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The phase transition in PbTiO 3 is discussed quantitatively from the microscopic free energy based upon the mean field approximation, where the Ti ions shift is considered as the order parameter in the lattice having the spontaneous deformation. From our calculation of the microscopic free energy, the ionic shift of the Ti ion and the coefficient of the expanded free energy, we concluded that the transition temperature and the order of cubic-tetragonal transition are well explained by this model.

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PACS 77.22.Ej, 77.84.DyThe spontaneous polarization and the refractive indices in the tetragonal, orthorhombic and rhombohedral phases of KNbO 3 are discussed quantitatively from the microscopic consideration. The shift of the Nb ion situated at the centre of the lattice is calculated at various temperatures from the mean field approximation model. The spontaneous polarization has been calculated by the dipole-dipole model using the calculated values of the shift of the Nb ions, the vertical strains and the shearings.1 Introduction The oxygen-octahedra ferroelectrics ABO 3 perovskite structure constitutes a very attractive class of coumponds for various propreties. At high temperatures KNbO 3 is paraelectric with cubic structure. On cooling, KNbO 3 crystal transforms successively from cubic to tetragonal at 435 °C, then to orthorhombic at 215 °C and finally from orthorhombic to rhombohedral structure at -50 °C [1]. As for the origin of the ferroelectricity in the tetragonal phase of KNbO 3 that has been discussed in previous work [2], the physical origin of this property in these three ferroelectric phases is assumed to be related to the change of the dipole-dipole interactions due to the lattice deformation and the shift of Nb ion caused by the change of temperature. In this paper, we discuss, in Section 2 the method of calculation of the displacements by using a mean field approximation model, in Section 3 the dipole-dipole interaction due to the local field acting on the constituent ions. Finally, in Section 4 we give the results and some discussions.

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