On clean grain-boundaries involving growth of nonequilibrium crystalline-amorphous superconducting materials addressed by a phenomenological viewpoint

This study deals with a problem of clean grain-boundary geometric quasi universal feature, and its representative value characteristic of superconducting cuprate polycrystals. The emergence of the superconducting phase goes via a thermally activated and massive, as well as spherulites' coarsening assisted, nucleation-growth phase transformation. It has been shown by exploiting mainly the space dimension as the principal degree of freedom in transformations of the type that random close packing and self-avoiding walk conceptions, when applied together, corroborate a characteristic value of the fractal grain-boundary dimension, D-f - 7/3 congruent to 2.3(3). This value is of practical importance, as provided by computer simulation based on modified Eden-cluster algorithm, and co-supported within a certain accuracy by an accompanying laboratory experiment. A working assumption of the sensitivity of the phase transformation to characteristic time scales has been exploited to accomplish the final goal.