Effective elastic modulus of nano-particles

Atoms at a free surface experience a different local environment than do atoms in the bulk of a material. As a result, the equilibrium position and energy of these atoms will, in general, be different from bulk positions and bulk energies. In traditional continuum mechanics, such interfacial free energy is typically neglected because it is associated with only a couple of layers of atoms near the surface and the ratio of the volume occupied by the surface atoms and the total volume is extremely small. However, for nano-size particles, the surface to volume ratio becomes significant, so does the effects of surface free energy. In this paper, a framework is developed to incorporate the surface free energy into the continuum mechanics theory. Based on this approach, it is shown that the effective modulus of a particle does depend on the particle size. Although such size dependency is negligible for larger size particles, it becomes significant when the particle shrinks to nanometer size.