Dissipation mechanisms in polycrystalline YBCO prepared by sintering of ball-milled precursor powder

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Dissipation mechanisms in polycrystalline YBCO prepared by sintering of ball-milled precursor powder E. Hannachi, M.K. Ben Salem, Y. Slimani, A. Hamrita, M. Zouaoui, F. Ben Azzouz, M. Ben Salem

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Received date: 6 July 2013 Revised date: 15 August 2013 Accepted date: 18 August 2013 Cite this article as: E. Hannachi, M.K. Ben Salem, Y. Slimani, A. Hamrita, M. Zouaoui, F. Ben Azzouz, M. Ben Salem, Dissipation mechanisms in polycrystalline YBCO prepared by sintering of ball-milled precursor powder, Physica B, http://dx.doi.org/10.1016/j.physb.2013.08.028 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Dissipation mechanisms in polycrystalline YBCO prepared by sintering of ball-milled precursor powder

E. Hannachi, M. K. Ben Salem, Y. Slimani, A. Hamrita, M. Zouaoui, F. Ben Azzouz, M. Ben Salem * L3M, Department of Physics, Faculty of Sciences of Bizerte, University of Carthage, 7021 Zarzouna, Tunisia

Corresponding author:

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Prof. Ben Salem Mohamed Department of physics Faculty of Sciences of Bizerte 7021 Zarzouna, Bizerte, Tunisia 00 216 72 591 906 00 216 72 590 566 [email protected] [email protected]

Abstract Magnetoresistivity ( ρ(T, H) ) measurements of polycrystalline YBa2Cu3Oy (Y-123) and YBa2Cu3Oy embedded with nanoparticles of Y-deficient Y-123, generated by the planetary ball milling, have been compared and analyzed by the Ambegaokar and Halperin phase slip model (AH) and thermally activated flux creep (TAFC). Phase analysis by X-ray diffraction (XRD), granular structure examination by scanning electron microscopy (SEM) coupled with energy dispersive X-ray spectroscopy (EDXS), were carried out. SEM analyses show that nanoparticles of Y-deficient Y-123, generated by ball milling, are embedded in the superconducting matrix. The broadening of the resistive transition under magnetic field is found to possess two distinct regions, which suggests that dissipation phenomenon in milled and unmilled samples is caused by two mechanisms: the order parameter fluctuations and the vortex-dynamics separated by a crossover temperature T* . The critical current J c (0) at zero

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temperature in the grain boundaries decreases as a power law, H n , which is an indication of the sensitivity of a single junction between the superconducting grains to the applied magnetic field. J c (0) of the milled material is higher than the one of the unmilled and the activation energies of vortex flux motion U(H) behavior in the applied magnetic field is enhanced by the presence of the nanoparticles embedded in the matrix.

Keywords: YBCO superconductor, planetary ball milling, electrical properties, dissipation phenomena.

1. Introduction Transport properties such as electrical conductivity and electrical current density of high Tc superconductors (HTS) are largely affected by the application of external magnetic fields. One of the most prominent features of these materials is the peculiar broadening of the resistive transition under an applied magnetic field. The broadening phenomenon gives valuable information on the pinning and vortex motion. Much attention has been paid to the relationship between the dissipative flux motion and the flux pinning mechanisms, induced by thermal activation [1]. The mixed state of the resistivity is divided into two dissipative regions, called the vortex-glass and vortex-fluid states. There are different models for the interpretation of the resistivity broadening under a magnetic field such as superconducting glass [2], flux creep [3], flux flow [4], Kosterlitz–Thouless transition [5], fluctuations [6], Josephson coupling [7], Ambegaokar and Halperin [8], thermally activated flux flow [9], etc. Some studies [10-13] have shown that the Ambegaokar and Halperin (AH) model perfectly fits the experimental data of single and bulk HTS materials. Furthermore, other authors [3,14,15], have applied the thermally activated flux creep (TAFC) model to describe the broadening of the resistivity near the transition temperature. Bhalla et al [16], using AH

