Open AccessTOPOLOGICAL LOCALISATION OF DEFECTS AT ATOMIC SCALE
Author(s) -
JeanPaul Jernot,
Patricia Jouannot-Chesney,
Christian Lantuéjoul,
G. Nouet,
P. Ruterana
Publication year - 2011
Publication title -
image analysis and stereology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.237
H-Index - 27
eISSN - 1854-5165
pISSN - 1580-3139
DOI - 10.5566/ias.v21.p191-198
Subject(s) - tessellation (computer graphics) , partition (number theory) , euler characteristic , topology (electrical circuits) , neighbourhood (mathematics) , mathematics , space (punctuation) , euler's formula , geometry , computer science , mathematical analysis , combinatorics , operating system
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