Impact of obstacles on dislocation patterning and stress correlations

By virtue of their long-ranged nature, elastic stresses due to dislocations may provide a mechanism for the spatial organization of alloys with misfitting constituents. Here, we first explore the connection between dislocation patterning and correlations in elastic stress fields associated with dislocations. Specifically, we examine the impact of obstacles, such as impurities and grain boundaries, on the pattern formation in a collection of mutually interacting dislocations. This is accomplished by characterizing the order in terms of various dislocation structure factors that reflect the tendency to form dislocation wall segments. We find that random stationary impurities frustrate wall formation without altering the characteristic length scale of the dislocation patterning, while grain boundaries promote wall formation via dislocation incorporation, and frustrate polygonization away from the boundaries. We then discuss the implication of the results of induced solute patterning in phase-separating alloys.