Theoretical Determination of the Orders of the Ferroelectric Phase Transitions

Following the recent recognition that there are, in all, 83 possible kinds of ferroelectric phase transitions of paraelectric crystals, we attempt to determine theoretically the orders of these phase transitions. For this purpose, we introduce four postulates, one of which, as an example, is that the free energy under zero stress of the crystal can be expressed as an infinite power series in the components of the polarization vector the vicinity of the Curie temperature. As a result, it is found that 50 of the 83 kinds of ferroelectric phase transitions must be of first order (in the thermodynamic sense), and that the remaining 33 kinds can be either of first order or of second order. (Properly speaking, it is, at present, not a logical conclusion but a conjecture that all of the 33 kinds can be of second order.) No disagreement is detected between the predictions of this theory and existing experimental results.