X-Ray Diffraction by Disordered Lamellar Structures

Abstract

Saying that X-ray diffraction reveals the atomic structure of solids would be commonplace if one were not to add that two types of problems are involved, each requiring its own method of approach. It is possible to obtain, from a "proper", isolated crystal of adequate size, a diffraction pattern yielding the atomic structure unambiguously, even if the number of atoms in the lattice is large. The problem can be considered as solved, as witnessed by the importance of its results in chemistry, biology, etc. A different matter is that of imperfect crystals, in which the periodicity of the atomic positions is only partial, or even approximate. The difficulty is further compounded by the fact that, in general, only microcrystalline and poorly oriented powders are on hand. The experimental data are then insufficient for a complete determination of the structure at the atomic level since X-ray diffraction is not equivalent to a microscope with a resolution of the order of the atomic diameters, enabling us to "see" the structure. What could then be the maximum information to be drawn from the experimental determinations? The answer to this question is provided by the authors for lamellar solids, a very numerous class of imperfect crystals, of which clays are the best known example. The method consists in calculating the diffraction pattern of a model drawn up using all the available information on the sample, then in adjusting arbitrarily chosen parameters to obtain the best fit with the experimental data. The corresponding structure is thus a possible structure, it may even be the likely one, but it has not been proved to be the actual true structure.