Section 9.2.2.1. The notion of polytypism

The common property of the structures described in Section 9.2.1 was the stacking ambiguity of adjacent layer-like structural units. This has been explained by the geometrical properties of close packing of equal spheres, and the different modifications thus obtained have been called polytypes.

This phenomenon was first recognized by Baumhauer (1912, Baumhauer, 1915) as a result of his investigations of many SiC single crystals by optical goniometry. Among these, he discovered three types and his observations were formulated in five statements:

Baumhauer recognized the special role of these types within modifications of the same substance and called this phenomenon polytypism – a special case of polymorphism. The later determination of the crystal structures of Baumhauer's three types indicated that his results can be interpreted by a family of structures consisting of identical layers with hexagonal symmetry and differing only in their stacking mode.

The stipulation that the individual polytypes grow from the same system and under (nearly) the same conditions influenced for years the investigation of polytypes because it logically led to the question of their growth mechanism.

In the following years, many new polytypic substances have been found. Their crystal structures revealed that polytypism is restricted neither to close packings nor to heterodesmic `layered structures' (e.g. CdI₂ or GaSe; cf. homodesmic SiC or ZnS; see 9.2.1.2.2 to 9.2.1.2.4), and that the reasons for a stacking ambiguity lie in the crystal chemistry – in all cases the geometric nearest-neighbour relations between adjacent layers are preserved. The preservation of the bulk chemical composition was not questioned.

Some discomfort has arisen from refinements of the structures of various phyllosilicates. Here especially the micas exhibit a large variety of isomorphous replacements and it turns out that a certain chemical composition stabilizes certain polytypes, excludes others, and that the layers constituting polytypic structures need not be of the same kind. But subsequently the opinion prevailed that the sequence of individual kinds of layers in polytypes of the same family should remain the same and that the relative positions of adjacent layers cannot be completely random (e.g. Zvyagin, 1988). The postulates declared mixed-layer and turbostratic structures as non-polytypic. All this led to certain controversies about the notion of polytypism. While Thompson (1981) regards polytypes as `arising through different ways of stacking structurally compatible tabular units [provided that this] should not alter the chemistry of the crystal as a whole', Angel (1986) demands that `polytypism arises from different modes of stacking of one or more structurally compatible modules', dropping thus any chemical constraints and allowing also for rod- and block-like modules.

The present official definition (Guinier et al., 1984) reads:

This definition was elaborated as a compromise between members of the IUCr Ad-Hoc Committee on the Nomenclature of Disordered, Modulated and Polytype Structures. It is a slightly modified definition proposed by the IMA/IUCr Joint Committee on Nomenclature (Bailey et al., 1977), which was the target of Angel's (Angel, 1986) objections.

The official definition has indeed its shortcomings, but not so much in its restrictiveness concerning the chemical composition and structural rigidity of layers, because this can be overcome by a proper degree of abstraction (see below). More critical is the fact that it is not `geometric' enough. It specifies neither the `layers' (except for their two-dimensional periodicity), nor the limitations concerning their sequence and stacking mode, and it does not state the conditions under which a polytype belongs to a family.

Very impressive evidence that even polytypes that are in keeping with the first Baumhauer's statement may not have exactly the same composition and the structure of their constituting layers cannot be identical has been provided by studies on SiC carried out at the Leningrad Electrotechnical Institute (Sorokin, Tairov,Tsvetkov & Chernov, 1982; Tsvetkov, 1982). They indicate also that each periodic polytype is sensu stricto an individual polymorph. Therefore, it appears that the question whether some real polytypes belong to the same family depends mainly on the idealization and/or abstraction level, relevant to a concrete purpose.

This very idealization and/or abstraction process caused the term polytype to become also an abstract notion meaning a structural type with relevant geometrical properties,¹belonging to an abstract family whose members consist of layers with identical structure and keep identical bulk composition. Such an abstract notion lies at the root of all systemization and classification schemes of polytypes.

A still higher degree of abstraction has been achieved by Dornberger-Schiff (1964), Dornberger-Schiff (1966), Dornberger-Schiff (1979) who abstracted from chemical composition completely and investigated the manifestation of crystallochemical reasons for polytypism in the symmetry of layers and symmetry relations between layers. Her theory of OD (order–disorder) structures is thus a theory of symmetry of polytypes, playing here a role similar to that of group theory in traditional crystallography. In the next section, a brief account of basic terms, definitions, and logical constructions of OD theory will be given, together with its contribution to a geometrical definition of polytypism.