Abstract
We present a quantum-mechanical study of silver decahedral nanoclusters and nanoparticles containing from 1 to 181 atoms in their static atomic configurations corresponding to the minimum of the ab initio computed total energies. Our thermodynamic analysis compares T = 0 K excess energies (without any excitations) obtained from a phenomenological approach, which mostly uses bulk-related properties, with excess energies from ab initio calculations of actual nanoclusters/nanoparticles. The phenomenological thermodynamic modeling employs (i) the bulk reference energy, (ii) surface energies obtained for infinite planar (bulk-related) surfaces and (iii) the bulk atomic volume. We show that it can predict the excess energy (per atom) of nanoclusters/nanoparticles containing as few as 7 atoms with the error lower than 3%. The only information related to the nanoclusters/nanoparticles of interest, which enters the phenomenological modeling, is the number of atoms in the nanocluster/nanoparticle, the shape and the crystallographic orientation(s) of facets. The agreement between both approaches is conditioned by computing the bulk-related properties with the same computational parameters as in the case of the nanoclusters/nanoparticles but, importantly, the phenomenological approach is much less computationally demanding. Our work thus indicates that it is possible to substantially reduce computational demands when computing excess energies of nanoclusters and nanoparticles by ab initio methods.
Highlights
The silver nanoparticles are widely used as antiviral agents [1,2], sensors [3,4], catalysts [5], as nanoparticle solders [6,7] as well as in numerous others application
The volumes obtained from the direct calculations of the electronic structure of nanoclusters/nanoparticles are represented by the Density Functional Theory (DFT) black data points, and the molar volumes from our phenomenological thermodynamic approach are continuous blue and red lines for the volumes based on the Murnaghan equation and the definition of the bulk modulus, respectively
It is evident that the volumes from direct DFT calculations of nanoclusters/nanoparticles agree very well with those based on the definition of the bulk modulus (Equation (10))
Summary
The silver nanoparticles are widely used as antiviral agents [1,2], sensors [3,4], catalysts [5], as nanoparticle solders [6,7] as well as in numerous others application. Nanoclusters, as extreme cases of nanoparticles, have a yet greater surface/volume ratio and different geometries and electronic structures when compared with their bulk counterparts. Theoretical computations constitute a very advantageous tool when studying nanoclusters as they can accurately determine many of their characteristics, such as their surface type, strain energies [8,9], phase diagrams [10] or information on their catalytic activity. Many studies reported that modifications of the surface energy can change the shape of a (nano-)particle and/or its melting temperature [11,12,13]. The most stable surface geometry for nanoparticles of pure fcc transition metals is the {111} facet [14] but the situation can differ in multi-component cases [15]
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