Applicable Scope Of Landau Theory In Ferroelectric Phase Transition And Discussion Of Correlation Length In The Critical Region

Phase transition and critical phenomenon are fields full of challenges and sudden discoveries. Once Landau theory of phase transition was used to deal with ferroelectrics phase transition. It introduces symmetry breaking into phase transition theory and associates it with order parameter to find the necessary condition of occurrence of phase transition. The theory has settled plenty of problems. When temperature is very close to the temperature of phase transition, critical phenomena appear in the system. Fluctuation of order parameters leads to the failure of Landau theory of phase transition.In the thesis, mechanism of ferroelectrics phase transition is discussed. Researchers think fluctuations of order parameters are not independent, but are associated in the critical region. So there are Ginzburg grads in the expansion of Ag (density of free energy) in terms of fj (order parameter), which is used to deduce the probability of fluctuations. Correlation function is then introduced to denote the correlation degree of order parameters of different points in the system. We deduce the correlation functions of order parameter by hyperboloid function (T > TC,T < Tc), and then compare the two functions to get the change of specific heat, and to get correlation length ?as the token of correlation degree. So we can make clear the applicable scope of Landau theory of phase transition.In the system, the dipoles' appearance and parallel arrangement lead to occurrence of spontaneous polarization, which is the essence of ferroelectrics phase transition. The interaction between dipoles is long-distance Coulomb force. Because of the interaction, correlation of the potentials between dipoles comes into being in the critical region, and then lead to the occurrence of ferroelectrics phase transition. Cumulative integral is used to research the phenomenon. Comparing this conclusion with that of applicable scope of Landau theory, we discuss the relation between them and the essence of coefficient K and correlation length ?...