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Investigation of the Interlayer Organization of Water And Ions in Smectite from the Combined Use of Diffraction Experiments and Molecular Simulations. A Review of Methodology, Applications, and Perspectives

Published online by Cambridge University Press:  01 January 2024

Eric Ferrage
Eric Ferrage*
Affiliation:
Université de Poitiers, CNRS, UMR 7285 IC2MP, Equipe Hydrasa, 5 rue Albert Turpain, Bât. B8, TSA 51106, 86073, Poitiers cedex 9, France
*
*E-mail address of corresponding author: [email protected]
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Abstract

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Investigation of the organization of interlayer water and cations in smectite is a permanent topic in clay science for environmental science, civil engineering, materials science, and industrial applications. Experimental X-ray (or neutron) diffraction methods and molecular simulations are key techniques to probe the organization of the smectite structure at a similar molecular length scale. The combination of both of these experimental and numerical methods represents a complementary approach to reveal the structural heterogeneity of real samples, design and model a wide range of smectite structures, and validate the simulation results through comparison with experimental data.

This paper first revisits establishment of the original interlayer model as developed in the 1930s for the organization of water and ions in the smectite structure using X-ray diffraction (XRD) techniques. Then, based on a simplified approach, key theoretical tools are provided to calculate XRD pattern 00l reflections for a periodic smectite structure with a wide range of interlayer compositions and organizations using conventional spreadsheet software. In addition to educational purposes, this theoretical description is used to describe the principal parameters governing the positions and intensities of experimental XRD 00l reflections. This calculation toolbox is also used to determine better the layer-to-layer distances considered in molecular simulations and to validate these simulations through a detailed collation procedure using experimental data.

Recent examples of the application of such a procedure to collate experimental diffraction data and molecular simulations are presented for the specific case of deciphering the molecular organization of interlayer water and cations in the different smectite hydrates (mono-, bi-, and tri-hydrated layers). The extension of this approach to the interlayer refinement of organo-clays is also detailed, and perspectives regarding the characterization of other lamellar compounds are discussed.

Keywords

Interlayer Ion OrganizationInterlayer Water OrganizationMolecular SimulationNeutron DiffractionSmectitesX-ray Diffraction
Type
Article
Information
Clays and Clay Minerals , Volume 64 , Issue 4 , August 2016 , pp. 348 - 373
Copyright
Copyright © The Clay Minerals Society 2016

Footnotes

This paper is published as part of a special issue on the subject of ‘Computational Molecular Modeling’. Some of the papers were presented during the 2015 Clay Minerals Society-Euroclay Conference held in Edinburgh, UK.

References

Akai, J. Nomura, N. Matsushita, S. Kudo, H. Fukuhara, H. Matsuoka, S. and Matsumoto, J., 2013 Mineralogical and geomicrobial examination of soil contamination by radioactive Cs due to 2011 Fukushima Daiichi nuclear power plant accident Physics and Chemistry of the Earth, Parts A/B/C 58–60 57–67.CrossRefGoogle Scholar
