Investigation of microstructural, Vickers microhardness and superconducting properties of YBa2Cu3−xGdxO7−δ (0 ≤ x ≤ 0.150) superconducting ceramics via experimental and theoretical approaches

This study manifests the change of pinning mechanism, electrical, structural, physical, mechanical and superconducting properties of YBa₂Cu_3?xGd_xO_7?δ superconductors samples prepared by the conventional solid-state reaction method (x = 0, 0.025, 0.050, 0.100 and 0.150) by use of dc resistivity, X-ray analysis (XRD), scanning electron microscopy (SEM) and Vickers microhardness measurements. Zero resistivity transition temperatures (T _c ^offset ) of the samples are deduced from the dc resistivity measurements. Additionally, the lattice parameters are determined from XRD measurements when the microstructure, surface morphology and microhardness of the samples studied are examined by SEM and mechanical measurements, respectively. The results obtained demonstrate that T _c ^offset values of the samples decrease slowly with the increase in the Gd content. The maximum T _c ^offset (92.0 K) is obtained for the pure sample prepared at 940 °C for 20 h in air atmosphere while the minimum value of 83.3 K is found for the sample doped with 0.150 Gd content. Moreover, it is obtained that J _c values reduce from 132 to 34 A/cm² with the enhancement of the Gd level in the crystalline structure. Further, the peak intensities belonging to Y123 (major) phase are obtained to decrease whereas the peak intensities of the minor phases such as BaCuO₂ and Y211 are found to enhance systematically with the increment in the Gd content in the system, illustrating that partial substitution of Cu²⁺ ions by Gd³⁺ ions are carried out successfully. Moreover, SEM images display that the undoped sample obtains the best crystallinity and connectivity between superconducting grains and largest grain size whereas the worst surface morphology is observed for the maximum doped sample (x = 0.150). At the same time, Vickers microhardness, elastic modulus, load independent hardness, yield strength, fracture toughness and brittleness index values, playing important roles on the mechanical properties, are computed for all the samples. The experimental results of the microhardness measurements are examined using the Meyer’s law, PSR (proportional specimen resistance), modified PRS, Elastic–Plastic deformation model (EPD) and Hays–Kendall (HK) approach. The microhardness values obtained increase with the enhancement of the Gd content in the samples. Besides, it is noted that the Hays–Kendall approach is the most successful model explaining the mechanical properties of the samples studied in this work.     

Effect of annealing temperature on magnetoresistivity, activation energy, irreversibility and upper critical field of the Cu-diffused MgB2 bulk superconductors

This study manifests the change of the pinning mechanism, superconducting and physical properties of Cu-diffused MgB₂ superconductors prepared at different annealing temperature from 650 to 850 °C by means of the magnetoresistivity measurements conducted at several applied magnetic fields in a range of 0–7 T as a function of temperature from 15 to 50 K. The onset (T _c ^onset ) and offset (T _c ^offset ) critical temperatures, activation energies (U₀), irreversibility fields (μ₀H_irr), upper critical fields (μ₀H_c2), residual resistivity ratios (R_R), cross-sectional area fractions (A_F), penetration depths (λ), coherence lengths (ξ) and electronic mean free path ( $ \ell $ ) of the samples are evaluated from the magnetoresistivity curves. Thermally activated flux creep (TAFC) model is used for the determination of the U₀ values; likewise, the μ₀H_irr and μ₀H_c2 values are obtained by resistivity criteria of 10 and 90 % normal-state resistivity, respectively. At absolute zero temperature (T = 0 K), the extrapolation of the μ₀H_irr(T) and μ₀H_c2(T) curves is used to find the μ₀H_irr(0) and μ₀H_c2(0) values of the samples. Moreover, the ξ values are deduced from the μ₀H_c2(0) values when the λ values are calculated from the Ginzburg–Landau parameter ( $ \kappa $ ). It is found that the superconducting and physical properties of the samples improve with the increment of the diffusion-annealing temperature; however, the presence of the magnetic field leading to the decrease of the flux pinning in the samples causes the reduction of these properties. Namely, the T _c ^onset and T _c ^offset values are found to increase from 38.4 to 39.3 K and 36.9 and 38.3 K with the enhancement in the diffusion-annealing temperature at zero filed. Similarly, the U₀ values increase significantly with the increase of the annealing temperature. In fact, the U₀ of 9,162 K belonging to the sample annealed at 850 °C is determined to be the maximum activation energy value. On the other hand, the minimum T _c ^onset of 30.9 K, T _c ^offset of 27.6 K and U₀ of 1,365 K at 7 T applied magnetic field are obtained for the pure sample, indicating that the sample annealed at 850 °C obtains much stronger flux pinning, better crystallinity and connectivity between grains compared to the other samples prepared. Based on these results, the superconducting and physical properties of the MgB₂ superconductors produced in this work are observed to enhance with the increase of the diffusion-annealing temperature as a result of the improvement of pinning abilities, crystallinity and connectivity between grains. The magnetic field and temperature dependence of the activation energy are also discussed.     

