Changes in the structural symmetry of crystals of the classes D4and C4hin second-order phase transitions

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Abstract
Applying Landau's thermodynamical group theory, the permitted changes in the space structure of D4 and C4h class crystals, at the temperature of their structural second-order phase transition, are determined. Crystals with symmetry of all space groups of the classes D4 and C4h are considered except the C4h6 group, the symmetry changes of which have been determined by Lyubarskii (1960). It is found that crystals of symmetry D4n (n=1, 2, 3, 4, 5, 6, 7, 8, 9, 10) and C4hn (n=1, 2, 3, 4, 5), as the result of a structural second-order phase transition, can either undergo changes in symmetry within the tetragonal system (D4 to D4, C4 and C4h to C4h, S4, C4) or change their symmetry from tetragonal to rhombic (D4 to D2, C2 and C4h to C2h, C2) or from tetragonal to triclinic (C4h to Ci). The volume of the unit cell can remain unchanged, or can increase twice, three times or even eight times in the phase transition. The calculations do not take into account phenomena occurring in the critical region but deal only with the static properties of the crystals.