Effect of size on energy and elastic constants of Ni nanoparticles studied using the embedded-atom method

Abstract

Using the embedded-atom method potential, the energy and elastic constants of Ni nanoparticles are investigated as a function of size. It is found that a simple formula derived from the total energy can be used to explain the change characteristics of the size-dependent energy and C11 and C44 of Ni nanoparticles. The change characteristics of the size-dependent C12 are slightly different from the situation of C11 and C44 and they perhaps depend on its strain character when the nanoparticle is larger than ∼2.0 nm in size. It is also found that a transition occurs from a fast change of these size-dependent properties to a slow one. Such a transition occurs at ∼1.5 nm in size for the nanoparticles, i.e. the energy and elastic constants of Ni nanoparticles show approximately no change as long as their size is larger than 2 nm. It is also demonstrated that when the size of the nanoparticle is large enough (>20 nm) the calculated elastic constants and the cohesive energy are in agreement with those of their respective bulk counterpart.

Review Article: Case studies in future trends of computational and experimental nanomechanics

“…[131][132][133] Both of them influence elastic moduli variations: the smaller the system, the more the effective moduli differ from their bulk counterpart. Atomistic simulations show significant variations of the effective elastic moduli below 10-15 nm sized NPs only, 134 while changes are still observed at rather greater sizes in the experiments (see, for example, Mook et al 135 ). Many differences between the two approaches need to be explained, and there is still no method to predict the evolution of elastic moduli due to size diminution for a given material (see Gerard and Pizzagalli for quantitative examples 136 ).…”

“…210) and GaAs. 211 We should point out, however, that some very small length scale studies of silicon nanospheres by both atomic force microscopy 134 and transmission electron microscopy 212 resulted in similar flow stress behavior. Considering dopant levels, extensive studies 205,213 have demonstrated that n-doping can favor enhanced dislocation velocities compared to intrinsic silicon.…”