Transformations of the coordinate system (unit-cell transformations)

Abstract

Transformations of the coordinate system are useful when nonconventional descriptions of a crystal structure are considered, for instance in the study of relations between different structures, of phase transitions and of group–subgroup relations. Unit-cell transformations occur particularly frequently when different settings or cell choices of monoclinic, orthorhombic or rhombohedral space groups are to be compared or when `reduced cells' are derived. In this chapter, matrix notation is used to describe a general transformation. Selected frequently occurring transformation matrices are tabulated and illustrated by diagrams. This chapter is also available as HTML from the International Tables Online site hosted by the IUCr.