Energetics of Polar and Nonpolar Facets of PbSe Nanocrystals from Theory and Experiment

ABSTRACT: Surface energies of the distinct facets of nanocrystals are an important factor in the free energy and hence determine the nanocrystal morphology, chemical and physical properties, and even interparticle dipole interactions. Here we investigate the stability and atomic structure of polar and nonpolar PbSe surfaces by combining first-principles calculations with high-resolution transmission electron microscopy (TEM). For uncapped surfaces, the calculations predict that the nonpolar {100} surface is the most stable with a surface energy of 0.184 J m
2, while the nonpolar {110} and reconstructed {111}-Pb surfaces have surface energies of 0.318 J m
2 and 0.328 J m
2, respectively. Fully polar {111} surfaces are structurally unstable upon relaxation. These findings are in good agreement with TEM observations showing that capped nanocrystals have a nearly spherical, multifaceted morphology, while cubical shapes with predominantly {100} facets are obtained when the capping molecules are removed through heating in va uum. During this process, however, also multipolar surfaces can temporarily exist just after the removal of the surfactants. These metastable {111} surfaces consist of ribbon-like nanodomains, whereby the ribbons are alternating in polarity. The calculations confirm that these multipolar surfaces are energetically more favorable than fully polar surfaces. The consequences for capped nanocrystals (a dominant Pb-oleate termination) and nanocrystal fusion (a shorter interaction range of dipole interactions) are discussed.

Figure left: Configuration of {100}, {110}, and {111} PbSe surfaces. Full circles indicate surface atoms (top layer) and quasisurface atoms (these atoms are only partially covered; they have at most one atomic bond to the top layer). Empty circles indicate subsurface atoms (having two or more bonds with atoms at an elevated layer). Subfigure (c) shows a fully polar configuration with one Pb-terminated surface and one Se-terminated surface in order to maintain stoichiometry. The bottom two configurations (d,e) are reconstructed {111} surfaces. There is one reconstructed variant {111}-Pb whereby half the Pb atoms are absent in the surface layer, and a domain-wise polar variant {111}
2Pb with ribbons of Pb atoms on top of a Se atomic layer. {111}-Se and {111}
2Se surfaces can be constructed analogously.

Figure left: High-resolution TEM images showing the morphology of PbSe NCs: (a) PbSe nanocrystals in a [011] projection, so that the {100}, {110}, and {111} surfaces can be observed simultaneously; (b) example of the Wulff diagrams (in this case corresponding to panel a) that were used to derive relative surface energies; (c,d) other PbSe NCs in a [011] projection; (e) other NCs in various orientations; (f) nanowires are formed in low-density areas after annealing at 120 °C; (g) in general, cubical shapes start to dominate after longer annealing times as the surfactants evaporate; the corners of the cubes display {100} nanofaceting, as indicated with white arrows.