Fractal geometry as a descriptor of superconducting performance in Bi-2223 samples

Abstract This study investigates the influence of grain boundary geometry on superconducting performance in Bi-2223 polycrystalline samples subjected to different uniaxial compaction pressures. Samples prepared by solid-state reaction were compacted at 148 MPa (low-pressure sample), 199 MPa (medium-pressure sample), and 248 MPa (high-pressure sample). SEM micrographs were examined using multiscale fractal analysis combined with a refined region of interest protocol designed to exclude edge artifacts. Increasing compaction enhanced superconducting performance, with J c (0) rising from 293 to 547 A/cm 2 , residual resistivity ρ 0 decreasing from 1.06 to 0.76 mΩ cm, and texture factor F (00 l ) increasing from 0.63 to 0.70. ROI-based analysis revealed a systematic reduction of the grain boundary fractal dimension D gb from 1.483 ± 0.067 (powder) to 1.285 ± 0.047 (high-pressure sample), while no statistical difference was observed between the low- and medium-pressure samples; log ( B ), D 2 , and log-transformed unit scale lacunarity log ( Λ 1 ) exhibited the same invariance before changing significantly at the highest pressure. These results demonstrate that interface geometry evolves under pressure in a threshold-dependent rather than continuous manner, with a geometric invariance regime between 148 and 199 MPa followed by a statistically significant transition at 248 MPa. Strong correlations between fractal descriptors and transport parameters confirm that multiscale fractal analysis provides a sensitive, nondestructive probe of the critical geometric thresholds governing granular Bi-2223 superconductivity.