Scripta METALLURGICA Vol. 28, pp. 773-778, 1993 Pergamon Press Ltd. et MATERIALIA Printed in the U.S.A. All rights reserved

ANELASTIC CREEP AND AFTEREFFECT STUDIES OF OXYGEN RELAXATION IN YBa2Cu30~_ a

J. R. Cost, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

and James T. Stanley, Arizona State University,

Tempe, Arizona 85287, USA

(Received December 2, 1992) (Revised January 15, 1993)

Introduction

It is desirable to better understand the atomic mobility of oxygen in YBa2Cu3OT_8 because the oxygen stoichiometry and thus the superconducting properties are determined by diffusion of oxygen into the bulk. Ar~lastic relaxation studies, especially those which involve jumping of atoms between sites, have in the past been important to our understanding of atomic mobility in many materials. Our focus for this paper is to extend earlier anelastic investigations of oxygen mobility in YBa2Cu3OT_ 8 to a new regime of relaxation times, those greater than 100 s. We use the anelastic creep and aftereffect (ACA) method which complements internal friction (IF) studies by measuring relaxation times at much lower temperatures.

Prior Anglastic Studies

An IF peak due to orientational ordering of oxygen atoms in YBa2CusO~_ a was first reported by Berry (1). This anelastic relaxation was manifested by a peak at 330°C measured at roughly 350 Hz and it was inferred that it was due to jumping of oxygen atoms between sites on the CuO plane. It should be noted that Berry and other investigators also observed IF peaks due to oxygen in YBa.2Cu307. 8 at subambient temperatures; however, these anelastic relaxations are not considered in this paper since their low activation energies indicate that they do not involve lattice jumps of oxygen atoms.

Other researchers independently found and investigated this oxygen relaxation soon after Berry. Tallon and coworkers (2) reported a peak at 530°C measured at 40 kHz. Later they investigated the same peak when they extended their measurements to frequencies of 8 and 144 kHz (3). Subsequently, this relaxation was studied at torsional pendulum frequencies by Zhang and coworkers (4-6), Xie et al (7), Cost and Stanley (8), and Woirgard et al (9). Other investigations studied this relaxation at or near kilocycle frequencies: Cost and Stanley (8), Berry and coworkers (10), Bonetti et al (11), and Cannelli et al (12).

The relaxation times obtained from the IF peaks by all the above researchers follow the predicted Arrhenius relation, ~ - z o exp(Q/kT), reasonably well over more than seven orders of magnitude. All of the IF results, except those of Bonetti et al (1 I), lie within a factor of three of a best fit line having an activation energy Q= 1.05 eV and a pre-exponential factor ~0--8. lxl0 q3 s. This Arrhenius behavior is strong evidence that the relaxation has a single rate-controlling mechanism over the temperature range studied (130°C to 610°C). This agreement is quite good since the measurements were, of course, performed on different samples prepared in different laboratories, often by different methods. It indicates that the rate of the oxygen relaxation is not highly structure sensitive.

There is, however, a measurable effect of stoichiometry upon the relaxation time. This has been shown by Berry and coworkers (10) as a shift in peak temperature Tp with loss of oxygen. This shift corresponds to a deviation

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774 OXYGEN RELAXATION IN YBa2Cu3OT_ 6 Vol. 28, No. 7

in the relaxation time at constant temperature of almost one decade. Interestingly, the relaxation time first decreases and then increases with loss of oxygen. Similial changes of relaxation time with oxygen content were also shown by Xie et al (7).

In all of the above IF studies the peaks are wider than predicted for a single relaxation time. This is not unexpected; it indicates that oxygen atoms involved in the relaxation are jumping from a spectrum of local environments each of which has a different relaxation time. To know more about the relaxation of oxygen atoms, it is desirable to investigate this spectrum, especially its width and shape. This requires deconvolution of the ACA measurements. Fortunately, ACA curves, because they are isothermal and do not require assumptions concerning the temperature dependence of the relaxation parameters, can be deconvoluted more accurately than IF versus temperature peaks.

