chemical diffusion coefficient of oxygen in polycrystalline yba2cu3o7−x at room temperature

Physica C 174 ( 1991 ) 273-279 North-Holland

Chemical diffusion coefficient of oxygen in polycrystalline YBaECU307_x at room temperature

Yosef Scolnik, Eyal Saba tan i and Dav id Cahen i The Weizmann Institute of Science, Rehovot, Israel 76100

Received 20 December 1990

Diffusion of oxygen at room temperature in polycrystalline pellets and thin films of YBa2CuaO7_x (123) is measured from the current decay at constant potential in an electrochemical cell with a liquid electrolyte, using 123 as the cathode. The effective chemical diffusion coefficient is found to be 10-it_ 10-t2cm2/s, thus explaining the relatively facile movement of oxygen in such samples.

1. Introduction

While it is well established that the oxygen content ofYBa2CuaO7_x ( 123 ) can be changed between x = 0 and l, at temperatures above 400 ° C [ 1 ], the idea, that oxygen diffusion is also relatively facile at room temperature, at least in polycrystalline samples, has become accepted only recently. Such low temperature oxygen diffusion is not only of interest from the point of view of solid state chemistry, but also because it can yield reduced material that behaves in some aspects different from that which is accessible by high temperature diffusion, such as the occur- rence of a Tc around 20 K [2 ].

In view of our success in reducing polycrystalline pellets and thin films of 123, in a wet electrochemical set-up, at room temperatures, it was of interest to try to measure the chemical diffusion coefficient of oxygen,/~(ox), in such samples at this temperature. Up till now mostly high temperature values for /~(ox) have been reported (except for the estimate made in ref. [3] on the basis of weight gain "~"-:-" , U U I l l l ~

reoxygenation of thin films at < 160°C). Thus, for example, measurements of L3(ox) from the time dependence of the resistance of pellets and thin films at ~ 550°C gave values of ~ 10-12 c m E / s [4-6]. For

Author for correspondence.

single crystals Maier et al. reported a much higher value of ~ 10 -6 c m 2 / s for/3(ox) in the ab-plane, at 300°C [7]. Extrapolation of their data (taken between 440 and 350°C) suggests a room temperature value of ~ 10-~o cm2/s. While this value is similar to that estimated by extrapolating from 900-300°C data on polycrystalline pellets, from observing the interface between the orthorhombic and tetragonal phases by polarized light microscopy [8], it is not a realistic one. This can be seen by calculating that the time needed to deplete 1-10 pm grains totally from oxygen would be seconds to minutes, something that is nol borne out by experiment. On the other hand if we extrapolate self diffusion data, obtained from tracer experiments between 600 and 300 °C on crystals and oriented polycrystalline samples we find a room temperature value of ~ 10-~9 cm2/s [9]. If this were similar to the effective value for D(ox) at room temperature, it would limit oxygen loss to a very nar- row region ( 1 nm or less) near the 3urface of each grain. This is incompatible with our results from r o o m 4 . . . . . . * . . . . o l a , ' , ¢ r ~ , ' , h ~ - ~ ; r ~ l r e d u c t i o n , ~¢ t h e Ik lk.¢ 1 1 1 l . J t . . . l l g 4 lib ~l . l I t , . '11.¢ 1 ~ ¢ ' ~ . Ib I ' ~hJ ' l~ 1 l ~ ¢ I i a a ~*," ~,,4, i . . . . . .

extent of this process is such that most of the volume of 5-10 pm sized grains and all of that of ~ 1 ~m ones is affected. We can make a rough estimate of /~(ox) under our conditions on the basis of the amount of oxygen tha" is removed over time from our samples, using their average grain size to esti-

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274 Y. Scolnik et al. / Chemical diffusion coefficient o f oxygen in polycrystailine YBa2Cu jOt_ x at room temperature

mate the diffusion path. This suggests that the effective value of/~(ox) at room temperature is some- where around 10-m1-10-12 cm/s in our polycrystalline samples. Such a value is not unrea- sonable, in view of the estimates made above and in ref. [ 3 ], or when we compare it to room temperature data for polycrystalline samples of Ndo.sSr0.sCoO3_y [0<y<0 .25 ] [10], Ndo.sSro.2CoO3_y [0_<y<0.1 ] [ 10 ] and Lao.sSr, o.sCoO2.9a9 [ 11 ], which gave values of 7.6× 10 -L4, lAX 10 -I~ and 5X 10 -15 cm2/s, respectively. These data were obtained by galvano- static changes in potential [ 10], or potentiostatic changes of current with time [ 11 ]. The latter method is the one more readily applicable to porous polycrystalline samples, because by using a time-bounded three-dimensional diffusion model. Van Buren et al. [ 11 ] could est imate/)(ox) polycrystaliine samples of La-Sr-Co perovskite, without spec~6c knowledge of surface area or suaface concentration of oxygen vacancies. We report here the results of applying this method to a number of 123 samples. Due to the polycrystalline, often porous nature of our samples, the values that we obtain represent effective ones.