Aplin, A.C. Matenaar, I.F. McCarty, D.K. and van der Pluijm, B.A., 2006 Influence of mechanical compaction and clay mineral diagenesis on the microfabric and porescale properties of deep-water Gulf of Mexico mudstones Clays and Clay Minerals 54 500–514.CrossRefGoogle Scholar
Aristilde, L. Lanson, B. and Charlet, L., 2013 Interstratification patterns from the pH-dependent intercalation of a tetracycline antibiotic within montmorillonite layers Langmuir 29 4492–4501.CrossRefGoogle ScholarPubMed
Bailey, S.W., 1982 Nomenclature for regular interstratifications American Mineralogist 67 394–398.Google Scholar
Ben Brahim, J.B. Armagan, N. Besson, G. and Tchoubar, C., 1983 X-ray diffraction studies on the arrangement of water molecules in a smectite. I. Homogeneous two-water-layer Na-beidellite Journal of Applied Crystallography 16 264–269.CrossRefGoogle Scholar
Ben Brahim, J. Besson, G. and Tchoubar, C., 1984 Etude des profils des bandes de diffraction X dune beidellite-Na hydratée à deux couches deau. Détermination du mode dempilement des feuillets et des sites occupés par leau Journal of Applied Crystallography 17 179–188.CrossRefGoogle Scholar
Bérend, I. Cases, J.M. François, M. Uriot, J.P. Michot, L.J. Masion, A. and Thomas, F., 1995 Mechanism of adsorption and desorption of water vapour by homoionic montmorillonites: 2. The Li+, Na+, K+, Rb+ and Cs+ exchanged forms Clays and Clay Minerals 43 324–336.CrossRefGoogle Scholar
Bergmann, J. Kleeberg, R., Delhez, R. and Mittemeijer, E.J., 1998 Rietveld analysis of disordered layer silicates Proceedings of the European Powder Diffraction (EPDIC5) 300–305.CrossRefGoogle Scholar
Bethke, C.M. and Altaner, S.P., 1986 Layer-by-layer mechanism of smectite illitization and application to a new rate law Clays and Clay Minerals 34 136–145.CrossRefGoogle Scholar
Botan, A. Rotenberg, B. Marry, V. Turq, P. and Noetinger, B., 2010 Carbon dioxide in montmorillonite clay hydrates: Thermodynamics, structure, and transport from molecular simulation Journal of Physical Chemistry C 114 14962–14969.CrossRefGoogle Scholar
Bradley, W.F. Grim, R.E. and Clark, G.F., 1937 A study of the behavior of montmorillonite upon wetting Zeitschrift für Kristallographie 97 216–222.Google Scholar
Breu, J. Seidl, W. Stoll, A.J. Lange, K.G. and Probst, T.U., 2001 Charge homogeneity in synthetic fluorohectorite Chemistry of Materials 13 4213–4220.CrossRefGoogle Scholar
Brigatti, M.F. Galán, E. and Theng, B.K.G., 2006 Structure and mineralogy of clay minerals Handbook of Clay Science 1 19–86.CrossRefGoogle Scholar
Busch, A. Alles, S. Gensterblum, Y. Prinz, D. Dewhurst, D. Raven, M. Stanjek, H. and Krooss, B., 2008 Carbon dioxide storage potential of shales International Journal of Greenhouse Gas Control 2 297–308.CrossRefGoogle Scholar
Calarge, L. Lanson, B. Meunier, A. and Formoso, M.L., 2003 The smectitic minerals in a bentonite deposit from Melo (Uruguay) Clay Minerals 38 25–34.CrossRefGoogle Scholar
Cases, J.M. Bérend, I. Besson, G. François, M. Uriot, J.P. Thomas, F. and Poirier, J.E., 1992 Mechanism of adsorption and desorption of water vapor by homoionic montmorillonite. 1. The sodium-exchanged form Langmuir 8 2730–2739.CrossRefGoogle Scholar
Cases, J.M. Bérend, I. François, M. Uriot, J.P. Michot, L.J. and Thomas, F., 1997 Mechanism of adsorption and desorption of water vapor by homoionic montmorillonite: 3. The Mg2+, Ca2+, Sr2+ and Ba2+ exchanged forms Clays and Clay Minerals 45 8–22.CrossRefGoogle Scholar
