Appendix: Tables for the determination of d in Å from 2θ° for the Kᾱ and Kβ radiations of copper, cobalt and iron
G. Brown, 1980. "Appendix: Tables for the determination of d in Å from 2θ° for the Kᾱ and Kβ radiations of copper, cobalt and iron", Crystal Structures of Clay Minerals and their X-Ray Identification, G. W. Brindley, G. Brown
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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 Kα1, Kα2 doublet is rarely resolved. By contrast, corresponding to the stronger Kα reflections, weak reflections arising from Kβ radiation are not uncommon, especially if, as sugggested (Chapter 5, Section 3.2), thin β-filters are used.
Figures & Tables
In the years 1930—1950 clay mineral identification involved mainly a combination of X-ray powder diffraction and chemical analysis with some assistance from other techniques, notably differential thermal analysis. In the period 1950—1970 additional procedures have emerged including infrared analysis, electron optical methods and a variety of thermal methods. These procedures are now treated in other monographs sponsored by the Mineralogical Society and in many other publications. Despite the availability of other techniques, X-ray diffraction remains a basic tool for studying minerals and we hope that this monograph will continue to serve, as did the previous editions, both those concerned with the more academic aspects of clay mineralogy and also those, such as geologists, civil engineers and soil scientists, for whom identification and quantitative estimation of the minerals in natural clayey materials is a practical requirement.