Symmetry and cation sites

Mainly because of a dimensional misfit between the T and O sheets (cf below), in real mica structures the Pauling model (in which there are no structural distortions) is too abstract and must be replaced at least by a model which takes into account a rotation of the tetrahedra within the (001) plane. This ditrigonal rotation is discussed below the resulting model has been called the trigonal model by Nespolo et al. (1999c). 

In the homo-octahedral family, the three M sites are by definition identical in content and size. Any difference in one of the M sites violates the H centering, lowering the symmetry of the O sheet to that of the meso-octahedral family. A difference between the other two M sites destroys also the inversion center and lowers the symmetry of the O sheet to that of the hetero-octahedral family. From the practical viewpoint, differences among the M sites are often small and must be evaluated on statistical grounds. As discussed by Bailey (1984c) for the specific case of micas [cf. an application in Amisano-Canesi et al. (1994)], if o/ is taken as the estimated standard deviation (esd) of an individual quantity and o = Oiln is the esd of the mean of n values, the esd of a difference (A) between two mean values is given by (3 = Two quantities are 

Layergvupsymmep C m ). The m mirror plane coincides with the ac plane of the 

Layergoupsymmep C12(l). The two-fold axis is along the b axis of the layer and the M2 and M3 sites are no longer equivalent. Two symmetrically independent tetrahedral sites are present in each sheet, but the two T sheets of a layer are symmetrically equivalent Tlu = T l and T2u = T21. This symmetry occurs in some meso- and hetero-octahedral IM polytypes and in the hetero-octahedral 3T polytypes. 

Layergoujsymmep Cl. The three M sites and the four T sites are all symmetrically independent. This symmetry occurs, e g., in ephesite-2Mi (Slade et al. 1987). 

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