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Rietveld Refinement of Disordered Illite-Smectite Mixed-Layer Structures by a Recursive Algorithm. I: One-Dimensional Patterns
- Kristian Ufer, Reinhard Kleeberg, Jörg Bergmann, Reiner Dohrmann
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- Journal:
- Clays and Clay Minerals / Volume 60 / Issue 5 / October 2012
- Published online by Cambridge University Press:
- 01 January 2024, pp. 507-534
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X-ray diffraction patterns of oriented mounts of clay minerals are often used in clay mineralogy for qualitative and quantitative purposes. Fequently occurring stacking defects, in particular, can be characterized by this technique. Modeling of these diffraction profiles has become an important tool in obtaining structural information about the nature of stacking order. Manual matching of calculated and observed patterns is time consuming and user dependent. Automatic refinement procedures are, therefore, desirable. An improved approach for the treatment of disordered layer structures within a Rietveld refinement is presented here. The recursive calculation of structure factors, similar to that of the simulation program DIFFaX, was introduced in the Rietveld code BGMN. Complete implementation is formulated within the interpreter language of the Rietveld code and is transparent as well as flexible. Such a method has opened the application of Rietveld refinement to patterns of oriented mounts where only basal reflections of stacking disordered structures were recorded. The DIFFaX code was used to simulate basal reflections of illite-smectite mixed layers (I-S) with different ratios of illitic and smectitic layers and with different degrees of long-range ordering (Reichweite). Rietveld refinements with these simulated patterns were used to evaluate the application of this new approach. Several I-S with different degrees of ordering were also chosen as tests for the refinement of basal reflections. The samples were prepared as standard airdried and ethylene glycol-solvated, oriented specimens. Realistic structural parameters were obtained for the composition and ordering of the I-S.
Rietveld Refinement of Disordered Illite-Smectite Mixed-Layer Structures by a Recursive Algorithm. II: Powder-Pattern Refinement and Quantitative Phase Analysis
- Kristian Ufer, Reinhard Kleeberg, Jörg Bergmann, Reiner Dohrmann
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- Journal:
- Clays and Clay Minerals / Volume 60 / Issue 5 / October 2012
- Published online by Cambridge University Press:
- 01 January 2024, pp. 535-552
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X-ray diffraction (XRD) of powdered materials is one of the most common methods used for structural characterization as well as for the quantification of mineral contents in mixtures. The application of the Rietveld method for that purpose requires structure models for each phase. The recursive calculation of structure factors was applied here to the Rietveld refinement of XRD powder patterns of illite-smectite (I-S) minerals. This approach allowed implementation of stacking disorder in structural models. Models for disordered stacking of cis-vacant and trans-vacant dioctahedral 2:1 layers as well as rotational disorder were combined with models for mixed layering of illitic and smectitic layers.
The DIFFaX code was used to simulate non-basal (hk) reflections of illites with different degrees of disorder. Rietveld refinements of these simulated patterns were used to evaluate the application of this new approach. A model describing rotational disorder (n·120° and n·60° rotations) and mixed layering of cis-vacant and trans-vacant dioctahedral layers was tested. Different starting parameters led to identical results within the ranges of standard deviations and confirmed the stability of the automatic refinement procedure. The influence on the refinement result of an incorrect choice of fixed parameters was demonstrated.
The hk model was combined with models describing the basal reflections of disordered I-S and tested on measured data. A glauconitic mineral (Urkut, Hungary), an ordered I-S (ISCz-1, a special clay in the Source Clays Repository of The Clay Minerals Society), and a dioctahedral I-S (F4, Füzérradvány, Hungary) were used as test substances. Parameters describing the mixed layering of illitic and smectitic layers were compared with the results from refinements of oriented mounts and showed good agreement. A pattern of a physical mixture of an I-S mineral and a turbostratically disordered smectite was analyzed in order to test the new approach for application in quantitative phase analysis. The quantitative Rietveld phase analysis results were found to be satisfactory.
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. 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Dillon, Robert DiSalle, Mary Domski, Alan Donagan, Paul Draper, Fred Dretske, Mircea Dumitru, Wilhelm Dupré, Gerald Dworkin, John Earman, Ellery Eells, Catherine Z. Elgin, Berent Enç, Ronald P. Endicott, Edward Erwin, John Etchemendy, C. Stephen Evans, Susan L. Feagin, Solomon Feferman, Richard Feldman, Arthur Fine, Maurice A. Finocchiaro, William FitzPatrick, Richard E. Flathman, Gvozden Flego, Richard Foley, Graeme Forbes, Rainer Forst, Malcolm R. Forster, Daniel Fouke, Patrick Francken, Samuel Freeman, Elizabeth Fricker, Miranda Fricker, Michael Friedman, Michael Fuerstein, Richard A. Fumerton, Alan Gabbey, Pieranna Garavaso, Daniel Garber, Jorge L. A. Garcia, Robert K. Garcia, Don Garrett, Philip Gasper, Gerald Gaus, Berys Gaut, Bernard Gert, Roger F. Gibson, Cody Gilmore, Carl Ginet, Alan H. Goldman, Alvin I. Goldman, Alfonso Gömez-Lobo, Lenn E. Goodman, Robert M. Gordon, Stefan Gosepath, Jorge J. E. Gracia, Daniel W. Graham, George A. Graham, Peter J. Graham, Richard E. 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- Edited by Robert Audi, University of Notre Dame, Indiana
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- Book:
- The Cambridge Dictionary of Philosophy
- Published online:
- 05 August 2015
- Print publication:
- 27 April 2015, pp ix-xxx
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