Exoerimental Method

The experimental method for making ACA measurements in YBa2CB3OTq ~ has previously been described (13). Briefly, the loading (i. e., anelastic creep) experiments measured the anelastic strain in torsion as a function of time following application of a constant torsional stress. The unloading (i. e., anelastic aftereffect) experiments measured anelastic strain following removal of the same stress. The anelastic strain curves were subsequently analyzed to obtain an average time for the relaxation, which in this study is related to the atomic jump time for oxygen in the YBa2Cu3074 lattice. Prior to each measurement the sample was held at constant stress until the anelastic strain saturated. All measurements were made isothermally at temperatures from 50°C to 110°C. Also, all the experiments met the test of full reversibility of strain following a loading and unloading cycle indicating that none of the strain was plastic. Two wire samples were used; these were the same ones used for previous IF measurements (8). Oxygen stoichiometries of the two samples were measured as 6=0.10 and 0.17. ACA experimental results from the two samples were essentially the same.

For both the anelastic aftereffect and the anelastic creep experiments, the strain versus time curves were analyzed to obtain ¢inn, the time at the inflection point on the plot of anelastic strain versus time on a logarithmic scale. This gives an average relaxation time which is near the center of the relaxation time spectrum. The uncertainty in measurement of ¢ina is estimated at 40%.

One of the most interesting and important results to be obtained by analysis of ACA curves is information about the spectrum of relaxation times which controls the relaxation. Details of this spectrum and its temperature dependence provide basic understanding of the atomic jump process. We have developed a method for analysis of ACA data when the kinetics of the anelastic behavior are controlled by a continuous spectrum of relaxation times. Referred to as the Direct Spectrum Analysis (DSA) method, this technique deconvolutes ACA data to give a reliable approximation of the position, shape, width, and magnitude of the relaxation time spectrum (14, 15). It has been shown to calculate dependable approximations of a wide variety of known input spectra (14) and to have an accuracy for the calculated spectra which is roughly the same as the experimental error in the data.

Results and Discussion

Results from a typical ACA experiment on YBa2Cu307. ~ ale shown in Fig. 1, which is a plot of the fractional anelastic strain ¢,n at 79.8°C versus time on a logarithmic scale. That the ACA data span a much longer time than for a single relaxation time can be seen in Fig. 1 by comparing the time span of the measured data with that for the dashed curve which is for an anelastic relaxation having a single relaxation time (i. e., giving simple exponential decay) of 5500 s. For ACA the strength of the relaxation is given by A=¢o~h,Jcehai c. For the isothermal measurements in Fig. 1 A=0.172. This agrees with A=0.166 and the monotonic decrease of A with temperature reported for the same sample using an IF measurement with peak temperature of 211°C (8).

Relaxation time svectrum

The ACA data in Fig. 1 have been analyzed by DSA to obtain a best estimate of the spectrum of relaxation times which governs the kinetics. This spectrum is shown for an analysis with 33 bins of ln(r i) in Fig. 2. Here the

Vol . 28, No. 7 OXYGEN RELAXATION IN YBa2Cu307_ 6 775

spectral amplitude, NOn ri), for each bin is plotted versus the r i value. Other DSA calculations done on the same data, but with the analysis parameters varied (e.g., number of bins or the r limits) showed spectra which only differed from that in Fig. 2 by a few percent. Also, this DSA spectrum is typical of others of this experiment.

Note that the relaxation time spectrum is quite broad, ranging from 400 s to 70,000 s at half height. Also, it is nearly symmetrical on the log(ri) scale. This combination of breadth and symmetry suggests that it may be a good fit to a lognormal distribution. The tendency for relaxation time spectra of thermally activated processes to fit a lognormal distribution and the properties of such a distribution have been discussed in detail by Nowick and Berry (16). A lognormal curve fit to the DSA spectrum is shown as the solid curve in Fig. 2. This fit gives fro=5130 s for the center of the distribution and 8=3.25 for the width parameter. The inflection point analysis of these data gave ri~n=3700 s, roughly 30% less than r m obtained by DSA; this is an intrinsic difference due to the averaging of the r spectrum.

