Quantitative analysis of meandering and dimensional crossover of conduction path in 3D disordered media by percolation modeling

Abstract

Listen

Translate article

Conduction in disordered media has been the subject of interest in applications and basic research. Percolation theory is used to study conduction, and mean-field theory has been used to describe macroscopic conduction. However, such an approximation theory cannot provide specific insights into the local limiting factors of conduction. In this study, a finite element simulation based on the site percolation model is used to investigate the effect of microstructural defects in materials on transport current. Statistical analysis of the local current obtained by the simulation experiment shows that the meandering of the transport current because of the disturbance of the current path increases as the concentration of defects increases, thus observing a dimensional crossover of the transport current from 1D to 3D. Λ, which represents the degree of current meandering, has a value of 5.3 in the vicinity of the singularity of the percolation threshold (Pc). The governing mechanisms of the transport current differ depending on the concentration and correlation of defects. The main limiting factors of the transport current are the following: ‘shadow effect’ derived from isolated defects in the quasi-1D region where the defects are dilute; the meandering of the current path including the reverse current in the 3D region where the defects are highly concentrated and begin to correlate. These results can be used to understand the current limiting mechanisms in 3D polycrystalline superconducting materials and are expected to provide guidelines for controlling complex microstructures in iron-based superconductors, MgB2, and BSCCO.