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Nanomaterials 2020, 10, 767 7 of 15 Due to various shape of nanoparticles, the mean surface energy of nanoclusters/nanoparticles is computed according to the approach suggested by Guisbiers and Abudukelimu in [57] σsur =∑Ahkl·σhkl/∑Ahkl, (12) where Ahkl are areas of facets with different {hkl} crystallographic orientation on the surface of a nanocluster/nanoparticle. In the following, we put the energy σ{111} equal to the surface energy σsur of the whole decahedron particle as its surface contains only the {111} facets. Next to the energy we also make an attempt to determine the molar volume of the studied nanoparticles from our quantum-mechanical calculations by the following steps. We first compute the mean radius as a half of the average inter-atomic distance between all the atoms and all their nearest neighbors—see Figure 4. Second, we put this mean radius equal to a radius of equally sized touching spheres in a fcc bulk crystal (as when computing the atomic packing factor, for fcc equal to 0.74). Third, we assign the atomic volume in such a fcc bulk crystal to each atom in our nanocluster. Figure 4. Computed bond lengths between pairs of nearest neighbors in the studied nanoclusters/nanoparticles. Blue symbols represent all inter-atomic distances in calculated nanoparticles, orange color marks the mean inter-atomic distances and the black dashed line shows the inter-atomic distance of bulk fcc structure of Ag. The figure neatly shows that the studied nanoclusters/nanoparticles are highly strained. The majority of bond lengths (interatomic distances) is well below the bulk value of fcc Ag (see the horizontal black dashed line in Figure 4). In particular, this is true for the two nanoclusters with the number of atoms equal to 7 and 23. The mean (average) interatomic distance (see the orange data points) clearly demonstrates this reduction of the interatomic distances. It is worth noting that internal elastic strains (and the corresponding energies) are not included in our approximative phenomenological thermodynamic description of nanoclusters/nanoparticles (as described in the subsection above) but all particles are subject to a fictitious hydrostatic pressure (which we put equal to the surface stress value).PDF Image | Quantum-Mechanical of the Energetics of Silver Decahedron Nanoparticles
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