The role of Lu doping on microstructural and superconducting properties of Bi2Sr2CaLuxCu2Oy superconducting system

Lutetium (Lu) added Bi₂Sr₂CaLu_xCu₂O_y superconducting samples with x = 0, 0.1, 0.3, 0.5, 0.7 and 1.0 are prepared by solid-state reaction method and annealed at 840 °C for 50 h. The heating and cooling rates of the furnace are adjusted to be 10 and 3 °C/min, respectively. For the comparison, undoped sample is subjected to the same annealing conditions. The prepared samples are characterized using X-ray powder diffraction (XRD), scanning electron microscope (SEM), energy dispersive spectroscopy (EDS), and dc resistivity (ρ?T) measurements. The volume fraction, grain size, texturing and lattice parameters are determined from the XRD measurements. The microstructure, surface morphology and element composition analysis of the samples produced are investigated by SEM and EDS measurements, respectively. Moreover, the resistivity (at room temperature), critical transition (onset and offset) temperature, variation of transition temperature and hole carrier concentration values of the samples studied are estimated from the dc resistivity measurements. According to the results obtained, the samples prepared exhibit the polycrystalline superconducting phase with less intensity of diffraction lines with the enhancement in the Lu addition due to the effect of the minor phase (Bi-2201). The lattice parameter c and volume fraction of Bi-2212 phase reduce systematically whereas the cell parameter a and minor phase fraction enhance with ascending the Lu content in the system, leading to the decrement in the superconducting properties. Scanning electron microscope measurements show that not only do the surface morphology and grain connectivity degrade but the grain sizes of the samples decrease with the increase of the Lu addition, as well. Energy dispersive spectroscopy results reveal that the Lu³⁺ ions might enter into the crystal structure by replacing Sr²⁺ ions, confirming why the superconducting properties of the pure sample are more superior to the samples doped. At the same time, dc resistivity results obtained show that the room temperature resistivity systematically increases with the enhancement of the Lu content as a result of the hole filling when the onset (T _c ^onset ) and offset (T _c ^offset ) temperatures determined from the resistivity curves decrease from 99.5 to 93.0 K and 85.0 to 60.0 K, respectively, illustrating not only the increment in the relative percentage of Bi-2201 phase formation and the reduction of the mobile carrier concentration but also the presence of impurities and weak links between the superconducting grains.     

