A new classification of twinning in crystals

A comprehensive and informative classification of twinning in crystals is proposed. It is based on the nature of the twin mapping operation. If the mapping operation is a symmetry element of a certain prototype space group (in Aizu's sense), the twin is called an “Aim twin”. Otherwise it is called a “Bollmann twin”. Aim twins are essentially transformation twins. They may be further divided into ferroic twins and translation twins. Ferroic twins, in turn, can be of two types: ferroelastic or F-twins (e.g. the 90° twins of BaTiO₃), and nonferroelastic-ferroic or N-twins (e.g. the Dauphiné twins of quartz). The antiphase domains in Cu₃Au are a typical example of translation twins (T-twins). The three types of Aim twins (F, N and T) have distinctive macroscopic physical properties. Bollmann twins are divided into two main categories: C-twins and M-twins, where C stands for coincidence lattice and M for miscellaneous. C-twins are further categorized into two types, depending on the “total” or “partial” nature of the coincidence sublattice. M-twins can be of three types, depending on the dimensionality of the dichromatic pattern being 0, 1 or 2. Illustrative examples are discussed. A compact and informative twin symbol is introduced.