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.