rhombic 123 [ 12 ]. The oxygen content was deduced from iodometric titration which determined the fractions of Cu 2+ and Cu 3+. It was found to be 6.97+0.02. Grain sizes were mostly between 5-10 ~m, as determined by Scanning Electron Microscopy (cf. fig. 1 ).

The procedure of ref. [ 11 ] was used to prepare Lao.sSro.sCoO3_r This yielded single phase material as determined by X-ray powder diffraction. The oxygen content was ~i:~und to be 2.99, as determined by iodometric titration, and in agreement with results from ref. [ 3 ]. The grain size was typically 1.5 iam.

Thin f'dms of 123 were obtained from Tel Aviv University's Dept. of Physics. They were prepared by electron gun sputtering of 123 targets on sapphire substrates. Subsequently they were sintered and annealed to maximize their oxygen content. The dif- fractograms of the films that resulted after annealing in oxygen showed non-epitaxial growth of orthorhombic 123. The films were some 1 ~tm thick (cf. fig. 1).

2.2. Modifications of pellets

2. Experimental

2.1. Preparation of 123

Pellets were prepared by heating a mixture of ni- trates, precipitated by evaporating to dryness the solution, that resulted from dissolving stoichiometric quantities ef Y203, BaCO3 and CuO in concentrated nitric acid. This precipitate was redissolved in dilute nitrate and again heated to dryness. This procedure was repeated 3 times, after which the final precipitate was heated in air overnight at 120 ° C. Pellets, 8 mm in diameter and some 0.5 mm thick, were prepared from the thoroughly ground powder. They were heated in flowing oxygen for 12 h at 950°C, cooled to 50 ° C, reground and reheated. After a final step of re-grinding and passing the resulting powder through a 400 mesh (37 ~tm) sieve, the final pellet was pressed and heated as above with a 12 h annealing step at 500°C, before cooling to room temperature.

The resulting material was single phase, as far as could be judged from the X-ray powder diffracto- grams, which agreed well with the pattern of ortho-

To check for the effects of the density, porosity and nature of the surface of the pellets on the measurements, samples were modified in several ways. By varying the final heat treatment pellets with densi- ties between 4.2 and 5.0 g/cm 3 and grain sizes between 5 and l 0 l~m could be prepared. The porosity was increased first by grinding up the final pellets and then repressing without sintering. Such treatment preserves superconductivity of the individual grains, as shown by AC magnetic susceptibility measurements. A further increase in porosity was achieved by preparing pellets (after grinding up the pellets that were obtained after final anneal) that contained 10% (w/w) of tetrabutyl ammonium perchlorate (TBAP), the salt used to prepare the organic liquid electrolyte. The, TBAP was then removed from the pellet by soaking the pellet overnight in propylene carbonate. A further change in porosity was achieved by covering the side of the pellet, that was exposed to the liquid electrolyte, by a micro- porous teflon membrane with 40-60% porosity volume and 0.2 ~tm pore radius (Raychem). Changes in porosity were observed by scanning electron microscopy.

Y. Scolnik et aL / Chemical diffusion coefficient of oxygen in polyerystalline YBa2Cu ~O7_.~ at room temperature 275

The surfaces of some pellets were etched in 1% (w/ w) Br2/ethanol solution for 10-40 min. Such etch is reported to clean the surface of hydroxides and car- bonates, that form upon exposure to air ( 10 min etch removes ca. l ~tm of pellet, according to ref. [ 13 ]. On the surface of other pellets 50-60 nm Ag was evaporated. Such treatment is reported to form a layer of Ag on the grain surfaces, which then lowers the surface barrier for out-diffusion of oxygen [ 14 ]. One set of pellets with 50 nm Ag on the pellet surface, to be exposed to the solution, was used as is. Another set, with 60 nm Ag on both sides, was annealed for 20 h at 750°C and then cooled at 50°C/ h to room temperature.

