An Analytical Lattice Model Study of fcc Nanowires

Size-dependent elastic moduli are investigated theoretically for a face-center-cubic single-crystalline nanowire. A three-dimensional lattice model is constructed only considering the interactions between the nearest and second nearest atoms and the interactions are represented as harmonic springs. Unlike the classical continuum theory, this lattice model directly takes the discrete nature in the cross sectional directions into account. The constitutive relation of the nanowire is then derived by using the energy approach and the analytical expressions of the elastic moduli of nanowires, including axial, transverse Young's modulus and Poisson's ratio, are obtained. The model is validated through comparison with molecular simulation data from the literature. Once validated, the model is used to study the size-dependent elastic moduli. It is shown that the 〈100〉 nanowires are always softer than its bulk counterpart in both axial and transverse directions.