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.