Effect of diffusion-annealing time (0.5 h ≤ t ≤ 2 h) on the mechanical and superconducting properties of Cu-diffused bulk MgB2 superconductors by use of experimental and different theoretical models

This study reports the effect of different annealing time (0.5 h ≤ t ≤ 2 h) on the electrical, physical, microstructural, mechanical and superconducting properties of Cu-diffused bulk magnesium diboride (MgB₂) system by means of dc resistivity, X-ray diffraction analysis (XRD), scanning electron microscopy (SEM) and microhardness measurements (H _v ). The room temperature resistivity (at 300 K), critical transition (T _c ^offset and T _c ^onset ) temperature, variation of transition temperature, grain size, phase purity, lattice parameter, texturing, surface morphology, crystallinity and Vickers microhardness values of the samples are evaluated and compared with each other. The resistivity results obtained reveal that the (T _c ^offset and T _c ^onset ) values of the samples produced ascend with the enhancement in the annealing time up to 1 h beyond which these values start to reduce systematically and in fact the smallest T _c ^onset of 38.1 K and T _c ^offset of 36.2 K are observed for the sample annealed for 2 h. Similarly, the SEM micrographs display that the surface morphology, crystallinity and grain connectivity improve until a certain diffusion-annealing time (1 h), and after this point, all the properties obtained start to degrade with the increase of the annealing time. Furthermore, the peak intensities, grain sizes and lattice parameters deduced from the XRD measurements illustrate that a systematic elongation in the a and c axis lengths is detected with the annealing time until 1 h beyond which a regular contraction in the lattice parameters is observed for the samples. Likewise, the peak intensities belonging to MgB₂ phase enhance with the increment of the annealing time up to 1 h after which they reduce slowly; however, a new peak belonging to Mg₂Cu phase appears in the sample annealed for the duration of 2 h, confirming both the reduction of the grain size and degradation of the critical temperature. Additionally, we have focused on the microhardness measurements for the examination of the mechanical properties of the samples studied. Experimental results of microhardness measurements are estimated using the various models such as Meyer’s law, proportional sample resistance model, modified proportional sample resistance model and Hays-Kendall (HK) approach. Based on the simulation results obtained, the Hays-Kendall (HK) approach is determined as the most suitable model describing the mechanical properties of samples prepared.     

Role of Gd content in Cu(1) and Cu(2) sites on electrical, microstructural, physical, mechanical and superconducting properties of YBa2Cu3−xGdxO7−δ ceramics

This study deals with the effects of partial Gd³⁺ substitution for the Cu sites on the electrical, microstructural, physical, mechanical and superconducting properties of YBa₂Cu_3?xGd_xO_7?δ ceramic superconductors with x = 0, 0.025, 0.050, 0.100 and 0.150 with the aid of dc resistivity, transport critical current density (J _c ), X-Ray analysis (XRD), scanning electron microscopy (SEM), electron dispersive X-Ray (EDX), Vickers microhardness (H _v ) and density measurements. The samples studied in this work are prepared by the standard solid-state reaction method. The resistivity (at room temperature), critical (onset and offset) temperature, variation of transition temperature, critical current density, hole-carrier concentration, grain size, phase purity, lattice parameter, texturing, surface morphology, element distribution, density, porosity, crystallinity, Vickers microhardness and elastic modulus (E) values of the samples are obtained and compared with each other. The obtained results show that the room temperature resistivity systematically increases with the increment of the Gd content as a result of the hole filling when the onset (T _c ^onset ) and offset (T _c ^offset ) critical temperatures determined from the resistivity curves are found to decrease from 95.2 to 93.6 K and 92.0 to 83.3 K, respectively, showing the presence of impurities and weak links between the superconducting grains. As for the critical current density measurements, the J _c values decrease from 132 to 34 A/cm² as the Gd doping increases. The XRD results give that although the Gd³⁺ ions substituted tend to occupy both the Cu(1) and Cu(2) sites, the ions are more favorable for the Cu(2) site as a consequence no change of the crystal structure. Besides, the peak intensities belonging to major phase (Y123) decrease monotonously with the increment of the Gd content in the system; however, new peaks belonging to the minor phases start to appear after the doping level of x = 0.0250 beyond which these peaks enhance monotonously, resulting in the decrement of the grain size. Further, the Lotgering indices calculated from the XRD patterns indicate that the texturing of the Y123 grains reduces systematically with the Gd content. According to the SEM investigations, the microstructures of the samples prepared degrade slightly with the content up to the doping level of x = 0.025 after which the morphology suddenly deteriorates due to the appearance of the different phases in the system. EDX measurements show that not only do the elements used for the preparation of the Y123 superconductors with and without Gd content distribute homogeneously but also the level of Cu element rapidly decreases with the increment of the Gd content compared to the other elements, illustrating that the Cu²⁺ ions may partly be substituted by Gd³⁺ ions. Moreover, the porosity analyses for the samples depict that the porosity increases with the Gd content, leading to the degradation of the grain connectivity. We also discuss on the mechanical properties of the samples to examine both the elastic modulus and the strength of connection between superconducting grains.     

