Periodic intensity distribution (PID) of mica polytypes: symbolism, structural model orientation and axial settings

Following a preliminary revisitation of the nomenclatures in use for mica polytypes, the properties of the periodic intensity distribution (PID) function, which represents the Fourier transform of the stacking sequence, are analysed. On the basis of the relative rotations of neighbouring layers, mica polytypes are classified into three types; for each type, the PID exists in different subspaces of the reciprocal space. A revised procedure to compute the PID, in which further restrictions on the structural model orientation are introduced, is presented. A unifying terminology based upon the most common symbols used to describe mica polytypes (RTW, Z and TS) is derived; these symbols represent the geometrical basis for the computation of the PID. Results are presented for up to four layer polytypes and are compared with the reflection conditions derived by means of Zvyagin's functions. Both the PID values and the reflection conditions are expressed in suitable axial settings and compared with previous partial reports, revealing some errors in previous analyses. A computer program to compute PID from the stacking symbols is available.