Periodic Space Partitioners (PSP) and their relations to Crystal Chemistry

Abstract

AbstractWe are looking back on 30 years development of periodic space partitioners (PSP) and their relations to their periodic relatives,i.e.minimal surfaces (PMS), zero potential surfaces (P0PS), nodal surfaces (PNS), and exponential scale surfaces. Hans-Georg von Schnering and Sten Andersson have pioneered this field especially in terms of applications to crystal chemistry. This review relates the early attempts to approximate periodic minimal surfaces which established a systematic classification of all PSP in terms space group symmetry and consecutive applications in a variety of different fields. A consistent nomenclature is outlined and different methods for deriving PSP are described. Characteristic structure factor sets which solely define PNS by can be used to discriminate structure types of a given symmetry or even to determine complicated crystal structures. The concept of PSP relates space group symmetry, topology, and chemical bonding in an intriguing way and tessellations on PSP which can be generated in a straight forward way allow to predict new framework types. Through transformation of such continuous topological forms a new entry has been found for understanding and interpreting reconstructive phase transitions. Finally we indicate the importance of PSP models for soft matter science.