Eur. Phys. J. B (2012) 85: 416
https://doi.org/10.1140/epjb/e2012-30897-y

Regular Article

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

University of Technology and Life Sciences, Institute of Mathematics and Physics, 85796 Bydgoszcz, Poland

^a e-mail: nkruszewska@utp.edu.pl

Received: 3 October 2012
Published online: 24 December 2012

Abstract

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 ≅ 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.