表面能对纳米颗粒的晶格收缩和固有频率的影响

由于纳米颗粒具有很大的比表面积，因此，表面能对它的力学性能有着不可忽略的影响．本文给出了由表面能所导致的纳米颗粒晶格收缩效应的解析结果，与试验观察定量上相当一致；计算了表面能对纳米颗粒固有频率的影响，预测了由于表面能的影响，纳米颗粒出现的“振动软化”现象．

EFFECTS OF THE SURFACE ENERGY ON THE LATTICE CONTRACTION AND EIGENFREQUENCY OF A NANO GRAIN

Nano grains are single phase or multiphase polycrystals with a grain size in the range of 1 to 100 nm. Compared with bulk materials with the same chemical composition, nano grains exhibit rather high surface energy due to the large volume fraction of particles (atoms and molecules) residing in the grain boundaries. Therefore, the influence of surface energy to the mechanical properties of grain, such as Young's modules, lattice size and eigenfrequency, is not negligible. This is confirmed by experiments. In this paper, based on continuum mechanics, a theoretical model used to predict the effect of surface energy of nano grain is established. Firstly, the motion equations, in which the effect of surface energy of nano grain is involved, are derived according to the virtual work's principle. By using these equations, the effect of the lattice contraction induced by surface energy is studied and the analytical result, which is consistent with the experimental data in quantity, is obtained. The prediction about the influence of surface energy to the eigenfrequency of nano grain is given. Numerical results show that there exists `frequency softening' in the vibration of nano grain due to surface energy. This conclusion approaches that of dynamical theory of crystal lattices.