Generating functions for stoichiometry and structure of single- and double-layer sheet-silicates. (1st December 2015)

• Record Type: Journal Article
• Authors: Hawthorne, Frank
• Is Part Of: Mineralogical magazine. Volume 79:Number 7(2015)
• Page Start: 1675
• Page End: 1709
• Publication Date: 2015-12-01
• Subjects: Mineralogy -- Periodicals; Mineralogy -- Great Britain -- Periodicals; 549.05
• DOI: 10.1180/minmag.2015.079.7.17
• Languages: English
• ISSNs: 0026-461X

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)1 and (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 topology of 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 two single-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 functions with 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.