Thermodynamic Considerations
Shape of crystal is dependent on relative specific surface energies associated with facets of crystal. At equilibrium, a crystal has to bound by facets giving a minimum total surface energy (Wulff facets theorem).
Hence, the equilibrium shape often reflect the intrinsic symmetry of corresponding lattice (i.e. cubic materials → cubic morphologies). In addition, the equilibrium shape, although faceted, has low aspect ratio to minimize surface A.
Kinetic Considerations
Growth rate of a crystal facet depends exponentially on surface energy, so at high growth rates (kinetically controlled growth regime), high energy facets grow more quickly, leaving behind low energy planes as facets of the product. Hence, nanocrystal shapes may be controlled via the use of appropriate capping agent(s) to change the free energy of various crystallographic surfaces, to kinetically control growth rates of various facets of seed .
Shape of crystal is dependent on relative specific surface energies associated with facets of crystal. At equilibrium, a crystal has to bound by facets giving a minimum total surface energy (Wulff facets theorem).
Hence, the equilibrium shape often reflect the intrinsic symmetry of corresponding lattice (i.e. cubic materials → cubic morphologies). In addition, the equilibrium shape, although faceted, has low aspect ratio to minimize surface A.
Kinetic Considerations
Growth rate of a crystal facet depends exponentially on surface energy, so at high growth rates (kinetically controlled growth regime), high energy facets grow more quickly, leaving behind low energy planes as facets of the product. Hence, nanocrystal shapes may be controlled via the use of appropriate capping agent(s) to change the free energy of various crystallographic surfaces, to kinetically control growth rates of various facets of seed .
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