Simultaneous inductive determination of grain and intergrain critical current densities of YBa2Cu3O7−x coated conductors A. Palau, T. Puig, X. Obradors, E. Pardo, C. Navau et al. Citation: Appl. Phys. Lett. 84, 230 (2004); doi: 10.1063/1.1639940 View online: http://dx.doi.org/10.1063/1.1639940 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v84/i2 Published by the AIP Publishing LLC.
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APPLIED PHYSICS LETTERS
VOLUME 84, NUMBER 2
12 JANUARY 2004
Simultaneous inductive determination of grain and intergrain critical current densities of YBa2 Cu3 O7À x coated conductors A. Palau, T. Puig,a) and X. Obradors Institut Cie`ncia Materials Barcelona, CSIC, Campus U.A.B., 08193 Bellaterra, Spain
E. Pardo, C. Navau, and A. Sanchez Grup d’Electromagnetisme, Department Fı´sica, U.A.B., 08193 Bellaterra, Spain
A. Usoskin and H. C. Freyhardt Zentrum fur Funktion Wekstoffe, 37073 Go¨ttingen, Germany
L. Ferna´ndez and B. Holzapfel IFW Dresden, 01069 Dresden, Germany
R. Feenstra Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6057
共Received 5 August 2003; accepted 15 November 2003兲 An inductive methodology simultaneously enabling the determination of grain- and intergrain critical current densities of YBa2 Cu3 O7⫺x coated conductors is developed. This noninvasive method is based on the identification of a clear peak in the reverse branch of the magnetization loop at a positive magnetic field, as a signature of the electromagnetic granularity inherent to these materials. A quantitative evaluation of the return magnetic field at the grain boundaries allows us to understand the existence of this magnetization peak and quantify the grain critical current density. This methodology is envisaged to sort out granularity effects from vortex pinning effects on coated conductors. © 2004 American Institute of Physics. 关DOI: 10.1063/1.1639940兴
thick YBCO film grown by a BaF2 ex situ process using evaporated precursors on a CeO2 /YSZ/Y2 O3 /Ni/Ni– 3%W tape.9 Zero field cooled magnetic measurements were carried out with a standard SQUID magnetometer equipped with a 5.5 T superconducting coil on samples of 5⫻5 mm2 . Subtraction of the substrate magnetic signal was required in all cases. The right-hand side inset of Fig. 1 shows a typical hysteresis loop for RABiTS-b after substrate subtraction for a maximum applied field H m ⫽5000 Oe at 5 K. Remarkably, the hysteresis loop appears to be anomalous with a maximum on the reverse branch of the magnetization at an applied
With a few years of very intensive effort, high criticalcurrent biaxially textured coated conductors are presently a reality. Both ion-beam-assisted deposition 共IBAD兲 and rolling-assisted biaxially textured substrates 共RABiTS兲 techniques1 have been shown to be suitable for the preparation of high J c conductors. Magneto-optic flux imaging and transport measurements have demonstrated that the supercurrent flow in these conductors is of percolative nature through low angle grain boundaries.2– 4 Therefore, complex flux patterns of currents circulating within the grains and currents crossing grain boundaries are foreseen.5 Some attempts6 have been made in order to develop noninvasive experimental methodologies to determine the intergrain critical current density associated with the grain boundary network, J GB c , . In this letter we and the grain critical current density, J G c present an inductive methodology very suitable to calculate J GB and J G c c for a single conductor from a set of hysteresis loops. This method is based on the anomalous behavior of the hysteresis loops of coated conductors and reflects the effect of the return field from the grains into the grain boundaries. A number of high-quality IBAD and RABiTS coated conductors from different laboratories have been analyzed. A YBCO–IBAD sample, IBAD-a, is a 1 m thick YBa2 Cu3 O7⫺x film grown by a high rate PLD process, on an IBAD–YSZ/Ni–Cr stainless steel substrate.7 Additionally, two RABiTS samples have also been analyzed: RABiTS-a is an 800 nm YBCO film deposited by PLD on a YSZ/CeO2 /Ni– 0.1%Mn tape,8 and RABiTS-b is a 1 m
FIG. 1. Magnetic hysteresis loops at 50 K of 共䊉兲 RABiTS-b for H m ⫽1000, 2000, and 5000 Oe and 共〫兲 IBAD-a for H m ⫽600, 1000, and 5000 Oe. Left inset shows a schematic drawing of the magnetic fields at a grain boundary. Right inset shows the M (H) curve at 5 K for H m ⫽5000 Oe for 共䊉兲 RABiTS-b and 共䊊兲 YBCO thin film.
a兲
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© 2004 American Institute of Physics
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Palau et al.