2.3. Electrochemical set-up

A standard 3-electrode cell was used with 123 as the electrode and Pt wires as counter- and quasi reference electrodes. In the 0.1M solution of TBAP in propylene carbonate, such a quasi reference electrode was found to be at a potential of +0.25 V versus SCE. Both thin films and pellets of 123 were used as working electrode. They were contacted by at- taching a Cu wire to them, with Ag paint. To avoid parasitic reactions with the solution, the contact region was covered with electrically insulating epoxy cement. The electrolyte was de-aerated by bubbling Ar through it, prior to starting the experiment, and kept under Ar during the experiment. In some experiments we used dry acetonitrile, instead of propylene carbonate as the solvent. The working voltage was varied between - 1 . 0 and - 0 . 5 V (versus the quasi-reference electrode), depending on the experiment.

2. 4. Measurement o f D(ox)

The theoretical background for the electrochemical determination of/9(ox) by measuring the time dependence of current decay under potentiostatic conditions has been given in ref. [ 15]. The deriva- tion is based on a time-bounded, three-dimensional model for diffusion. This model is applicable to materials whose electronic conductivity depends on their stoichiometry (via control over the concentration of electronic carriers) in a continuous fashion over a certain range of stoichiometry. This particular ver-

sion of the current decay method is suitable for use with porous, polycrystalline samples. Originally it was used for samples in aqueous solutions. However, because of the interactions of H20 with the surface of 123, we used a non-aqueous electrolyte. The reaction that takes place during passage of current at the 123 electrode can be written as follows:

[YBa2Cu3OT, 2h,~b] + 2ze-

[YBa2Cu3OT_x, zVo] + z{O} = , (1)

where {O} is a reactive oxygen species that reacts further in solution (to give mainly propanal, in propylene carbonate, cf. ref. [ 16 ] ). The square brackets indicate species in the electrode, where Vo stands for an oxygen vacancy. The reaction that determines the potential between the 123 electrode and the solution can be written as:

[06],23 + 2e- ¢> [V o - 2hvt,],23 + {0} = , (2)

where -2h~b indicates the removal of two holes from the valence band (vb) of 123. The diffusion model assumes that the rate of this reaction is determined by the slow out (in) diffusion of Oo (Vo) inside the porous electrode material. The pellet is thought to be made up of small particles of identical size and shape that contact each other electrically, i.e. are the same potential.

A problematic assumption of the original model is that inside each particle oxygen diffusion is taken to be isotropic. In 123 it has been shown that diffusion along the ab-plane is much faster (up to 106 times) than along the c-direction [9]. Thus in polycrystalline samples one measures essentially diffusion along the ab-plane only. While these results have been obtained at elevated temperatures, it is diffic~dt to see why diffusion at room temperature would be isotropic. By modifying the derwation of Van Butch's model (given in the appendix oercf. [ 15] ) but now assuming that the diffusion occurs o~ly in the ab- plane, it can be shown that the average currem density, i, is now given by:

k (,j+! / ' = ~ \ ,f72 j .rcr+2 (3)

rather than by:

276 E Scoinik et al. / Chemical diffusion coefficient o f oxygen in polycrystalline YBazCu~Oz_,, at room temperature

k ( 4 2( /+1) '~ (4)

for samples made up of parallelopipeds with edges 2p, 2fq and 2~. Here ~ is a dimensionless length factor, determined by the average form of the grains. It is defined as:

a

x/O(ox)t (5)

The factor k also contains the diffusion coefficient, /)(ox) and the grain size, a, as well as the surface concentration of Vo. By extrapolating the plot of the measured decay current, i, versus 1/x/~ (t is the time m seconds since the start of the experiment), and from knowledge of it and a , /~(ox) can be obtained from the intercept of the linear part of this plot, with the 1/x/~ axis, i.e. we extrapolate to zero current (exhaustion of oxygen in the grain). This intercept yields to which is then substituted in eq. (5). The shape parameter, ;t, is taken to be 2, as intermediate between a cube and a sphere. In practice this parameter is probably less for the elongated shape of the grains in our pellets (cf. fig. l ). For f=5 , 2=0.7, so that the effect on/~(ox) will not be very large. We tested our experimental set-up by using this method to determine /)(ox) in polycrystalline pellets of Lao.sSro 5C002.99 in organic (propylene carbo,ate) solution. Our result, 5 × 10-~4 cm2/s agrees reason- ably well with the values obtained in ref. [ 15 ] for the same compound in aqueous KOH, 5 × 10- ~ cmE/s,

a ,d with the value of Kudo [ l 0 ] for the correspond- ing compound Ndo.sSro.sCoOa_y, 7.6× 10-,4 cmE/s.