Christidis, G.E. and Eberl, D.D., 2003 Determination of layer-charge characteristics of smectites Clays and Clay Minerals 51 644–655.CrossRefGoogle Scholar
Claret, F. Sakharov, B.A. Drits, V.A. Velde, B. Meunier, A. Griffault, L. and Lanson, B., 2004 Clay minerals in the Meuse-Haute Marne underground laboratory (France): Possible influence of organic matter on clay mineral evolution Clays and Clay Minerals 52 515–532.CrossRefGoogle Scholar
Cuadros, J., 1997 Interlayer cation effects on the hydration state of smectite American Journal of Science 297 829–841.CrossRefGoogle Scholar
Cygan, R.T. Liang, J. and Kalinichev, A.G., 2004 Molecular models of hydroxide, oxyhydroxide, and clay phases and the development of a general force field Journal of Physical Chemistry B 108 1255–1266.CrossRefGoogle Scholar
Cygan, R.T. Greathouse, J.A. Heinz, H. and Kalinichev, A.G., 2009 Molecular models and simulations of layered materials Journal of Materials Chemistry 19 2470–2481.CrossRefGoogle Scholar
Dazas, B. Lanson, B. Breu, J. Robert, J. Pelletier, M. and Ferrage, E., 2013 Smectite fluorination and its impact on interlayer water content and structure: A way to fine tune the hydrophilicity of clay surfaces? Microporous and Mesoporous Materials 181 233–247.CrossRefGoogle Scholar
Dazas, B. Ferrage, E. Delville, A. and Lanson, B., 2014 Interlayer structure model of tri-hydrated low-charge smectite by X-ray diffraction and Monte Carlo modeling in the grand canonical ensemble American Mineralogist 99 1724–1735.CrossRefGoogle Scholar
Dazas, B. Lanson, B. Delville, A. Robert, J. Komarneni, S. Michot, L.J. and Ferrage, E., 2015 Influence of tetrahedral layer charge on the organization of interlayer water and ions in synthetic Na-saturated smectites Journal of Physical Chemistry C 119 4158–4172.CrossRefGoogle Scholar
de la Calle, C. and Suquet, H., 1988 Vermiculite Hydrous Phyllosilicates (Exclusive Of Micas) 19 455–496.CrossRefGoogle Scholar
Delville, A., 1991 Modeling the clay-water interface Langmuir 7 547–555.CrossRefGoogle Scholar
Delville, A., 1993 Structure and properties of confined liquids: A molecular model of the clay-water interface Journal of Physical Chemistry 97 9703–97102.CrossRefGoogle Scholar
Drits, V. Srodon, J. and Eberl, D.D., 1997 XRD measurement of mean crystallite thickness of illite and illite/smectite: Reappraisal of the Kubler index and the Scherrer equation Clays and Clay Minerals 45 461–475.CrossRefGoogle Scholar
Drits, V.A. Sakharov, B.A. Lindgreen, H. and Salyn, A., 1997 Sequential structure transformation of illite-smectite-vermiculite during diagenesis of Upper Jurassic shales from the North Sea and Denmark Clay Minerals 32 351–371.CrossRefGoogle Scholar
Drits, V.A. and Tchoubar, C., 1990 X-ray Diffraction by Disordered Lamellar Structures: Theory and Applications to Microdivided Silicates and Carbons Berlin Springer-Verlag 371 pp..CrossRefGoogle Scholar
Dzene, L. Tertre, E. Hubert, F. and Ferrage, E., 2015 Nature of the sites involved in the process of cesium desorption from vermiculite Journal of Colloid and Interface Science 455 254–260.CrossRefGoogle ScholarPubMed
Ferrage, E. Lanson, B. Sakharov, B.A. and Drits, V.A., 2005 Investigation of smectite hydration properties by modeling experimental X-ray diffraction patterns: Part I. Montmorillonite hydration properties American Mineralogist 90 1358–1374.CrossRefGoogle Scholar
