Non-uniform composition distribution in alloy quantum structures

Based on 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 alloy quantum crystals. We demonstrate 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. 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.