Excess Conductivity Analysis of Tl1−x Y x Ba2Ca2Cu3O10−δ Superconductors

Excess conductivity analyses of resistivity data of Tl_1?x Y _x Ba₂Ca₂Cu₃O_10?δ (x=0, 0.04, 0.06, 0.08, 0.1) samples have been carried out by following Lawrence & Doniach (LD) and Maki-Thompson (MT) models. In the critical regime important superconductivity parameters have been elucidated by employing Ginzburg-Landau number N _G of Ginzburg Landau theory. Our samples have shown a decrease in the T _c (R=0) and magnitude of diamagnetism with increased Y-doping. The cell parameters and volume of the unit cell increase with doping of Y⁺³ in Tl_1?x Y _x Ba₂Ca₂Cu₃O_10?δ (x=0, 0.04, 0.06, 0.08, 0.1) which shows a decrease in the density of charge carriers in the conducting CuO₂ planes. Since the Fermi vectors of the carriers, K _F=[3π ² N/V]^1/3=[3π ² n]^1/3, their coherence length along the c-axis, ξ _c=?K _F/2mΔ, and the Fermi velocity, V _F=?K _F/m depend on density of mobile charge carriers, the doping of Y⁺³ suppresses it and hence the superconductivity parameters. We have confirmed these conjectures with the excess conductivity analyses (FIC) of our conductivity data. The FIC analysis of conductivity data has shown a decrease in the values of ξ _c, V _F, B _c(0), B _c1(0) and J _c(0) with increase doping of Y (except for the samples with x=0.04). The width of two dimensional conductivity regimes is shrunken with increased Y-doping. From these studies it is concluded that presence of Y⁺³ in the unit cell of TlBa₂Ca₂Cu₃O_10?δ impedes the flow of the mobile charge carriers to the conducting CuO₂ planes which induce suppression in the superconductivity parameters. The studies also stress the vital role of mobile charge carriers in the mechanism of high temperature superconductivity.     

Synthesis and Excess Conductivity Analyses of Ce-Doped Tl1−x Ce x Ba2Ca2Cu3O10−δ Superconductors

The role of mobile carriers density supplied by TlBa ₂ O _4?δ charge reservoir layer is investigated by doping Ce in TlBa ₂Ca ₂Cu ₃ O _10?δ superconductors. The T _c(onset) and T _c(R= 0) versus Ce contents have shown almost a parabolic-shaped phase diagram which is interpreted in terms of hole’s doping. The magnetic measurements showed that magnitude of diamagnetism is gradually suppressed with Ce doping at Tl site. Fourier transform infrared (FTIR) revealed that the phonon modes associated with apical oxygen atoms type Cu(2)–O _A –Tl are softened, whereas the planar oxygen modes are hardened with the doping of Ce the unit cell. In the excess conductivity, analyses of conductivity data of Tl _1?x Ce _x Ba ₂Ca ₂Cu ₃ O _10?δ samples have shown a suppression of T _{c m f} (K) and the width of 2D conductivity regimes, whereas the coherence length along the c-axis ξ _c(0) and the interlayer coupling J are enhanced with the doping of Ce ⁺⁴ in the charge reservoir. The increase in ξ _c(0) is interpreted in the form of homogenization of the carrier’s density of carriers the CuO ₂ planes. The process of homogenization is accomplished with the reduction of density of carriers in the outer CuO ₂ that consequently promotes increase in the phase relaxation time, τ _? , of the carriers, their Fermi velocity, and the energy required to break apart the Cooper pairs.     

Superconductivity and Fluctuation-Induced Conductivity (FIC) Analysis of (Cu0.5Tl0.5?x M x )Ba2Ca2Cu3O10?δ