Ferrage, E. Lanson, B. Malikova, N. Plançon, A. Sakharov, B.A. and Drits, V.A., 2005 New insights on the distribution of interlayer water in bi-hydrated smectite from X-ray diffraction profile modeling of 00l reflections Chemistry of Materials 17 3499–3512.CrossRefGoogle Scholar
Ferrage, E. Tournassat, C. Rinnert, E. and Lanson, B., 2005 Influence of pH on the interlayer cationic composition and hydration state of Ca-montmorillonite: Analytical chemistry, chemical modelling and XRD profile modelling study Geochimica et Cosmochimica Acta 69 2797–2812.CrossRefGoogle Scholar
Ferrage, E. Lanson, B. Sakharov, B.A. Geoffroy, N. Jacquot, E. and Drits, V.A., 2007 Investigation of dioctahedral smectite hydration properties by modeling of X-ray diffraction profiles: Influence of layer charge and charge location American Mineralogist 92 1731–1743.CrossRefGoogle Scholar
Ferrage, E. Kirk, C.A. Cressey, G. and Cuadros, J., 2007 Dehydration of Ca-montmorillonite at the crystal scale. Part I: Structure evolution American Mineralogist 92 994–1006.CrossRefGoogle Scholar
Ferrage, E. Lanson, B. Michot, L.J. and Robert, J., 2010 Hydration properties and interlayer organization of water and ions in synthetic Na-smectite with tetrahedral layer charge. Part 1. Results from X-ray diffraction profile modeling Journal of Physical Chemistry C 114 4515–4526.CrossRefGoogle Scholar
Ferrage, E. Sakharov, B.A. Michot, L.J. Delville, A. Bauer, A. Lanson, B. Grangeon, S. Frapper, G. Jiménez-Ruiz, M. and Cuello, G.J., 2011 Hydration properties and interlayer organization of water and ions in synthetic Nasmectite with tetrahedral layer charge. Part 2. Toward a precise coupling between molecular simulations and diffraction data Journal of Physical Chemistry C 115 1867–1881.CrossRefGoogle Scholar
Ferrage, E. Vidal, O. Mosser-Ruck, R. Cathelineau, M. and Cuadros, J., 2011 A reinvestigation of smectite illitization in experimental hydrothermal conditions: Results from X-ray diffraction and transmission electron microscopy American Mineralogist 96 207–223.CrossRefGoogle Scholar
Fripiat, J.J. Cruz, M.I. Bohor, B.F. Thomas, J Jr, 1974 Interlamellar adsorption of carbon dioxide by smectites Clays and Clay Minerals 22 23–30.CrossRefGoogle Scholar
Gates, W.P. Bouazza, A. and Churchman, G.J., 2009 Bentonite clay keeps pollutants at bay Elements 5 105–110.CrossRefGoogle Scholar
Gieseking, J.E., 1939 The mechanism of cation exchange in the montmorillonite-beidellite-nontronite type of clay minerals Soil Science 47 1–14.CrossRefGoogle Scholar
Giesting, P. Guggenheim, S. Koster van Groos, A.F. and Busch, A., 2012 X-ray diffraction study of K- and Ca-exchanged montmorillonites in CO2 atmospheres Environmental Science and Technology 46 5623–5630.CrossRefGoogle ScholarPubMed
Giesting, P. Guggenheim, S. Koster van Groos, A.F. and Busch, A., 2012 Interaction of carbon dioxide with Na-exchanged montmorillonite at pressures to 640 bars: Implications for CO2 sequestration International Journal of Greenhouse Gas Control 8 73–81.CrossRefGoogle Scholar
Glaeser, R. and Méring, J., 1954 Isothermes dhydratation des montmorillonites bi-ioniques (Ca, Na) Clay Mineral Bulletin 2 188–193.CrossRefGoogle Scholar
Glaeser, R. and Méring, J., 1968 Domaines dhydratation des smectites Comptes-Rendus de lAcadémie des Sciences de Paris 267 463–466.Google Scholar
Glaeser, R. Mantine, I. and Méring, J., 1967 Observations sur la beidellite Bulletin du Groupe Français des Argiles 19 125–130.CrossRefGoogle Scholar
Gruner, J.W., 1932 Crystal structure of kaolinite Zeitschrift für Kristallographie 83 75–88.CrossRefGoogle Scholar
