Journal of Low Temperature Physics, Vol 117. Nos. 5/6. 1999

Percolation Analyses on Transport Properties ofYBa2Cu3O7-s-Ag System
Manabu Ikebe and Hiroyuki Fujishiro
Faculty of Engineering, Iwate University, 4-3-5 Veda, Morioka 020-8551,
Japan.

The transport properties of YBa2Cu3O7-s-Ag composite ceramic system have beenstudied from the viewpoint of the percolation theory. The percolation thresholdvolume fraction fc of Ag determined from the electrical resistivity and from thethermal conductivity is fc=0.125±0.005. This markedly smaller value than thetheoretical value (f c =0.16) suggests the segregative distribution of Ag. The
critical exponent t depends on the component conductivity ratio h=aYBCO/aAg,
which can be explained on the basis of the scaling hypothesis.
PA CS number: 72.15. Cz, 71.30. + h

1. INTRODUCTION
One main hurdle against the application of high T c oxide superconductors inceramic forms is the occurrence of the weak-links at the border of grains, which
practically limit the effective transport critical current Iceff of bulk cuprate superconductors. The addition of Ag metal to cuprates is often effectual to make up forthe weak-links. It is physically interesting and also useful for an applicational
purpose to investigate the behavior of Ag clusters on the basis of the percolation
theory. The accumulated data and analyses from the viewpoint of the percolation
theory, however, are somewhat scattered and sometimes inconsistent with eachother.1-4
In this study, we try to develop synthetic analyses about the percolative
behavior of Ag clusters in YBa2Cu3O7-s (YBCO) by measuring the electrical resistivity and the thermal conductivity. The conductivity ratio of Ag metal to thecuprate is widely changed by varying the amount of oxygen deficiency 6 ofYBCO. The experimental results are analyzed on the basis of the scaling theory
for the percolation of Ag clusters.

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M. Ikebe and H. Fujishiro

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2.

OUTLINE OF THE SCALING LAW

In a two component random composite of M and I, clusters of M with an
infinite scale are formed when the volume fraction fM of M exceeds a certain
threshold value fc. Assuming M to be a metal and / to he an insulator, a power law
holds for the hulk effective conductivity a E of the composite in the critical region;

The values of t=1.9±0.1 and fc=0.16 were predicted for three-dimensional continuum media. 5 If I component is also somewhat conductive and the conductivity
ratio h=a1/aM is not strictly zero, the power law of eq. (1) breaks down as Af=
fM-fC tends to zero. In this case, aE is expected to follow the scaling hypothesis,6

where z=h/Aft+s,s(=0.73) is the critical exponent governing the divergence of theconductivity in a superconductor-metal composite for 0<f C -f M «1. The universal scaling function 0(z) can he expanded in the power series of z:

For non-zero values of h, the conductivity data must he carefully handled taking
proper account of region of z in which the application of eq. (3) is justified. In thispaper, h dependence of the t exponent is mainly discussed.4,73.

EXPERIMENTAL

YBCO powder and Ag2O powder (Dowa Mining Co. Ltd.) were mixed with anappropriate weight ratio and pressed into pellets. The pellets were pre-sintered at
935°C for 15h in air and furnace cooled. The pre-sintered pellets were crushed,
mixed and again pressed into pellets. They were sintered at 930°C for 30h in air
and then furnace cooled in 15h. After the obtained pellets were cut into squarepillars (~3x3xl5mm 3 ), they were heated again and quenched into liquid N 2 fromvarious temperatures to prepare 'quenched samples'.
The density of the samples was determined by measuring the size and the mass.
Figure 1 shows the filling factor of the samples, which increases with increasing
nominal Ag volume fraction fAgN. In this paper, the Ag volume fraction is corrected using the least square fitting curve in Fig. 1. The electrical resistivity andthe thermal conductivity were automatically measured between 10K and 260K in
a Gifford-McMahon refrigerator. 8

Percolation Analyses of YBa2Cu3O7-s -Ag System

1291

0.8

Fig. 1. Filling factor of YBCO-Ag samples
as a function of nominal Ag volume fraction
fAgN. /fAgN was corrected using the least square
fitting line to give f Ag .

4.

Fig. 2. Temperature dependence of the electrical resistivity p(T) of YBCO nonquenched and quenched from 700°C, 800°Cand 900°C.

