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Nanomaterials 2020, 10, 767 3 of 15 Figure 2. A schematic visualization of studied decahedron nanoclusters and nanoparticles (for higher number of atoms) with each of them accompanied by the number of atoms. 2.1. Phenomenological Thermodynamic Modeling The phenomenological thermodynamic approach based on the CALPHAD method is very often used for calculations of the total energy of particles as well as for the prediction of phase diagrams [22–26,43]. The computations use an approximation when bulk variables are applied in the case of nanoparticles but not all properties of the (nano-)particles are included (for example, a structural disorder is sometimes omitted). The molar total Gibbs energy Gtot is decomposed into a sum of relevant contributions [24]: Gtot = Gref +Gid +GE +Gmag +GP +Gsur, (1) where Gref is the molar reference Gibbs energy, Gid is the molar energy of ideal mixing of an alloy, GE is the molar excess Gibbs energy, Gmag is the molar contribution related to magnetism (which could be particularly complicated in the case of magnetic nanoparticles, including spin and orbital moment contributions as discussed, e.g., in Ref. [44]), GP accounts for the influence of pressure P and Gsur for the molar contribution of surface energy. When adapting the Equation (1) to the studied case of silver nanoclusters/nanoparticles, i.e., an unary non-magnetic metal at the temperature T = 0 K, only the reference Gibbs energy Gref and the surface Gibbs energy Gsur remain: Gtot = Gref + Gsur. (2) The surface energy contribution is in the case of spherical nanoparticles equal to: Gsur = Asph ·σsur = Asph · Vsph ·σsur = 3· Vm ·σsur, (3) n nVsph r where σsur is surface energy, Asph = 4πr2 is the surface area of a spherical nanoparticle with the volume Vsph = (4/3)πr3, n is is the number of moles and the Vm is the molar volume. As the volumePDF Image | Quantum-Mechanical of the Energetics of Silver Decahedron Nanoparticles
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