The above width parameter 8 =3.25 obtained from the ACA data at 79.8°C is significantly larger than B = 2.74 obtained by IF (8). This is due to the temperature dependence of 8 for anetastic relaxations. Nowick and Berry (16) point out that from the temperature dependence of B one can distinguish whether a thermally activated relaxation tends to be controlled either by (i) a distribution of activation energies (with a constant p~-exponential frequency factor) or (ii) a distribution of frequency factors (with a constant activation energy). For the latter case the distribution parameter 13 is independent of temperature. For the former case, if the distribution of relaxation times is lognormal as our results indicate, then there must be a normal distribution of activation energies which is independent of temperature. As a result of this the spectrum of relaxation times must broaden with decreasing temperature.

by For the intermediate case where distributions in both Q and ln(r0) occur, the distribution parameter is given

B(T) --- [ 13o + BQ/kTI, (1)

where B 0 and 13Q are the distribution parameters for log(r o) and the activation energy Q, respectively. ACA measurements at several temperatures of this experiment have been analyzed using the DSA method and then given a lognormal fit as in Fig. 2 to obtain 13 at several temperatures. (Unfortunately the relaxations at 100°C and above occurred too rapidly for reliable use of the DSA method.) The results, both for ACA measurements and for a single IF measurement (8) are shown in Fig. 3. A linear fit of these results to Eq. 1 (see the solid line) yields 60=0.83(-1-0.14) and BQ=0.077(+0.014) eV with the second term of Eq. 1 being positive. The values for the second term, which is the one associated with a distribution in Q, range from 2.4 to 2.9 depending upon the temperature. Note that this is roughly a factor of three greater than the first term 13o=0.83, which is associated with the distribution of the preexponential frequency factor, log(to). Thus we find that the distribution of activation energies, rather than of log(to), dominates this oxygen relaxation.

Temperature d _ependence of the relaxation time

In Fig. 4 the results from all of the anelastic studies of this oxygen relaxation in YBa2Cu3OT. * are shown. Included are all known IF investigations (1-12) plus the ACA results of this and other studies. Our ACA results were measured at temperatures from 50°C to l l0°C and are from both anelastic creep and aftereffect experiments. These two types of experiments were found to have the same r~n at a particular measurement temperature. The relaxation times range from 102 to 10 ~ s and show the expected Arrhenius behavior. The activation energy and r 0 values from a linear fit to the ACA data of this study are shown in Table 1. Note that these values agree well with those obtained from a fit of just the IF results (I-10, 12) which are also listed in Table 1.

Examination of the combined ACA and IF results in Fig. 4 shows that the ACA relaxation times are a consistent extension of the IF findings. The solid line in Fig. 4 is for a linear fit to our ACA data and the combined IF data (1-10, 12). It is a remarkably good fit for over eleven orders of magnitude of relaxation time. (This range ties the record set by the anelastic measurements of the Shock peak for carbon in iron.) The activation energy and r 0 parameters for the combined ACA and IF data are also shown in Table 1 and agree well with those obtained by either method alone. Clearly, the same relaxation is being measured by the two different anelastic techniques. Thus we

776 OXYGEN RELAXATION IN YBa2Cu307_ 6 Vol. 28, No. 7

deduce that the oxygen relaxation has the same rate-limiting step over the entire temperature range from 50°C to 600°C. Although the values of all of the parameters mentioned above are nearly the same, probably the best assessment is obtained from the combined ACA results of this study and the IF results of reference (8), since these measurements cover nine orders of magnitude and were all made on the same two samples. These data give Q= 1.13 eV and r0=l.9xl0 -13 s, see the bottom row of Table 1.

