Abstract
It has been suggested that interstratified illite-smectite (I-S) minerals are composed of aggregates of fundamental particles. Many attempts have been made to measure the thickness of such fundamental particles, but each of the methods used suffers from its own limitations and uncertainties. Small-angle X-ray scattering (SAXS) can be used to measure the thickness of particles that scatter X-rays coherently. We used SAXS to study suspensions of Na-rectorite and other illites with varying proportions of smectite. The scattering intensity (I) was recorded as a function of the scattering vector, q = (4 π/λ) sin(θ/2), where λ is the X-ray wavelength and θ is the scattering angle. The experimental data were treated with a direct Fourier transform to obtain the pair distance distribution function (PDDF) that was then used to determine the thickness of illite particles. The Guinier and Porod extrapolations were used to obtain the scattering intensity beyond the experimental q, and the effects of such extrapolations on the PDDF were examined. The thickness of independent rectorite particles (used as a reference mineral) is 18.3 Å. The SAXS results are compared with those obtained by X-ray diffraction peak broadening methods. It was found that the power-law exponent (α) obtained by fitting the data in the region of q = 0.1–0.6 nm−1 to the power law (I = I0q−α) is a linear function of illite particle thickness. Therefore, illite particle thickness could be predicted by the linear relationship as long as the thickness is within the limit where α <4.0.
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References
Ando, H. and Konishi, T. (2000) Structure analysis of regenerated cellulose hydrogels by small-angle and ultra-small-angle X-ray scattering. Physical Review E, 62, Part B, 727–733.
Bradley, W.F. (1950) The alternating layer sequence of rectorite. American Mineralogist, 35, 590–595.
Carlson, R.D. and Schmidt, P.W. (1969) Tests of a Hankel transform method of determining electron densities of long cylinders from small angle X-ray scattering data. Journal of Applied Crystallography, 2, 297–300.
Dékány, I., Szekeres, M., Marosi, T., Balázs, J. and Tombácz, E. (1994) Interaction between ionic surfactants and soil colloids: adsorption, wetting and structural properties. Progress in Colloid & Polymer Science, 95, 73–90.
Dékány, I., Turi, L., Fonseca, A. and Nagy, J.B. (1999) The structure of acid treated speiolites: small-angle X-ray scattering and multi MAS-NMR investigations. Applied Clay Science, 14, 141–160.
Drits, V.A., Środoń, J. and Eberl, D.D. (1997) XRD measurement of mean thickness of illite/smectite; reappraisal of the Kübler index and the Scherrer equation. Clays and Clay Minerals, 45, 461–475.
Drits, V.A., Eberl, D.D. and Środoń, J. (1998) XRD measurement of mean thickness, thickness distribution and strain for illite and illite-smectite crystallites by the Bertaut-Warren-Averbach technique. Clays and Clay Minerals, 46, 38–50.
Dudek, T., Środoń, J., Eberl, D.D., Elsass, F. and Uhlik, P. (2002) Thickness distribution of illite crystals in shales. I: X-ray diffraction vs. high-resolution transmission electron microscopy measurements. Clays and Clay Minerals, 50, 562–577.
Eberl, D.D., Środoń, J., Lee, M., Nadeau, P.H. and Northrop, H.R. (1987) Sericite from the Silverton caldera, Colorado: Correlation among structure, composition, origin, and particle thickness. American Mineralogist, 72, 914–934.
Eberl, D.D., Drits, V.A., Środoń, J. and Nüesch, R. (1996) MudMaster: A program for calculating crystallite size distributions and strain from the shapes of X-ray diffraction peaks. US Geological Survey Open File Report 96–171, 44 pp.
Eberl, D.D., Nuesch, R., Šuchá, V. and Tsipursky, S. (1998) Measurement of fundamental illite particle thicknesses by X-ray diffraction using PVP-10 intercalation. Clays and Clay Minerals, 46, 89–97.
Glatter, O. (1982) Data treatment and interpretation. Pp. 119–196 in: Small-Angle X-ray Scattering (O. Glatter and O. Kratky, editors). Academic Press, New York.
Glatter, O. (1995) Modern methods of data analysis in small-angle scattering and light scattering. Pp. 107–180 in: Modern Aspects of Small-Angle Scattering (H. Brumberger, editor). Proceedings of the NATO Advanced Study Institutes, Como, Italy, May 1993, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Henderson, G.V. (1970) The origin of pyrophyllite rectorite in shales of north central Utah. Clays and Clay Minerals, 18, 239–246.
Jaboyedoff, M, Kübler, B. and Thélin, Ph. (1999) An empirical Scherrer equation for weakly swelling mixed-layer minerals, especially illite-smectite. Clay Minerals, 34, 601–617.
