Least-squares profile of randomly interstratified clay mineral structures

Abstract

A profile refinement method is described for the analysis of randomly interstratified clay mineral structures from their basal 00l reflections. The basis of the technique is similar to that of Rietveld refinement, allowing least-squares estimation of the variable parameters in the model, but a more elaborate calculation of the diffraction pattern is used including explicitly the effects of disorder and small particle size, via the analytical approximation of Wright [Clays Clay Miner. (1975), 23, 278–288] for random interstratification. The method allows the determination of the spacing and relative amount of each interlayer type, together with other information such as atomic z coordinates, site occupancies and the coherently diffracting domain size. Two examples are used as illustrations, a hydrated calcium montmorillonite and an interstratified illite–smectite soil clay. In both cases the results are shown to be an improvement on those previously obtained from the same diffraction patterns by more conventional methods. Although designed primarily for use in clay mineralogy, the method may also have applications in studies of other disordered systems such as graphite intercalation compounds and liquid crystals.