International audienceThe present study aims primarily at refining a structure model for interlayer cations and H2O molecules in tri-hydrated (3W) smectite (d(001) = 18-19 angstrom). The <2 mu m fraction of the SWy-2 source clay (low-charge montmorillonite) was saturated by Mg2+, Ca2+, Ba2+, or Na cations, before collection of X-ray diffraction (XRD) patterns at 98% relative humidity. Experimental d(001) values derived for the essentially homogeneous 3W hydrates provided volume constraints for Grand Canonical Monte Carlo (GCMC) simulations. Computed atomic density distribution of interlayer species were used in turn to calculate XRD intensities of 00l reflections. The agreement between calculated and experimental 00l intensities allowed val...