Modeling the Size Dependency of the Stability of Metal Nanoparticles

Abstract

In this work, we use density functional theory (DFT) to study cuboctahedral, octahedral and cubic nanoparticles of the late transition metals as well as Al and Mg in order to identify their stability as a function of size. We developed a simple model that not only includes the surface energies as in the commonly used Wulff construction but additionally accounts for energies related to edges and corners. Importantly, this model only requires the bulk cohesive energy and the surface energies of the fcc(111) and fcc(100) surfaces, which are used to extrapolate to lower coordination numbers. We find that our model estimates the stability of nanoparticles with a mean absolute error of only 0.09 eV.

Theoretical Investigation of the Size Effect on the Oxygen Adsorption Energy of Coinage Metal Nanoparticles

“…For Cu, the effect of geometry optimization is studied explicitly. For free standing metal Cu clusters ranging from 13 to 923 atoms, a linear relation between the mean Cu-Cu distance, the chemical potential which is approximated by the average energy per atom, and the number of atoms to the power of -1/3 (see Figure S3) is observed, similarly to what has been found for other metals [13,34,[38][39][40][41][42][43][44][45]. Figure 1 shows the adsorption energy of an oxygen atom on the Cu clusters with increasing size.…”

Structure‐Dependent Strain Effects

“…The reactivity is, moreover, affected by the fact that the surface atoms of nanoparticles are strained. One reason for the strain, is the finite size and the arrangement to shapes that minimize the surface energy [6,7] . Nanoparticles may additionally be strained by the lattice mismatch to the support [8] .…”

A review on the use of DFT for the prediction of the properties of nanomaterials

“…Dietze et al have employed DFT to identify the stability of different shapes (e.g., cuboctahedral, octahedral, and cubic) of nanocatalysts of the late transition metals as well as Al and Mg as a function of size. 123 Liu et al have investigated the interaction between the stable structures of TiAu 4 with a different number of H 2 O molecules (1, 2, 4, and 12) by using a DFT-based basin-hopping global optimization approach. 124 DFT calculations of heterogeneous reactions on catalyst surfaces can provide insights about the reactivity and mechanisms, and can potentially allow in silico screening and design of catalysts.…”