Effect of Nb addition on magnetic,structural and superconducting properties of (Bi,Pb)-2223 superconductors

In this work, the effects of Nb₂O₅ addition with different ratios on the structural and magnetic properties of Bi_1.7?xPb_0.3Nb_xSr₂Ca₂Cu₃O_y (x = 0.00–0.20) superconducting samples were investigated. (Bi, Pb)-2223 superconducting samples were prepared by conventional solid-state reaction method. The phase formation, phase fraction and lattice parameters were determined from X-ray powder diffraction (XRD) measurements, the microstructure, surface morphology analyses of the samples were carried out using scanning electron microscope (SEM). Additionally, ac susceptibility measurements were done in order to determine the critical current density (J_c) and hole concentration (p) of the samples. AC susceptibility measurements were done at various ac fields (ranging from 20 to 160 A/m) to understand the effect of Nb addition on magnetic properties of Bi_1.7?xPb_0.3Nb_xSr₂Ca₂Cu₃O_y superconductor. Critical onset (T _c ^on ) and loss peak temperatures (T_p) were estimated from the ac susceptibility curves. It was observed from ac susceptibility measurements that the critical onset temperatures decreased from about 108–98 K with increasing Nb addition (x = 0.00–0.20). The imaginary part of susceptibility was used to calculate the intergranular critical current density (J_c) by means of the Bean’s model. X-ray diffraction analysis revealed that the samples consisted of a mixture of Bi-2223 and Bi-2212 phases as the major constituents and non-superconducting phase Ca₂PbO₄ as the minor. It was also shown from XRD measurements that volume fraction of high-T_c phase decreases with increasing Nb addition up to x = 0.20. The sample with Nb addition of x = 0.20 showed the highest volume fraction of Bi-2223 phase (86 %). When Nb addition was increased, the surface morphology and grain connectivity are found to degrade, the grain sizes decrease and porosity of the samples were observed to increase from SEM images except the sample with x = 0.20 Nb addition.     

Superconducting transition temperature of aluminum,indium, and lead fine particles

Aluminum, indium, and lead fine particles with free surfaces were made by evaporation in helium gas to study the size dependence of the superconducting transition temperatureT _c in very small particles. The transition temperature was determined from the change of diamagnetic susceptibility with temperature. The present experiment shows thatT _c rises with decrease of the average diameter \(\bar d\) for aluminum and indium, while it remains nearly constant for lead. The enhancement factorsT _c /T _c ^b (T _c ^b isT _c for the bulk material) in the case of \(\bar d = 100 {\AA}\) are determined as 1.45, 1.15, and 1.0 for aluminum, indium, and lead, respectively. The effect of the soft phonon mode arising from the increasing fraction of surface satisfactorily explains the experiment with respect to both the size dependence and the difference among elements by a rather simple model.     

Electrical and Magnetic Behaviour of PrFeAsO_{\mathbf{0.8}}F_{\mathbf{0.2}} Superconductor

