Dielectric properties of (Zn)x/CuTl-1223 nanoparticle-superconductor composites

Zinc (Zn) nanoparticles and (Cu0.5Tl0.5)Ba2Ca2Cu3O10−δ (CuTl-1223) superconducting phase were prepared separately by sol-gel and solid-state reaction methods, respectively. Zn nanoparticles were added in CuTl-1223 superconducting matrix with different weight percentage during the final sintering process to obtain (Zn)x/CuTl-1223 (x = 02-4 wt%) nanoparticle-superconductor composites. The effect of Zn nanoparticles on structural, morphological, superconducting, and dielectric properties of CuTl-1223 phase was investigated. The addition of these Zn nanoparticles has not affected the crystal structure of host CuTl-1223 superconducting phase. Superconducting properties were enhanced after the addition of Zn nanoparticles up to certain optimum content (i.e., x = 1 wt%), which were due to improved inter-grain connectivity by healing up of micro-cracks and reduction of defects like oxygen deficiencies, etc. The activation energy (U) was increased after the addition of Zn nanoparticles in CuTl-1223 phase. The dielectric properties of these samples (i.e., dielectric constant, dielectric loss) were determined by experimentally measured capacitance (C) and conductance (G) as a function of frequency at room temperature. The addition of metallic Zn nanoparticles in CuTl-1223 matrix has overall suppressed the dielectric parameters of (Zn)x/CuTl-1223 nanoparticle-superconductor composites. The metallic Zn nanoparticles played a significant role in inter-grain couplings by filling the voids and pores.

The key objective of this research is the progression of inter-grain connectivity and to scrutinize its effects on superconductivity and dielectric properties of (Zn) x / CuTl-1223 nanoparticle-superconductor composites.
In CuTl-1223 phase, the charge reservoir layer (Cu 0.5 Tl 0.5 )Ba 2 O 4δ consists of Tl 3+ , Cu 2+ , and Ba 2+ ions, which can localize the charge carriers, while the conducting CuO 2 plane consists of mobile charge carriers. The dielectric constant ascends from the accretion of carriers in between (Cu 0.5 Tl 0.5 )Ba 2 O 4δ charge reservoir layer and CuO 2 plane [11,12]. The charge reservoir layer, inter-grain boundaries, and micro-cracks act as dielectric media, which can be polarized by the displacement of charge carriers with the assistance of an external electric field from their equilibrium position. The material may undergo four primary mechanisms of polarization [13][14][15][16] each of which involves a short-range motion of charges and subsidizes to the total polarization of the material: · Electronic polarization ( e  ). It arises when shifting of electronic charge clouds of atoms and ions takes place. This is observed at very high frequencies such as 10 16 Hz, i.e., in ultra violet optical region. · Lattice polarization ( a  ). The origin of this polarization is the combined displacement of ion cores and their electronic charge distribution. This is observed at frequencies ranging from 10 10 to 10 13 Hz, i.e., in infrared optical region. · Dipolar polarization ( 0  ). It originates from the permanent dipoles or from the presence of charge carriers, which is active at lower frequencies from 10 3 to 10 6 Hz, i.e., in the sub-infrared optical region due to their longer relaxation time. · Interfacial polarization ( i  ). This polarization is sensitive at low frequency range of 10 3 Hz and may extend to a few kHz [6,13,17]. Dielectric properties of Cu 0.25 Tl 0.75 Ba 2 Ca 3 Cu 4 O 12δ superconductor with addition of MgO nanoparticles were investigated in frequency range from 100 Hz to 4 MHz [7]. Volume fraction and connectivity between grains were found to be increased by the addition of these nanoparticles by healing micro-cracks. Increase in r   and decrease in ac  were observed up to certain optimum level of the nanoparticle content. Dielectric constants ( r   , r   ) and dielectric loss ( tan ) of Tl-based high temperature superconductors (HTSCs) were found to depend strongly on operating temperature and frequency of external applied ac-field [6]. Negative capacitance (NC) phenomenon was observed in Cu 0.5 Tl 0.5 Ba 2 Ca 3 Cu 4y Zn y O 12δ (y = 0, 3) superconductor at different frequencies and temperature [13,18]. Effect of oxygen post-annealing on superconductivity and dielectric properties of Cu 0.5 Tl 0.5 Ba 2 Ca 3 (Cu 4y Cd y )O 12δ was investigated [19]. A strong dielectric dispersion was observed at low frequencies and temperature, while reverse effects were observed at high temperature and frequencies. The dielectric constant determines the nature of the superconducting material, i.e., the binding forces to which the mobile carriers are tied among the conducting CuO 2 planes and Cu 0.5 Tl 0.5 Ba 2 O 4−δ charge reservoir layers. The real part of the dielectric constant (   ) shows energy stored within the material when exposed to electric field. The imaginary part of the dielectric constant (   ) indicates the absorption and the attenuation of energy across the interfaces under an external electric field. Electrical nature of materials can be described by dielectric properties. Materials with high dielectric constant are used in micro-electronic devices. In this article, we reported the frequencydependent dielectric measurements for (Zn) x /CuTl-1223 nanoparticle-superconductor composites. Different parameters related to dielectric measurements like dielectric constant (both real and imaginary parts), tangent loss, and ac-conductivity have been calculated in the frequency range of 10 1 to 10 7 Hz at room temperature, i.e., 293 K.

