In this investigation we create a variety of dioctahedral, interlayer (cation)-deficient mica clay mineral models of the 1M-illite series, using the ab initio method of density functional theory (DFT), employing plane waves, pseudo potentials, and super cells. The structures we create are modelled on an average formula of illite such as (Ca0.059, K0.655)(Si3.597, Al0.403)(Fe0.628, Al0.969,Mg0.428)O10(OH)2, as well as existing crystal structures and experimental data. This study investigates the relative positions of both octahedral and tetrahedral cation substitutions (e.g. Fe3+ for Al3+ and Al3+ for Si4+) in both trans- and cis-vacant structures. The purpose of this work is to create robust, representative models of single layers (I) and double layers (I-I) of illite found within gas shale, that can be used in future investigations. We examine lattice parameters, interatomic distances of tetrahedral and octahedral sheets, K–O distances, and K positions, and find reasonable agreement with experimental data, and excellent agreement with simulated data of similar structures. Finally, to enable experimental characterization of samples of illite with different compositions, we provide simulated X-ray powder diffraction (XRPD) patterns including up to the first ten (h k l) reflections, and find characteristic identifiers of trans- and cis-vacant micas in agreement with previous theoretical and experimental studies. We conclude that the models we create are feasible models of I and I-I layers of illite found within shale and are ready for use in future work.

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