The superconducting and ground state samples of PrFeAsO_0.8F_0.2 and PrFeAsO have been synthesised via the easy and versatile single step solid state reaction route. X-ray and Reitveld refine parameters of the synthesised samples are in good agreement to the earlier reported value of the structure. The ground state of the pristine compound (PrFeAsO) exhibited a metallic-like step in resistivity below 150 K followed by another step at 12 K. The former is associated with the spin density wave (SDW)-like ordering of Fe spins and later to the anomalous magnetic ordering for Pr moments. Both the resistivity anomalies are absent in case of the superconducting PrFeAsO_0.8F_0.2 sample. Detailed high field (up to 12 Tesla) electrical and magnetization measurements are carried out for the superconducting PrFeAsO_0.8F_0.2 sample. The PrFeAsO_0.8F_0.2 exhibited superconducting onset ( $T_{c}^{\mathrm{onset}}$ ) at around 47 K with T _c (ρ=0) at 38 K. Though the $T_{c}^{\mathrm{onset}}$ remains nearly invariant, the T _c (ρ=0) is decreased with applied field, and the same is around 23 K under an applied field of 12 Tesla. The upper critical field (H _c2) is estimated from the Ginzburg–Landau equation (GL) fitting, which is found to be ～182 Tesla. Critical current density (J _c ), being calculated from high field isothermal magnetization (MH) loops with the help of Beans critical state model, is found to be of the order of 10³ A/cm². Summarily, the superconductivity characterization of the single step synthesised PrFeAsO_0.8F_0.2 superconductor is presented.     

Investigation of Lu effect on YBa2Cu3O7−δ superconducting compounds

This study reports the effect of Lu addition on the microstructural and superconducting properties of YBa₂Lu_xCu₃O_7?δ (Y123) superconducting samples with x = 0, 0.1, 0.3, 0.5 and 0.7 by means of X-ray diffraction (XRD) analysis, scanning electron microscopy (SEM), electron dispersive X-ray (EDX), electrical resistivity and transport critical current density (J_c) measurements. The samples prepared by the liquid ammonium nitrate and derivatives are exposed to various annealing time (20, 40 and 60 h) and temperature (950, 960 and 970 °C), and the best ambient for the sample fabrication is determined to be 970 °C for 20 h. Zero resistivity transition temperatures (T_c), critical current densities (J_c), variation of transition temperatures, hole-carrier concentration, grain size, lattice parameter, surface morphology, element distribution, crystallinity and resistivity (at room temperature) values of the bulk superconducting samples prepared at 970 °C for 20 h are compared with each other. T_c and J_c values of the samples are inferred from the dc resistivity and the critical current measurements, respectively. The results show that the T_c value of the pure sample is about 90.6 K while the sample doped with 0.1 wt% Lu has the maximum T_c value (92.5 K). However, beyond x = 0.1, the T_c value is observed to decrease toward to 83.5 K with increment in the Lu addition. Similarly, the J_c values measured are found to reduce from 142 to 76 A/cm² with the addition. Moreover, XRD measurements show that both pure and Lu-doped samples exhibit the polycrystalline superconducting phase with the changing intensity of diffraction lines and contain Y123 and Y211 phase, confirming the incorporation of Lu atoms into the crystalline structure of the samples studied. At the same time, comparing of the XRD patterns of samples, the intensity ratio of the characteristic (110) and (013) peaks on the sample doped with 0.1 wt% Lu is more than that on the other samples prepared. Additionally, SEM images display that the sample doped with 0.1 wt% Lu obtains the best crystallinity, grain connectivity and largest grain size whereas the worst surface morphology is observed for the maximum doped sample (x = 0.7). Further, EDX results demonstrate that the Lu atoms doped are successfully introduced into the microstructure of the Y123 samples studied and the maximum Cu element level is observed for the sample doped with 0.1 wt%, explaining that why this sample obtains the best superconducting properties compared to others. According to all the results obtained, it is concluded that the 0.1 wt% Lu addition into the Y123 system improves the microstructural and superconducting properties of the samples studied.     

