  Cation exchange is a useful tool for post-synthetic modification of
nanocrystals, yet its mechanisms 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 cation exchange
and suggest principles for the rational design of compositionally-patterned
nanomaterials.