Gruner, J.W., 1934 The structures of vermiculites and their collapse by dehydration American Mineralogist 19 557–575.Google Scholar
Guinier, A., 1964 Théorie et Technique de la radiocristallographie Paris Dunod 740 pp..Google Scholar
Harris, G.L. Nicholls, P.H. Bailey, S.W. Howse, K.R. and Mason, D.J., 1994 Factors influencing the loss of pesticides in drainage from a cracking clay soil Journal of Hydrology 159 235–253.CrossRefGoogle Scholar
Heinz, H. Koerner, H. Anderson, K.L. Vaia, R.A. and Farmer, B.L., 2005 Force field for mica-type silicates and dynamics of octadecylammonium chains grafted to montmorillonite Chemistry of Materials 17 5658–5669.CrossRefGoogle Scholar
Heinz, H. Lin, T. Mishra, R. and Emami, F.S., 2013 Thermodynamically consistent force fields for the assembly of inorganic, organic, and biological nanostructures: The INTERFACE force field Langmuir 29 1754–1765.CrossRefGoogle ScholarPubMed
Hendricks, S. and Teller, E., 1942 X-ray interference in partially ordered layer lattices Journal of Chemical Physics 10 147–167.CrossRefGoogle Scholar
Hendricks, S.B. and Fry, W.H., 1930 The results of X-Ray and microscopical examinations of soil colloids Soil Science 29 457–480.CrossRefGoogle Scholar
Hendricks, S.B. and Jefferson, M.E., 1938 Structures of kaolin and talc-pyrophyllite hydrates and their bearing on water sorption of the clays American Mineralogist 23 863–875.Google Scholar
Hendricks, S.B. Nelson, R.A. and Alexander, L.T., 1940 Hydration mechanism of the clay mineral montmorillonite saturated with various cations 1 Journal of the American Chemical Society 62 1457–1464.CrossRefGoogle Scholar
Hofmann, U. and Bilke, W., 1936 Über die innerkristalline Quellung und das basenaustauschvermogen des montmorillonits Kolloid-Zeitschrift 77 238–251.CrossRefGoogle Scholar
Hofmann, U. Endell, K. and Wilm, D., 1933 Kristallstruktur und quellung von Montmorillonit (Das Tonmineral der Bentonittone) Zeitschrift für Kristallographie 86 340–348.CrossRefGoogle Scholar
Holmboe, M. Wold, S. and Jonsson, M., 2012 Porosity investigation of compacted bentonite using XRD profile modeling Journal of Contaminant Hydrology 128 19–32.CrossRefGoogle ScholarPubMed
Howard, S.A. and Preston, K.D., 1989 Profile fitting of powder diffraction patterns Modern Powder Diffraction 20 217–275.CrossRefGoogle Scholar
Hubert, F. Caner, L. Meunier, A. and Ferrage, E., 2012 Unraveling complex <2 μm clay mineralogy from soils using X-ray diffraction profile modeling on particle-size sub-fractions: Implications for soil pedogenesis and reactivity American Mineralogist 97 384–398.CrossRefGoogle Scholar
Inoue, A. Lanson, B. Marques-Fernandes, M. Sakharov, B.A. Murakami, T. Meunier, A. and Beaufort, D., 2005 Illite-smectite mixed-layer minerals in the hydrothermal alteration of volcanic rocks: I. One-dimensional XRD structure analysis and characterization of component layers Clays and Clay Minerals 53 423–439.CrossRefGoogle Scholar
Iwasaki, T. and Watanabe, T., 1988 Distribution of Ca and Na ions in dioctahedral smectites and interstratified dioctahedral mica/smectites Clays and Clay Minerals 36 73–82.CrossRefGoogle Scholar
Lanson, B., 2011 Modelling of X-ray diffraction profiles: Investigation of defective lamellar structure crystal chemistry Bulk and Surface Structures of Layer Silicates and Oxides: Theoretical Aspects and Applications 11 151–202.Google Scholar
Lanson, B. Sakharov, B.A. Claret, F. and Drits, V.A., 2009 Diagenetic smectite-to-illite transition in clay-rich sediments: A reappraisal of X-ray diffraction results using the multi-specimen method American Journal of Science 309 476–516.CrossRefGoogle Scholar
