An empirical Scherrer equation for weakly swelling mixed-layer minerals, especially illite-smectite
The Scherrer equation links the measured width of an X-ray diffraction peak (Scherrer width, SW) to the number of stacked cells (N) in the direction normal to the diffracting planes. The formula is only valid for one d-value occurring in the coherently diffracting domain. This equation can be modified for weakly swelling mixed-layer minerals. This assumes that the peak broadening caused by the mixed-layering is proportional to the amount of swelling component (S) and that the effects of size and mixed-layering are additive. If two SW can be measured on XRD patterns from samples treated in two different ways (such as air dried or glycolated), N and S can be determined. This equation is applicable to illite-smectite mixed-layer minerals with high illitic content. The results are most accurate for N >30. The use of Scherrer's equation is discussed.
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