Superconductivity has been improved by partial substitution of slightly higher electronegative (M=Bi, Hg) elements at Tl sites in (Cu_0.5Tl_0.5?x M _x )Ba₂O_4??? (x=0,0.25) charge reservoir layer of (Cu_0.5Tl_0.5?x M _x )Ba₂Ca₂Cu₃O_10??? superconductor. These samples were characterized by X-ray diffractometry, dc-resistivity, ac-susceptibility, FTIR absorption spectroscopy, and fluctuation-induced conductivity (FIC) analysis. The FIC analysis has been carried out in the light of Aslamasov?CLarkin (AL) theory on the resistivity versus temperature curves of (Cu_0.5Tl_0.5?x M _x )Ba₂Ca₂Cu₃O_10??? superconductor. The microscopic parameters such as cross-over temperature (T _o ), zero-temperature coherence length ?? _c (0), inter-layer coupling (J), and critical exponents (?? _2D and ?? _3D) have been determined from FIC analysis of these samples and tried to correlate them to the superconductivity order parameters. A?direct correlation between the cross-over temperatures (T _o ) and zero resistivity critical temperature {T _c (R=0)} and carrier concentration in these samples has been observed. The improvement in T _c (R=0) and the shift of 3D AL region to higher temperature values with the doping of Bi and Hg have also been observed.     

Magneto-resistance and Excess Conductivity Studies of Tl(Ba2−y Mg y )Ca 2 Cu 3 O 10−δ Samples

The flux pinning characteristics of T l(B a _2?y M g _y )C a ₂ C u ₃ O _10?δ(0.0≤y≤ 1.5) samples have been studied under the influence of various dc magnetic fields in the light of thermally activated flux flow model. It was observed form the magneto resistivity measurements that the activation energy U has been increased in the sample with Mg incorporation of y=0.5, however, it is decreased in the samples with higher Mg doping. This shows that lower Mg doping concentration promotes enhancement, whereas its higher concentration suppresses the flux pinning characteristics of Tl(Ba _2?yMg _y )Ca ₂Cu ₃ O _10?δ (0.0 ≤y≤1.5) samples. The excess conductivity analysis of Tl(Ba _2?yMg _y )Ca ₂Cu ₃ O _10?δ (0.0 ≤ y ≤ 1.5) samples has shown that the coherence length along the c-axis ξ _c(0), the interlayer coupling J, the phase relaxation time of the carriers τ _? , and the Fermi velocity v _F of the carriers are suppressed with Mg doping. However, the values of B _c0(T), B _c1(T), and J _c(0) are enhanced which complement the magnetoresistivity analysis. These results showed that the flux pinning characteristics are enhanced for lower doping concentration of Mg at the charge reservoir layer sites.     

Fluctuation Conductivity of RE1−2x Ca x M x Ba2Cu3O7−δ (RE=Nd,Y and M=Pr,Th) Superconductors

Polycrystalline samples of RE_1?2x Ca _x M _x Ba₂Cu₃O_7?δ with RE=Nd, Y and M=Pr, Th (with 0.0≤x≤0.10), superconductors were prepared by the standard solid-state method. Resistivity was measured as a function of temperature and doping concentration x. Excess conductivity was analyzed using the modified Lawrence-Doniach (LD) expressions. The fluctuation regions, crossover temperatures, coherence lengths, and effective layer thickness were obtained and the values were compared for both samples. For both samples, it was found that with increasing doping, the crossover temperatures were reduced, while the coherence length decreased. The upper critical field and critical current density were increased with increasing doping concentration due to the introduction of disorder and the enhancement of flux pinning by charge neutral doping. Furthermore, the coherence lengths of the Nd-based samples are larger than that for the Y-based samples by a factor 2. It was found that the value of critical current density in Nd(CaPr)-123 is higher than Y(CaTh)-123, from which it is suggested that CaPr doping is more effective than CaTh doping.     

Enhanced Inter-grain Connectivity in Nano-particles Doped (Cu0.5Tl0.5)Ba2Ca2Cu3O10?δ Superconductors

Polycrystalline (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_10??? superconductors show strong composition variations at the termination ends of the crystals which compromise over-all superconducting properties of the final compound. These composition variations are one of the root causes of void formation which produces a poor quality material. The better inter-grain coupling suppresses the Josephson losses required for higher transport critical current density (J _c ). The lower losses across the inter-grain Josephson junctions are essential for wire and microelectronic applications. We have fixed such inadvertent composition variation in (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_10??? superconductors by doping them with nano-particles of CuO, BaO and CaO₂. Nano-particles doped (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_10??? superconductors were synthesized at 860?°C and characterized using X-ray diffraction (XRD), resistivity (??), ac-susceptibility (??), scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR) measurements. The magnitude of superconductivity is significantly enhanced with the doping of nano-particles. The samples with 15?wt.?% addition of CuO nano-particles have even shown textured elongated crystalline with extremely low population of voids.     

