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Physics Procedia 36 (2012) 1609 – 1613

Superconductivity Centennial Conference

Speciﬁc heat and thermal diﬀusivity of YBCO coatedconductors
Tomoyuki Naitoa , Hiroyuki Fujishiroa , Yasuhisa Yamamurab , Kazuya Saitob ,Hiroshi Okamotoc , Hidemi Hayashic , Yoshihiro Goshod , Takeshi Ohkumad , Yuh
Shioharada Faculty of Engineering, Iwate University, Morioka 020-8551, Japanb Department of Chemistry, Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571, Japanc Kyushu Electric Power Co., Inc., Fukuoka 815-8520, Japand Superconductivity Research Laboratory, ISTEC, Tokyo 135-0062, Japan

Abstract
We have measured the temperature dependence of speciﬁc heat, C(T ), for Ag deposited YBCO coated conductor(YCC), YCC reinforced by a thin Cu tape (YCC-Cu), and the Hastelloy substrate with buﬀer layer. C(T ) of Hastelloy C276 with buﬀer layer agrees well with the reported one of Hastelloy C-276, indicating that the contribution of the buﬀer
layer to the measured C(T ) is negligibly small. C(T ) of both YCC and YCC-Cu tapes was successfully reproducedby the simple sum rule using the C(T ) values reported for Hastelloy, Ag and Cu. The results demonstrate that C(T )of various YCC tapes can be estimated using the reported C(T ) of constitutional materials. The estimated thermal
diﬀusivity, α = κ/C, at 300 K of YCC, which was estimated using the thermal conductivity, κ, did not agree with thereported α of Ag. This result was inconsistent with the fact that the applied heat ﬂew through the Ag layer, suggestingthat a relation of α = κ/C for homogeneous material cannot be applicable for the layered material such as YCC.

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Keywords: Keywords: YBCO coated conductor, speciﬁc heat, thermal diﬀusivity

1. Introduction
Since the degradation of the critical current density, Jc , in YBa2 Cu3 O7−δ (YBCO) is not as large evenat 77 K in a high magnetic ﬁeld as that of Bi-based compounds, YBCO is a promising material for thehigh temperature and high magnetic ﬁeld applications. In past decade, YBCO coated conductor (YCC)
tapes, which consists of metal substrate, buﬀer and cap layers, YBCO ﬁlm, and stabilizing Ag layer, hasbeen developed for the power applications such as power cables, motors,transformers, and fault current
limiters [1].
Thermal properties such as the thermal conductivity, κ(T ), thermal diﬀusivity, α(T ), and the speciﬁcheat, C(T ), are very important to evaluate the thermal stability of the superconducting materials. The heat
intrusion or exhaust, Q, through the tape is shown by the following relation,
 T2SQ=
κ(T )dT.
L T1

1875-3892 © 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Guest Editors.
doi:10.1016/j.phpro.2012.06.316

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Tomoyuki Naito et al. / Physics Procedia 36 (2012) 1609 – 1613

0.5
YCC-Ag20
YCC-Ag10Cu300
Hastelloy+buffer

C (J/g-K)

0.4
0.3
0.2

CuAg
YBCObuffer
Hastelloy

0.1
00100

200300T(K)Fig. 1. Temperature dependence of the speciﬁc heat, C(T ), of YCC-Ag20, YCC-Ag10Cu300 and Hastelloy+buﬀer tapes.

