  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.