RESULTS AND DISCUSSION

Figure 2 shows the temperature dependence of the electrical resistivity p(T) ofYBCO non-quenched, and quenched from 700°C, 800°C and 900°C. p(T) ofYBCO rapidly increases with increasing quenching temperature T q . In the figure,p(T) of Ag+0.22at.%Au alloy whose residual resistivity ratio (RRR) is nearly
equal to the estimated RRR of Ag clusters in YBCO is also shown.
Figures 3(a)-3(c) show typical plots of log aE vs log (fAg-fC) to determine theexperimental values of critical exponent tex and the percolation threshold fc. The
conductivity values at 150K were used because RRR of Ag cluster is verified todepend on fAg to some extent9 and theaYBCO/aAgvalues become dependent on RRRof Ag cluster at low temperatures. The most suitable value of fc was determined tobe 0.125 for the present Ag+YBCO ceramics system. This fc value is remarkably
smaller than the generally accepted value of fc~0.16 for 3D continuum media.
The smaller value of observed fc should reflect selective distribution of Ag clusters into voids at grain boundaries of YBCO; the filling factor in Fig. 1 rapidly
increases with increasing Ag composition, which also suggests that Ag metals fillup the voids of ceramic YBCO preferentially.
In order to determine tex, the region of Af(=f A g -f c ) must be carefully setup.
Eqs.(2) and (3) are valid for Af >(aYBCO /a Ag ) 1/s+t which corresponds to the condition, z<1. On the other hand, if we go too far from fc, we pass through the criticalregion and enter into the region where the effective medium approximation(EMA) becomes valid. In this work, we set the region to determine tex as(aYBCO/aAg)l/s+t<Af<0.2. The determined tex values depend on the conductivity
ratio h and are larger for smaller h as shown in Fig. 4. In the following, we esti-1292

M. Ikebe and H. Fujishiro

mate the relation between observed tex value and h on the basis of the scaling law
given by eqs. (2) and (3).4,6,7To calculate aE based on eq. (2), the scaling function 0+ of eq. (3) must beknown. As a trial function, we set 0+(z)=A+(l +z) and calculated aE in the range,(aYBCO / a Ag) 1/s+t <Af<0.2. Then average slope between Af=(aYBCO /aAg) 1/s+t and Af=
0.2 was defined as t* and obtained t* is given by the dotted line in Fig. 4. In thepresent calculation, the t value of 1.8 and s value of 0.73 were used. The t* values

Fig. 3. The typical plots of log aE vs log (f A g -f c ) to determine experimental values ofcritical exponent tex and the percolation threshold fc for (a) Tq=900oC, (b) non-quenched and (c)Tq=800oC, respectively. Note that (c) is for the thermal conductivity. The vertical dashed line
represents Af value for respective samples which corresponds to z=l.

Fig. 4. The experimentally determined tex values and calculated t* values as a function of
conductivity ratio h=a(YBCO)/a(Ag) (see text).

Percolation Analyses of YBa2Cu3O7-s -Ag System

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Table I. The parameter values used for the calculation of t* and experimental tex values. For
the p(T) analyses, aAg=1621mQ-1cm-1 was used from Fig. 2.

Tq

conductivity at 150K

h(=aYBCO/ aAg)

tex

t*K

800° C

KAg=4300mW/cmKKYBCO=31.3mW/cmK

7.3X10-3

0.86

0.78

PPPP

non-Q
700°C
800oC
900° CaYBCO=1.36 mQ-1cm-1
aYBCO=0.26 mQ-1 cm-1
aYBCO=0.114mQ-1cm-1
aYBCO=0.015mQ-1cm-1

8.4xl0-4
1.6X10-4
7.0x10-5
9.3X10-6

1.20
1.481.73
1.58

1.27
1.43
1.49
1.99

measurementin Fig. 4 agree fairly well with the experimental tex values. The parameter values
used for the calculation are summarized in Table I.

5.

SUMMARY(1) The electrical resistivity p and the thermal conductivity K were measured for
Ag+YBa2Cu3O7-s composites and the results were analyzed. The percolationthreshold volume fraction fc of Ag is determined to be 0.125, which is remarkably smaller than the generally accepted value of 0.16 for random binary mixing
in three-dimensional continuum media. The observed small fc value supports thesegregative distribution of Ag particles in this system.
(2) Observed critical exponent tex for fAg >fC is dependent on the conductivity
ratio h=a(YBa2Cu3O7-s)/a(Ag), which was varied in this study by quenching thecomposites from various temperatures.
(3) On the basis of the scaling law, the trial scaling function, 0+(z)=A(l+z), explains fairly well the h dependence of the observed tex values.

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