Size-Dependent Elastic Modulus and Vibration Frequency of Nanocrystals

The elastic properties and the vibration characterization are important for the stability of materials and devices, especially for nanomaterials with potential and broad application. Nanomaterials show different properties from the corresponding bulk materials; the valid theoretical model about the size effect of the elastic modulus and the vibration frequency is significant to guide the application of nanomaterials. In this paper, a unified analytical model about the size-dependent elastic modulus and vibration frequency of nanocrystalline metals, ceramics and semiconductors is established based on the inherent lattice strain and the binding energy change of nanocrystals compared with the bulk crystals, and the intrinsic correlation between the elasticity and the vibration properties is discussed. The theoretical predictions for Cu, Ag, Si thin films, nanoparticles, and TiO2 nanoparticles agree with the experimental results, the computational simulations, and the other theoretical models