Experimental details
nanoparticle-superconducting composites were synthesized by using solid-state reaction method. Initially Cu(CN), Ba(NO 3 ) 2 , and Ca(NO 3 ) 2 compounds were mixed in appropriate ratios to prepare bulk Cu 0.5 Ba 2 Ca 2 Cu 3 O 10δ precursor material. The mixed material was ground in agate mortar and pestle for 2 h. After grinding, the mixed material was loaded in quartz boat and fired at 860 ℃ for 24 h in pre-heated chamber furnace followed by furnace cooling to room temperature. The firing step was repeated after 2 h grinding under the same conditions. The calculated amounts of Tl 2 O 3 and Zn nanoparticles were mixed in Cu 0.5 Ba 2 Ca 2 Cu 3 O 10δ precursor material. The mixed material obtained was pelletized under 3.8 tons/cm 2 pressure by using hydraulic press [20,21]. The pellets were wrapped in gold capsules (to avoid Tl leakage) and sintered for 10 min at 860 ℃ in pre-heated chamber furnace followed by quenching to room temperature in order to obtain the final product (Zn) x /CuTl-1223 (x = 0-4 wt%) nanoparticlesuperconductor composites.
These composites were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), temperature-dependent resistance measurements, and dielectric properties. The structural phases of nanoparticles and composites were determined by XRD. The average size of nanoparticles was calculated by using Debye-Scherrer's formula. The cell parameters were determined by using Check Cell computer software. The surface morphology and chemical composition were examined by SEM and energy dispersive X-ray (EDX) analysis, respectively. Conventional four-probe method was used to measure temperature-dependent resistance of these samples. The frequency-dependent dielectric measurements were carried out by using an LCR meter at frequencies from 10 1 to 10 7 Hz. Typical two-probe technique was used for frequency-dependent dielectric measurements. Silver paint was applied to both the surfaces and was dried at room temperature. By measuring the conductance (G) and capacitance (C), the dielectric constant ( r  ), dielectric loss ( tan ), and ac-conductivity ( ac  ) of the samples were determined by using following equations [13,20]: where d is the thickness of pellets, A is the area of electrode, G is the conductance, 2πf   is the angular frequency, f is the frequency of applied ac-field, m  is the permittivity of material, 0  is the permittivity of free space, and r  is the relative permittivity.

Results and discussion
XRD spectrum exhibits prominent sharp diffraction peaks indexed with hexagonal structure of Zn nanoparticles as shown in Fig. 1. XRD analysis shows the distinct diffraction peaks at 2θ = 36.34°, 39.06°, 43.28°, 54.36°, which are indexed to (002), (010), (011), and (012) planes, respectively. The hexagonal structure of Zn nanoparticles matches well with the database of JCPDS, indicating that Zn nanoparticles have crystalline structure. The average size of Zn nanoparticles calculated by Debye-Scherrer's formula is 50 nm. No prominent peak of impurity is found in XRD spectrum of Zn nanoparticles. The XRD spectra of (Zn) x /CuTl-1223 nanoparticle-superconducting composites with different weight percentage of Zn nanoparticles (i.e., x = 0-4 wt%) are shown in Fig. 2.
