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Cell-twinning is a structure-building mechanism in which one or more types of building blocks (modules) are juxtaposed next to another to build a three-dimensional triperiodic structure called a modular crystal structure. The building blocks are three-dimensional but less than triperiodic and can thus be:

  • finite and non-periodic, with symmetry described by a point group;
  • monoperiodic, with symmetry described by a rod group;
  • diperiodic, with symmetry described by a layer group.

The juxtaposition of modules can produce an interface which is homogeneous with the structure of the module, or may create a heterogeneous interface where coordination polyhedra are modified, created or annihilated. This heterogeneity may lead to a modulation of the chemical composition of the resulting structure with respect to that of the archetype(s) corresponding to the composition of the building module(s). Accordingly, the following hierarchy of structures has been introduced:

  • polytypes: cell-twins without alteration of the coordination at the interface;
  • chemical twins: with alteration of the coordination at the interface;
    • isochemical, without chemical variation at the interface;
    • heterochemical, with chemical variation at the interface.

The phenomenon in which the cell-twinning mechanism leads to a series of structures where the composition is directly related to the size of the modules is called tropochemical cell-twinning.