Effect of diffusion-annealing time on magnetoresistivity of Cu-diffused bulk MgB₂ superconductors with experimental and theoretical approaches

This study reports the role of various annealing time such as 0.5, 1, 1.5 and 2 h on the flux pinning mechanism, physical and superconducting properties of Cu-diffused bulk MgB₂ superconductors prepared at 850 °C with the aid of the magnetoresistivity measurements performed in the magnetic filed range from 0 to 7 T. The critical transition (both \( T_{c}^{onset} \) and \( T_{c}^{offset} \)) temperatures, 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 paths (\( \ell \)) of the MgB₂ materials are derived from the magnetoresistivity curves. At the same time, activation energy (U₀) values are determined from thermally activated flux creep model. Furthermore, resistivity criteria of 10 and 90 % normal-state resistivity serve as the important parameters for the description of μ₀H_irr and μ₀H_c2 values, respectively. At absolute zero temperature (T = 0 K), the extrapolation of the μ₀H_irr(T) and μ₀H_c2(T) curves gives the μ₀H_irr(0) and μ₀H_c2(0) values of the samples prepared. Similarly, the ξ values are derived from the μ₀H_c2(0) values when the λ values are deduced from the Ginzburg–Landau parameter (\( \kappa \)). It is noted that the pinning mechanism, physical and superconducting properties of the samples improve with the enhancement of the diffusion-annealing time up to 1 h beyond which these properties start to destroy systematically and in fact reach the local minimum point for the sample annealed at 850 °C for 2 h as a consequence of the degradation of pinning ability, density, crystallinity and connectivity between grains. Additionally, the presence of the magnetic field leads to reduce these properties due to the decrement of the flux pinning in the samples. Namely, the maximum \( T_{c}^{onset} \) and \( T_{c}^{offset} \) values are found to be about 39.3 and 38.3 K for the sample annealed at 850 °C for 1 h. With the increment in the applied magnetic field up to 7 T, these values decrease to 32.0 and 29.2 K, respectively. Likewise, the U₀ value of the sample reduces from 9,162 to 2,968 K with the increase of the applied field. On the other hand, the minimum \( T_{c}^{onset} \) of 30.9 K, \( T_{c}^{offset} \) of 27.4 and U₀ of 898 K at 7 T applied magnetic field are obtained for the sample annealed at 850 °C for 2 h, pointing out that the latter sample obtains much weaker flux pinning, lesser crystallinity and connectivity between grains compared to the other samples. The dissipation mechanism is also discussed from the results of the magnetic field and temperature dependence of the activation (flux pinning) energy.