Ordered and disordered structures in borosilicates with a pentasil-type framework

X-ray diffraction patterns of two different zeolite-like borosilicates, BOR-C and BOR-D, are subjected to investigation. The structure of BOR-C is interpreted in terms of a regular stacking of `pentasil' layers correlated by inversion centres (i-type stacking). Conversely, the structure of BOR-D may only be described as a layer sequence in which the prevailing i-type stacking is interrupted by faults consisting of mirror-related layers (σ-type stacking). A statistical model where both the crystal surfaces and the stacking faults (with a 25% probability) are randomly distributed (Bernoullian model) leads to Lorentzian profiles and the resulting calculations show a good fit with experiment. In view of the very strong X-ray similarity among BOR-D, the ZSM-11 aluminosilicate and the pure silica analogue silicalite-2, the same statistical model is proposed for the two latter structures.