OD structures

This chapter starts with some motivations leading to the concept of Ordered Derivative (OD) structures and corresponding theory to deal with one-dimensional disorder of two-dimensionally ordered layers. It introduces the terminology and procedures through the use of wollastonite structure which played a prominent role in inspiring the foundation of OD theory by Dornberger-Schiff. Basic terms and definition are given for OD structures of equivalent layers and also for those of M kinds of layers: partial operations of λ- and σ-type, OD families, categories of OD structures, NFZ formula, and MDO...

This chapter starts with some motivations leading to the concept of Ordered Derivative (OD) structures and corresponding theory to deal with one-dimensional disorder of two-dimensionally ordered layers. It introduces the terminology and procedures through the use of wollastonite structure which played a prominent role in inspiring the foundation of OD theory by Dornberger-Schiff. Basic terms and definition are given for OD structures of equivalent layers and also for those of M kinds of layers: partial operations of λ- and σ-type, OD families, categories of OD structures, NFZ formula, and MDO structures. The diffraction features of OD structures (family reflections and characteristic reflections) are presented and discussed. Numerous examples of OD families both of equivalent layers and with two or more kinds of distinct layers are illustrated, with indication of the heuristic power of the OD approach. The chapter contains also a table of monoclinic and orthorhombic OD groupoid families.