Eckhaus instability - a possible wavelength changing mechanism in the evolution of dislocation patterns

Phase modulations of periodic dislocation patterns observed in transmission electron microscopy (TEM) studies of some single crystalline metals, are a nalyzed using the methods of nonlinear dynamics. The Ginzburg-Landau (GL) e quation for the soft mode instability in the weakly nonlinear regime is der ived for the Walgraef-Aifantis (WA) model for a coupled system of two popul ations of dislocations. The bulk of results is obtained using the GL equati on, and, therefore, the results are more general than the WA-model itself. We demonstrate that phase modulations of dislocation patterns can be descri bed using the concept of the Eckhaus instability which describes one of the most fundamental "generic" mechanisms of wavelength-changing The timescale of wavelength-changing processes in dislocation systems can be very large when the system is close to the Eckhaus stability limit. This means that me tastable phase modulations of dislocation patterns can survive nearly uncha nged for a long time. The results of numerical simulations for realistic va lues of the parameters show that the Eckhaus instability could be the under lying physical reason of modulated ladder structures of persistent slip ban ds (PSBs) in cyclically deformed metallic alloys. (C) 2001 Elsevier Science B.V. All rights reserved.