How stacking disorder can conceal the actual structure of micas : the case of phengites

The present study deals with how stochastic stackings of tetrahedral/octahedral phengitic sheets bearing diverse cation distributions affect diffraction signals and the structural inferences therefrom derived. The interest for such minerals is dictated by that the stability of phengite polytypes, their cation distributions and P/T conditions of crystallization are related to each other. We focus our attention on layers' probabilistic sequences that preserve the topology of the polytypes 2M1(SG: C2/c) and 3T(SG: P3112). Neutron diffraction intensities are modelled by a Monte Carlo approach and then used as artificial experimental data for conventional structure refinements that yield the occupancy factors in the fourfold (Si, Al) and sixfold (Al, Mg) coordination sites of 2M1 and 3T. The cation ordering from structure refinement tallies with the one of the "average structure" of a stochastic stacking, but it can significantly differ from those of the individual tetrahedral/octahedral sheets. For instance, sheets having ordered cation arrangements can lead to a stochastic structure which is supposed to bear a fully disordered cation partitioning according to structure refinement. This affects the configuration entropy contributions: the values obtained by conventional refinements can deviate from the correct ones up to 30 %. The analysis of the equivalent reflection intensities brings to light the anomalies hinting at the occurrence of such stacking disorder (using modelled reflections, the mean ratio between standard deviation and average intensity of symmetry equivalent reflections is ideally 0 for perfect crystal structures, but it can amount up to 6 in stochastically disordered phengites). However, taking into account the instrumental uncertainties and the deviations from ideality of actual crystals, such phenomena are very difficult to be detected experimentally.