Appl. Phys. Lett., Vol. 84, No. 2, 12 January 2004
FIG. 2. Numerically calculated dimensionless factors g and x as function of a/L. Shown in the inset are H peak as a function of H m at 50 K for 共⽧兲 sat IBAD-a, 共夝兲 RABiTS-a, and 共䊊兲 RABiTS-b. Also indicated are the H peak and H msat values for the RABiTS-b sample.
field, H a ⬃2300 Oe, instead of at H a ⬃0 as expected for a superconducting film 共see result for a 230 nm thin film in right-hand side inset of Fig. 1兲. A maximum in the reverse magnetization at H a ⬎0 has been observed earlier10,11 ascribed to granularity effects and explained by the same mechanism as that of the hysteretic behavior of J c observed in transport measurements.12,13 As the magnetic field is ramped up, flux enters the material and gets pinned into the grains. Subsequent decrease of the magnetic field results in a reverse magnetic field component through the grain boundaries due to the flux lines trapped in the superconducting grains. Thus, the local magnetic field at the grain boundary, GB , results from the vectorial sum of the applied magnetic H loc field, H a , and the return field coming from each grain that contributes at the boundary, H return 共see upper left-hand side GB GB ⫽H a – H return . In this letter H loc has inset of Fig. 1兲, H loc been considered to be uniform over the sample because the contribution of the self-magnetic field arising from the percolating intergrain critical current density can be neglected in thin films materials, as it has been evidenced by critical-state model calculations for this particular geometry.14,15 GB Therefore, when H loc ⫽0, the magnetization peaks and H peak⬃H return . Magnetization measurements are then a very powerful method to infer the granularity effects of coated conductors. Figure 1 shows hysteresis loops at different H m for IBAD-a and RABiTS-b at 50 K. It is confirmed that both types of coated conductor samples display the maximum in the reverse magnetization at H a ⬎0. However the magnetization of both samples peaks at different H a , H peak , and this peak evolves differently by increasing H m . The inset of Fig. 2 shows H peak as a function of H m for the three samples analyzed, IBAD-a, RABiTS-a, and RABiTS-b at 50 K. Clearly, H peak increases for low values of H m and then it sat , and the saturation saturates. Both, the saturation field, H m sat value of H peak , H peak , are magnitudes characteristic of each type of coated conductor. sat The relation H peak⬃H return establishes that 共i兲 H peak is reached when the grain magnetization saturates, thus sat max sat H peak (T)⬃H return (T), and 共ii兲 H m is a measure of the magsat (T) netic field required to saturate the grains, i.e., H m
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FIG. 3. Temperature dependence of J cGB 共closed symbols兲 and J cG 共open symbols兲 for 共⽧兲 IBAD-a, 共夝兲 RABiTS-a, and 共䊉兲 RABiTS-b. Shown in the lower inset is the magnetic field dependence and hysteretic behavior of J cGB(H) for 共〫兲 IBAD-a, 共夝兲 RABiTS-a, and 共䊉兲 RABiTS-b at 50 K and H m ⫽5000 Oe. Upper inset shows the temperature dependence of the average grain radius obtained for the three samples, 共⽧兲 IBAD-a with 具a典⫽1.7 m, 共夝兲 RABiTS-a with 具a典⫽20 m, and 共䊉兲 RABiTS-b with 具a典⫽12 m.