TABLE 1 Activation Energies and Preexponential Factors

Type of study Q (eV)

6Q, uncertainty (eV) (s)

6.5x10 "t3

log(fo) (s)

ACA, this study 1.09 +0.030 -12.18 (+0.10)

All IF (1-10, 12) 1.05 +0.019 8.1x10 -13 -12.09 (+0.22)

ACA and all IF 1.14 +0.012 1.2x10 -13 -12.93 (+0.24)

+0.009 1.13 1.9xlO "13 ACA and IF (8) -12.72 (4-0.12)

Other anelastic experiments using ACA have been performed by Turner (17) and Seidel et al (18). Their data are also shown in Fig. 4. The relaxation times measured by Turner tend to be smaller than those of this study while those of Seidel et al are larger. Although each of these studies only reports two data points, it may be seen that both investigations find the same temperature dependence. The variations between the results of these two ACA studies and the present one are probably due to differences in oxygen stoichiometry as was observed by Berry and coworkers (10).

Comvarison with diffusion results

Rothman and coworkers have studied oxygen diffusion in YBa~Cu3OT. ~ using tracer techniques (19, 20), and their results provide the best values of the activation energy for mass transport of oxygen in YBa2Cu3OT. ~. Relationships between oxygen mobility as studied by mass transport methods (i.e., tracer diffusion) compared to atomic jump methods (i.e., anelastic) have been discussed by Cost and Stanley (8). An important concept from this discussion is that because of the spectrum of relaxation times, the activation energy obtained by diffusion methods is expected to be less than that obtained by anelastic techniques. This agrees with the findings for YBa2Cu3OT.~, Qdi~ion--0.97 eV (19) and Q~, l ,~= 1.13 eV. This important difference is understood as follows: The spectrum of relaxation times measured in this study shows that a spectrum of local environments exists in the sample. The activation energy obtained by anelastic methods averages the times for single (or nearly single) jumps of oxygen atoms to a neighboring site in each of these local environments, thus sampling all the local environments and the furl activation energy spectrum. That obtained by diffusion methods, on the other hand, averages the times for a sequence of jumps by individual atoms between adjacent local environments. These sequential jumps will tend to take place between connected regions having fast jump rates, thus sampling only the low activation energy portion of the spectrum. Because of this different averaging, we predict then Qdif~,on < Q,w-~c, which is what we now know to be true for the mobility of oxygen in YBa2Cu30-/. 8.

This work was performed under the auspices of the U. S. Department of Energy. Appreciation is expressed to T. J. Turner for permission to show some of his ACA results prior to publication and to R. B. Pceppel for preparation and characterization of the YBa2Cu30~_ ~ samples.

Vol . 28, No. 7 OXYGEN RELAXATION IN YBa2Cu307_ ~ 777

Re. ferenc¢~

1. B.S. Berry, Bull. Am. Phys. Soc., 33 (3), 512 (1988). 2. J .L . Tallon, A. H. Schuitema, and N. E. Tapp, Appl. Phys. Lett., 52, 507 (1988). 3. J .L . Tallon and M. P. Staines, J. Appl. Phys., 68, 3998 (1990). 4. T. Chen, J. Zhang, J. Huang, Y. Chen, M. Yang, X. Xie, T. Li, and L. Xie, Chinese Phys. Lett., 5, 185

(1988). 5. J .X. Zhang, G. M. Lin, Z. C. Lin, K. F. Liang, P. C. W. Fung, and G. G. Siu, J. Phys. Condens. Matter,

1, 6939 (1989). 6. J .X. Zhang, G. M. Lin, W. G. Zeng, K. F. Liang, Z. C. Lin, G. G. Siu, M. J. Stokes, P. C. W. Fung,

Supercond. Sci. Technol., 3, 163 (1990). 7. X .M. Xie, T. G. Chen, and Z. L. Wu, Phys. Rev. B, 40, 4549 (1989). 8. J .R . Cost and J. T. Stanley, J. Mater. Res., ~, 232 (1991). 9. J.Woirgard, A. Riviere, P. Gadaud, and P. Tal, Europhys. Lett., 17, 601 (1992). 10. B.S. Berry, W. C. Pritchet, and T. M. Shaw, Defect and Diffusion Forum, 75, 34 (1991). 11. E. Bonetti, E. G. Compari, P. Cammarota, A. Casagrande, and S. Mantovani, L Less Com. Metals, 164-5.

