In silico determination of surface entropy of 1-D copper nanostructures

Abstract

Metallic one-dimensional (1-D) nanostructures are widely studied owing to their important role in developing electronic and electromechanical systems at the nanoscale. In the context of their structures, the large surfaces play a governing role in dictating many of their fundamental characteristics and hence, the surface properties are the most vividly studied issues. In the present work, we employ the harmonic oscillator model to analyze the thermodynamic properties of 1-D copper nanostructures. Our simulations reveal that owing to the large surface to volume ratio, the structural energies of these nanomaterials significantly exceed that of the bulk copper. Nevertheless, the harmonic oscillator approach enables us to directly evaluate the free energy of the system and eventually provides the associated entropy. The calculations are performed for three different crystal orientations and the results clearly indicate that the per atom entropy of thinner nanostructures is larger than their bulk counterpart. This increment in entropy is attributable to the increased degrees of freedom of the surface atoms and has the tendency of stabilizing the surface structure. The harmonic oscillator model works over a reasonable range of temperature and the technique demonstrated here is well extendable to other nanomaterials of interest.

Simulation of thermal stress and buckling instability in Si/Ge and Ge/Si core/shell nanowires

“…In this relation, m i and m j denote the atomic mass corresponding to the coordinate variables r i and r j , respectively. Assuming the validity of the harmonic approximation model [ 34 ], the diagonalization of the dynamical matrix yields the squared-eigenfrequencies (ω 2 ) that link the classical and real temperatures of an N -atom system:…”