* (T) where H G* is the full penetration field of the ⬃2H G grains. Therefore, by using the experimental values, sat sat (T) and H m (T), we will be able to determine the grain H peak critical current density, J G c , and the grain size if the relations G * (H ) and J (H ) JG return c c G are known. We have calculated the return field for saturated cylinders with constant J c 共Bean critical-state model兲 assuming that two isolated adjacent grains 共zero separation兲 contribute to the return field at the grain boundary. Calculations have been derived for cylinders of different aspect ratios a/L (a⫽cylinder radius and L⫽cylinder thickness兲 in order to emulate the grains composing IBAD and RABiTS coated conductors. Using a numerical simulation based on energy minimization in the Bean critical-state model we have then also determined the full penetration field16 for isolated cylindrical grains of different aspect ratios.14,17 The two equations obtained are: JG c⫽
max sat 10 H return 10 H peak ⬃ , 4 xL 4 xL
共1兲
JG c⫽
* 10 H msat 10 H G ⬃ , 4 na 4 2na
共2兲
where x and n are numerically calculated dimensionless factors depending on the ratio a/L. These equations derived for isolated cylindrical grains do not need to be corrected for any component of the intergranular self-field for thin film samples,14,15 as already mentioned above. Therefore, comsat sat /H m ) bining Eqs. 共1兲 and 共2兲 we obtain the relation, (H peak ⫽(x/2n)/(a/L)⫽g(a/L), which can be used to estimate the average grain size by means of the function g(a/L) shown in sat sat /H peak . For all IBAD Fig. 2, and the experimental value H m and RABiTS samples analyzed the grain size obtained is indeed temperature independent 共see the upper inset of Fig. 3兲. The average grain radius, a, obtained for IBAD-a sample is ⬃1.7 m while the RABiTS-a and RABiTS-b samples gave average grain radius of ⬃20 and ⬃12 m, respectively. Notice that the obtained grain radius, a, for both IBAD
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and RABiTS coated conductors are consistent with the structural grains determined by TEM and EBSD.8,9,18 The determination of the aspect ratio a/L enables us to estimate J G c using the x(a/L) dependence shown in Fig. 2 and Eq. 共1兲. Results are presented in Fig. 3 共open symbols兲. Values for J G c are in the expected range of YBCO thin films. However, RABiTS-b sample, grown by BaF2 ex situ process, displays a slightly smaller temperature dependence than the other samples grown by PLD. This feature deserves further investigation because it could indicate that different pinning mechanisms are relevant in these films. Positive errors bars have been introduced in the J G c valsat ues in order to consider that J G c has been calculated at H peak , where we have determined H return from the grains. The desat has been estimated from crease in J c from H a ⫽0 to H peak results of thin films. On the other hand the hysteresis loop measurements for H m ⬎2H S* , where H S* is the full penetration field of the sample, allow us to determine the percolating intergrain critical current density, J GB c . The total measured magnetic moment, m⬃m GB, where m GB is the magnetic moment of the intergranular part, because the magnetic moment of the grains is m G ⭐10⫺2 – 10⫺3 m in all the samples. This indicates that the large current loops of the intergrain percolating currents generate a larger magnetic moment than the grain current loops associated to J G c . Thus, it can be considered that the measured magnetic moments of the m(H) cycles solely correspond to the magnetic moment of the intergranular component though strongly influenced by the return field of the grains.19 Then, the temperature dependence of J GB c at GB ⬃0 can be calculated from the equation, J GB H loc c ⫽(30 m/R s V s ), where m is the value of the magnetic moment at the peak, and R s and V s are the total sample radius and volume, respectively. Results are shown in Fig. 3 共closed symbols兲 for the three samples. Notice that the J GB c (T) values for the IBAD and RABiTS samples are just two to four times smaller than the corresponding J G c (T), indicating that these coated conductors are of very high quality. Finally, by applying the same equation, J GB c ⫽(30 m/R s V s ), to both, the initial and reverse branches of the m(H) curve, we have determined the magnetic field dependence of J GB and the associated hysteretic behavior rec sponsible of the anomalous hysteresis loops 共see lower inset of Fig. 3兲. Therefore, we encounter now by inductive magnetic measurements, the hysteretic behavior of J GB c (H) reported12,13 earlier from transport measurements. In conclusion, we have demonstrated that solely from magnetic hysteresis loops measured at different maximum applied magnetic fields, we are able to determine simultaneously the grain and intergrain critical current densities of IBAD and RABiTS coated conductors. The simplicity of the method paves the way to a full investigation of the relationship existing between granularity and vortex pinning effects.
This inductive contactless methodology is based on the anomalous behavior of the hysteresis loops of high critical current granular materials, induced by the return field from the grains into the grain boundaries. Numerical calculations determining the return field and full penetration field of saturated finite grains in the Bean critical-state model have been required in order to properly quantify the grain critical current and give relevant evidence for grain size structure of both types of conductors. This work has been supported by MCyT 共MAT200202642 and BFM2000-0001兲, Generalitat de Catalunya 共SGR 2001-00189 and CeRMAE兲 and EU 共SOLSULET G5RDCT2001-00550兲. A.P. wishes to acknowledge MCyT for a Doctoral Fellowship. B.H and L.F acknowledge support from the German BMBF 共Grant No. 13N7267A兲 1
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