Compositional patterning in coherent and dislocated alloy nanocrystals

Variations in the distribution of the alloy components can significantly influence the electronic properties of self-organized alloy nanocrystals. Using a combination of finite element and quadratic programming optimization methods, we have developed an efficient numerical technique to compute the equilibrium composition profiles in coherent and dislocated nanocrystals. We show that the variations in composition profiles arise due to the competition between chemical mixing effects and the relaxation of composition-dependent mismatch strain as well as strain due to dislocations. We find that the composition profiles in these crystals depend strongly on morphological features such as the slopes and curvatures of their surfaces and the presence of corners, edges and dislocations at the nanocrystal-substrate interface. This approach provides the means for a quantitative description of the factors controlling equilibrium composition profiles in various coherent and dislocated self-organized alloy systems.