Enumeration of polytypes MX and MX2 through the use of the symmetry of the Zhdanov symbol

Acta Crystallographica. Section A, Foundations of Crystallography
Juan E Iglesias

Abstract

The different close-packed polytypes MX and MX2 have been enumerated for each of the possible space groups by counting the corresponding Zhdanov symbols for each space group and period of stacking, P, by the use of elementary combinatorial techniques. In special cases, simple closed formulae are obtained for these numbers as functions of P. The symmetry properties of the Zhdanov symbol have been investigated with the help of its cyclotomic representation and the two-color symmetry point group thereof. Zhdanov-like rules have been developed for MX2 polytypes. The SiC cases have been generated to P = 18 under the ;1-exclusion' rule and the possible diamond polytypes have been examined.

Citations

Apr 24, 2013·Chemphyschem : a European Journal of Chemical Physics and Physical Chemistry·Antti J Karttunen, Thomas F Fässler
Jun 1, 2016·Chemical Science·Yi Li, Jihong Yu
May 30, 2014·Physical Chemistry Chemical Physics : PCCP·Kathryn A BradleyMatthew J Rosseinsky
Apr 22, 2014·Physical Review Letters·Yu-ichiro Matsushita, Atsushi Oshiyama

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