Size-Dependent Surface Energy Density of Spherical Face-Centered-Cubic Metallic Nanoparticles

Abstract

The surface energy density of nano-sized elements exhibits a significantly size-dependent behavior. Spherical nanoparticle, as an important element in nano-devices and nano-composites, has attracted many interesting studies on size effect, most of which are molecular dynamics (MD) simulations. However, the existing MD calculations yield two opposite size-dependent trends of surface energy density of nanoparticles. In order to clarify such a real underlying problem, atomistic calculations are carried out in the present paper for various spherical face-centered-cubic (fcc) metallic nanoparticles. Both the embedded atom method (EAM) potential and the modified embedded atom method (MEAM) one are adopted. It is found that the size-dependent trend of surface energy density of nanoparticles is not governed by the chosen potential function or variation trend of surface energy, but by the defined radius of spherical nanoparticles in MD models. The finding in the present paper should be helpful for further theoretical studies on surface/interface effect of nanoparticles and nanoparticle-reinforced composites.

Surface Energy of Au Nanoparticles Depending on Their Size and Shape

“…Unlike the energy change related to forming the free surface of a nanoparticle, the area is not well defined. Consequently, small changes of the radius/size yield large changes of the surface area, especially for nanometre-sized particles [12]. The rather geometrical argumentation of Ref.…”

“…Wei and Chen [12] pointed out that, from the theoretical point of view, the trend could be qualitatively altered by changing the definition of a nanoparticle surface area. Unlike the energy change related to forming the free surface of a nanoparticle, the area is not well defined.…”

“…The rather geometrical argumentation of Ref. [12] was later linked to a physical quantity, a spatial expansion of the electronic cloud [13]. Using a refined, physically-based surface for small nanoparticles consequently leads to a weak-to-no size dependence of surface energy [14,15].…”

Segregation Phenomena in Size-Selected Bimetallic CuNi Nanoparticle Catalysts

“…In reduced chemical state and in the absence of surface adsorbates, Cu is expected to segregate toward the surface of the particles due to its lower surface free energy. 14,36,37 In the presence of oxides or oxygencontaining adsorbates, the situation is much more complex. In bulk bimetallic systems, the Gibbs free energy for NiO is higher (less negative) than that of CuO but lower than that of Cu 2 O.…”

“…Given that the atomic radii of Cu and Ni are very similar (128 pm versus 124 pm), the size misfit does not play an important role with respect to segregation in this system. In reduced chemical state and in the absence of surface adsorbates, Cu is expected to segregate toward the surface of the particles due to its lower surface free energy. ,, In the presence of oxides or oxygen-containing adsorbates, the situation is much more complex. In bulk bimetallic systems, the Gibbs free energy for NiO is higher (less negative) than that of CuO but lower than that of Cu 2 O. , This means that, in bulk CuNi alloys, the segregation trends for Cu + and Cu 2+ are in principle opposite to each other, with Cu 2+ preferentially segregating to the surface and Cu + inward.…”