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modified model demonstrated that two mechanisms have to be used to explain the dissipation with a possible crossover from one mechanism to another. The preparation method and the nature of the chemical doping and additives can introduce additional defects in the form of single atom, grain boundaries or impurity phases in the superconductor material, which lead to increase the number of disorder in the compound. Disorder is assumed to play a leading role in the superconducting properties of high-Tc superconductors in an external magnetic field [17–19]. The aim of this paper is to analyze the effect of disorder induced by a high density of interfaces between Y-123 and the embedded nanophases generated by ball milling, on the dissipative phenomenon. The high energy ballmilling facilitates the formation of an optimal microstructure with a high grain boundary density and lattice strain, which is expected to enhance the magnetic flux pinning ability and to improve the critical current in external magnetic fields [20-21]. Since our samples contain a complex three-dimensional network of Josephson weak links formed at grain boundaries, a logical choice for a physical model in these materials is the AH theory. We report here a comparative analysis of the physical mechanisms responsible for the broadening of the ρ (T, H) of pure YBa2Cu3Oy and YBa2Cu3Oy embedded by nanoparticles induced by planetary ball milling. We show that ‘glassy’ dynamics and phase slippage, are able to account for the behaviour of the experimental data as a function of both the magnetic field H and the temperature T.

2. Experimental details Details on the preparation of YBa2Cu3Oy polycrystalline samples and the effect of the planetary ball milling have been reported elsewhere [21] and therefore we only give a brief description. A mixture of Ba2CO3, Y2O3, and CuO powders was pelletized and then calcined at 950oC for 12 h in air in order to produce an oxide precursor without remainder of any carbonates. The resulting oxide precursor was divided into two parts, one part was milled via

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the planetary milling and the other part was grounded by hand in an agate mortar. In the present work, we considered the sample milled by planetary ball milling for 4 h with a milling speed of 600 rpm and a ball-to-powder weight ratio of about 5:2. Both milled and hand grinding oxide precursors were then pressed uniaxially into pellets. These pellets were sintered in air at 950oC for 8 h. The samples are labeled as “milled” (for the planetary milled precursor) and “unmilled” (for the hand grinded precursor). The structure and phase purity of the powder sample ground from sintered pellets were examined by powder X-ray diffraction using a Philips 1710 diffractometer with CuK α radiation. The microstructure of samples was characterized using a scanning electron

microscope (JEOL-JEM 5510). The temperature dependence of the electrical resistivity was measured under an applied magnetic field in the range of 0 to 200 mT. A low current of 40 µA is used in order not to affect the behavior of the resistivity transition for the milled and unmilled samples.

3. Results and discussion XRD patterns for the umilled and the milled samples are shown in Fig. 1 and they were indexed by an orthorhombic lattice with space group Pmmm. A small quantity of Y2BaCuO5 has been observed. Moreover, compared to unmilled sample the intensity of ( 00A ) peaks are lower in the milled sample. This can be related to an increase of planar defects along the caxis generated by the embedded nanoparticles in the matrix. The XRD data have been analyzed by the Rietveld refinement procedure using the FULLPROF program with multiphase capability. The Rietveld method was successfully applied to determine quantitatively phase abundances of the different crystallographic phases in the compound. According to the SEM coupled with EDXS analyses, the milled sample exhibits nanoscale entities of Y-deficient YBCO submerged within the Y-123 crystallites. Therefore a fitting of the XRD data of ball milled sample was tried considering stoichiometric Y-123, Y-deficient

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YBCO and secondary phases such as (Y-124 and Y-211). The Y-deficient YBCO phase concentration is 8 wt.% in the milled sample. The grain size was calculated using the well known Scherrer equation. The estimated average grain size of Y-123 is about 95 and 80 nm respectively in unmilled and milled samples and about 15 nm for Y-deficient YBCO. Fig. 2 shows the SEM micrographs of the transverse cross-section morphology of the unmilled (Fig. 2-a) and milled (Fig. 2-b) samples. The microstructure of samples exhibits a granular structure with a dominant YBCO phase. The milled sample exhibits a smaller grain size. A closer look at higher magnification (Fig. 3) reveals that the spherical shape entities appear as a clumping of fine particles with a particle size of about 15 nm into coral-like agglomerates [21]. The EDXS resolution in the SEM is about 1–2µm, so it is impossible to determine precisely the composition of the entities by conducting a spot analysis on a single particle. To estimate the elemental composition of the entities, comparative analyses have been carried out in the regions where entities are present and regions where they are absent. For the milled sample the EDXS analysis performed on areas with a high-density of entities shows the presence of Y, Ba, Cu, and O with a small deviation of the yttrium content compared to the nominal composition of YBa2Cu3Oy [21]. The microstructure of milled sample is characterized by a high density of interfaces between the Y-deficient YBCO nanoparticles and the YBCO matrix. In the Fig. 4 we show the magnetoresistivity measurements of the unmilled and milled samples under different magnetic fields. Both samples show metallic behavior in the normal state (Inset of Fig.4). Note that the normal state resistivity of the milled sample is higher. The larger the number of defects, heterogeneities etc, the higher their scattering offered to the mobile carriers. This is confirmed by the higher residual resistivity ρ n (0) values for milled sample. The mechanism of the resistive transition under the influence of a magnetic field seems to be similar for both milled and unmilled samples. The broadened region is extremely

