Twinsvs. modular crystal structures

Abstract

AbstractThe crystallographic nature of modular structures is analysed and discussed in terms of their symmetry and structure building operations. The modular crystal structures we discuss in this paper are homogeneous edifices, built by one or more types of modules related by a point-space operation, and the whole structure is described by an ordinary three-dimensional triperiodic space group. Because the term “twin” is often used, with or without modifiers, to describe symmetry operations that act as building mechanisms in modular structures, a comparison is made with twins, that are instead heterogeneous edifices, described not by a space group but by a (polychromatic) point group, where the individuals are related by operations in the vector space. A unifying scheme is proposed where the passage from heterogeneous to homogeneous structures, only apparently justified by a change of dimensions of the individuals, implies a change of space where the operations are defined.