Abstract: The Periodic Intensity
Distribution (PID) analysis of the diffraction pattern of mica
polytypes can be applied to single crystals. Since micas often
appear as twins, general criteria are established to investigate
the presence of twinning. These criteria are derived through a
geometrical approach based on the general symmetry features of
the layer stacking. Nonorthogonal polytypes have been classified
into Class a and Class b, depending on the direction along which
c axis is inclined. Common twinning in micas is by reticular pseudo-mero-hedry;
for Class a polytypes its presence can be recognized by careful
inspection of the geometry of the diffraction pattern. On the
other hand, a pseudo-rhombohedral primitive cell exists in case
of Class b polytypes: for them, two of the five pairs of twin
elements common to non-orthogonal polytypes correspond to twinning
by pseudo-merohedry, which does not modify the geometry of the
diffraction pattern.
It is proved that the geometrical features of mica diffraction
pattern can be divided into two types: 1 ) the number and position
of diffractions common to all polytypes built on the same structural
principle, calledfamily reflections, derived by calculating the
reflection conditions; 2) the number of planes with orthogonal
geometry. The analysis takes into account that most of the mica
polytypes reported to date are OD structures belonging to two
subfamilies, and that a third, rare kind of polytypes, called
mixed-rotation polytypes, consists instead of non-OD structures.
For mixed-rotation polytypes the definition of the family reflections
differs from that of the two subfamilies. It is shown that these
three kinds of polytypes are easily recognized by analyzing the
reflections with h ≠O(mod 3) and k = O(mod 3). Then, the number
of reflections along family rows and the number of orthogonal
planes in the diffraction pattern permit to investigate the presence
of twinning.
*Mineralogical Institute, Graduate School ofScience, University
of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
Present address : National Institute for Research in Inorganic
Materials, Research Center for Creating New Materials, 1-1 Namiki,
Tsukuba-shi, Ibaraki 305-0044, Japan.