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.
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