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TOPOLOGICAL LOCALISATION OF DEFECTS AT ATOMIC SCALE

DOI: 10.5566/ias.v21.p191-198

Keywords: defects , Euler-Poincare characteristic , HREM images , interfaces , tessellations , topology

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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.

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