Excess Conductivity Analysis and the Critical Region in Be-Doped Cu0.5Tl0.5Ba2Ca1?y Be y Cu0.5Zn1.5O8?δ Superconductors

The excess conductivity analysis of as-prepared and oxygen-annealed Be-doped Cu_0.5Tl_0.5Ba₂Ca_1?y Be _y (Cu_0.5Zn_1.5)O_8??? (y=0, 0.15, 0.3, 0.45) superconducting samples is carried out in the critical regimes and beyond. Various superconducting parameters, like the zero resistance critical temperature T _c , mean field critical temperature $T_{c}^{mf}$ , onset temperature of superconductivity T ^?, the crossover temperature T _G of the critical and 3D fluctuations and dimensionality of fluctuations are determined. From the 3D to 2D crossover, and at the termination of 2D fluctuations, the coherence length ?? _c (0) along the c-axis, the coupling constant?J, the phase relaxation time ?? _?? , the Fermi velocity V _F of the carriers and Fermi energy E _F are calculated. Using the Ginzburg?CLandau (G?CL) equations in the critical regime, the thermodynamic critical magnetic field B _c(0), the lower critical field B _c1(0), the upper critical field B _c2(0) and the critical current density J _c(0) are also calculated from these analyses. Four fluctuation regions above T _c are observed for all of the samples, namely the critical (cr), three-dimensional (3D), two-dimensional (2D) and zero-dimensional (0D) fluctuations regions. It is observed that with the increased Be content at Ca sites, ?? _c (0), V _F and the coupling constant J are increased, which shows that the inter-planar coupling is improved by the incorporation of Be atoms at the Ca sites.     

Fluctuation Induced Conductivity in Hg-Doped (Cu0.5Tl0.5?x Hg x )Ba2Ca3 Cu 4O12?δ Superconductor

The fluctuation induced conductivity (FIC) analysis on resistivity data of the Hg-doped (Cu_0.5Tl_0.5−x Hg _x )Ba₂Ca₃Cu₄O_12−δ (x=0, 0.15, 0.25, 0.35) superconductor has been carried out in the light of the Aslamazov–Larken (AL) theory. The superconducting properties have been improved with Hg-doping (up to x=0.25) at Tl sites in the Cu_0.5Tl_0.5Ba₂O_4−y charge reservoir layer. These samples are also post-annealed in oxygen to improve intergrain connectivity and to optimize the carriers’ density in CuO₂ planes. The results of FIC analysis have shown three-dimensional (3D) and two-dimensional (2D) fluctuations in the order parameters. It has been observed that there is an increase in the cross-over temperature (T _o) as well as in zero resistivity critical temperature {T _c(0)} with Hg-doping. These properties have been further improved after post-annealing in oxygen, which may be due to improved inter-grain coupling and optimization of mobile carriers in CuO₂ planes. A direct correlation between T _o, T _c(0) as well as zero temperature coherence length ξ _c(0) has been observed.     

Temperature and Frequency Dependent Dielectric Properties of Cu0.5Tl0.5Ba2Ca3(Cu4−y Cd y )O12−δ Bulk Superconductor

The temperature and frequency dependent dielectric properties of polycrystalline Cd-doped Cu_0.5Tl_0.5Ba₂Ca₃(Cu_4?y Cd _y )O_12?δ (y=0,0.25,0.5,0.75) bulk superconductor samples are investigated. The zero resistivity critical temperature {T _c(R=0)} has decreased and normal state resistivity has increased with the increase of Cd-doping in Cu_0.5Tl_0.5Ba₂Ca₃(Cu_4?y Cd _y )O_12?δ samples. The dielectric properties such as dielectric constants (ε′,ε″), dielectric loss tangent (tanδ) and ac-conductivity (σ _ac ) are investigated by measuring the capacitance (C) and conductance (G) in the frequency range of 10 KHz to 10 MHz at different temperature from 80 K to 300 K. The negative capacitance (NC) is observed in all Cu_0.5Tl_0.5Ba₂Ca₃(Cu_4?y Cd _y )O_12?δ samples. The large values of NC observed at lower frequencies and temperatures may be due to reduced thermal vibrations and enhanced polarizability of the material. The effect of Cd-doping on bulk properties, dc-resistivity (ρ) and ac-electrical conductivity (σ _ac ) of these superconductor samples are investigated. The polarization in Cu_0.5Tl_0.5Ba₂Ca₃(Cu_4?y Cd _y )O_12?δ samples is most likely arising from the displacement of charges in CuO₂/CdO₂ planes relative to the static charges at Ba²⁺, Tl³⁺, and Cu²⁺ sites in Cu_0.5Tl_0.5Ba₂O_4?δ charge reservoir layers by external applied field.     