Most of the diffraction peaks are well indexed in accordance to CuTl-1223 tetragonal structure, following P4/mmm space group. These peaks correspond to CuTl-1223 phase with lattice parameters a = 4.01 Å,  48 Å for x = 4 wt%. A few un-indexed peaks of low intensity also appear, which are possibly due to presence of impurities or some other superconducting phases. A slight shift of the diffraction peaks to lower angles is observed, which may be due to strains produced in the material after the addition of Zn nanoparticles. Figure 3 shows SEM images of (Zn) x / CuTl-1223 nanoparticle-superconductor composites with x = 0, 2 wt%. High porosity, weak inter-grain connectivity, and disorientation of grains in pure CuTl-1223 superconducting phase can be visualized in Fig. 3(a). Inter-grain connectivity and improved grain size after addition of Zn nanoparticles in CuTl-1223 superconducting matrix can be seen in Fig. 3(b). The improvement in inter-grain connections and grain size may be due to healing up of inter-grain voids after inclusion of metallic Zn nanoparticles. EDX spectra of (Zn) x /CuTl-1223 nanoparticlesuperconductor composites (x = 2, 4 wt%) are shown in Fig. 4, which show the presence of different elements in the composites. XRD, SEM, and EDX show that Zn nanoparticles occupy the interstitial spaces between the grains and do not affect the crystal structure of host CuTl-1223 phase. The temperature-dependent resistance measurements of (Zn) x /CuTl-1223 nanoparticlesuperconductor composites (x = 0, 1, 3 wt%) are shown in Fig. 5. The metallic variation in resistance from room temperature down to onset of superconductivity with critical temperature c (0) T around 92, 101, and 100 K for x = 0, 1, 3 wt% has been observed, respectively.
These measurements indicate the increase in critical temperature c (0) T from 92 to 101 K after the addition of 1 wt% of Zn nanoparticles. The increase in c (0) T is due to the facilitation of mobile free carriers and improvement in the inter-grain connectivity after addition of Zn nanoparticles in CuTl-1223 phase. The initial rise in   c 0 T is due to increase in superconducting volume fraction and improved weak-links after the addition of Zn nanoparticles at the grain boundaries of CuTl-1223 matrix.
where U is the activation energy; B k is the Boltzmann constant; and 0  is the normal state resistivity. The plot of 0 ln( / ) showing the activated behavior is given in the inset of Fig. 5. To calculate the activation energy, the region close to superconducting transition is chosen and it is observed that the activation energy is increased after the addition of Zn nanoparticles in CuTl-1223 matrix. The maximum value of activation energy is found in the sample with x = 1 wt%. The increase of activation energy may be due to interaction of carriers with the metallic Zn nanoparticles at grain boundaries.
Dielectric properties of (Zn) x /CuTl-1223 nanoparticle-superconductor composites with x = 0-4 wt% have also been examined. The variation in frequency-dependent dielectric constant ( r  ) of the samples at room temperature is shown in Fig. 6. The dielectric constant is decreased with increase of frequency. The carriers can not follow the frequency of external applied electric ac-field at high frequencies and dielectric response becomes ineffective. The maximum values of r  at frequency 10 1 Hz are found around 8.96×10 12 , 1.53×10 13 , 3.74×10 12 , 1.181×10 12 , and 1.22×10 13 for x = 0, 1, 2, 3, 4 wt%, respectively. The variation of r  is non-monotonic, which can be due to heterogeneous mixing of Zn nanoparticles in CuTl-1223 matrix, but the overall suppression of dielectric properties may be due to reduction of defects after the addition of metallic Zn nanoparticles. The variation of maximum values of r  with Zn nanoparticle content in (Zn) x /CuTl-1223 nanoparticlesuperconductor composites is given in the inset of Fig. 6. The increase of maximum values of r  may be due to agglomeration and segregation of Zn nanoparticles in the bulk CuTl-1223 phase at higher concentration of Zn nanoparticles.