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sensitive to the magnetic field and moves to lower temperatures on increasing the applied magnetic field. It is clear that the milling process strengthens ΔT = Tc (0) − Tc (H) ; Tc is the zero resistivity temperature. The ΔT data are well fitted according to a power law scaling relation ΔT = a H -n with n equal to 0.35 ± 0.03 and 0.37± 0.01 for both samples; the value of the factor a is found to be 1.7 and 1.09 in the milled and unmilled samples respectively. The factor a is significantly higher in the former case. This result confirms that nanoparticles generated during the planetary ball milling and embedded in the matrix increase the number of interfaces and defects. To analyze the broadening of the resistive transition of our samples, we have considered the AH and TAFC models. Fig. 5 is a schematic view of the broadening of the resistive transition under magnetic field showing the different regimes of energy dissipation. For a high-Tc superconductor, the AH model is directly applicable in the range of

TAH < T < Tp and a quantitative comparison between the experimental data and the model can be made. TAH is the temperature at which the experimental data coincide with the theoretical curve for the AH model. Within this theory, the resistivity, ρ( Τ, H ) , in the limit of low current I << I c (Ic is the critical current), is given by ρ(T ) = ρ p [ I o ( γ / 2)]−2 [8] where ρ p is the average

normal resistivity of the junction, I o is the modified Bessel function and γ is the normalized barrier height for thermal phase slippage defined as γ ( Η, Τ ) = C( Η ) (1 - t ) q where t = Τ/Τp is the reduced temperature. In the fitting process, we start by using the values of the resistivity ρ p and the corresponding temperature TP of the branching point of the curves, while the

parameter C(H) and the exponent q were left free. Fig. 6 shows AH fits of the resistivity under magnetic field in the temperature range TAH < T < Tp for the unmilled and the milled samples. The distribution of interfaces plays an important role in the broadening of the resistivity under applied magnetic field and on the thermal fluctuation of the order parameters phases across 6

these interfaces. Besides the Y-123/Y-123 junction, other interfaces between Y-deficient nanophases and Y-123 matrix are added to the milled sample and as a consequence the AH model describes a larger zone in the milled sample compared to unmilled one. The value of ρ p is unaffected by the applied magnetic field and equals to 0.115 ± 0.003 m Ω cm and 0.126

± 0.005 m Ω cm for the unmilled and milled samples respectively. The value of TP is equal to 88.7K and 91.7K respectively for the milled and unmilled samples. For each curve C(H) and

q have been determined from the fit. It is observed that on increasing the magnetic field, the temperature TAH shifts to a lower value and the parameter C(H) decreases. The average of the exponent q is 1 ± 0.05 for both samples. The variation of the C(H) parameter with the magnetic field is shown in Fig. 7. The C(H) parameter in both samples show a similar behavior. The

C(H)

data are well fitted according to a power law scaling

relation C(H) = c H -n ; the power law dependence of C(H) to the magnetic field n is 0.38 ± 0.003 for the milled and 0.29±0.03 for the unmilled sample. Our results are consistent with other studies such as for the Ca-doped GdPr-123 system [22]. C(H) depends on the size and orientation of the weak link Josephson junctions, which are determined by the sample microstructure. Within the range of the applied magnetic field, the C(H) factor, c, is comparable for both samples. From the AH theory, the parameter C(H) at temperature close to the transition temperature TP is given by [23]: C(H) = (J c (0)= 2 a 2 ) /(ek B Tp ) , where J c (0) is the critical current density in the grain boundary at zero temperature and a is the average grain size. Given that the C(H) and Tp values deduced from the fitting are essentially the same for both samples and SEM observations show that the average grain size for the milled sample is twice larger than that of the milled one, the Jc(0) of the milled sample is higher compared to the unmilled one. To confirm this result, the transport critical current density Jc values were determined at various temperatures under applied magnetic field using a 5µV/cm criterion. 7

