2D and 3D percolation in high-temperature superconductors

A quantitative model is presented for the high critical current densities ((Formula presented)) supported by superconducting materials with uniaxial alignment, such as c-axis textured Bi-Sr-Ca-Cu-O tapes. Current follows percolative paths across small-angle grain boundaries. Because (Formula presented) is low for intragranular conduction parallel to the c axis, the 3D flow required for percolation is produced by conduction perpendicular to the c axis in tilted grains. For optimized microstructures, (Formula presented) ranging from 3 to 30 % of the intragranular value is predicted for percolation across small-angle grain boundaries with misorientations below 10° and 20°, respectively.