Superlattices and Microstructures, Vol. 21, No. 3, 1997

Model analyses of thermal conductivity and purity of doped Ag in
Ag + YBa2 Cu3 O7
H. Fujishiro, M. Ikebe, Y. Minato, H. Ogasawara, K. Noto
Faculty of Engineering, Iwate University, 4-3-5, Ueda, Morioka 020, Japan(Received 8 July 1996)

The thermal conductivities κ(T ) of Ag-doped YBa2 Cu3 O7 sintered materials were measured
for various Ag fractions up to f Ag = 0.67. By analyzing the κ(T ) data based on a proposed
phenomenological model, the purity of doped Ag in YBa2 Cu3 O7 could be determined.
c 1997 Academic Press Limited
Key words: thermal conductivity, Ag doped YBa2 CU3 O7 , purity of Ag.

1. Introduction
Ag-doping of sintered high-Tc cuprates is often effective in improving superconducting characteristics,
reinforcing the weak links between the grain boundaries. The transport properties, such as the thermal conductivity κ(T ) and the electrical resistivity ρ(T ), of Ag-doped materials are heavily influenced by the contentand the purity of the doped Ag. κ is an important parameter which dictates the dynamic stability of a superconducting material. We previously studied the Ag distribution and the Ag purity in Ag-doped Bi2212
crystals fabricated by a floating zone (FZ) method and proposed a simple phenomenological model to analyze
the thermal and electrical transport in this composite system [1, 2]. The crystal grains and Ag distribution
were highly anisotropic in the FZ crystals.
In this paper, we report the temperature dependence of κ(T ) of Ag-doped YBa2 Cu3 O7 (YBCO) sinteredmaterials with Ag volume fractions up to f Ag = 0.67. We apply the phenomenological model to analyze theκ(T ) data of Ag + YBCO composite materials.
.

.

.

.

2. Experimental
The Ag-doped YBCO samples were fabricated as follows; YBCO powder and Ag2 O powder (Dowa MiningCo. Ltd) were mixed with an appropriate weight ratio and pressed into pellets. The average sizes of each powder
were about 7 µm and 10 µm, respectively. After they were sintered at 550 ∼ 880 ◦ C for 8 hours in air, theywere pulverized, again pressed into pellets and sintered at 925 ∼ 935 ◦ C for 30 hours in air followed by furnacecooling. The Ag volume fraction f Ag was calculated from ideal densities dAg = 10.25 and dYBCO = 6.24 andthe initial weight ratio wAg /wYBCO . The thermal conductivity κ(T ) was measured from 10 to 200 K using an
automated measuring system which employed a GM refrigerator as a cryostat [3].
.

.

0749–6036/97/030349 + 04 $25.00/0

sm960397

c 1997 Academic Press Limited

350Superlattices and Microstructures, Vol. 21, No. 3, 1997
510Ag(RRR=257)
Ag(RRR=37)
Ag(RRR=15)
fAg=0.67

Thermal conductivity (mW cm–1 K–1)

104

fAg=0.44
fAg=0.34
fAg=0.26
fAg=0.22
fAg=0.18

103

fAg=0.12
fAg=0.09
fAg=0.05
fAg=02

10101

Ag+YBCO050

100
Temperature (K)150200Fig. 1. The temperature dependence of the thermal conductivity κ(T ) of Ag + YBCO materials with various Ag concentrations f Ag ,together with that of Ag-Au alloys [5].
.

.

.

.

3. Results and discussion
It was confirmed from the analyses by an electron probe microanalyzer (EPMA) that the doped Ag2 O
powder was uniformly and isotropically dispersed in the form of metal particles and that the content of Ag
particles increased with increasing nominal Ag2 O concentration [4]. The ρ(T ) values of Ag-doped YBCO
decreased with increasing Ag content, and the Tc of about 92 K was observed up to f Ag = 0.34. The κvalues increased with increasing Ag content as shown in Fig. 1. In Ag + YBCO composite materials, the heatshould flow through a YBCO path, a Ag path or series of YBCO and Ag paths. Then the thermal resistance ofAg + YBCO composites is given by the general equivalent circuit in Fig. 2A. Taking account of the isotropic
nature of this sintered material, we propose a simplified model cube of Ag + YBCO specimen in Fig. 2B,
which exemplifies the equivalent circuit of Fig. 2A [1, 2]. In this model the doped Ag particles are divided into
two groups. One group consists of linked Ag particles, presumably situated mainly in the grain boundaries,
which form Ag pillars and contribute to a parallel heat path. The other group consists of isolated Ag particles
which form a smaller inside cube and contribute to the series path of Ag and YBCO. The sum of volumes ofpillars and a cube is postulated to be equal to f Ag . The total thermal resistance W of the circuit in Fig. 2A isgiven by1
11
1
1+++.
(1)
=W
WY1
WAg1
WY2 + WAg2
WY3 + WAg3
.