The dependence of the transport critical current densities Jc versus temperatures at applied magnetic field of 2 mT for milled and unmilled samples is shown in Fig .8. Both samples show an enhancement of the critical current with temperature. Note that the milled sample exhibits higher transport critical current density over the entire temperature range compared to unmilled one. In the region Tg < T < TFC (Fig. 5), the broadened resistivity curves of ρ (T, H) cannot be adequately explained by the AH theory as predicted by some authors [13, 24-26]; where Tg is the glass transition temperature and TFC is the temperature at which the experimental data coincide with the theoretical curve for the TAFC model. Many previous studies [27-32] report that vortex-dynamics plays a dominant role in dissipation in the region below TFC . Therefore the resistivity can be described using Arrhenius equation ρ( Τ, Η ) = ρ p exp( -U( Τ, Η )/k Β Τ ) , where k B is the Boltzmann constant, ρ p is the pre-exponential factor independent of the applied magnetic field and U(H, T) = U( Η )U( Τ) with U(H) = ( ΤP /Τg( Η ) - 1) −1 [33] and U(T ) = U(0)(1 - Τ/ΤP ) m . Tg (H) can be extracted by a linear extrapolation of the plot of

(d ln(ρ/ρ p )/dΤ ) -1

versus

T

and the

U(T)

dependence can be expressed as:

U(T ) = - [k Β Τ ( Τp - Τg ( Η ))/Τg ( Η )] ln(ρ/ρ p ) . One can therefore extract the magnetic field dependence of the activation energies U(H) from the slope of ln(ρ/ρ p ) versus (1 - Τ/ΤP ) m / T curves. The m and TP parameters have been determined by fitting the experimental data. The

U(T ) results for the unmilled and milled samples are presented in Fig. 9. The fitting parameters m are found to be 1.5 for the unmilled sample, corresponding to a 3D vortex anisotropy state and 2 in the milled one which corresponds to 2D behavior of pinning of vortices induced by interface between grains. These values of m are consistent with those obtained for the high temperature superconducting materials [34, 35]. TFC can be extracted by

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a linear extrapolation of the plot of U(T ) . Fig. 10 shows curves of ln(ρ/ρ p ) versus (1 - Τ/ΤP ) m / T for the unmilled and milled samples under varying magnetic fields. The slope

of the linear data in the tail of these curves gives the activation energy U(H) . The value of

U(H) decreases as the magnetic field increases (Fig. 11). For the applied magnetic field in the range 0 < H < 200mT , the activation energy U(H) of milled sample is higher than of the unmilled one, which confirms the strengthening of pinning of vortices in the milled sample. Therefore the ball milling can enhance the flux pinning properties of materials and improve their transport capabilities. This result is supported by the improvement of the critical current density under applied magnetic field, the flux pinning force, the irreversibility magnetic field and the upper critical magnetic field of the milled sample [21]. The decrease of pinning energy with an increase of the applied magnetic field can be scaled with a power law relation, U(H) ∝ H -n , where n equals to 0.45 for the unmilled sample and 0.75 for the milled sample. In some reports, the value of n has been found to be 0.35 for GdPrCa-123 [22], 0.5 for Y-123 [25, 31], and 0.67 for Gd(Ba,La)-123 [36], 0.73 in Y-123 thin film [37, 38], 0.9 in BiSrCaCuO tape samples [39] and 0.55 for GdLaPr-123 [40]. Our results clearly show that in milled and unmilled samples two distinct dissipation mechanisms are operating (Fig 12). A crossover from the AH to the TAFC dissipation mechanisms occurs at the dissipation transition temperature around T * (Inset Fig. 12). The AH mechanism dominated by a phase slip process governed by the order parameter fluctuations is operating in the upper region of the ρ(T, H)

curves, i.e. above

TAH = T * + ΔTAH , while the TAFC mechanism corresponding to a motion of the vortices is

operating below TFC = T * − ΔTFC . In between, a small temperature range, i.e. TAH to TFC the dissipation phenomenon is possibly governed by both mechanisms i.e. the order parameter fluctuations and the vortex-dynamics. Widths of the overlapping region around T* ,

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ΔT * = TAH − TFC as a function of the applied magnetic field in the range 0 < H < 200mT for the unmilled and milled samples are summarized in Fig. 13. This figure shows that the overlapping region is larger in the milled sample. The inset of Fig. 13 highlights the crossover temperature T * as function of applied magnetic field for unmilled and milled samples. 4. Conclusion

