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Typical synthesis of core/shell nanostructures involves a rigorous two-step protocol. It is common to synthesize the semiconducting core first, followed by the overgrowth of a thin shell of a different band-gap material. The few attempted single-step and one-pot synthesis approaches have been limited in their use and specific to the type of precursors involved. The core/shell nanocrystals prepared by over-coating methods enclose interfaces of lattice-mismatched core and shell regions that lead to undesirable misfit strain and defect-induced states in the band gap. Motivated by the need for single-step synthesis routes to design minimally strained core/shell-like nanostructures, we study the equilibrium properties of a prototypical ternary compound semiconductor nanocrystal system, emphasizing on equilibrium surface segregation, as a potential means to self-assemble core/shell-like semiconductor quantum dots.