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Determination of Illite Crystallite Thickness Distributions Using X-Ray Diffraction, and the Relation of Thickness to Crystal Growth Mechanisms Using Mudmaster, Galoper, and Associated Computer Programs

Eberl, D.D. (2002) Determination of illite crystallite thickness distributions using X-ray diffraction, and the relation of thickness to crystal growth mechanisms using MudMaster, GALOPER, and associated computer programs: In CMS Workshop Lectures, Vol. 11, Teaching Clay Science, A. Rule and S. Guggenheim, eds. The Clay Mineral Society, Aurora, CO, 131-142.

D. D. Eberl
D. D. Eberl
U.S. Geological Survey3215 Marine St., Suite E-127Boulder, CO
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January 01, 2002


These exercises involve determination of crystallite thickness distributions (CTDs) for illite by evaluation of X-ray diffraction (XRD) data using the MudMaster computer program. These data are used to infer crystal-growth mechanisms for the samples using the GALOPER computer program. The programs employed in this exercise, together with the instruction manuals, are available at: (or /pc_version). It is recommended that relevant sections of the instruction manuals (MudMan, p. 6-21; and GalopMan, p. 6-15) be read before the exercises below are undertaken.

Size distributions for crystallites can be measured by XRD because the widths of the XRD peaks broaden as crystallite size decreases. A detailed analysis of crystallite size is possible because the intensity function for XRD peaks can be represented as a Fourier series. Fourier analysis (a mathematical method used to determine the collection of cosine waves, differing in frequency and amplitude, that is necessary to approximate a function) of the interference function for illite yields Fourier coefficients for the various crystallite thicknesses that can then be treated according to Bertaut-Warren-Averbach (BWA) theory to yield crystallite-thickness distributions (Drits et al.,1998). These distributions are found by calculating the second derivative of a plot of the Fourier coefficients versus n, the number of illite layers in the crystallites. The interference function for an illite is found by dividing the intensity of its basal XRD peaks by the Lorentz polarization factor (Lp) and by the layer scattering intensity (G2), both of which can be calculated independently (Moore and Reynolds, 1989).

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Clay Minerals Society Workshop Lectures

Teaching clay science

Audrey C. Rule
Audrey C. Rule
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Stephen Guggenheim
Stephen Guggenheim
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Clay Minerals Society
ISBN electronic:
Publication date:
January 01, 2002




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