## Polytypism of Micas: OD-Interpretation, Stacking Symbols, Symmetry Relations

K. Dornberger-Schiff^{1, †}, K.-O. Backhaus^{1} and S. Ďurovič^{2}

^{1} Akademie der Wissenschaften der Deutschen Demokratischen Republik, 1199 Berlin-Adlershof, Rudower-Chaussee 5, Deutsches Demokratisches Republik.

^{2} Institute of Inorganic Chemistry, Slovak Academy of Sciences, 809 34 Bratislava, Czechoslovakia.

^{†}
Deceased July 27, 1981.

**Abstract:** From the symmetry point of view, micas may be classified as follows: those with all three octahedrally coordinated sites occupied by the same cation (homo-octahedral micas), those with only two of these sites occupied by the same cation (meso-octahedral micas), and those with the three sites occupied by different cations or by two different cations and a void, in an ordered manner (hetero-octahedral micas). For any of these three classes, mica polytypes, idealized in accordance with the generalized Pauling model, can be interpreted as OD structures consisting of octahedral OD layering and tetrahedral OD layering in which an interlayer cation plane is sandwiched between tetrahedral sheets. A mica layer built up by an octahedral sheet and two halves of tetrahedral sheets on either side consists of two OD packets linked by a two-fold rotation.

The orientation of any OD packet may be given by a number from 0 to 5 (related to a hexagonal coordinate system). A dot behind or before these numbers is used to denote the position of the octahedral layer (number + dot = orientational character). The displacement of a packet against its predecessor is characterized by a vector from the origin of a packet P_{n} (or q_{n−1}) to the origin of the adjacent packet P_{n+1} (or P_{2n}). These displacements may also be symbolized by numbers from 0 to 5 (displacement characters); a zero displacement is symbolized by *. Any mica polytype (ordered or disordered) can thus be described by a two-line symbol. The orientational characters are located on the first line, and the displacement characters on the second. Any symbol, therefore denotes unequivocally the stacking layers in a polytype. The space-group symmetry of ordered polytypes follows directly from the symbol.