Here, T 1 and T 2 are the temperatures of the terminals of the tape, S the cross section, and L the length ofthe tape.
We have measured κ(T ) of various YCC tapes and found that the applied heat mainly ﬂew through thehigh thermal conductive layer such as stabilizing Ag and the reinforcing Cu using an equivalent heat current
circuit with simple sum rule [2, 3]. In this paper, we report the temperature dependence of the speciﬁcheat, C(T ), of the Ag deposited YCC tape and a YCC tape reinforced by thin Cu tape. The contribution ofeach constitutional material of the YCC tape to C(T ) is discussed by simple sum rule using the C(T ) values
from the literature. Thermal diﬀusivity was estimated by the relation of α = κ/C which was approvedin homogeneous materials. The validity of this relation in a layered material such as YCC tape is also
discussed.
2. Experimental procedure
YCC tapes were fabricated by an ion beam assisted deposition (IBAD) and a pulsed laser deposition(PLD) method. The details of fabrication technique have been described elsewhere [4]. Hastelloy C-276(5 mm wide and 100 μm thick) was used as a substrate. Gd2 Zr2 O7 (GZO) (about 1 μm thick) and CeO2
(0.7 μm thick) ﬁlms were deposited on the Hastelloy as a buﬀer layer by the IBAD and PLD method,respectively. YBCO ﬁlm (about 1.5 μm thick) were grown by the PLD method. Finally, Ag (10-20 μmthick) was deposited on YBCO/CeO2 /GZO/Hastelloy as a thermal stabilizer. YCC tape reinforced by Cutape (300 μm thick) and the Hastelloy with the buﬀer layer, named YCC-Ag10Cu300 and Hastelloy+buﬀer,
respectively, were also prepared.
Speciﬁc heat, C(T ), was measured by a relaxation technique using the Physical Properties Measurement
System (PPMS, Quantum Design Inc.) from 10 K to 300 K.
3. Results and Discussion
3.1. Speciﬁc heat
Figure 1 shows the temperature dependence of the speciﬁc heat of YCC-Ag20, YCC-Ag10Cu300 andHastelloy+buﬀer. C(T ) of all the samples decreases monotonically with decreasing temperature. Absolute values of C(T ) at 300 K are about 0.37, 0.39 and 0.40 J/g-K for YCC-Ag20, YCC-Ag10Cu300 and
Hastelloy+buﬀer, respectively.

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Tomoyuki Naito et al. / Physics Procedia 36 (2012) 1609 – 1613

0.5
Hastelloy+buffer(measured)
Hastelloy(ref.[5])C (J/g-K)

0.4

0.3

0.2

0.1(a)
00100

200

300

T (K)
0.5

0.5
YCC-Ag20(measured)
YCC-Ag20(estimated)
Hastelloy(ref.[5])Ag(ref.[6])

0.4

0.3

C (J/g-K)

C (J/g-K)

0.4

YCC-Ag10Cu300(measured)
YCC-Ag10Cu300(estimated)
Hastelloy(ref.[5])Ag(ref.[6])Cu(ref.[6])

0.2

0.1

0.3

0.2

0.1(b)

(c)

00
0

100

2003000T (K)

100200300

T (K)Fig. 2. (a) Temperature dependence of the speciﬁc heat, C(T ), of Hastelloy+buﬀer and the reported C(T ) of Hastelloy. (b) and (c)show the measured and estimated C(T ) of YCC-Ag20 and YCC-Ag10Cu300, respectively. The reported C(T ) of Hastelloy, Ag andCu is also plotted.

Figure 2(a) shows the measured C(T ) of Hastelloy+buﬀer and the reported one of Hastelloy C-276 [5].
The measured C(T ) coincides well with the reported one, meaning that the contribution of the buﬀer layer
is negligibly small because of a very small volume fraction of the buﬀer layer.
We estimate the C(T ) for YCC-Ag20 and YCC-Ag10Cu300 using the reported C(T ) of Hastelloy [5],Ag [6] and Cu [6]. In a composite material which consists of n kinds of materials, the total quantity of heat,
Qtot , is given by the sum of that of each constitutional material as follows:
Qtot =nQi ,i=1where, Qi is the quantity of heat of the i-th part. When the speciﬁc heat per unit weight, C i , is known, Qi isgiven as C i ×(V i ×di ). Here, V i and di are the volume and density of the i-th part, respectively. Consequently,

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Tomoyuki Naito et al. / Physics Procedia 36 (2012) 1609 – 1613

105

αcal-Ag20

α (mm2/sec)

104

αcal-YCC-Ag20

103

Ag(ref.[7])1021010100200

300T (K)Fig. 3. Temperature dependence of the estimated thermal diﬀusivity, α(T ), of YCC-Ag20 tape and Ag20. The reported α(300 K) at300 K of Ag is also plotted.