2.5. AC impedance measurements

! i ii !ii !i iiii iii : !iliiii!il !~iiii!ii~iiiiiiiii!i!iii~i!: '/~II~ ilili~

: ~ili i̧!~!i!iiii~i!::i!ii~i ii~ i ̧ !i i ̧ i ~ ii i,i~ ~!/i ~ !

: :: :::7%:

III

~ }::;::~ !!i

Impedance measurements were done in acetonitrile (dried analytical grade) solution containing 0.5 mM trimethyl ammonium methyl ferrocence (TMAMFc +/z+ ) and 0.1 M TBAP in a three-electrode ceil with a platinum counter electrode and an Ag/0.1 M Ag + electrode as a reference electrode. An alternating voltage of 5 mV amplitude (rms) in the frequency range of 0.001-65000 Hz was applied to the 123 electrode, which was held at a bias equal to the equilibrium potential (0.26 V versus Ag/0.1 M Ag +). A Solartron frequency response analyzer

Fig. 1. Scanning electron micrographs of some of the samples of YBa2Cu307_, used in this study. The bars indicate 10 ~m. (a) Surface of pellet, without further surface treatment accelerating voltage 20 kV: (b) surface of pellet after etching in Br2/ethanol, accelerating voltage 20 kV; {c) surface ofnon-epitaxial polycrystalline thin film. accelerating voltage 30 kV.

Y. Scolnik et aL / Chemical diffusion coefficient o f oxygen in polycrystalline YBa2CusO:_.~ at room temperature 2 7 7

model 1250 coupled with a Solartron potentiostat (1286), was used to control the e ~periment.

3. Results and discussion

The evidence for oxygen reduction, i.e. the occur- rence of reaction (1) to account for the current passed during the experiment, has been given else- where [ 16 ]. Suffice it to say here that we can exclude corrosion or surface catalysis as the rate determining steps for current flow, on the basis of X-ray diffraction, determimation of oxygen content by iodometric titration plus coulometry, and magnetic susceptibility measurements of reduced samples. In addition, chemical analysis of the electrolyte solution after reduction supports our conclusion [ 16] that reaction [ 2 ] is the rate determining process for current flow.

The AC impedance experiments were performed to measure the diffusion coefficient of electroactive ions in the pores of the 123 electrode and to see if porous diffusion determines the diffusion coefficient derived from the i versus 1/x/~ plot. The simple approach to solve the problem of porous interface impedance is based on the use of transmission line analogy assuming that the pores are cylindrical, uni- form and semi-infinite in depth [ 17-19 ]. As a result of this approach the phase angle of the impedance of a porous electrode is half of the phase angle of the equivalent impedance at a regular planar electrode. For example, the phase angle of.the radial diffusion impedance in a pore is 22.5 ° instead of 45 ° as is the case for the diffusion impedance at a planar electrode. The above anproach also implies that the impedance of a porous electrode is proportional to to- ,/4 and not to oJ - '/2 [ 17 ].

A typical complex impedance plot of an 123 pellet electrode, which was treated for 10 min with 10% bromine solution in ethanol, is shown in fig. 2. The radial diffusion process is clearly distinguishable from other electrode processes. The frequency range cor- responding to the radial diffusion, which shows a transmission line behaviour with a constant phase angle of 24 ° (close to the expected value of 22.5 ° ) is expanded in the insert of fig. 2. The radial diffusion coefficient in the pores, Dpor~, was calculated

15000 -

12000

E 9000

,= o

6000

3000

0 0

. . . L _ U _ . L _ J I . ~ , , , I , ,

1200

1000 .

E 800.

E 600 -

v

.. 400.

200 '

. . . . ~ , . ~ . . . . l i l t . . . . . . . . . . . .

2 t

0 e

2~ o'" .

2 e ee°

11 . . . . i . . . . i . . . . , . . . . u . . . .

