1. To conduct measurementswith NRAOL technique, powder particles were pressed into an indiumplate. As a result, near the plate surface an oxide layer was formedwith a thickness of about 100 μm. This value meets the approximationof a semi-infinite media which was used when deriving Eqs. (7) and(8). Recall that the characteristic depth xo, at which an “instantaneous”plane diffusion source is located in the NRAOL technique, makes upseveral microns.

Experiments were conducted at room temperature at a 2 МV Vande Graaf accelerator. For measuring the distribution of deuterium ionsc(x,t) in the zone of irradiation, the 2H(d,p)3H reaction was used withthe particle energy in the incident beam of 650 keV. The samplesunder study were set perpendicular to the axis of the incident beam.Registration of the products of nuclear reactions was performed withthe use of a silicon surface-barrier detector having a diameter of about10 mm, and angle of detecting 160°. The diameter of the incidentbeam was 2 mm. The current of the deuteron beam falling onto thesample was varied in the range from 60 to 380 nA and in each casewas kept constant with an accuracy of about 20%. To measure the cur-rent, a secondary monitor was used which was calibrated by the Fara-day cup. The statistic error in the determination of the irradiationdose for the samples made up about 1%. The mathematical processingof the initial data was done by comparing the spectra from the samplesunder studywith those from the reference samplewith the constant-in-depth concentration of deuterium. As a reference, there was used apowder of the ZrCr2D4 deuteride. Experimental conditions at the accel-erator and methods of spectra processing are reported inmore detail in[14].

4. Results and discussion

The experiments on the determination of the diffusion coefficient Dconsisted in a continuous irradiationwith deuterons of the samples con-taining dissolved protium ions and the simultaneous registration of theproton spectra from the 2H(d,p)3H reaction. The exposure to the contin-uous irradiation amounted up to several hours, while the duration ofcollecting one spectrum varied from 200 to 600 s. With such experi-mental setting, the number of counts from the 2H(d,p)3H reaction wasinsufficient for high-accuracy measurements of the concentration–distance distributions for the deuterium atoms into the sample. Forthis reason,when treating the experimental data, we employed average

concentrations of deuterium C(t) in the zone under analysis. They weredetermined as follows:

C tð Þ ¼ 1xS

ZxS0

c x; tð Þdx; ð9Þ

where xS is the depth into the sample to which the measurements ofdeuterium concentration were performed. According to the results ofcalculations with the use of the SRIM program [11,12], the depth xo, atwhich the internal diffusion source was located, made up 3.71 μm forthe La0.9Sr0.1ScO3H0.1 oxide and 3.93 μm for BaZr0.9Y0.1O3H0.1, the corre-sponding values of xS were 3.3 and 3.5 μm.

In Fig. 4, as example, several spectra obtained in the study areshown. They illustrate that with increasing the irradiation time t, theyield of protons in the nuclear reaction 2H(d,p)3H and, correspondingly,deuterium concentration in the zone under analysis increased.

When treating the results of measurements with the use of Eqs. (8)and (9), it was established (see Fig. 5) that the experimental depen-dences C(t) corresponded to stationary conditions, i.e., constant valuesof the deuteriumdiffusion coefficients. Thismaymean that either no re-markable effect of sample heating and radiation defects on the diffusioncoefficients was exerted at all or stationary values of temperature andradiation defect concentrations were reached in our experiments veryquickly, in 10 min or quicker. The values of the deuterium diffusion co-efficientsDwere chosen so that tofit the experimental data on C(t)withthe calculations in the best way, themethod of least squares being used.The error in the determination of the diffusion coefficients is condi-tioned by the scatter of the experimental points around the calculatedcurves C(t), it did not exceed 20%. From Fig. 5 it is seen that deviationsof the experimental points from the calculated curves C(t) in the mainwere lower than a priori mean-square errors of measurements.

The obtained data on the diffusion coefficients D are given in thecaption to Fig. 5. For the La0.9Sr0.1ScO3H0.1 oxide, forwhich themeasure-ments were performed at various currents of the beam, the D valuesgrow with increasing the current. In a general case, it can be caused byincreasing concentration of radiation defects in the sample and its tem-perature upon irradiation. Estimationwith the use of Arrhenius relationD ¼ Do exp −Q

�kT

showed that the observed changes in the D values

can be traceable to the fact that the sample temperature in the experi-ments at the current 380 nA was higher by ΔT = 14 K than in experi-ments at 60 nA (it was taken that the activation energy for thedeuterium diffusion Q= 0.5 eV, which is typical of hydrogen in protonconductors [2]). The estimates made in our work based on the thermalcalculations [15] showed that ΔT ~ I, and at I = 380 nA, the maximal

Fig. 5. Dependence of the average deuterium concentration C in the zone under analysison the time of irradiation t. Points are experimental data, lines are the results of calcula-tions by Eqs. (8) and (9). The radius of the deuterons beam R = 1 mm, energy of theincident-beam particles 650 keV. 1 — La0.9Sr0.1ScO3H0.1, I=60 nA, D = 0.72·10-13m2/s.2 – BaZr0.9Y0.1O3H0.1, I=382 нА;, D = 0.79·10-14 m2/s. 3 – La0.9Sr0.1ScO3H0.1, I=180 nA,D = 0.77·10-13m2/s. 4 – La0.9Sr0.1ScO3H0.1, I=380 nA, D = 1.9·10-13m2/s.This is the cor-rect version of the caption for Fig.5.

