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Structure of ice Ih and ice Ic as described in the language of Delaunay simplices

Structure of ice Ih and ice Ic as described in the language of Delaunay simplices Classification of the Delaunay simplex forms is carried out for the ideal structures of ice Ih and ice Ic. Classification according to the number of edges of different length reveals six types of simplices, while classification according to the number and mutual positions of edges of the unit length (equal to the length of the hydrogen bond) reveals five types of indices. Ice Ic is composed of simplices of three types (one of which has the form of a perfect tetrahedron), ice Ih from six simplices. Degeneracy is removed in computer models of slightly distorted ice by means of insignificant shifting of water molecules from their ideal positions. This makes it possible to provide the unambiguous partition of the crystal structure into Delaunay simplices. It is found that degeneracy removal results in the appearance of Delaunay simplices of specific forms with a very small volume (Kije simplices). The shape characteristics of simplices of different types and their percentage are calculated in the large computer models of ice. In particular, the fraction of the Kije simplices is found to be about 7.5% in ice Ih. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A Foundations of Crystallography Wiley

Structure of ice Ih and ice Ic as described in the language of Delaunay simplices

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References (11)

Publisher
Wiley
Copyright
Copyright © 2011 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S0108767311034039
pmid
22011465
Publisher site
See Article on Publisher Site

Abstract

Classification of the Delaunay simplex forms is carried out for the ideal structures of ice Ih and ice Ic. Classification according to the number of edges of different length reveals six types of simplices, while classification according to the number and mutual positions of edges of the unit length (equal to the length of the hydrogen bond) reveals five types of indices. Ice Ic is composed of simplices of three types (one of which has the form of a perfect tetrahedron), ice Ih from six simplices. Degeneracy is removed in computer models of slightly distorted ice by means of insignificant shifting of water molecules from their ideal positions. This makes it possible to provide the unambiguous partition of the crystal structure into Delaunay simplices. It is found that degeneracy removal results in the appearance of Delaunay simplices of specific forms with a very small volume (Kije simplices). The shape characteristics of simplices of different types and their percentage are calculated in the large computer models of ice. In particular, the fraction of the Kije simplices is found to be about 7.5% in ice Ih.

Journal

Acta Crystallographica Section A Foundations of CrystallographyWiley

Published: Jan 1, 2011

Keywords: ;

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