Detailed survey on minimum activation energy for penetration of Ni nanoparticles into Bi-2223 crystal structure and temperature-dependent Ni diffusivity

The primary contributions of this study are not only to explore the role of diffusion annealing temperature interval 650 to 850 °C on the formation of effective electron–phonon coupling or cooper-pair probabilities (percentage of clusters in the superconducting path), densities of active and dynamic electronic states at Fermi energy level, stabilization of superconductivity in the homogeneous regions, overlapping of Cu-3d and O-2p wave functions and bond strengths in the crystal matrix of Ni surface-layered Bi-2223 polycrystalline ceramics, but also to determine the temperature-dependent diffusion fast-rate and required minimum activation energy for the diffusion of Ni foreign impurities into the bulk Bi-2223 superconducting crystal structure for the first time. The dc electrical measurement results obtained show that the optimum diffusion annealing temperature is found to be 700 °C for the penetration of optimum Ni concentration into the Bi-2223 crystal lattice so that the ceramic compound exposed to 700 °C annealing temperature exhibits the highest electrical and superconducting properties. In this respect, the material with the minimum electrical resistivity parameters of Δρ, ρ _115K , ρ _res and ρ _norm obtains the maximum superconducting characteristics of \(T_{c}^{{onset}}\), \(T_{c}^{{offset}}\) and RRR. Accordingly, the annealing temperature of 700 °C promotes the Bi-2223 ceramics for usage in the engineering, electro-optic, industrial and large scale applications. At the same time, the diffusion coefficients [D = D_oexp(E/k_BT)] determined at annealing temperature ranging from 650 to 850 °C are observed to be much more significant at rather higher temperatures as compared to lower temperatures. The temperature-dependent Ni diffusion coefficient is determined to be D = 3.9707 × 10^− 7exp[− 1.132 eV/k_BT] for the Bi-2223 particulate solid material. Namely, the diffusion coefficient is calculated to be about 3.9707 × 10^− 7cm² s^− 1 when the required minimum activation energy for the introduction of heavy metal Ni ions to the bulk Bi-2223 crystal structure is computed to be about 1.132 eV, being one of the most striking points deduced form this work.