156 V.B. Vykhodets et al. / Solid State Ionics 263 (2014) 152–156

possible heating of the sample being not higher than 14 K. This givesgrounds to consider the values of D found in our work to correspondto those at room temperature. Judgingby our results, the influence of ra-diation defects on the diffusion coefficients for deuteriumwas very poor(no more than two times) or was absent at all. Yet, this question needsadditional experiments to be performed, as it is important for under-standing the mechanism of proton diffusion in oxides.

We also performed deuteron irradiation of the La0.9Sr0.1ScO3D0.1

oxide. Prior to irradiation the oxide had contained deuterium ions andvirtually no protium ions. In principle, the formation of the diffusiondistributions of deuterium ions could take place in this case as well.However, it was established that the deuterium concentration in theanalysis zone of the La0.9Sr0.1ScO3D0.1 samples upon their irradiationwith deuterons was virtually constant. The same effect was observedin our work [14], where the BaZr0.9Y0.1O3D0.1 oxide was irradiatedwith deuterons. The results obtained in [14] testified that the certaintype of hydrogen isotope exchange took place during irradiation of theoxides. In this frame, the total amount of deuterium and protium ionsin the samples upon their irradiation with deuterons remained almostconstant, while the samples were predominantly losing protium ionsand, instead, gaining deuterium ions. Basing on these results, one cansuggest that the values of D obtained in this work correspond to theapproximately unchanged summed concentration of hydrogen ions inthe oxides.

In a general case, the values of the diffusion coefficients for deuteri-um can depend on concentration of each isotope rather than on only thetotal amount of protium and deuterium ions in an oxide. Prior to irradi-ation, only protium ionswere present in the samples. In the La–Sr–Sc–Ooxide, by the completion of irradiation, the atomic concentration ofdeuterium ions in the hydrogen subsystem was 3% at the current ofthe deuteron beam 60 nA. For the Ba–Zr–Y–O oxide the correspondingvalue was 38%. These data show that with the use of the NRAOLtechnique, one can obtain the D values at very low concentrations ofdeuterium in the diffusion zone. In the experiments performed, theconditions for measuring the diffusion coefficients for tracers werefulfilled for the La0.9Sr0.1ScO3H0.1 oxide at the current of the deuteronbeam I = 60 nA.

For the BaZr0.9Y0.1O3H0.1 oxide, the D value obtained for deuteri-um by the direct method, was compared with the charge diffusioncoefficients Dσ for protons. The corresponding measurementswere carried out in [2] in the temperature range of 50–150 °С,and the extrapolated value of the diffusion coefficient at 300 K

made up Dσ = 1.53∙10−14 m2/s. It is close to that obtained for thisoxide in our work — D =0.79∙10−14 m2/s. Strictly speaking, uponcomparison of these results, it is necessary to take into accountthe isotopic effect in diffusion. In the given case, this correctiondoes not exert any principal effect, and one can state on the virtual-ly coinciding values of D and Dσ. Judging by the results of this singlecomparison, unambiguous conclusions can hardly be made. Suchcoincidence of the values D and Dσ may testify to the absence of dif-ference in these diffusion coefficients in any case or to the correctdetermination of the diffusion coefficients in work [2] and in our re-search. This problem needs further investigation.

In the current work, at room temperature, we obtained the D valuefor the La0.9Sr0.1ScO3Н0.1 oxide one order of magnitude higher thanthat for BaZr0.9Y0.1O3H0.1. This result is interesting because protonconductors with high values of the hydrogen diffusion coefficientsshow up much promise as materials for solid oxide fuel cells andother electrochemical devices. In early works it was found that it isthe BaZr0.9Y0.1O3H0.1 oxide that is characterized by the maximal valuesof the proton mobility.

5. Conclusions

In literature, data on the diffusion coefficients for hydrogen in protonconductors that are gainedwith the use of a directmethod are lacking. Inthe current work, suchmeasurements were performed for the first timeand room-temperature values of the deuterium diffusion coefficients inthe proton conductors La0.9Sr0.1ScO3Н0.1 and BaZr0.9Y0.1O3H0.1 were de-termined. For the BaZr0.9Y0.1O3H0.1 oxide, the value of the diffusion coef-ficient for deuterium obtained at room temperature in our workvirtually coincides with that for the charge coefficient for the proton dif-fusion [2]. For the La0.9Sr0.1ScO3Н0.1 oxide, we obtained the value of thedeuterium diffusion coefficient at room temperature, which is approxi-mately by the order of magnitude higher than for the BaZr0.9Y0.1O3H0.1.

Acknowledgments

The authors are very grateful to V.V. Kondratiev and A.G. Kesarev forthe discussion of the mathematical problem given in Section 2 of thiswork. The work was supported by the Russian Foundation for BasicResearch (grant no. 13-03-00310) and by the Presidium of RussianAcademy of Sciences (grant no. 12-P-23-2006 “Hydrogen isotopes inoxides”).

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