components including metals, semiconductors, and insulators into various coreshell configurations. The compositional flexibility and structural tunability of coreshell nanocrystals open up tremendous opportunities for obtaining highly designable physical and chemical properties. [5] For most combinations of materials, the epitaxy is associated with the buildup of elastic strains that result from mismatched lattices of the constituent parts. The misfit strain has long been recognized as an important factor that affects the formation and property of epitaxial structures. For example, misfit strain can induce lattice defects such as dislocations, which degrade the quality of the epitaxial layers and cause problems in device fabrication. [6] On the other hand, misfit strain in defect-free epilayers is very useful for optimizing the properties of heterostructures. Elastic strain has been shown to stabilize single crystallite cubic formamidinium lead iodide (FAPbI 3) thin films that offer high quantum efficiency for photodetection. [7] The strain controlled ferroelastic switching in PbTiO 3 thin films also demonstrates high sensitivity for potential applications in pressure sensors and switches. [8] Misfit stain holds more leverage in heteroepitaxial core-shell nanocrystals than in epitaxial thin-films grown on bulk substrates. Owing to the large specific surface area, nanocrystals are enclosed by various crystal facets with distinct crystallographic parameters. Accordingly, nanocrystal heteroepitaxy is characterized by concurrent deposition of epilayers on all the exposed crystal facets of the core nanocrystals. [9] From a crystallographic point of view, epitaxial deposition on different crystal facets may be subjected to a variation of interfacial strains. Besides, misfit strains in core-shell nanocrystals are usually shared by the epilayer and substrate, [10] which gives rise to diversified strain build-up and relaxation processes. Consequently, epitaxial kinetics in different crystallographic directions are largely manipulated by the structure symmetry as well as the size and morphology of the core nanocrystals. [11] On a separate note, nanocrystals are more amenable to strain than the bulk counterparts due to the increase of elasticity at the nanometer length scale. [12] Therefore, strain engineering is increasingly employed to control the formation and functionality of heteroepitaxial nanostructures in recent years. [13] In this review, we summarize recent developments in the understanding and exploitation of misfit strain in heteroepitaxial core-shell nanocrystals (Figure 1). In Section 2, we Heteroepitaxial modification of nanomaterials has become a powerful means to create novel functionalities for various applications. One of the most elementary factors in heteroepitaxial nanostructures is the misfit strain arising from mismatched lattices of the constituent parts. Misfit strain not only dictates epitaxy kinetics for diversifying nanocrystal morphologies but also provides rational control over materials prope...