Jaboyedoff, M., Kübler, B., Sartori, M. and Thélin, Ph. (2000) Basis for meaningful illite crystallinity measurements: an example from the Swiss PreAlps. Schweizerische Mineralogische und Petrographisches Mitteilungen, 80, 75–83.
Jaboyedoff, M., Bussy, F., Kübler, B. and Thélin, Ph. (2001) Illite “crystallinity” revisited. Clays and Clay Minerals, 49, 156–167.
Kasama, T., Murakami, T., Kohyama, N. and Watanabe, T. (2001) Experimental mixtures of smectite and rectorite: Reinvestigation of ‘fundamental particles’ and ‘interparticle diffraction’. American Mineralogist, 86, 105–114.
Kodama, H. (1966) The nature of the component layers of rectorite. American Mineralogist, 51, 1035–1055.
Laird, D.A. and Nater, E.A. (1993) Nature of the illitic phase associated with randomly interstratified smectite/illite in soils. Clays and Clay Minerals, 41, 280–287.
Laird, D.A., Barak, P., Nater, E.A. and Dowdy, R.H. (1991) Chemistry of smectitic and illitic phases in interstratified soil smectite. Soil Science Society of America Journal, 55, 1499–1504.
Levitz, P., Lecolier, E., Mourchid, A., Delville, A. and Lyonnard, S. (2000) Liquid-solid transition of laponite suspensions at very low ionic strength: Long-range electrostatic stabilisation of anisotropic colloids. Europhysics Letters, 49, 672–677.
Lindgreen, H., Garnæs, J., Hansen, P.L., Besenbacher, F., Lægsgaard, E., Stensgarrd, I., Gould, S.A.C. and Hansma, P.K. (1991) Ultrafine particles of North sea illite/smectite clay minerals investigated by STM and AFM. American Mineralogist, 76, 1218–1222.
Morvan, M., Espinat, D., Lambard, J. and Zemb, Th. (1994) Ultrasmall- and small-angle X-ray scattering of smectite clay suspensions. Colloids and Surfaces A, 82, 193–203.
Nadeau, P.H., Wilson, M.J., McHardy, W.J. and Tait, J.M. (1984) Interstratified clays as fundamental particles. Science, 225, 923–925.
Peacor, D.R. (1998) Implications of TEM data for the concept of fundamental particles. The Canadian Mineralogist, 36, 1397–1408.
Porod, G. (1982) General theory. Pp. 17–51 in: Small-Angle X-ray Scattering (O. Glatter and O. Kratky, editors). Academic Press, New York.
Sawhney, B.L. (1989) Interstratification in layer silicates. Pp. 789–828 in: Minerals in Soil Environments (J.B. Dixon and S.B. Weed, editors). Soil Science Society of America, Madison, Wisconsin.
Schmidt, P.W. (1995) Some fundamental concepts and techniques useful in small-angle scattering studies of disordered solids. Pp. 1–56 in: Modern Aspects of Small-Angle Scattering (H. Brumberger, editor). Proceedings of the NATO Advanced Study Institutes, Como, Italy, May 1993, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Shang, C. and Rice, J.A. (2003) Invalidity in deriving inter-particle distance in clay-water systems using the experimental structure factor maximum obtained by small-angle scattering. Langmuir (submitted).
Shang, C., Rice, J.A. and Lin, J.S. (2001) Thickness and surface characteristics of colloidal 2:1 aluminosilicates using indirect Fourier transform of small-angle X-ray scattering data. Clays and Clay Minerals, 49, 277–282.
Środoń, J., Morgan, D.J., Eslinger, E.V., Eberl, D.D. and Karlinger, M.K. (1986) Chemistry of illite/smectite and end-member illite. Clays and Clay Minerals, 34, 368–378.
Środoń, J., Elsass, F., McHardy, W.J. and Morgan, D.J. (1992) Chemistry of illite-smectite inferred from TEM measurements of fundamental particles. Clay Minerals, 27, 137–158.
Uhlík, P., Šuchá, V., Elsass, F. and Čaplovičová, M. (2000) High-resolution transmission electron microscopy of mixed-layer clays dispersed in PVP-10: a new technique to distinguish detrital and authigenic illitic material. Clay Minerals, 35, 781–189.
Wignall, G.D., Lin, J.S. and Spooner, S. (1990) The reduction of parasitic scattering in small-angle X-ray scattering by three pinhole collimating system. Journal of Applied Crystallography, 23, 241–246.
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Shang, C., Rice, J.A., Eberl, D.D. et al. Measurement of Illite Particle Thickness using a Direct Fourier Transform of Small-Angle X-ray Scattering Data. Clays Clay Miner. 51, 293–300 (2003). https://doi.org/10.1346/CCMN.2003.0510305
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DOI: https://doi.org/10.1346/CCMN.2003.0510305