Estimating the similarity measure of crystal lattices by coordinates of their nodes in three-dimensional space
A.V. Kupriyanov, D.V. Kirsh

Full text of article: Russian language.

Abstract:
In presented paper the problem of determining the similarity measure of crystal lattices in three-dimensional space is considered. The description the developed method is presented. The algorithm is based on determining the six basic parameters of elementary cell for each of the comparable pair of lattices and calculating the corresponding metrics of similarity. By using this method, an experiment on mass comparison of the crystal lattices of all systems is carried out and the analysis of derived results is fulfilled.

Key words:
crystal lattice, Bravais cell, translational vectors, basic parameters of elementary cell, similarity measure.

References:

  1. Physical encyclopedia in 5 volumes / edited by A.M. Prochorova at al. – Moscow: “Soviet encyclopedia Publisher”, 1988. – (in Russian).
  2. Kupriyanov, A.V. Texture analysis and identification of the crystal lattice type upon the nanoscale images / A.V. Kupriyanov // Computer Optics. – 2011. – V. 35, ¹ 3. – P. 128-135. – (in Russian).
  3. Soifer, V.A. Analysis and recognition of the nanoscale images: conventional approach and novel problem statement / V.A. Soifer, A.V. Kupriyanov // Computer Optics. – 2011. – V. 35, ¹ 2. – P. 136-144. – (in Russian).
  4. Brandon, D Microstructure of materials. Methods of research and monitoring / D. Brandon, U. Kaplan. – Ìoscow: “Technosphere Publisher”, 2004. – 384 p. – (in Russian).
  5. Hammond, C. The Basic of Crystallography and Diffraction. Third Edition / C. Hammond. – Oxford University Press Inc., 2009. – 449 p.
  6. Egerton, R. Physical Principles of Electron Microscopy/ Ray F. Egerton – Ìoscow: “Tehnosfera Publisher”, 2010. – 304 p. – (in Russian).
  7. Hernandez, Y. Aberration-corrected HRTEM image of a graphene monolayer obtained by exfoliation of graphite in liquid phase / Y. Hernandez, V. Nicolosi [et al.] // Nature Nanotechnology. – 2008. – N. 3(9). – P. 563-568.
  8. Kessler, E.G. Precision Comparison of the Lattice Parameters of Silicon Monocrystals / E.G. Kessler, A. Henins, R.D. Deslattes, L. Nielsen, M. Arif // Journal of Research of the National Institute of Standards and Technology. – 1994. – Vol. 99, ¹1. – P. 1-18.
  9. Smith, William F. Foundations of Materials Science and Engineering / William F. Smith // McGraw-Hill Education, 2004. – 864 p.
  10. Patera, J. Centered cubic lattice method comparison / J. Patera, V. Skala // Proceedings of Algoritmy. – 2005. – P. 309-319.
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