Group-theoretical description of domain and phase boundaries in crystalline solids

The theory is reviewed of domains and domain boundaries arising in phase transitions accompanied by symmetry breaking. Conclusions concerning the number, the crystallographic type and the spatial orientation of coherent interfaces between crystals of the same structure (domain boundaries) and between different structures of the same material (interphase boundaries) are presented in terms of the space group theory and of the Landau theory of phase transitions. The application of the two-dimensional space groups and the diperiodic groups in three dimensions to the discussed objects is described. The conditions for the coexistence of domains and phases without macroscopic stress are given. An example of the group-theoretical analysis of domain structure is given for a real material: NaO₂.