Different approaches to modularity
Published:January 01, 1997
Some families of inorganic compounds form an array of more or less closely related, very complex structures with a number of independent atomic positions and unit cells of large dimensions. These structures can be broken up into a number of fragments (modules) that have relatively simple substructures but are joined into a more complex whole. Some modules occur in many members of these families, often in variably expanded/contracted forms as well as combined with elements of other kinds. From the point of view of the bond strength distribution these modules/elements may form independent units, weakly bonded on the outside, or they are only geometrical (configurational) entities that otherwise merge into the bonding pattern of the structure.
The same category of complex structures can also be approached from the opposite direction. Increasingly dense arrays of iso- or allochemical, extended structural defects lead to a formation of progressively smaller moduli of undisturbed, relatively simple structure decreasing in size (Wadsley, 1963) until they match in defect density and modulus (fragment) size those from the above mentioned, structurally and chemically complex families.
These opposite structural trends produced different schools of thought and modes of description. The concept of homologous series was coined for such compounds by Magnéli in 1953; the parallel concept of polysomatic series by Thompson in 1970. In the realm of intermetallic structures a very similar concept was introduced by Gladyshevskii & Krypyakevich (1972). For the latter two concepts, the starting point was a similarity (analogy) of the observed phenomena to polytypism,
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Modular Aspects of Minerals
Since the first beginning of the crystal chemical study of the inorganic compounds, a simple modular approach was developed, by looking at the crystal structures as built up through the assembling of simple polyhedral units. This approach was no only useful for a vivid and insightful description of the complex atomic arrangements of natural and synthetic compounds, but, through the use of simple and powerful rules for assembling polyhedral units, it displayed an extraordinary heuristic power, suggesting reliable models for many complex structural assemblages. The polyhedral approach also laid the basis for meaningful classifications which were applied to all the classes of inorganic compounds.