Abstract
Chemical transformations, such as ion exchange, are commonly employed to modify nanocrystal compositions. Yet the mechanisms of these transformations, which often operate far from equilibrium and entail mixing diverse chemical species, remain poorly understood. Here we explore an idealized model for ion exchange in which a chemical potential drives compositional defects to accumulate at a crystal's surface. These impurities subsequently diffuse inward. We find that the nature of interactions between sites in a compositionally impure crystal strongly impacts exchange trajectories. In particular, elastic deformations which accompany lattice-mismatched species promote spatially modulated patterns in the composition. These same patterns can be produced at equilibrium in core/shell nanocrystals, whose structure mimics transient motifs observed in nonequilibrium trajectories. Moreover, the core of such nanocrystals undergoes a phase transition-from modulated to unstructured-as the thickness or stiffness of the shell is decreased. Our results help explain the varied patterns observed in heterostructured nanocrystals produced by ion exchange and suggest principles for the rational design of compositionally patterned nanomaterials.
Highlights
Chemical transformations, such as ion exchange, are commonly employed to modify nanocrystal compositions
Cation exchange in particular has been used to produce a variety of heterostructured nanocrystals, metal chalcogenides, whose mixed compositions exhibit diverse morphologies [4, 5]
We show that a strong driving force for exchange among differentsized species creates nonequilibrium patterns within model nanocrystals
Summary
Elastic forces drive nonequilibrium pattern formation in a model of nanocrystal ion exchange. Elastic deformations which accompany lattice-mismatched species promote spatially modulated patterns in the composition These same patterns can be produced at equilibrium in core/shell nanocrystals, whose structure mimics transient motifs observed in nonequilibrium trajectories. The nanocrystal’s interior evolves through diffusive steps that swap the states of adjacent lattice sites (σR → σR , σR → σR, where R and R are nearest neighbors), with configurationdependent rate kdiff Such a swap may represent a series of microscopic barrier-crossing events, perhaps involving transient vacancies or interstitials [6, 13, 14]; we resolve only the net transport of ion density. Similar to previous simulations by Ott et al [15], these stochastic rate processes are numerically realized with a KMC algorithm (Materials and Methods)
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