The Free Energy Of The Ferroelectric Phase Transition And The Order Parameter Of The Antiferroelectric Phase Transition

The full free energy expansion was proposed. The physics significations of every part of the free energy expansion are illuminated. The significations of the coefficient of free energy expansion and that of conjugate variable of the independent variable are indicated. The first order partial differential of Gibbs free energy are thermodynamics variable. The second order and the higher order partial differential of Gibbs free energy are substance property tensors, i.e. they are all the coefficients of the physical effects. The term numbers of free energy expansion are studied during the phase transition process when the order parameter is more than one variable. The corresponding terms are retained in free energy expansion according to the specific conditions when Landau theory is used. Furthermore, the order of the phase transition can be obtained by the coefficients in free energy expansions. Besides, by using the traditional method, the order parameter of the possible phase can be obtained by the first order derivative of free energy and the stability condition of the phase can be reached when the Jacobi ordered-main subdeterminant of the second order derivative of the order parameter is definitely positive.As far as Landau theory is concerned, the key is to write out the correct free energy expansion. The expansion can be constructed by the base functions of point group. Generally speaking, the sixth order terms should be retained in the free energy expansion. In order to obtain the correct free energy expansion rapidly, we recalculate the base functions of the irreducible representations for thirty-two point groups corresponding to the specific representative matrix and supplement the third-order base fuctions. Eighteen kinds of point groups are found having third-order invariant. If the group of the high-temperature crystal structure is one of these point groups, then the ferroelectrics will undertake the first orderphase transition.Landau theory is used to describe the ferroelectric phase transition of Boracites. All the possible proper ferroelectric phases are obtained. They are ferroelectric orthogonal phase, ferroelectric trigonal phase and ferroelectric monoclinic phase. The temperature zones of the three possible phases are calculated respectively by using the stability conditions of more variables. There are only five kinds of boracites that have the ferroelectric trigonal phase. The spontaneous polarization and the Curie temperature as well as the temperature dependence of the principal reciprocal susceptibility are obtained respectively. The calculated result shows that at the Curie temperature Tc, spontaneous polarization jumps. The component of the principal reciprocal susceptibility perpendicular to polarization jumps but the component parallel to polarization does not jump. Considering the speciality of the principal reciprocal susceptibility in trigonal boracite, the experiment scheme on the measurement of the principal reciprocal susceptibility components is presented.On the basis of Curie principle, the order parameter of the antiferroelectric phasetransition is investigated by taking crystal PZT, crystal SrTiO and the antiferroelectricmodels of simple cubic lattice as examples. A method of searching for the suitable order parameter is given. Firstly, according to Curie principle, the symmetry of the order parameter is decided by using the symmetry of the crystal before and after phase transition. Then by using the physical tensor matrix, searching from the first order tensor, we can finally obtain a suitable order parameter. A third-order complete symmetry polarizationtensor ijk is put forward as the order parameter of phase transition. The matrix of ijkhas been calculated for PZT and SrTiO3 respectively. We find that this order parameter can reflect the symmetry changes of the two crystals perfectly. There are two kinds of antiferroelectric models for the simple cubic lattice. We called them model A and model Brespectively. The symmetry of model A is D2d and the symmetr...