Incommensurate and commensurate modulated structures

This chapter discusses incommensurate and commensurate modulated structures. After an introduction to the concepts used to describe modulated structures, including the basic ideas of higher-dimensional crystallography, four-dimensional space groups and displacive and occupational modulation, superspace-group determination is outlined. Tables of Bravais lattices, geometric and arithmetic crystal classes, and superspace groups (with reflection conditions) are presented and their use is illustrated with different examples. Keywords: arithmetic crystal classes; basic structural features; Bravais classes; centring reflection conditions; composite crystal structures; crystallographic systems; higher-dimensional crystallography; holohedry; incommensurate modulated structures; lattices; Laue classes; modulated crystal structures; modulations; occupation modulations; point groups; structure factors; superspace groups