Translational symmetry changes in second-order phase transitions on clean crystal surfaces

The group theory approach, within the Landau-Lifshitz theory of phase transitions, is presented to predict the possible translational symmetry changes (possible surface superstructures) in second-order phase transitions on clean crystal surfaces. 80 diperiodic groups in three dimensions are used to describe the symmetry of the surface layer. A comparison of the theoretical results with experimental data is given.