Knight, K.S. (2022) Crystallographic parameterisation of distortions in the SOD framework in the sodalite and helvine groups: an analysis in condensed normal modes of an aristotype phase. Mineralogical Magazine, 86 (1). pp. 87-102. ISSN 0026-461X
Abstract
Crystallographic distortions in the alternating aluminium and silicon tetrahedral framework of sodalite (Na8Al6Si6O24Cl2), and beryllium and silicon in helvine (Mn8Be6Si6O24S2), (framework designated SOD) are described in terms of a set of condensed normal mode amplitudes and phases derived from an ideal tetrahedron of a theoretical aristotype phase. For a sodalite-structured hettotype phase in space group P43n, these normal modes transform as the irreducible representations A1, E(α) and T1(z) of point-group 43m, where to a good approximation A1 acts as a pure breathing mode, E(α) as a polyhedral distortive mode and T1(z) as a rigid unit rotation about the unique 4 axis of the T-site under consideration. Parameterisation of the mode amplitudes in terms of low-order polynomials as a function of thermodynamic variable permits the crystal structure of sodalite-structured phases to be accurately interpolated at intermediate values of the thermodynamic variable. Published data for the high-temperature behaviour of sodalite have been re-analysed in terms of mode amplitudes which accurately reproduce the temperature dependence of the bond lengths, bond angles and the Al–O–Si inter-polyhedral angle. Full expressions for these derived structural parameters in terms of mode amplitudes and the lattice parameter are tabulated and agree with experimental results to within one estimated standard deviation of the experimental parameter. The potential for mode decomposition in lower symmetry SOD framework crystal structures is illustrated by deriving an aristotype structure for tugtupite (Na8Al2Be2Si8O24Cl2) at room temperature in space group I4.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s), 2022. Published by Cambridge University Press on behalf of The Mineralogical Society of Great Britain and Ireland. This is an author produced version of a paper subsequently published in Mineralogical Magazine. Article available under the terms of the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | sodalite; danalite; SOD framework; crystal structure; mode decomposition |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Materials Science and Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 18 Mar 2022 14:54 |
Last Modified: | 13 Jul 2022 00:14 |
Status: | Published |
Publisher: | Mineralogical Society |
Refereed: | Yes |
Identification Number: | 10.1180/mgm.2022.4 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:184907 |