Lanson, B. Ferrage, E. Hubert, F. Prêt, D. Mareschal, L. Turpault, M. and Ranger, J., 2015 Experimental aluminization of vermiculite interlayers: An X-ray diffraction perspective on crystal chemistry and structural mechanisms Geoderma 249-250 28–39.CrossRefGoogle Scholar
Lindgreen, H. Drits, V.A. Sakharov, B.A. Jakobsen, H.J. Salyn, A.L. Dainyak, L.G. and Krøyer, H., 2002 The structure and diagenetic transformation of illite-smectite and chlorite-smectite from North Sea Cretaceous-Tertiary chalk Clay Minerals 37 429–450.CrossRefGoogle Scholar
Madsen, F.T., 1998 Clay mineralogical investigations related to nuclear waste disposal Clay Minerals 33 109–129.CrossRefGoogle Scholar
Maegdefrau, E. and Hofmann, U., 1937 Die Kristalstruktur des montmorillonits Zeitschrift für Kristallographie 98 299–323.Google Scholar
Marshall, C.E., 1935 Layer lattices and base-exchange clays Zeitschrift für Kristallographie 91 433–449.CrossRefGoogle Scholar
Martins, M.L. Gates, W.P. Michot, L. Ferrage, E. Marry, V. and Bordallo, H.N., 2014 Neutron scattering, a powerful tool to study clay minerals Applied Clay Science 96 22–35.CrossRefGoogle Scholar
McCarty, D.K. Sakharov, B.A. and Drits, V.A., 2008 Early clay diagenesis in Gulf Coast sediments: New insights from XRD profile modeling Clays and Clay Minerals 56 359–379.CrossRefGoogle Scholar
McCarty, D.K. Sakharov, B.A. and Drits, V.A., 2009 New insights into smectite illitization: A zoned K-bentonite revisited American Mineralogist 94 1653–1671.CrossRefGoogle Scholar
Méring, J., 1946 On the hydration of montmorillonite Transactions of the Faraday Society 42 B205–B219.CrossRefGoogle Scholar
Méring, J., 1949 L’interfé rence des rayons X dans les systèmes àstratification dés ordonée Acta Crystallographica 2 371–377.CrossRefGoogle Scholar
Méring, J. and Glaeser, R., 1954 Sur le rôle de la valence des cations échangeables dans la montmorillonite Bulletin de la Société Francaise de Minéralogie et Cristallographie 77 519–530.CrossRefGoogle Scholar
Michels, L. Fossum, J.O. Rozynek, Z. Hemmen, H. Rustenberg, K. Sobas, P.A. Kalantzopoulos, G.N. Knudsen, K.D. Janek, M. Plivelic, T.S. and da Silva, G.J., 2015 Intercalation and retention of carbon dioxide in a smectite clay promoted by interlayer cations Scientific Reports 5 8775.CrossRefGoogle Scholar
Michot, L.J. Ferrage, E. Jiménez-Ruiz, M. Boehm, M. and Delville, A., 2012 Anisotropic features of water and ion dynamics in synthetic Na- and Ca-smectites with tetrahedral layer charge. A combined quasi-elastic neutron-scattering and molecular dynamics simulations study Journal of Physical Chemistry C 116 16619–16633.CrossRefGoogle Scholar
Möller, M.W. Hirsemann, D. Haarmann, F. Senker, J. and Breu, J., 2010 Facile scalable synthesis of rectorites Chemistry of Materials 22 186–196.CrossRefGoogle Scholar
Moore, D.M. and Hower, J., 1986 Ordered interstratification of dehydrated and hydrated Na-smectite Clays and Clay Minerals 34 379–384.CrossRefGoogle Scholar
Moore, D.M. Reynolds, R.C. Jr., 1997 X-ray Diffraction and the Identification and Analysis of Clay Minerals New York Oxford University Press 322 pp..Google Scholar
Nagelschmidt, G., 1936 On the lattice shrinkage and structure of montmorillonite Zeitschrift für Kristallographie 93 481–487.CrossRefGoogle Scholar
Pezerat, H., 1967 Recherches sur la position des cations échangeables et de l’eau dans les montmorillonites Comptes-Rendus de lAcadémie des Sciences de Paris 265 529–532.Google Scholar
