Domain-size evolution upon switching of the states of a one-dimensional system with defects

The decay kinetics of metastable states in highly perfect materials is well described by Kolmogorov–Johnson-Mehl statistical theory. We generalize this theory to a one-dimensional system with regard to the effect of chaotically distributed defects that hinder new phase propagation. We calculate a phase transformation pattern that is randomly inhomogeneous in space and time depending on the density of defects and delay times caused by them. The theory is applicable to the extended contacts of large-scale integrated circuits, magnetic nanowires, quasi-one-dimensional semiconductors encapsulated in carbon nanotubes, biological macromolecules, and many other systems.