Atomic Displacement Relationship to Curie Temperature and Spontaneous Polarization in Displacive Ferroelectrics

The phase transition from nonpolar to polar in displacive ferroelectric crystals is accompanied by the displacement of certain atoms from their higher-temperature symmetry positions. A study of all displacive ferroelectrics in which atomic positions have been determined has shown that a fundamental relationship exists between and the Curie temperature T₂. This relation has been form T₂= (K2k) () ^2, where K has the dimensions of a force constant, k is Boltzmann's constant, and T₂ is in absolute units. A least-squares fit, based on and T₂ for ten different ferroelectrics, gives K2k= (2. 000. 09) 10^4^K ^-2. In addition, the spontaneous polarization Pₒ is found to be related to by the equation Pₒ= (2589) cm^-2. K is discussed in terms of the interatomic force constant along the polar axis.