Effect of grain size on the electrical and magnetic properties of MgB2 thick films deposited on the Al2O3 single crystal substrates

MgB₂ films having thicknesses of approximately 10 μm have been prepared on the Al₂O₃ single crystal substrates by using ultrasonic spray pyrolysis technique. The films fabricated were then analyzed by means of microstructural, structural, transport and magnetic properties. The influence of grain size, depending on the ex-situ and in situ heating, were investigated. The results obtained showed that the size of MgB₂ grains has an effect on the transport and magnetic properties of the films. Films prepared with in situ heating have small particle size (<50 nm) and were found to be much better properties than the films prepared ex-situ heating, which have larger grains (~1 μm). The best T _c value and critical current density, J _c ^mag , were obtained to be ~36 K and 9.88 × 10⁵ A cm^?2 respectively for the films prepared with small grains. The results were showed that the smaller grain size and in situ heating cycles are essential points for quality thick film MgB₂ fabrication.     

3He Vapor Pressure near Its Critical Point

Between 0.65 K and 3.2 K, the temperature dependence of the vapor pressure P of ³He is defined by the International Temperature Scale of 1990 (ITS-90). However, the ITS-90 vapor pressure equation was not designed to be consistent with the scaling law required for the second temperature derivative of the vapor pressure in the vicinity of the liquid-vapor critical point. In this paper, two scaling-type equations are used to describe the ³He vapor pressure in the region near the critical point. The first scaling equation contains two unknown coefficients which are obtained by taking as reference the temperature $\bar{T}$ at which the product (T _c ?T)P presents a maximum ( $\bar{T}=2.56736$  K). The second scaling equation contains three unknown coefficients which are obtained by using as references $\bar{T}$ and T _up=3.2 K, the upper value of the ITS-90 interval. In both equations we take for the critical temperature and pressure the values T _c =3.31554 K and P _c =114?632.7 Pa. The proposed equations, specially the second one, are satisfactorily compared with experimental data for P and dP/dT within the temperature range (T _c ?T)/T _c ≤0.065 and with semiempirical data for d ² P/dT ² within the temperature range 0.0001≤(T _c ?T)/T _c ≤0.03.     

The effect of Nd 2 O 3 addition on superconducting and structural properties and activation energy calculation of Bi-2212 superconducting system

The effect of Nd ₂ O ₃ addition on the micro-structural and the superconducting properties of Bi-2212 superconductor ceramics, prepared by solid state reaction method, was analyzed by performing X-ray diffraction (XRD), scanning electronic microscope (SEM), energy dispersive spectroscopy (EDS) and dc Resistivity (ρ-T) measurements. The magnetoresistivity of the samples was measured for different values of the applied magnetic field strengths (0–7 T). Also, the activation energies were calculated using the Arrhenius equation. According to these results, the T _c ^offset value of the undoped sample was decreased from 79 to 42 K with the growth of magnetic field. In the same way, the activation energy (U _o ) values were significantly diminished by the increasing of magnetic field. A similar situation was observed in other doped samples. Activation energy for 0.05 % Nd ₂ O ₃ doped sample under 7 T magnetic field was 550 J/mol the least. In addition, lattice parameter c, calculated by analysis of XRD data, was decreased with doping while lattice parameter a was increased. SEM analysis shows that particles were shrinking with the addition. When compared with other elements for EDS analyses, it was analyzed an important decrease in the percentage of Sr with the increasing of Nd contribution.     

On the Presence of 1D-Like Stripes in Superconducting Epitaxial La2 -x Sr x CuO4 thin Films

A large positive magnetoresistance (up to tens of percents) is observed in both underdoped (x?<?0.15) and overdoped superconducting La_{2? x}Sr_xCuO₄ (LSCO) epitaxial thin films, at temperatures far above the superconducting critical temperature T _c . In the underdoped regime, this magnetoresistance cannot be described by the Kohler rule and is due to the influence of superconducting fluctuations. On the other hand, in the overdoped regime, the Kohler rule does not seem to be violated. ?The strong magnetoresistance above T _c can be related to the preformed superconducting pairs existing well above T _c but forming a phase coherent superconducting state below T _c . The observations support the idea of a close relation between the pseudogap and the superconducting gap and provide evidence for the presence of pre-pairs above T _c . Both the observed fluctuations and the observed magnetoresistance are in accordance with the existence of 1D-like stripes. These results are further supported by recent high magnetic field measurements (up to 55 T) of the transverse magnetoconductivity σ _xy, which goes to zero for T→0 K.     

