  Atomistic simulations are performed to study the statistical mechanical
property of gold nanoparticles. It is demonstrated that the yielding behavior
of gold nanoparticles is governed by dislocation nucleation around surface
steps. Since the nucleation of dislocations is an activated process with the
aid of thermal fluctuation, the yield stress at a specific temperature should
exhibit a statistical distribution rather than a definite constant value.
Molecular dynamics simulations reveal that the yield stress follows a Gaussian
distribution at a specific temperature. As the temperature increases, the mean
value of yield stress decreases while the width of distribution becomes larger.
Based on numerical analysis, the dependence of the mean yield stress on
temperature can be well described by a parabolic function. Present study
illuminates the statistical features of the yielding behavior of nanostructured
elements.
