Continuum Simulation of the Elastic Behavior of Nanosized Diamond Single Crystals

Two continuum models are proposed for predicting stress fields and elastic properties of nanosized diamond monocrystals. The first model is a boundary value problem of the elasticity theory formulated for a sphere with a thin shell, which ensures consideration of the effect of the free surface energy on the elastic behavior of a diamond nanocrystal. In the second model, the surface energy is taken into account through the boundary condition in accordance with the Gurtin–Murdoch theory of material surfaces. The geometric and material parameters of the models are determined by comparison with the results of classical molecular dynamics. A parametric analysis of the developed models is carried out, and the trends in the influence of the nanoparticle size on the lattice parameter, stress concentration, and bulk elastic modulus of diamond are determined.