Vacancy defects are known to play an important role in the structural and chemical properties of metallic and semiconductor nanoparticles. Here, we investigate the likelihood of vacancy formation at the surface, in the subsurfaces, and in the interior of a model system of Al nanocrystals. The depth dependence of the vacancy formation energy (VFE) in 14–17 layered low-indexed surfaces of aluminium is studied using LDA, PBE, and PBEsol exchange-correlation functionals. Within a depth of two subsurface layers, the functionals make a transition from a similar description of surfaces to the differences in VFEs observed in bulk Al. The VFE converges to the bulk value within 0.01 eV beyond a maximum depth of 3–6 atomic layers, depending on the crystallographic surface plane. We find that the different convergence behaviors are related to the relaxations of atomic planes, normal to the surface, which in turn depend on the packing density of these surfaces. For the (111) subsurfaces, surprisingly, the defect formation energies are found to be higher than that of bulk Al, which is related to the hindered relaxations in its close-packed atomic planes. Although our results predict considerably lower VFE for the topmost layers of all the surfaces, the likelihood of forming a vacancy in the immediate subsurfaces of multifaceted Al nanoparticles is predicted to be lower than in bulk Al, which is in contrast to expectation.

Cation exchange is a powerful tool for the synthesis of nanostructures such as core–shell nanocrystals, however, the underlying mechanism is poorly understood. Interactions of cations with ligands and solvent molecules are systematically ignored in simulations. Here, we introduce the concept of pseudoligands to incorporate cation-ligand-solvent interactions in molecular dynamics. This leads to excellent agreement with experimental data on cation
exchange of PbS nanocrystals, whereby Pb ions are partially replaced by Cd ions from solution. The temperature and the ligand-type control the exchange rate and equilibrium composition of cations in the nanocrystal. Our simulations reveal that Pb ions are kicked out by exchanged Cd interstitials and migrate through interstitial sites, aided by local relaxations at core–shell interfaces and point defects. We also predict that high-pressure conditions facilitate strongly enhanced cation exchange reactions at elevated temperatures. Our approach is easily extendable to other semiconductor compounds and to other families of
nanocrystals.