There has been wide speculation about the structural factors responsible for the observed frequency of the different mica polytypes. The purpose of this investigation is to identify the important factors and to test the relevant ones by using calculated cohesive energies to discriminate between alternative model structures. Sets of structures were constructed, based on talc, pyrophyllite, muscovite, biotite, and anandite. Each model set was specifically designed so that all structures in a given set would have essentially the same short-range repulsive forces and essentially the same van der Waals forces. The difference between the cohesive energies of two structures could then be ascribed essentially entirely to long-range Coulomb electrostatic forces. The method is a natural extension of the polyhedral approach to crystal chemistry.

Of the various parameters designed to characterize deviations from structural ideality, only Δz and α are specifically related to the articulation of the various coordination polyhedra. Other parameters measure the departure from ideal geometry of individual coordination polyhedra. We identify Δz as the best parameter for predicting the stable polytype. Most micas with Δz less than 0.1 Å are 1M polytypes, regardless of composition and other structural parameters. Most micas with Δz greater than 0.1 Å are 2M1 polytypes regardless of composition and other structural parameters. The conspicuous exceptions include the lithian micas and the brittle mica anandite, [Ba(Mg,Fe)3(Si3Fe)O10(OH)S]. Though significantly variable, α bears no apparent relationship to the stability of the 1M versus the 2M1 polytype.

The calculations support both theoretical and empirical observations regarding (a) the predominance of 1M and 2M1 polytypes and (b) the scarcity of 2M2 and 2O polytypes. Al-Si “disordering” in micas is subject to certain rules: (a) the principle of aluminum avoidance and (b) the same ratio of Al to Si in all tetrahedral sheets. The relative positioning of tetrahedral Al cations on opposite sides of the octahedral sheet seems not to be important. For muscovite-2M1, there are at least 48 crystal-chemically reasonable Al-Si orderings with very nearly the same low energy. The different orderings should be more or less equally represented in actual structures. Calculated energies are most sensitive to interlayer Al-Al separations. In 1M and 2M1 polytypes, Al-Si orderings consistent with a 21 axis parallel to b are especially favorable.

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