200 400 600 800 1000 1200

z' (ohm m 21

o, •

e

o e

@e e

3000 6 0 0 0 9000 12000 15000

Z' (ohm cm 2)

Fig. 2. The complex impedance plot of an electrode of a pellet of YBa2Cu307_ x (treated in a 10% ethanolic solution of bromine ) measured in 0.5 mM (TMAMFc)(CIO4)+0.5 mM (TMAMFc) (CIO4h+0.1 M TBAP in acetonitrile at an applied potential Etn=0.260 V versus Ag/0. l M Ag +.

from this transmission line using Warburg impedance equations for planar diffusion:

Zair, = a~o ' /4, (6)

~= ~F" ~ + (7)

Here Zo.ff is the diffusion impedance magnitude [ 11,12], w is the angular frequency, R, 7", n and F are the gas constant, the absolute temperature (in K), the number of electrons and the Faraday constant, respectively. The real electrode area, ,4, was calculated from the ratio of the capacitance of a pellet electrode and a thin film electrode measured by cyclic voltammetry in 0.1 M TBAP in acetonitrile. For this purpose we used an epitaxial film, grown on SrTiOa, by laser ablation (from G. Koren, Technion, Haifa). (7, and CR are bulk concentrations of the oxidized form (TMAMFc +2) and the reduced form (TMAMFc ~- ), respectively. Do and DR, the diffusion coefficients of the oxidized and reduced forms, respectively, were assumed to be equal (Do=DR=Dpor¢). Dpore was found to be 1.5- 1.6× l0 -8 cm2/s. We note that the Warburg imped-

278 Y. Scolnik et al. / Chemical diffusion coefficient of oxygen in polyc~, stalline YBa2CujOr_.~at room temperature

32

24

8

0 ).0

8 0

4 0

0

,

o.5 x . ,

1/~lt ( xxool

Fig. 3. Plot of reduction current, h vs. 1/x/~ (t = time in seconds) for a pellet of YBa2Cu3OT_x in propylene carbonate/tetra-butyl ammonium perchlorate electrolyte. The line shows the extrapolation of the data to zero current. Insert: same plot, including shorter times of reduction.

ance e q u a t i o n s can be used as long as the r e l a t ion

r2o t o /Dpo~> 100 holds (to is the pore r ad ius ) [ 17].

W i t h ro~ 5 lam (see fig. 1 ) th i s re la t ion ho lds for

to> ~ s - i wh ich is the f r e q u e n c y range cor respond-

ing to the rad ia l d i f fus ion process (see inser t in fig.

2) .

Figure 3 shows a represen ta t ive p lo t o f i versus 1 /

x/~ for a pellet . F r o m it we f i nd to = 7 × 104 s, wh ich

cor responds to D ( o x ) = 3 . 6 × l 0 -~2 c m 2 / s for 2 = 2

a n d a = 10 lxm. F o r A = 0 . 7 ( f = 5) , D ( o x ) = 3 × 10 - ~

cm-' /s . T a b l e 1 s u m m a r i z e s resul ts o b t a i n e d on a

n u m b e r o f 123 s a m p l e s o f v a r y i n g o x y g e n content ,

par t ic le s ize a n d dens i ty . In the t ab le we also give re-

sults whose p o r o s i t y was c h a n g e d b y use o f a mic ro-

porous m e m b r a n c e or by l each ing ou t o f T B A P a n d

on pellets w h o s e sur face h a d b e e n m o d i f i e d , as de-

scr ibed in sec t ion 2.

All o f the v a l u e s for pellets were ca l cu l a t ed by us-

ing it = 2 a n d g r a i n sizes, a, as i n d i c a t e d ; they shou ld

be m u l t i p l i e d b y 8 for i t=0 .7 . T h e resu l t s show tha t

/ ) is re la t ive ly i n d e p e n d e n t o f the v a r i o u s t r e a t m e n t s

g iven to the pel lets . W h i l e th is cou ld i n d i c a t e that we

are m e a s u r i n g / ~ for a s o l u t i o n - d e t e r m i n e d process,

the fact tha t c h a n g i n g the e lect rolyte h a d no great ef-

fect, argues aga ins t this. F u r t h e r m o r e , the i m p e d -

ance m e a s u r e m e n t s show tha t we are n o t m e a s u r i n g

a pore d i f f u s i o n process. T h e l i m i t e d effects o f sur-

face t r e a t m e n t s i nd i ca t e that the m e a s u r e d / ) va lues

do not reflect a sur face l i m i t e d process . It is there-

fore a p p a r e n t t ha t we m e a s u r e a so l id state, in t ra-

Table I Effective room temperature chemical diffusion coefficients for oxygen in polycrystallin~ samples of YBa2Cu3OT_x.

