Topological classification of defects in crystals |
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| Affiliation: | 1. School of Nuclear Technology and Chemistry & Biology, Hubei University of Science and Technology, Xianning 437100, China;2. Department of Energy Materials and Technology, General Research Institute for Nonferrous Metals, Beijing, China;3. Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong SAR, China;4. School of Materials Science and Engineering, Nanchang University, Nanchang, Jiangxi 330031, China;1. The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark;2. IMAPP, Radboud University, Nijmegen, PO Box 9010, the Netherlands;3. The M. Smoluchowski Institute of Physics, Jagiellonian University, Lojasiewicza 11, PL 30-348, Krakow, Poland |
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| Abstract: | Here we review the topological approach to the classification of defects in crystals, which are deviations from crystallinity. First, we illustrate this approach using the simpler case of dislocations. We show how the fact that dislocations are completely characterized by their Burgers vectors only, is related via topological considerations to the fact that a perfect crystal is exactly reproduced by translations through a lattice vector. Later, we present the developments of the French school and that of Rogula, comparing and contrasting them. These are attempts to generalize the above idea to include consideration of other transformations that leave a perfect crystal invariant. Finally, we discuss briefly some of the problems that still remain with this approach. |
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