| Reference Type | Journal (article/letter/editorial) |
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| Title | Generating functions for stoichiometry and structure of single- and double-layer sheet-silicates |
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| Journal | Mineralogical Magazine |
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| Authors | Hawthorne, Frank C. | Author |
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| Year | 2015 (December) | Volume | 79 |
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| Issue | 7 |
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| Publisher | Mineralogical Society |
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| DOI | doi:10.1180/minmag.2015.079.7.17Search in ResearchGate |
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| Generate Citation Formats |
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| Mindat Ref. ID | 244753 | Long-form Identifier | mindat:1:5:244753:1 |
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| GUID | 0 |
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| Full Reference | Hawthorne, Frank C. (2015) Generating functions for stoichiometry and structure of single- and double-layer sheet-silicates. Mineralogical Magazine, 79 (7) 1675-1709 doi:10.1180/minmag.2015.079.7.17 |
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| Plain Text | Hawthorne, Frank C. (2015) Generating functions for stoichiometry and structure of single- and double-layer sheet-silicates. Mineralogical Magazine, 79 (7) 1675-1709 doi:10.1180/minmag.2015.079.7.17 |
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| Abstract/Notes | AbstractTwo-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. |
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