Modelling the structural evolution and polytypism of micas by tetrahedral transformation and polyhedral volumes.

A computerized analysis of over 450 mica crystal structures is carried out. These data are accessed via the Inorganic Crystal Structure Database (ICSD), whereby unit-cell parameters, atomic coordinates and polyhedron generators resulting from this analysis are transferred to Microsoft Excel as an interactive working environment. This environment enables the rapid calculation of many crystal chemical parameters, including tetrahedral, octahedral or AO12 polyhedral volumes and areas. The forms of the O4 tetrahedra are quantified by transformation to pseudocubes with six independent parameters. Reversibility between crystal chemical and crystallographic parameters is provided by means of the Microsoft Excel Solver. This gives rise to a method of structure prediction by interpolation, which is demonstrated for a 1M phlogopite. Hypothetical structures at temperatures of 150 and 723 K are predicted, and a computationally generated structure at 673 K is compared with the experimentally known structure at this temperature. The crystal chemical parameterization is also used to identify the differences between the five principal mica polytypes: 1M, 2M1, 2M2, 3T and 2O. The Excel software developed is made available via a weblink, with instructions for carrying out structure predictions in the supporting information.