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Generating functions for stoichiometry and structure of single- and double-layer sheet-silicates

Part of: Foundations in mineralogy and crystallography

Published online by Cambridge University Press:  02 January 2018

Frank C. Hawthorne
Frank C. Hawthorne*
Affiliation:
Department of Geological Sciences, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
*
*E-mail: frank_hawthorne@umanitoba.ca
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Abstract

Two-dimensional nets may be used to generate the stoichiometry and structure of single-layer and double-layer sheet-silicate minerals. Many sheet-silicate minerals are based on the 3-connected plane nets 63, 4.82, (4.6.8)2(6.82)1and (52.8)1(5.82)1, and some more complicated nets, e.g. (5.6.7)4(5.72)1(62.7)1, (4.122)2(42.12)1, (52.8)1(5.62)1(5.6.8)2(62.8)1,have one or two representative structures. Many complicated sheet-silicate minerals are based on sheets of 2-, 3- and 4-connected tetrahedra that may be developed from 3- and 4-connected plane nets by a series of oikodoméic operations on 3- or 4-connected nets that change the topologyof the parent net. There are three classes of oikodoméic operations: (1) insertion of 2- and 3-connected vertices into 3- and 4-connected plane nets; (2,3) replication of single-layer sheets by topological mirror or two-fold-rotation operators, and condensation of the resulting twosingle-layer sheets to form double-layer sheets. The topological aspects of these sheet structures may be described by functions that express stoichiometry in terms of tetrahedron connectivities (formula-generating functions) and functions that associate these formula-generating functionswith specific two-dimensional nets. Using these functions, we may generate formulae and structural arrangements of single-layer and double-layer silicate structures with specific local and long-range topological features.

Keywords

sheet-silicate mineralsbond topologyformula-generating functionstructure connectivitystructure-generating functionstructure prediction
Type
Frontiers in Theoretical Mineralogy
Information
Mineralogical Magazine , Volume 79 , Issue 7 , December 2015 , pp. 1675 - 1709
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2015

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