Pezerat, H. and Méring, J., 1958 Dé tection des cations échangeable de la montmorillonite par l’emploi des séries diffé rences Bulletin du Groupe Français des Argiles 10 25–26.CrossRefGoogle Scholar
Prêt, D. Ferrage, E. Tertre, E. Pelletier, M. Robinet, J.C. Faurel, M. Bihannic, I. and Hubert, F., 2013 X-ray tomography and impregnation methods to analyze pore space heterogeneities at the hydrated state Proceeding of the Workshop of the Nuclear Energy Agency Clayclub Clay Characterisation from Nanoscopic to Microscopic Resolution Karlsruhe NEA/RWM/CLAYCLUB, OECD-NEA Press 75–83.Google Scholar
Reynolds, R.C. Jr., 1965 An X-ray study of ethylene glycolmontmorillonite complex American Mineralogist 50 990, 1001.Google Scholar
Reynolds, R.C. Jr., 1967 Interstratified clay systems: Calculation of the total one-dimensional diffraction function American Mineralogist 52 661–672.Google Scholar
Reynolds, R.C. Jr., 1968 The effect of particle size on apparent lattice spacings Acta Crystallographica Section A 24 319–320.CrossRefGoogle Scholar
Reynolds, R.C. Jr., 1985 NEWMOD: A Computer Program for the Calculation of One-Dimensional Patterns of Mixed-Layered Clays Hanover, NH RC Reynolds.Google Scholar
Reynolds, R.C. Jr., 1986 The Lorentz-polarization factor and preferred orientation in oriented clay aggregates Clays and Clay Minerals 34 359–367.CrossRefGoogle Scholar
Reynolds, R.C. Jr., 1989 Diffraction by small and disordered crystals Modern Powder Diffraction 20 145–182.CrossRefGoogle Scholar
Ross, M., 1968 X-ray diffraction effects by non-ideal crystals of biotite, muscovite, montmorillonite, mixed-layer clays, graphite, and periclase Zeitschrift für Kristallographie 126 80–97.CrossRefGoogle Scholar
Sakharov, B.A. and Drits, V.A., 1973 Mixed-layer kaolinite-montmorillonite: A comparison of observed and calculated diffraction patterns Clays and Clay Minerals 21 15–17.CrossRefGoogle Scholar
Sakharov, B.A. and Lanson, B., 2013 X-ray identification of mixed-layer structures. Modelling of diffraction effects Handbook of Clay Science. Developments in Clay, 2nd ed. Part B: Techniques and Applications 5B 51–135.CrossRefGoogle Scholar
Sakharov, B.A. Naumov, A.S. and Drits, V.A., 1982 X-ray diffraction by mixed-layer structures with random distribution of stacking faults Doklady Akademii Nauk SSSR 265 339–343.Google Scholar
Sakharov, B.A. Naumov, A.S. and Drits, V.A., 1982 X-ray intensities scattered by layer structure with short range ordering parameters S>1 and G>1 Doklady Akademii Nauk SSSR 265 871–874.Google Scholar
Sakharov, B.A. Lindgreen, H. Salyn, A. and Drits, V.A., 1999 Determination of illite-smectite structures using multispecimen X-ray diffraction profile fitting Clays and Clay Minerals 47 555–566.CrossRefGoogle Scholar
Sato, T. Watanabe, T. and Otsuka, R., 1992 Effects of layer charge, charge location, and energy change on expansion properties of dioctahedral smectites Clays and Clay Minerals 40 103–113.CrossRefGoogle Scholar
Sato, T. Murakami, T. and Watanabe, T., 1996 Change in layer charge of smectites and smectite layers in illite/smectite during diagenetic alteration Clays and Clay Minerals 44 460–469.CrossRefGoogle Scholar
Shashikala, H.D. Suryanarayana, S.V. and Nagender Naidu, S.V., 1993 Debye temperature and mean-square amplitudes of vibration of Ti3Al alloys Journal of Applied Crystallography 26 602–605.CrossRefGoogle Scholar
Skipper, N.T. Refson, K. and McConnell, J.D.C., 1989 Computer calculation of water-clay interactions using atomic pair potentials Clay Minerals 24 411–425.CrossRefGoogle Scholar
