On the structure and stability of nanoscale materials: a two-dimensional model

Abstract

We have investigated numerically using the Metropolis Monte Carlo algorithm two-dimensional systems of about 3000 classical particles interacting via a Lennard-Jones potential and being subjected to periodic boundary conditions. In this model we consider metastable structures of small crystalline grains which are randomly oriented relative to each other and which are interconnected by a network of boundaries. The atomic structure within the grains being composed of about 500 atoms each is a nearly ideal triangular lattice. The network of boundaries however has a highly defective structure which is determined by the boundary conditions enforced by the crystalline grains. It is the objective of our work to develop a conceptually simple model for nanocrystalline materials, which can be used for a qualitative description of their complex properties. The main ingredient of the model is its property to relax into a metastable state consisting of intrinsically well ordered crystalline grains connected by a highly defective intergranular component. For that state we compute the static structure factor and the pair correlation function.