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.