This study attempted to quantify the interstratificational broadening of the randomly interstratified illite/smectite (random I∕S) basal reflection and to evaluate the percentage of the interstratified illite layers (%I) from the result. The interstratificational broadening was quantified using the distributional discrepancy (D) defined as D=[∑t∣ft(obs)−ft(ref)∣]∕2, where ft(obs) is the frequency of a crystallite containing thickness, t (the number of layers), measured from a basal reflection broadened by interstratifications, and ft(ref) is the frequency for a basal reflection with no interstratificational broadening. The basal reflections at 5.2° 2θ under glycolation and 8.84° 2θ under thermal dehydration provided the ft(obs) and ft(ref) of random I∕S. The linear relation, D=2.17%I+2.49(0⩽%I⩽30), was obtained from simulations for SWy-2 (Wyoming, USA).