The variation in frequency-dependent real part of dielectric constant (   ) of these samples at room temperature is shown in Fig. 7. At lower frequency, dipolar polarization is dominant but when the frequency increases, the oscillation of the applied field increases and the dipolar polarization characteristic time becomes longer than the time constant of applied field. That is why decrease in   is observed. The maximum values of   at frequency 10 1 Hz are found around 1.   according to which a dielectric medium is assumed to be made of well conducting grains separated by grain boundaries. At lower frequencies, the grain boundaries are more effective, due to which charges hop, resulting in higher dielectric constant. The decrease observed with increasing frequency is due to decrease in polarization as the dipoles do not have the capacity to follow the applied field at high frequencies. The maximum values of   at frequency 10 1 Hz are found around 8.96×10 12 , 1.53×10 13 , 3.64×10 12 , 1.15×10 12 , and 1.23×10 13 for x = 0, 1, 2, 3, 4 wt%, respectively. The variation in frequency-dependent tangent loss ( tan ) of the samples at room temperature is shown in Fig. 9. The peaks appeared correspond to dispersion positions indicating the relaxation process. Maximum dissipation is observed because of relaxation time of electrical dipoles, which is near the applied electric field. The Fig. 9 Variation of dielectric loss factor ( tan ) of (Zn) x /CuTl-1223 nanoparticle-superconductor composites with frequency for x = 0-4 wt%. In the inset, there are shown the variation of maximum tan versus Zn nanoparticle content (i.e., x). maximum values of tan at frequency 10 1 Hz are found around 6.89×10 3 , 7.03×10 3 , 1.73×10 4 , 2.49×10 4 , and 6.92×10 3 for x = 0, 1, 2, 3, 4 wt%, respectively. A decreasing trend in tan is seen at low frequency, which is due to the effective grain boundaries. The peak in tan can be observed at different frequencies with the addition of these Zn nanoparticles, which is 7.8×10 4 at 48.48 Hz, 1.09×10 5 at 24.25 Hz, 2.39×10 5 at 16.50 Hz, 3.18×10 5 at 22.45 Hz, and 9.08×10 4 at 24.25 Hz for the samples with x = 0, 1, 2, 3, 4 wt%, respectively.
At relaxation frequency, the most apparent relaxation time,  , is given by 1   ( 7 ) where  is the angular frequency.
The variation in frequency-dependent acconductivity ( ac  ) of (Zn) x /CuTl-1223 nanoparticlesuperconductor composites at room temperature is shown in Fig. 10. Maximum values of ac  at frequency 10 7 Hz are found to be 0.69, 1.27, 0.21, 0.077, and 0.88 S/cm for x = 0, 1, 2, 3, 4 wt%, respectively. The value of ac  increases as a whole after the addition of Zn nanoparticles in CuTl-1223 superconducting matrix. The possible reason for this increase in ac  is due to healing up of the micro-cracks, which results in the improvement of inter-grain connectivity. The ac-conductivity ( ac  ) of our samples increases at high frequencies, which happens due to bound carriers trapped in the samples. When ac-conductivity ( ac  ) decreases with increasing frequency, it happens due to the free carriers. In the inset, there is shown the variation of maximum value of ac  versus Zn nanoparticle content, showing a random trend in variation, which may be due to inhomogeneous distribution of these nanoparticles in the CuTl-1223 matrix.

Conclusions
(Zn) x /CuTl-1223 nanoparticle-superconductor composites were synthesized successfully by solid-state reaction method and characterized by different experimental techniques. Structural, morphological, compositional, superconducting, and dielectric properties were explored by XRD, SEM, EDX, and dielectric parameters of these composites. Granular structure with improved grain size could be observed by SEM micrographs. Tetragonal crystal structure of CuTl-1223 matrix was not altered after the addition of Zn nanoparticles, which provided evidence about their occupancy at the grain boundaries in the bulk CuTl-1223 material. The value of U was increased after the addition of Zn nanoparticles in CuTl-1223 composites. The improvement of superconducting properties could be accredited to the metallic nature of Zn nanoparticles, which could facilitate the mobility of carriers by improving the weak-links. Dielectric parameters have been decreased with the increase of frequency and became saturated at higher frequencies.
The ac-conductivity ( ac  ) was seen to be increased non-monotonically due to heterogeneous distribution of Zn nanoparticles in CuTl-1223 matrix.