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Nanomaterials 2020, 10, 767 12 of 15 phenomenological approach can be extended from the bulk down to nanoclusters containing only a few atoms. Our work thus indicates that it is possible to substantially reduce computational demands when assessing thermodynamic properties of nanoclusters and nanoparticles by quantum-mechanical methods. We would also like to emphasize that, importantly, the agreement between (i) our phenomenological modelling and (ii) the DFT energies for the actual nanoclusters has not been found sensitive to minor deviations of the shape of the studied nanoclusters from a geometrically ideal decahedral case (due to atomic relaxations in our DFT calculations). On the other hand, it should be noted that (i) our study does not cover any excitations, such as phonons, and (ii) whenever the absolute value of the excess energy, i.e., not per atom, is needed when thermodynamically assessing the stability of nanoclusters/nanoparticles, the deviation of the absolute excess energies as obtained from our method may change with the number of atoms (with respect to absolute excess energies from direct ab initio calculations of the studied nanoclusters/nanoparticles). Author Contributions: Conceptualization, S.P. and M.F.; methodology, S.P., M.F. and M.V.; formal analysis, M.V.; resources, M.Š.; writing—original draft preparation, S.P.; writing—review and editing, M.F., M.V. and M.Š.; visualization, S.P. and M.V.; supervision, M.F.; project administration, M.Š. and M.F. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Education, Youth and Sports of the Czech Republic under the Project CEITEC 2020 (Project No. LQ1601) and by the Czech Science Foundation under the Projects “Stability and phase equilibria of bimetallic nanoparticles” (Project No. GA14-12653S) and “Structure and properties of selected nanocomposites” (Project No. GA 16-24711S). Acknowledgments: We are very grateful to Jana Pavlu ̊ from Masaryk University in Brno, Czech Republic, for many fruitful discussions related to the CALPHAD modeling. Computational resources were provided by the Ministry of Education, Youth and Sports of the Czech Republic under the Projects CESNET (Project No. LM2015042), the Project CERIT Scientific Cloud (Project No. LM2015085) and by IT4Innovations National Supercomputer Center (Project No. LM2015070) within the program Projects of Large Research, Development and Innovations Infrastructures. Figures 2 and 3 were visualized using the VESTA package [64–66]. Conflicts of Interest: The authors declare no conflict of interest.The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. References 1. Daniel, S.C.G.K.; Tharmaraj, V.; Sironmani, T.A.; Pitchumani, K. Toxicity and Immunological Activity of Silver Nanoparticles. Appl. Clay Sci. 2010, 48, 547–551. [CrossRef] 2. Galdiero, S.; Falanga, A.; Vitiello, M.; Cantisani, M.; Marra, V.; Galdiero, M. Silver Nanoparticles as Potential Antiviral Agents. Molecules 2011, 16, 8894–8918. [CrossRef] [PubMed] 3. Bindhu, M.R.; Umadevi, M. Silver and Gold Nanoparticles for Sensor and Antibacterial Applications. Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 2014, 128, 37–45. [CrossRef] [PubMed] 4. Chapman, R.; Mulvaney, P. Electro-Optical Shifts in Silver Nanoparticle Films. Chem. Phys. Lett. 2001, 349, 358–362. [CrossRef] 5. Grouchko, M.; Kamyshny, A.; Ben-Ami, K.; Magdassi, S. Synthesis of Copper Nanoparticles Catalyzed by Pre-Formed Silver Nanoparticles. J. Nanoparticle Res. 2009, 11, 713–716. [CrossRef] 6. Sopoušek, J.; Buršík, J.; Zálešák, J.; Buršíková, V.; Brož, P. Interaction of Silver Nanopowder with Copper Substrate. Sci. Sinter. 2011, 43, 33–38. [CrossRef] 7. Sopoušek, J.; Buršík, J.; Zálešák, J.; Pešina, Z. Silver Nanoparticles Sintering at Low Temperature on a Copper Substrate: In Situ Characterisation under Inert Atmosphere and Air. J. Min. Metall. Sect. B Metall. 2012, 48, 63–71. [CrossRef] 8. Ali, S.; Myasnichenko, V.S.; Neyts, E.C. Size-Dependent Strain and Surface Energies of Gold Nanoclusters. Phys. Chem. Chem. Phys. 2016, 18, 792–800. [CrossRef] 9. Patala, S.; Marks, L.D.; De La Cruz, M.O. Elastic Strain Energy Effects in Faceted Decahedral Nanoparticles. J. Phys. Chem. C 2013, 117, 1485–1494. [CrossRef] 10. Wang, J.; Lu, X.G.; Sundman, B.; Su, X. Thermodynamic Assessment of the Au-Ni System. Calphad Comput. Coupling Phase Diagrams Thermochem. 2005, 29, 263–268. [CrossRef]PDF Image | Quantum-Mechanical of the Energetics of Silver Decahedron Nanoparticles
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