Atomistic and continuum modeling of nanoparticles: Elastic fields, surface constants, and effective stiffness

VI Kushch, INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 183, 103806 (2023).

DOI: 10.1016/j.ijengsci.2022.103806

The elastic fields, surface constants and effective elastic moduli of nanoparticles are studied by means of classical molecular dynamics and continuum mechanics. Two analytical models of isotropic nanoparticles are considered. The first model is a sphere coated with a thin surface layer, which simulates the effect of the free surface energy in the nanoparticle. In the second model, the surface effect is taken into account by applying the boundary conditions in accordance with the Gurtin-Murdoch theory of material surfaces. The effective elastic moduli of nanoparticles are evaluated using the general and consistent from the micromechanical viewpoint surface averaging scheme. The geometric and material parameters of the continuum models are found by fitting the MD data for nanoparticles of three monocrystalline solids with diverse atomic mass, lattice type, and elastic moduli. It is shown that the properly calibrated analytical models correctly predict the size effect of surface free energy on the lattice contraction, residual stress, surface constants, and the elastic stiffness of nanoparticles. Applicability of the developed continuum models to the faceted nanocrystals is discussed. Comparison of the atomistic and continuum models of nanoparticles yields a simple and robust method for evaluating the surface constants. The parametric and asymptotic study of these models is performed. The established analytical relationships between the parameters of the continuum models facilitate using the surface layer model in the numerical simulation of nanostructures.

Return to Publications page