Synthesis and Comparative Analysis of Crystallite Size and Lattice Strain of Pb₂Ba_1.7Sr_0.3Ca₂Cu₃O_10+δ Superconductor

In this article, Pb₂Ba_1.7Sr_0.3Ca₂Cu₃O_10+δ superconductor material was synthesized using conventional solid-state reaction method. X-ray diffraction (XRD) analysis demonstrated one dominant phase 2223 and some impurities in the product powder. The strongest peaks in the XRD pattern were successfully indexed assuming a pseudo-tetragonal cell with lattice constants of a = 3.732, b = 3.733 and c = 14.75 Å for a Pb-Based compound. The crystallite size and lattice strain between the layers of the studied compound were estimated using several methods, namely the Scherrer, Williamson-Hall (W.H), size-strain plot (SSP) and Halder Wagner (H.W) approach. The values of crystallite size, calculated by Scherrer, W.H, SSP and H.W methods, were 89.4540774, 86.658638, 87.7555823 and 85.470086 Å, respectively. Moreover, the lattice strain values obtained by W.H, SSP and H.W methods were 0.0063240, 0.006325 and 0.006, respectively. It was noted that all crystallite size results are consistent; however, the best method is the size-strain plot because it gave a value of R² approaching one. Furthermore, degree of crystallites was calculated and found to be 59.003321%. Resistivity analysis suggests zero-resistance, which is typical of superconducting materials at critical temperature. Four-probe technique was utilized to measure the critical temperature at onset T_c(onset), zero resistivity T_{c(off set)}, and transition (width ΔT), corresponding to temperatures of 128 K, 116 K, and 12 K, respectively.