Coincidences of a Shifted Hexagonal Lattice and the Hexagonal Packing

• Authors: J. Arias , E. Gabinete , M. Loquias
• Languages of publication: EN

Abstracts

EN

A geometric study of twin and grain boundaries in crystals and quasicrystals is achieved via coincidence site lattices and coincidence site modules, respectively. Recently, coincidences of shifted lattices and multilattices (i.e. finite unions of shifted copies of a lattice) have been investigated. Here, we solve the coincidence problem for a shifted hexagonal lattice. This result allows us to analyze the coincidence isometries of the hexagonal packing by viewing the hexagonal packing as a multilattice.

Keywords

EN

61.50.Ah; 61.44.Br

Discipline

• 61.50.Ah: Theory of crystal structure, crystal symmetry; calculations and modeling
• 61.44.Br: Quasicrystals

• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 126
• Issue: 2
• Pages: 516-519

Dates

published

2014-08

Contributors

author

J. Arias

• Institute of Mathematics, University of the Philippines Diliman, C.P. Garcia St., UP Campus Diliman, 1101 Quezon City, Philippines

author

E. Gabinete

• Institute of Mathematics, University of the Philippines Diliman, C.P. Garcia St., UP Campus Diliman, 1101 Quezon City, Philippines

author

M. Loquias

• Institute of Mathematics, University of the Philippines Diliman, C.P. Garcia St., UP Campus Diliman, 1101 Quezon City, Philippines

References

• [1] W. Bollmann, Crystal Defects and Crystalline Interfaces, Springer, Berlin 1970, doi: 10.1007/978-3-642-49173-3
• [2] H. Grimmer, W. Bollmann, D.H. Warrington, Acta Crystallogr. A 30, 197 (1974), doi: 10.1107/S056773947400043X
• [3] D.H. Warrington, Mater. Sci. Forum 126-128, 57 (1993), doi: 10.4028/www.scientific.net/MSF.126-128.57
• [4] M. Baake, in: The Mathematics of Long-Range Aperiodic Order, (rev. version) Ed. R.V. Moody, Kluwer, Dordrecht 1997, p. 9 http://arxiv.org/abs/math/0605222
• [5] M.J.C. Loquias, P. Zeiner, J. Phys., Conf. Ser. 226, 012026 (2010), doi: 10.1088/1742-6596/226/1/012026
• [6] M.J.C. Loquias, P. Zeiner, preprint. http://arxiv.org/abs/1301.3689
• [7] M. Pitteri, G. Zanzotto, Acta Crystallogr. A 54, 359 (1998), doi: 10.1107/S010876739701667X
• [8] G.H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers, 6th ed., Oxford University Press, Oxford 2008
• [9] P.A.B. Pleasants, M. Baake, J. Roth, J. Math. Phys. 37, 1029 (1996), doi: 10.1063/1.531424
• [10] M. Baake, U. Grimm, Z. Kristallogr. 221, 571 (2006), doi: 10.1524/zkri.2006.221.8.571
• [11] E.D. Gabinete, M.Sc. Thesis, University of the Philippines Diliman, Quezon City 2013
• [12] J.C.H. Arias, M.J.C. Loquias, in preparation

Identifiers

DOI

10.12693/APhysPolA.126.516