TOPOLOGICAL LOCALISATION OF DEFECTS AT ATOMIC SCALE

Abstract

The problem addressed in this paper is the detection of defects on atomic structures. The procedure proposed is in two steps. At first a tessellation is built starting from the atoms. It consists of a partition of the space into cells, and is used to define the neighbourhood relationships between the atoms. Then, the local contribution to a topological parameter, namely the Euler-Poincare characteristic, is defined and measured for each cell. Within a regular tessellation, made of identical cells, this local contribution is equal to zero. Any local deviation from regularity corresponds to a tessellation containing cells with non-zero contributions. This allows us to locate the defects from a topological criterion and opens the way to a fully automatic detection of interfaces at atomic scale. The procedure is applied in 2D space for the detection of edge dislocations, grain boundaries and twins from HREM models and images. A 3D example is also given to illustrate its generality.