Optical study of charge dynamics along thec-axis in high-T c superconductors

Comparing the optical spectra withE∥c for typical high-T _c superconducting cuprates, we discuss the charge dynamics along thec-axis. The plasma energy or the mass anisotropic factorm _* ^c //m _* ^b is one of the key parameters determining the spectrum forE∥c. In Bi₂Sr₂CaCu₂O₈ and La_2?x Sr _x CuO₄ with a largem _* ^c /m _* ^b , the plasma energy is smaller than the superconducting gap energy, and thus the supercurrent along thec-axis is a kind of Josephson current flowing through insulating layers such as the BiO layers. On the other hand, in YBa₂Cu₃O₇ with a smallm _* ^c /m _* ^a , it seems that the coherent supercurrent flows along thec-axis. Although the spectrum forE∥c strongly depends on samples, presumably due to the difference in the hole concentration, a clear anisotropy between theab- and thec-directions is observed in the characteristics energy scales such as the plasma energy as well as the reflectivity knee energy.     

Properties of MgB2 Thin Films Deposited on Different Substrates Prepared by Ex-Situ Annealing Process

MgB₂ thin films were deposited on MgO (100) substrate and r-plane Al₂O₃ $(1\bar{1}02)$ substrate by ex-situ annealing of boron film in magnesium vapor. The thickness of ex-situ annealed MgB₂ films is approximately 600 nm according to data observation by ellipsometer. The magnetic properties of samples were determined using a vibrating sample magnetometer. The magnetic field dependence of the critical current density J _c was calculated from M–H loops and also the magnetic field dependence of F _p was compared for the different temperature ranges from 5 to 25 K. The critical current density J _c was found to be around 1.0×10⁶ A/cm² and 1.7×10⁶ A/cm² in zero field at 5 K for MgB₂ films deposited on MgO and r-plane Al₂O₃ substrates, respectively. It was found that the critical current density of the film deposited on MgO became stronger than that of r-plane Al₂O₃ in the magnetic field. The superconducting transition temperature was determined by ac susceptibility measurement using physical properties measurement system. ac susceptibility measurements for MgB₂ films deposited on MgO and r-plane Al₂O₃ substrates were performed as a function of temperatures at constant frequency and ac field amplitude in the absence of dc bias field. The critical current densities as a function of temperature were estimated from the ac susceptibility data.     

Thickness Dependence of Critical Current Density in MgB2 Films Prepared by Thermal Evaporation Method

MgB₂ films with the thickness of 350 to 1150 nm have been prepared on the Al₂O₃ (001) single crystal substrates from high purity B and Mg powder by the thermal evaporation method. Films were then heat treated ex-situ under Mg vapor at 950?°C to achieve actual MgB₂ stoichiometry. Thickness of the films, so the deposition time, was varied to investigate its influence on critical current density of the films. The films fabricated were analyzed by means of microstructural, transport, and magnetic properties. The best T _c and T _zero values were obtained to be 39.5 K and 38 K, respectively, and decreased with increasing the thickness. We found that the critical current density of the films prepared is highly thickness dependent. The maximum $J_{c}^{\mathrm{mag}}$ value was calculated to be 3.18×10⁶ A?cm^?2 at 10 K and zero field for 1150 nm thick films but dropped drastically by thickness.     