the total speciﬁc heat C tot per unit weight can be estimated by the following relation:n(C i × V i × di )totn
C = i=1iii=1 (V × d )Figures 2(b) and 2(c) show the temperature dependence of the measured and estimated C(T ) for YCCAg20 and YCC-Ag10Cu300, respectively. Here, the densities of Hastelloy, Ag and Cu are 8.89, 8.96 and10.49 g/cm3 , respectively. We ignore the contribution of the YBCO layer, because it is negligibly thin incomparison with those of other metallic parts. For both tapes, the measured C(T ) is well reproduced by theestimated one, indicating that the C(T ) of the composite samples with various thickness and species of eachlayered material can be estimated from the known C(T ) of each part using the simple sum rule.
3.2. Thermal diﬀusivity
Figure 3 shows the temperature dependence of the thermal diﬀusivity, αcal -YCC-Ag20 of YCC-Ag20tape, which is estimated from the measured C(T ) shown in Fig. 1 and the κ(T ) reported by us [2]. αcal YCC-Ag20 increased gradually with decreasing temperature and steeply upturned at lower temperatures.
The α(T ) behavior is a usual manner for ordinary materials. However, the absolute value of α(T ) should benoted. In the analysis of κ(T ) for YCC tapes, the heat mainly ﬂows in the stabilizing Ag layer, regardlessof the very thin thickness [2]. For the α value, which is closely related with the transient heat propagation,
it must be taken into consideration that the heat ﬂux preferentially ﬂows in the Ag layer. We estimatedthe revised thermal diﬀusivity, αcal -Ag20, as shown in Fig. 3, where the heat ﬂux is supposed to propagate
only through the high-thermal conductive Ag layer 20 μm in thickness in the YCC tape. The αcal -Ag20 wascalculated using κAg /CAg = κtot /((S Ag +S tot )/CAg ), where κtot is the thermal conductivity of the Ag stabilized
YCC tape, κAg is that of stabilizing Ag layer, S Ag and S tot are the cross section of the Ag layer and total
YCC tape, and CAg is the speciﬁc heat of Ag. The αcal -Ag20 value is about one order of magnitude larger
than αcal -YCC-Ag20. It should be noted that the αcal -Ag20 value at 300 K is quite reasonable agreementwith that of the reported Ag [7]. These results suggest that the heat ﬂux ﬂows in the Ag layer of the layered
superconducting tapes. The relation, α = κ/C, is applicable only for the homogeneous materials.
Finally, we comment on the use of the thermal diﬀusivity value for the thermal stabilizing design for thesuperconducting apparatus. If we use the αcal -YCC-Ag20 value as the thermal diﬀusivity of the tape, theamount of the heat ﬂow is underestimated. In this case, the additional thermal stabilizing materials mustTomoyuki Naito et al. / Physics Procedia 36 (2012) 1609 – 1613

be taken in consideration. In fact, the heat should propagate faster and no stabilizing materials such as Cu
inserting tape may be added. The measurement and application of the thermal parameters of the layered
structural system must be performed cautiously.
4. Summary
We have measured the temperature dependence of the speciﬁc heat, C(T ), of Ag deposited YBCO coatedconductor (YCC) tape, YCC reinforced by a thin Cu tape (YCC-Cu) and Hastelloy substrate with the buﬀerlayer. C(T ) of Hastelloy with the buﬀer layer almost coincided with that of Hastelloy C-276 reported
previously. This means the negligibly small contribution of the buﬀer layer to the measured C(T ). C(T )of both YCC and YCC-Cu tapes was well reproduced by the reported C(T ) of Hastelloy, Ag and Cu using
a simple sum rule. Thus, if we know the C(T ) values of all component of the YCC tape, whose unknown
C(T ) can be obtained by the calculation without a direct measurement. Thermal diﬀusivity, α(T ), of theYCC tape was estimated from the measured C(T ) and κ(T ) using the relation of α = κ/C, where κ isthermal conductivity. Since the main heat pass of the YCC tape is the stabilizing Ag layer, α(T ) of thestabilizing Ag layer was also estimated. The magnitude of α(T ) of the stabilizing Ag layer was one orderof magnitude larger than that of the YCC tape and nearly corresponded to that of the reported Ag at 300 K,
which suggested that the heat ﬂux propagated in the Ag layer of the YCC tape and that the obtained α(T ) ofthe YCC tape was underestimated. We can conclude that the relation of α = κ/C for homogeneous systemcannot be applicable for the layered system such as the YCC tapes.
Acknowledgement
This work was supported by the New Energy and Industrial Technology Development Organization(NEDO).
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