Analysis of family reflections of OD mica polytypes, and its application to twin identification

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. Non-orthogonal 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, called family 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≠0(mod 3) and k=0(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.