Constructing continuum models of ionic nanowires from quantum mechanics computations

We propose a modelling and computational approach based on atomistic computations to construct continuum models of nanostructures which are able to take into account surface and size effects in the Finite Element Method (FEM) context. First, we formulate the continuum problem in the Gurtin-Murdoch formalism [1] by introducing surface energies terms in the expression of the potential energy of the system. The stationary of this potential energy provides a variational form whic h can be applied to the FEM. To extract the surface energy parameters, we introduce a new methodology based on quantum mechanics (QM) computations using atomistic models of surfaces. A Density Functional Theory procedure (DFT) is applied to carry out the computations. The method to solve the continuum equations can be a simple FEM approach, with appropriate surface elements. We also propose another computational approach [2] to avoid the meshing of the surface by using an Extended Finite Element Method (XFEM) [3]. In that context, the surfaces are defined in an implicit manner via a level-set fu nction which is also used to construct the surface operators related to the Laplace-Young equation.