Skipper, N.T. Refson, K. and McConnell, J.D.C., 1991 Computer simulation of interlayer water in 2:1 clays Journal of Chemical Physics 94 7434–7445.CrossRefGoogle Scholar
Skipper, N.T. Chang, F.R.C. and Sposito, G., 1995 Monte Carlo simulation of interlayer molecular structure in swelling clay minerals. 1. Methodology Clays and Clay Minerals 43 285–293.CrossRefGoogle Scholar
Smith, D.E., 1998 Molecular computer simulations of the swelling properties and interlayer structure of cesium montmorillonite Langmuir 14 5959–5967.CrossRefGoogle Scholar
Stanjek, H., 2002 XRD peak migration and apparent shift of cell-edge lengths of nano-sized hematite, goethite and lepidocrocite Clay Minerals 37 629–638.CrossRefGoogle Scholar
Striolo, A., 2011 From interfacial water to macroscopic observables: A review Adsorption Science & Technology 29 211–258.CrossRefGoogle Scholar
Suquet, H. and Pezerat, H., 1987 Parameters influencing layer stacking types in saponite and vermiculite: A review Clays and Clay Minerals 35 353–362.CrossRefGoogle Scholar
Szczerba, M. Klapyta, Z. and Kalinichev, A., 2014 Ethylene glycol intercalation in smectites. Molecular dynamics simulation studies Applied Clay Science 91 87–97.CrossRefGoogle Scholar
Tertre, E. Prêt, D. and Ferrage, E., 2011 Influence of the ionic strength and solid/solution ratio on Ca(II)-for-Na+ exchange on montmorillonite. Part 1: Chemical measurements, thermodynamic modeling and potential implications for trace elements geochemistry Journal of Colloid and Interface Science 353 248–256.CrossRefGoogle ScholarPubMed
Tertre, E. Prêt, D. and Ferrage, E., 2011 Influence of the ionic strength and solid/solution ratio on Ca(II)-for-Na+ exchange on montmorillonite. Part 2: Understanding the effect of the m/V ratio. Implications for pore water composition and element transport in natural media Journal of Colloid and Interface Science 363 334–347.CrossRefGoogle Scholar
Tessier, D. Bouzigues, B. Favrot, J.C. and Valles, V., 1992 Influence of decimetric microrelief on clay texture evolution of hydromorphic soils of the Garonne River-differentiation of vertic and prismatic structures Comptes Rendus de l’Académie des sciences Paris Série II 315 1027–1032.Google Scholar
Trunz, V., 1976 Influence of crystallite size on apparent basal spacing of kaolinite Clays and Clay Minerals 24 84–87.CrossRefGoogle Scholar
Ufer, K. Kleeberg, R. Bergmann, J. and Dohrmann, R., 2012 Rietveld refinement of disordered illite-smectite mixed-layer structures by a recursive algorithm. I. One-dimensional patterns Clays and Clay Minerals 60 507–534.CrossRefGoogle Scholar
Vasseur, G. Djeran-Maigre, I. Grunberger, D. Rousset, G. Tessier, D. and Velde, B., 1995 Evolution of structural and physical parameters of clays during experimental compaction Marine and Petroleum Geology 12 941–954.CrossRefGoogle Scholar
Viennet, J. Hubert, F. Ferrage, E. Tertre, E. Legout, A. and Turpault, M., 2015 Investigation of clay mineralogy in a temperate acidic soil of a forest using X-ray diffraction profile modeling: Beyond the HIS and HIV description Geoderma 241-242 75–86.CrossRefGoogle Scholar
Waasmaier, D. and Kirfel, A., 1995 New analytical scattering-factor functions for free atoms and ions Acta Crystallographica Section A 51 416–431.CrossRefGoogle Scholar
Yang, N. and Yang, X., 2011 Molecular simulation of swelling and structure for Na-Wyoming montmorillonite in supercritical CO2 Molecular Simulation 37 1063–1070.CrossRefGoogle Scholar