Polytypism of crystal structures

AbstractPolytypism occupies a singular position in the structural crystallography uniting features of polymorphism and diversity of crystal structure built of definite units. In the structural systematics the polytype structures are considered in relation to fragmentary, interstratified, hybrid (both commensurate and incommensurate), order-disorder (OD) and modulated structures. The polytype diversity includes close packings of identical and different atoms, stackings of tetrahedral, octahedral and prismatic sheets, phyllosilicates and complex silicates having a wide variety of relative positions and/or orientations of the building units, combinations of structural units periodic in two and one dimensions or having finite dimensions, as well as purely chain-ribbon structures. Different polytypes require a variety of individual approaches in their consideration and symbolic description using symbols of the structural units, of their positions-displacements, orientations-rotations, or of the symmetry operations relating them. As a versatile notion polytypism presents an important crystallochemical phenomenon, a means to perceive crystalline substances not as isolated objects but as sets of interrelated members of united systems, and a cognition method effective in the solution of theoretical as well as applied problems