Theoretical study of the surface energy, stress, and lattice contraction of silver nanoparticles

Abstract

We employ first-principles and empirical computational methods to study the surface energy and surface stress of silver nanoparticles. The structures, cohesive energies, and lattice contractions of spherical Ag nanoclusters in the size range $0.5--5.5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ are analyzed using two different theoretical approaches: an ab initio density functional pseudopotential technique combined with the generalized gradient approximation and the embedded atom method. The surface energies and stresses obtained via the embedded atom method are found to be in good agreement with those predicted by the gradient-corrected ab initio density functional formalism. We estimate the surface energy of Ag nanoclusters to be in the range of $1.0--2.2\phantom{\rule{0.3em}{0ex}}\mathrm{J}∕{\mathrm{m}}^{2}$. Our values are close to the bulk surface energy of silver, but are significantly lower than the recently reported value of $7.2\phantom{\rule{0.3em}{0ex}}\mathrm{J}∕{\mathrm{m}}^{2}$ for free Ag nanoparticles derived from the Kelvin equation.