A Tensor Classification of Twinning in Crystals

A classification scheme for twinning in crystals is proposed. It is based on a tensor distinction of properties across the twin interface. The classification employs concepts from the theory of transformation twinning. The adequacy of such a scheme for other main types of twins, namely growth twins and nonferroelastic mechanical twins, is examined, and found to be satisfactory. All twins can be divided into four fundamentally distinct categories: ferroelastic or S-twins, nonferroelastic-ferroic or N-twins, Bollmann or B-twins and translation or T-twins. A comparison is made of the attributes of these four types of twins. A compact and informative twin symbol is introduced, which carries information about the tensor properties in which the twins differ. Information about any underlying total or partial coincidence sublattice is incorporated by attaching a subscript t or p to the main twin symbol. Several examples are discussed. This paper also introduces a rigorous definition of prototype symmetry in terms of the `nondisruption condition'.