We have studied the broadening of the resistive transition in bulk YBCO, embedded with nanoparticles of Y-deficient Y-123, generated by a planetary ball milling. The present study shows that the resistivity broadening under magnetic field can not be analyzed by a single model as reported by other investigations. Analysis of our experimental data, in a magnetic field ranging from 0 to 200mT, shows that at the vicinity of superconducting transition where critical fluctuations are believed to be absent, the vortex motion is described using the AH model in the temperature range TAH < T < Tp. At the temperatures below TFC the resistive features are modeled using the thermally activated flux creep formalism. Therefore there appears a small temperature range in which the dissipation may be due to the co-existence of both mechanisms i.e. the order parameter fluctuations and the vortex dynamics. This small range seems to be wider in milled sample. We have defined the crossover temperature which decreases with increasing magnetic field. It seems that the Y-deficient Y-123 nanoparticles embedded in the superconducting matrix, generated by the ball milling are the cause of the behavior and the improvement of flux pinning properties.

Acknowledgement

The authors are grateful to Prof G. Van Tendeloo (University of

Antwerp Belgium) for useful discussions and text corrections.

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Figure captions Fig. 1: X-Ray powder diffraction patterns of milled and unmilled samples. Fig. 2: SEM micrographs showing the overviews of (a) unmilled and (b) milled samples. Fig. 3: High magnification SEM micrograph showing nanosized particles within Y-123. Fig. 4: Variations of the electrical resistivity with temperature at different applied magnetic

field of unmilled and milled samples. Inset: Resistivity dependences on the temperature of milled and unmilled samples at self magnetic field. .Fig.

5: Schematic view of the broadening of the resistive transition under magnetic field

showing the different regimes of energy dissipation. Fig. 6: AH fitting data of the magnetoresistivity for unmilled and milled samples. Fig. 7: Variations of the factor C(H) with applied magnetic field for unmilled and milled

samples. Fig. 8: Critical current density as function of temperature measured at 2 mT for unmilled and

milled samples. Fig. 9: Variations of U(T) with temperature at different magnetic field for unmilled and

milled samples.

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Fig. 10: Plot of Ln(ρ / ρ p ) versus (1 - T/Tp) m / T at various magnetic fields for unmilled and

milled samples. Fig. 11: Variations of U(H) with applied magnetic field for unmilled and milled samples. The

inset shows LogU(H) − Log(H) variations of samples. Fig. 12: Dependence of the resistivity as a function of the applied magnetic field for unmilled

and milled samples. Solid and dashed lines cross at dissipation transition T* . The inset shows the magnified view of the transition region. Fig. 13: Dependence of the transition region ΔT* = TAH − TFC as a function of the applied

magnetic field for unmilled and milled samples. The inset shows variations of the crossover temperature T * with applied magnetic field for unmilled and milled samples.

20

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(116) (213)

(115) (016) (203) (007) (122)

(006) (200)

(005)

(113)

unmilled sample

(112)

(111)

Y2BaCuO5

(012) (102)

(003) (100)

(013) (103)

Intensity (a.u)

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-2

100

100

200

200

-3

-3

Ln ( ρ /ρp)

40

40

-2

-1

5

5

-1

-4 -4

-5 0.00

-5

0.05

0.10 -3

0.03

0.15 m

-1

10 (1-(T/Tp)) / T (K )

0.06

0.09 -3

-6

0.12 m

-1

10 (1-(T/Tp)) / T (K ) Fig.10 :E. Hannachi et al.

17

milled sample

unmilled sample

6 Log (U(H)/kB)

calculated curve

10

U(H)/kB

milled sample

unmilled sample

6

5

calculated curve

5

4

10

0

1

2

Log(μ0 H)

4

10

0

50

100

150

200 μ0H (mT)

Fig.11 :E. Hannachi et al.

unmilled sample

milled sample μ0H (mT)

0.10

0.10

2

0.10 ρ (mΩ.cm)

20

*

T

0.05

40 100 Fit AH

0.00

0.05

85

TFC TAH

Fit FC

90

0.05

T(K)

87

90

81

84

T(K)

87 T(K)

0.00

Fig.12 :E. Hannachi et al.

1.8

milled sample unmilled sample

1.5 1.2

milled sample

90

unmilled sample

88

0.9

86

*

T (K)

84

ΔT*(K)

0.00

ρ (mΩ.cm)

ρ (mΩ.cm)

5

0.6

84 82

0.3 0.0

0

0

20

40

60

30

80

60

90 120 μ0H(mT)

100 μ0H(mT)

Fig.13 :E. Hannachi et al.

18