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 n ormal to the diffracting planes. The formula is only valid for one d-value occurring in the coherently diffracting domain. This equation can be modifi ed for weakly swelling mixed-layer minerals. This assumes that the peak bro adening caused by the mixed-layering is proportional to the amount of swell ing component (S) and that the effects of size and mixed-layering are addit ive. If two SW can be measured on XRD patterns from samples treated in two diffe rent ways (such as air dried or glycolated), N and S can be determined. Thi s equation is applicable to illite-smectite mixed-layer minerals with high illitic content. The results are most accurate for N>30. The use of Scherre r's equation is discussed.