Fluctuation Induced Conductivity in (Cu0.5Tl0.5)Ba2Ca2Cu3O10?δ Superconductor Synthesized at Different Temperatures

The fluctuation induced conductivity (FIC) analysis of (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_10?δ superconductor synthesized at different temperatures has been carried out in the frame work of Aslamazov-Larkin (AL) theory. Almost all the superconducting parameters studied in this research work have been improved with the increase of synthesis temperature up to 850°C, which is most likely due to (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_10?δ superconducting phase stability at this synthesis temperature. The parameters calculated from FIC analysis are cross-over temperature (T ₀), zero temperature c-axis coherence lengths ξ _c (0), interlayer coupling strength (J) and the exponents (λ _3D and λ _2D). The FIC analysis has shown an increase in T ₀ and the shift of three dimensional (3D) Aslamazov-Larkin (AL) regions to the higher temperature with the increase in synthesis temperature up to 850°C.     

Self-doping Effects on the Superconducting Properties of Cu0.5Tl0.25M0.25Ba2Ca2Cu3O10−δ (M = Bi, Hg, Nb, Pd, Li, Na, K)

The effect of self-doping and substitution of elements of higher and lower electronegativity, such as Bi, Hg, Nb, Pd, Li, Na, K, on the superconducting properties of Cu_0.5Tl_0.5−x M _x Ba₂Ca₂Cu₃O_10−δ with x=0.25 is investigated. These experiments demonstrated that the elements of lower electronegativity such as Li, Na, and K can easily liberate their outer most s-electron that could be supplied to the conducting CuO₂ planes of Cu_0.5Tl_0.5−x M _x Ba₂Ca₂Cu₃O_10−δ superconductor, and as a result, we get enhanced superconducting properties. However, highly electro-negative elements hinder the transfer of carriers from charge reservoir layer to the conducting CuO₂ planes and promote inferior superconducting properties. In the present studies, we have investigated the effect of post-annealing in nitrogen and oxygen atmospheres for optimizing the carriers in conducting CuO₂ planes of Cu_0.5Tl_0.5−x M _x Ba₂Ca₂Cu₃O_10−δ (M=Bi,Hg,Nb,Pd,Li,Na,K) superconductor. These studies are important since the density of carriers in the conducting CuO₂ planes determines the Fermi-vector k _F and Fermi velocity v _F of the carriers, which ultimately brings about the final superconducting state of the system.      

The Effect of Simultaneous Substitution of Strontium at the Barium site of Tl0.6Pb0.4Ba2−x Sr x Ca2Cu3O9−δ Superconductors

High temperature superconductors, namely Tl_0.6⋅ Pb_0.4Ba_2−x Sr _x Ca₂Cu₃O_9−δ , have successfully been prepared by the solid state reaction method. The substitutions for this compound were taken as x=0.0, 0.10, 0.20, 0.30, 0.40 and 0.50. The optimum calcination was at 1073 K and for sintering was within 1128–1133 K. Electrical resistivity, using the four-probe technique, was used to find the transition temperature T _c. The highest T _c(offset) was 113 K for Tl_0.6Pb_0.4Ba_1.5Sr_0.5Ca₂Cu₃O_8.76. All samples were prepared by using O₂ flow. X-ray diffraction (XRD) analysis have shown a pseudotetragonal structure with an increase of the c-axis lattice constant for the samples which were doped with Sr as compared to those which have no Sr content.     

