Temperature-induced structural phase transitions in inorganic compounds: symmetry and information-entropy analysis

The tendency of crystal-structure symmetry increasing under increasing temperature (also known as a ‘Landau rule’) is one of the major empirical observations with regard to the temperature-induced phase transitions. The validity of the rule was investigated by means of the statistical analysis of the 502 temperature-driven phase transitions in inorganic compounds with known crystal-structure information for all polymorphs. The analysis was performed from the viewpoint of symmetry considerations (that is, the analysis in terms of the crystal-system hierarchy, where cubic system is the highest and triclinic is the lowest) and information-entropy calculations. It was revealed that the information-based structural complexity parameters (most importantly, the total information content per reduced unit cell) are more sensitive structural symmetry indicators than the symmetry classification in terms of the crystal-system hierarchy. The information-entropy measures decrease under increasing temperature in more than 77 % of phase transitions under consideration, which corresponds to the overall rise of symmetry under heating (the ‘Landau rule’). In contrast, the simple symmetry analysis confirms the ‘Landau rule’ in 60 % of cases only. The information-based parameters are especially efficient for the cases, when crystal system does not change (most numerous are monoclinic-monoclinic and orthorhombic-orthorhombic transitions). The deviations from the rule of increasing symmetry correspond to: phase transition sequences with intermediate (transitional) structures of high complexity, isosymmetric and reentrant phase transitions, and transitions that involve low-temperature metastable polymorphs. There are some exceptions that cannot be assigned to any of the phase-transition types mentioned above, where symmetry is decreasing under heating. The symmetry breaking results in the decrease in vibrational entropy, which may be considered as a major driving force behind the ‘Landau rule’. However, various phenomena such as formation and breaking of bonds, charge and orbital ordering, stereoactive activity of lone electron pairs, etc., may seriously influence polymorphic transformations under temperature changes.