Sample a, /~ (cm2/s) t) a (ltm) j) Potential Charged passed p [0] [0] (V) (C) (g/cm 3) initial final

Y - normal 9X 10-'2 10 - 1 4.66 4.78 7 6.85 Y-normal 4× 10-12 10 -0 .5 1.97 4.78 7 6.94 Y-etched b) 1 X 10-12 ~ 7 -0 .8 3.02 4.8 7 6.9 Y - Acetonitrile ¢) 4× 10-12 ~ 10 - 1 26.85 4.77 7 6.14 Y-Silver-covered d) 3X 10 -12 7 - 1 3.58 5.02 7 6.89 Y + Membrane e) 4× 10-12 10 -0 .7 2.6 4.77 7 6.92 Y-High porosity f) 2.5× 10 -12 ~8 -0 .7 0.3 - 7 - Y-not sintered 4× 10 -I~ --8 - 1 6.16 4.08 7 6.81 Y - oven-reduced ~ 1 O- t 2 ~ 5 - 1 1.14 5.02 6.48 6.44 Y- th in film g) 10-12-10 -13 ~ 1 -0 .5 0.07 - - - L-normal h) 5× 10 -~4 ~ 1.5 -- 1 "- 10 4.7 2.99 "-2.80

a~ Y=YBCO pellet or thin film; L= LaSrCoO3 pellet. t,, in ethanol/1% Br2 (see experimental). ¢ ~ Acetonitrile used as electrolyte instead of propylene carbonate. d, 50 nm Ag evaporated on both sides of pellet and annealed subsequently; see experimental. c, To decrease, artificially, solution movement in and out of the sample. f~ Pressed with TBAP (see experimental), subsequently TBAP leached out, to increase porosity. ~) Polycrystalline, non-epitaxial, from Tel-Aviv University. h, Lap ~Sro 5COO3 pellet prepared by method ofref. [ 11 ] (see experimental), but measured in propylene carbonate. ' ~ Calculated, t:sing 2 = 2 and a as indicated (see text, eq. ( 5 ) ). J' As determined by SEM.

Y. Scolnik et ai. / Chemical diffusion coefficient o f oxygen in polycrystailine YBa2Cu~Oz_ x at room temperature 2-~

grain diffusion process, probably reflecting a~so in part grain boundary diffusion. This conclusion is strengthened by the results on polycrystaUine films. These were found to behave like the pellets. How- ever, there is a greater uncertainty concerning the shape and size of grains in these films. Thus, the determination of the diffusion coefficient in these thin films is less precise. Still, we can state that the diffusion coefficient of these films is in the order of 10-12-10 -13 cm2/s. Samples that were fir=,t reduced, by quenching from high temperature, also gave similar values for D. We could also extract values of/~ from plots of reduction current versus time, during preparative room temperature reduction [ 16 ]. Again the results were, within experimental er- ror, similar to those obtained with fresh pellets, showing that no major changes in terms of diffusion coefficient/mechanism takes place during room temperature extraction of oxygen.

A possible explanation for this behaviour may be found in the shell model, used by us to explain our room temperature reduction results [ 16 ], and by Tu et al. [4 ] to explain their oxygen in- and out-diffusion data. In this model during reduction every grain acquires a reduced outer shell, through which oxygen out-diffusion has to occur. The diffusion coefficient that we measure is then determined by that of this reduced outer shell.

4. Conclusions

We found the effective chemical diffusion coefficient for polycrystalline 123 at room temperature to be 10 -~ -10 -~2 cm2/s. By comparing the results of the impedance and the potentiostatic step measurements, including those where porosity was varied, we conclude that the rate determining step in the out- diffusion process of oxygen is not due to a solution process. This is confirmed by the insignificant effect due to a change in electrolyte. This also shows that the reaction of the emerging oxygen at the surface is not rate limiting, either. This is confirmed by the mi- nor effects observed as a result of the changes of the surface due to etching and Ag deposition. Thus this leads us to conclude that the rate of determining step is the movement of oxygen inside th~ grains and that the value of D(ox) that we measure reflects that process.

Acknowledgements

YS is the recipient of a Stone postdoctoral fello~ ship. Part of this work was supported by the US-~s- rael Binational Science Foundation, Jerusalem, ts- rael. We thank G. Deutscher, U. Dai and N. Hess. from Tel Aviv University and G. Koren from th~ ~ Technion for thin film samples and N. Fleischer fo: bringing refs. [ l 0 ] and [ 15 ] to our attention.

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chemical diffusion coefficient of oxygen in polycrystalline yba2cu3o7−x at room temperature

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