Growth of (Cu0.5Tl0.5?x Hg x )Ba2Ca3Cu4O12?δ Superconductor with Optimal Carrier Density in CuO2 Planes and Fluctuation-Induced Conductivity

The growth of (Cu_0.5Tl_0.5?x Hg _x )Ba₂Ca₃Cu₄O_12??? (x=0, 0.25) superconductor with optimal carrier density in CuO₂ planes has been made possible by partial substitution of Hg at Tl sites in (Cu_0.5Tl_0.5)Ba₂O_4??? charge reservoir layer of (Cu_0.5Tl_0.5)Ba₂Ca₃Cu₄O_12??? superconductor. The fluctuation-induced conductivity (FIC) analysis has been carried out on resistivity vs. temperature curves by using Aslamazov?CLarkin (AL) theory and the results have shown three-dimensional (3D) and two-dimensional (2D) fluctuations in order parameters. The microscopic parameters deduced from FIC analysis such as crossover temperature (T _o ), zero temperature c-axis coherence {?? _c (0)} and the interlayer coupling strength?(J) have been improved with Hg substitution. Also, 3D region has been shifted to higher temperature with Hg substitution. In order to verify the optimal carrier density in CuO₂ planes with Hg substitution, the post-annealing experiments have been carried out on these samples in nitrogen and air. These post-annealing experiments have caused under-doping of carriers from the optimal level resulting into a decrease in T _c (R=0) as well as the magnitude of diamagnetism.     

Enhanced Magnetic Properties in Cu0.5Tl0.5Ba2Ca2Cu3O10−δ Superconductor Doped with Carbon Nanotubes

Fluctuation-induced conductivity (FIC) analysis in the critical fluctuation region (cr), three-dimensional (3D), two-dimensional (2D), and zero-dimensional (0D) regions is reported for undoped and carbon nanotubes (CNT)-doped Cu_0.5Tl_0.5Ba₂Ca₂Cu₃O_10?δ (CuTl-1223) superconductors. Samples were synthesized by well-known solid-state reaction method by adding CNT up to 7 wt %. The X-ray diffraction data confirms the single-phase orthorhombic structures following PMMM space group for all the samples. The scanning electron microscope (SEM) images reveal that the carbon nanotubes are present in the spaces between the grains and connect the grains electrically to help the intergranular current flow. From FIC analysis, it was found that the width of critical and 3D regimes are shrunken with the increased CNT doping in the final compound. Also, the coherence length (ξ_c(0)), the Fermi velocity (V _F), and the coupling constant (J) are suppressed with increased CNT doping except for the 0.25 wt % doped sample. The decrease in important superconductivity parameters most likely arises due to low CNT doping which indeed functions as columnar defects that are produced by heavy ion irradiation. In this analysis, we also found that the critical magnetic fields (B _c(0), B _c1(0)) and critical current density (J _c(0)) were found to increase with increased CNT concentration. These observations suggest that addition of CNT (efficient pinning centers) to CuTl-1223 compounds improve the electrical connection between the superconducting grains to result in the improvement of magnetic properties of the final compound.     

The Effect of Cadmium Substitution on the Superconducting Properties of Tl1−x Cd x Ba2Ca2Cu3O9−δ Compound

In order to study how Cd substitution for Tl changes, the superconducting properties of Tl_1?x Cd _x Ba₂Ca₂Cu₃O_9?δ compound with x=0, 0.1, 0.2 and 0.3. We have prepared samples with Cd in place of Tl by the solid state reaction method. It has been found that the increase of the Cd concentrations of all samples produced increases the transition temperature from 113 to 123 K and changes the mass density ρ _m, C/a and volume fraction V _Ph(1223).. XRD shows that the partial substitution of Tl with Cd is helpful to form the superconducting 1223 phase (TlBa₂Ca₂Cu₃O_9?δ ). It has been shown that samples mainly contain tetragonal phase 1223 with a few additional mixed 1212 and 1201 phases.     

Decoupling of CuO2 Planes and Superconductivity in (Cu0.5Tl0.5)Ba2Ca3Cu4O12-δ

Journal of Superconductivity and Novel Magnetism - (Cu0.5Tl0.5)Ba2(Ca3-xMgx)(Cu4-yZny)O12-δ (x?=?0, 2; y?=?0, 3) and (Cu0.5Tl0.5)Ba2(Ca3-xSrx)Cu4O12-δ...