Artificial Pinning Centers on MgB2 Superconducting Thin Films Coated by FeO Nanoparticles

MgB₂ thin films were fabricated on MgO (100) single crystal substrates. First, deposition of boron was performed by rf magnetron sputtering on MgO substrates and followed by a post deposition annealing at 850?°C in magnesium vapor. In order to investigate the effect of FeO nanoparticles on magnetic properties of MgB₂ thin films, the films were coated with different concentrations of FeO nanoparticles by spin coating process. The magnetic field dependence of the critical current density $J_{\mathrm{c}}$ was calculated from the M?CH loops and also magnetic field dependence of the pinning force density $f_{\mathrm{p}}(b)$ was determined for the films containing different concentrations of FeO nanoparticles. The values of the critical current density $J_{\mathrm{c}}$ in zero field at 5?K was found to be around 1×10⁶?A/cm² for pure MgB₂ film, 1.4×10⁶ for MgB₂ film coated with 25?%, 7.2×10⁵ for MgB₂ film coated with 33?%, 9.1×10⁵ for MgB₂ film coated with 50?% and 1.1×10⁶?A/cm² for MgB₂ film coated with 100?%. It?was?found that the film coated with 25?% FeO nanoparticles has slightly enhanced critical current density and it can be noted that especially the film coated with 25?% FeO became stronger in the magnetic field. The films coated with FeO were successfully produced and they indicated the presence of artificial pinning centers created by FeO nanoparticles. The superconducting transition temperature of the film coated with 25?% FeO nanoparticles was determined by moment?Ctemperature (M?CT) measurement to be 34?K which is 4?K higher than that of the pure film.     

Generalized Multiple Gap Model for the Superconductivity in MgB2

The free energy of the two-band superconductor is obtained taking into account all actual electron–phonon and Coulomb interactions. The temperature dependences of the superconducting gaps, the specific heat with its jump at T = T _c (T _c is the critical temperature) are calculated minimizing the free energy. The theory is applied to the MgB₂ superconductor.     

High Superconducting T c and Suppressed Isotope Effect in the Instantonic Condensate State of the Fermi-System: Analytic Solution

A superconducting pairing instability and isotope effect on the superconducting transition temperature T _c in the electronic system with instantonic condensate are derived analytically using previously proposed theory (Mukhin, J. Supercond. Nov. Magn. 22:75–80, 2009; J. Supercond. Nov. Magn. 24:1165–1171, 2011) of the instantonic nature of the “hidden order” in high-T _c cuprates. The self-organized instantonic condensate breaks Matsubara “time” invariance of the Fermi-system, and occurs due to strongly nonlinear interaction between antiferromagnetic or charge density fluctuations. The Cooper-channel susceptibility (polarization loop) is calculated using a single-particle Green’s function that we have derived recently (Mukhin and Galimzyanov, Physica B 407:1882–1884, 2012) for the Fermi-system with instantonic condensate. We found that superconducting T _c could be strongly enhanced and an isotope effect strongly suppressed in the presence of the instantonic condensate. The usual weak-coupling BCS results are recovered in the limit of vanishing the instantons. Relevance of the theoretical predictions for the high-T _c compounds is discussed.     

The High Pressure Superconductivity of CaLi2 Compound: The Thermodynamic Properties

The thermodynamic properties of the superconducting state in CaLi₂ at 60 GPa have been described in the paper. The numerical analysis has been carried out in the framework of the Eliashberg formalism. It has been shown that: (i) the critical value of the Coulomb pseudopotential is equal to 0.20, which corresponds to the value of 1795 meV for the Coulomb potential; (ii) the critical temperature (T _C ) cannot be correctly calculated by using the Allen-Dynes (AD) formula; (iii) the dimensionless ratios: $T_{C}C^{N} (T_{C} )/H^{2}_{C} (0 )$ , (C ^S (T _C )?C ^N (T _C ))/C ^N (T _C ) and 2Δ(0)/k _B T _C take the non-BCS values: 0.157, 1.78 and 3.85, respectively. The symbol C ^N represents the specific heat in the normal state, C ^S denotes the specific heat in the superconducting state, H _C (0) is the thermodynamic critical field near the temperature of zero Kelvin, and Δ(0) is the order parameter; (iv) the ratio of the electron effective mass ( $m^{\star}_{e}$ ) to the electron band mass (m _e ) assumes a high value, in the whole range of the temperature, where the superconducting state exists. The maximum of $m^{\star}_{e}/m_{e}$ is equal to 2.15 for T=T _C .