The phenomenon of dynamical scaling of structure factor—few open questions

Abstract

The phenomenon of new phase formation, a representative example of first order phase transition, is fundamental as an example of a highly nonlinear process far from equilibrium. New phases are the topological defects in an otherwise homogeneous medium of continuous symmetry. Very early stage of this phenomenon can be rigorously described by a linear theory, based on diffusion equation. The new phases grow with time with a self-similar growth pattern and in late stages all domain sizes are much larger than all microscopic lengths. The new phase forming systems exhibit scaling phenomenon, i.e., a morphological pattern of the domains at earlier times looks statistically similar to a pattern at later times apart from the global change of scale implied by the growth of a characteristic length scale L ( t ) —a measure of the time-dependent domain size of the new phase. The structure factor, for Euclidean systems, obeys simple scaling ansatz at late times. In the present work, we propose to examine some issues like (i) uniqueness of characteristic length; (ii) the extent of validity of the scaling laws for multicomponent systems; (iii) the extent of validity of the scaling laws for new phase formation in the case of non-Euclidean fractal systems. The need for investigations examining the extent and the nature of the validity of the scaling laws for confined systems and for systems subjected to random fields have been mentioned.