| Abstract: | Guided by the symmetry in a natural way, periodic potential surfaces partition the space in solid crystalline compounds. The arrangement of atoms, clusters and molecules obviously follows the (in general) curved shape of these ‘space partitioners’. In structures, the atoms therefore choose only a very limited subset of the infinite set of possible positions. In collective structures the periodic surfaces separate areas of different interactions between atoms, clusters, and molecules. In a certain sense, they can be considered as inner surfaces, a knowledge of which reveals insights into the organization of crystalline matter. There are many good indications that the weakly bonded electrons in the highest occupied orbitals are preferably localized in the region of the space partitioners. Dynamic processes as well can be correlated to the shape of the periodic surfaces. Moreover, the surfaces are didactically very helpful in making accessible the complicated three-dimensional relations in collective structures because the main features are projected onto (although curved) two-dimensional creations. The application of periodic potential surfaces to such a variety of compounds as quartz, brass and alpha-amylose underscores their general significance. Simple qualitative considerations already reveal the manifold relations to animate and inanimate nature through to mathematics, art and architecture. It appears that, in a very universal sense, the adaption of structures to a collective order finds a natural solution through curvature. |