231 (1990). 12. G. Cannelli, R. Cantelli, F. Cordero, F. Trequattrini, S. Ferraro, and M. Ferretti, Solid State Comm., 80,

715 (1991). 13. J .R . Cost, P. E. Armstrong, R. B. Poeppel, and J. T. Stanley, Proceedings of Symposium on Defects in

Materials, Materials Research Society, Pittsburgh, PA, 2__~, 819 (t991). 14. J .R . Cost, J. Appl. Phys., 54, 2137 (1983). 15. J .R . Cost, Nontraditional Method~ in Diffusion, G. E. Murch, ed., p. 111, TMS-AIME, Warrendale, PA

(1984). 16. A.S. Nowick and B. S. Berry, Anelastic Relaxations in Crystalline Solids, pp. 94-112, Academic Press, New

York (1972). 17. T . J . Turner, private communication. 18 D. Seidel, A. Homes, and H. Wipf, Europhys. Lett., 18, 307 (1992). 19. S.J . Rothman, J. L. Routbort, and J. E. Baker, Phys. Rev. B, 40, 8852 (1989). 20. S.J . Rothman, J. L. Routbort, U. Welp, and J. E. Baker, Phys. Rev. B, 44, 2326, (1991).

0.8

0 0.6

0.4

I 0.2

E 0 lo 1 lo 6

. . = . , o : / Y

,sA, s ° /

, , 10 2 10 3 10 4 10 5

TIME (s)

FIG. I. Fractional anelastic strain versus time (logarithmic scale) for anelastic creep at 79.8°C. The dotted line is for anelastic creep with a single relaxation time, r =5500 s.

~ 6

¢Jl

I I I I

• DSA calcu~tion

f , . 101 10 2 10 3 10 4 10 5 10 6

RELAXATION TIME, I;i(s )

FIG. 2. DSA calculated estimate of the relaxation time spectrum for the anelastic creep results of Fig. 1. The solid line is a lognormal fit to the calculated points.

778 OXYGEN RELAXATION IN YBa2Cu307_ 6 V o l . 28 , No. 7

4 . 0 I I I t I I I

• A n e l a s t i c c r e e p / a f t e r e f f e c t o Internal fiction "Y

r -

~= 3.0

2.5 = t = I t I I 1 . 8 2 . 2 2 . 6 3 . 0 3 . 4

looorr (1~:)

FIG. 3. Width parameter .6 versus reciprocal temperature for lognormal fit to DSA calculated relaxation time spectra of ACA and IF results. Solid line is a fit to Eq. 1.

IJJ

I-- Z o

5 uJ o-

FIG. 4.

TEMPERATURE (°C) 600 400 200 100 50

I I I I I I I / C )

_Y 10 4

1; 0 = 1.2 x 10 "13 s ~ ¢ Q = 1.14 (+0.012) eV _~

102 ~-

100

• Cost ~p(~r~=, 0 Turner,ACA

10-2 / m v Z hang, F!g. 3 _ / [] Zhang, Fig. 6

/ • Xie _ ~,~ vz~ zx Bonetti

10 -4 ~ ^ v Berry - / ~ e z~ • T allon

- / [] Woirgard - & / O Cannelli

10 -6 y • SeideI, ACA - I I I I

1.0 1.5 2.0 2.5 3.0 IO00/T" (1/10

Arrhenius plot for all anelastic results on YBa2Cu307. 6.