.

.

.

.

.

.

.

Superlattices and Microstructures, Vol. 21, No. 3, 1997

351

WAg1
WY1
WAg2

WY2

DL

WAg3

A

WY3

AB

Fig. 2. A, A general equivalent circuit of the thermal resistance of Ag + YBCO composites. B, A simplified model cube of thecomposite which takes into account the isotropic nature of the Ag distribution in this sintered material.
.

.

Thermal conductivity (mW cm–1 K–1)

1500
fAg=0.34
fAg=0.26
fAg=0.18
using κAg (RRR=257)
using κAg (RRR=37)
using κAg (RRR=215)

1000

500

050

100

150

Temperature (K)Fig. 3. Examples of the comparison of the measured κ(T ) with the calculated κ(T ) of Ag + YBCO composite materials using κAg (T )of R R R = 257, 37 and 15.
.

.

If one edge of the model cube has length L, if the edge of the inner cube is D and if the cross-section of a pillar
is A, each thermal resistance component is approximated as WY1 = L/{κYBCO (L − D − 2A)(L + D − 2A)},WY2 = (L − D)/(κYBCO D 2 ), WY3 = 1/(4κYBCO A), WAg1 = L/(4κAg A2 ), WAg2 = 1/(κAg D) and WAg3 =1/{2κAg (L − 2A)} with κYBCO and κAg being the thermal conductivities of YBCO and Ag, respectively. For
κYBCO we used the value for an undoped YBCO ( f Ag = 0) sample, and for κAg were used those of Ag + Aualloys [5] (residual resistivity ratio (RRR): ρ(280 K)/ρ(4.2 K) = 257, 37 and 15) which are also shown inFig. 1. A and D were determined so as to achieve the best fit to be observed κ(T ) values at three temperaturesof 80 K, 100 K and 150 K. Figure 3 shows examples of the fitting. The temperature dependence of κ(T ) waswell reproduced by the model.
As is well-known, κ(T ) of a pure metal only weakly depends on its purity in the high temperature region.

.

352

Superlattices and Microstructures, Vol. 21, No. 3, 1997
60Ag+YBCO50

RRR of Ag

4030
201000.1

0.20.3Ag volume fraction fAg

0.4

Fig. 4. Estimated R R R of Ag in Ag + YBCO versus Ag volume fraction f Ag .
.

.

(T > 70 K for Ag). In the low temperature region, however, κ(T ) is very sensitive to purity and is strongly
enhanced in purer metals. For the sample of f Ag = 0.18, the experimental κ(T ) is between the calculated
κ(T ) using κAg of R R R = 15 and that using R R R = 37, which means that the purity of doped Ag is between
R R R = 15 and 37. It was confirmed that the doped-Ag purity in the sample f Ag = 0.26 was nearly equal toR R R = 37 and that in f Ag = 0.34 was between R R R = 37 and 257. The relation between R R R of Ag andκAg (T ) was obtained by interpolation with reference to Cu data [6] in order to determine the R R R values ofAg particles in YBCO. Figure 4 shows the estimated R R R of doped Ag in YBCO versus Ag volume fractionf Ag . R R R was almost constant for f Ag below about 0.15 and then increased with increasing f Ag . The valueof f Ag ≈ 0.15 is consistent with the threshold volume fraction of percolation theory in a three-dimensional
medium [7]. The R R R of Ag in Ag-doped Bi2212 crystals in the previous report [1] was higher than thatof the present Ag-doped materials at the same Ag concentration. This probably results from the anisotropic
distribution of Ag in the latter [2].
.

.

.

.

.

.

.

.

References.

[1] M.
} Ikebe, H. Fujishiro, M. Matsukawa, F. Tatezaki, H. Ogasawara, K. Noto, K. Michishita, and Y. Kubo,Jpn. J. Appl. Phys. 33, 2004 (1994).
} Fujishiro, M. Ikebe, H. Ogasawara, K. Noto, K. Michishita, and Y. Kubo, Proc. 9th US-Japan Workshop[2] H.
on High-Field Superconducting Materials, Wires and Conductors, Kyoto, 61 (1995).
} Ikebe, H. Fujishiro, T. Naito, and K. Noto, J. Phys. Soc. Jpn. 63, 3107 (1994).
[3] M.
} Fujishiro, K. Kusaka, M. Ikebe, H. Ogasawara, and K. Noto, Cryogenics 34, ICEC Suppl., 231 (1994).
[4] H.
} Fujishiro, M. Ikebe, K. Noto, T. Sasaoka, and K. Nomura, Cryogenics 33, 1086 (1993).
[5] H.
} G. Hust and A. B. Lankford, NBS Report, NBSIR 84-3007 (1984).
[6] J.
[7] I.
} Webman, J. Jortner, and M. Cohen, Phys. Rev. B 14, 4737 (1976).
.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.
.