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POWDER diffraction patterns are almost always reported and compared in terms of the interplanar spacings, d, represented by the intensity maxima. In practice, d is obtained from the diffraction angle, θ, which is half the angle between the incident and diffracted rays, by means of the Bragg relationship


where λ is the wavelength of the radiation. The relation between these d-spacings and lattice spacings is discussed in Chapter 5, Section 3.7. Symmetrical reflection powder diffractometers are the instruments most widely used for examining clays by X-ray diffraction and they are usually calibrated in terms of 2θ rather than θ. To convert observed values of 2θ to d spacings it is convenient to have available solutions of the Bragg equation for radiations that are commonly used over the angular range normally encountered.

A number of compilations already exist in graphical or tabular form but these are either unnecessarily elaborate or too limited to be convenient for day-to-day use in studies of clays and related materials. Reflections with d spacings less than 1 Å are usually weak or absent in diffraction patterns of clays and when present they are of little value for identification. Because of structural defects and small crystal size, reflections from clays are usually broader than those obtained from materials such as quartz or feldspars and as a result the 1, 2 doublet is rarely resolved. By contrast, corresponding to the stronger reflections, weak reflections arising from radiation are not uncommon, especially if, as sugggested (Chapter 5, Section 3.2), thin β-filters are used.

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