| Traditionally, the macroscopic studies of ferroelectric phase transitions and other ferroic phase transitions were carried out within the limits of equilibrium thermodynamics. Devonshire theory, which is an equilibrium thermodynamic theory, describes ferroelectric phase transitions on the basis of Ginzburg-Landau theory. Its basic idea is expanding the elastic Gibbs free energy (G1=U-TS-X1X1) into an even power series of the electric displacement, and set up the relations between the coefficients of the series and certain macroscopic quantities that can be measured experimentally. Devonshire theory can be used to describe "heat hysteresis", which exists in the course of a ferroelectric phase transition. Since, there are a set of metastable states and several stability limit temperatures and, the interval between the ferroelectric phase stability limit temperature and the paraelectric phase stability limit temperature characterizes the degree of heat hysteresis. The ferroelectric phase transition temperature, which lies in the temperature interval, is always higher or lower than Curie temperature in the course of warming or cooling respectively. Normally, ferroics possesses domain structure. This phenomenon can be explained and described on the basis of the principle of minimum free energy and Curie principle. The surface of a ferroic system, as a discontinuous factor, enhances the system energy. Consequently, a ferroic system should be divided into domains, for the sake of minimum free energy. The size of domain, domain wall width andthe orientation relations between neighboring domains can be ascertained well.However it is an over-simple assumption that equilibrium thermodynamics deals with ferroelectric phase transitions and other ferroic phase transitions. A real phase transition process is very complicated. On the contrary, equilibrium thermodynamics, which is in view of infinite systems, is a kind of "static theory". For this reason, it is impossible that the description of phase transition systems, which vary with position and time, always in agreement with experimental facts well. Heat hysteresis, which exists in the course of first order ferroelectric phase transitions, exposes the limits of equilibrium thermodynamics. It is an irreversible process obviously. This can not be described by equilibrium thermodynamics in principle, but by thermodynamics of irreversible processes.Thermodynamics of irreversible processes, which is in view of inhomogeneous systems, consists of linear and nonlinear thermodynamics, according to the degree of deviation of a system's states from equilibrium. Linear thermodynamics is suitable for systems whose states slightly deviate from equilibrium. In fact, it has been assumed that ferroelectric phase transition process is in equilibrium. This is a reasonable assumption. Strictly speaking, equilibrium states can not exist in any a real process, otherwise it is impossible to achieve the transition between any two states. On the contrary, equilibrium thermodynamics is a kind of "static" theory. Because it is always to deal with problems forthe simplest case at first, stnall degree of deviation from equilibrium inferroelectric phase transition systems is assumed. It is no doubt that thecase of being far from equilibrium is more complicated. Only when theassumption can not reflect the nature of ferroelectric phase transitionsother more complicated factors are taken into account. In this work, asystem under study is in condition of "stationary" state was assumed.First, the assumption owns a basis of statistical physics. For the variationof a system, there are two scales of time that one is called "fast varying"and another is called "slow varying". The former reflects the microscopictime scale. By fast varying, the system will be in condition of "fluidstate", then relaxation towards equilibrium or non-equilibrium stationarystate unavoidably with a slow velocity (i.e. "slow varying", whichreflects the macroscopic time scale). Moreover, the assumption owns abasis of fact. Usually, a phase transition is achieved by "quasi-static"warming or cooling. So, it is possible that the system is in condition ofstationary state not far from equilibrium. Simultaneously, the principle ofminimum entropy production can be met, which is the result obtained byPrigogine in 1954. It is interesting to note that it was after the time whenDevonshire accomplished his works for ferroelectric phase transitions.Heat hysteresis of first order ferroelectric phase transitions can be described by thermodynamics of irreversible processes. First, system in condition of local equilibrium was assumed and Gibbs equation for a random local small region was given together with a set of conservation laws. Then, the entropy flux density vector and the rate of local entropyproduction were obtained. The course of a ferroelectric phase transition was analyzed by the principle of minimum entropy production. Existence of heat hysteresis is proved.The occurrence of domain structure in ferroics can not be property described by using equilibrium thermodynamics or dynamics of domain structure. Because the existing of domain structure is a prerequisite to dynamic studies of domain structure, and domain structure damages the homogeneity of systems. Moreover, equilibrium thermodynamics faces the awkward situation that the surface effect of a system (depolarization field, demagnetization field etc) has to be taken into account when the existing of domain structure is tried to be proved and domain configuration is tried to ascertained. These facts make equilibrium thermodynamics has to modify its theoretical foundation, for equilibrium thermodynamics is strictly correct only on condition that the thermodynamic limit can be met. This means a system is infinite without surface. Therefore, this conflicts with facts. The existing of a system surface should be a prerequisite if we describe the occurrence of domain structure in ferroics, because every part of an infinite system is identical according to its physical nature. The rate of local entropy production in view of different systems, i.e., ferroelectric, ferromagnetic and ferroelastic has been obtained. For the rate of entropy production of a stationary state is in its minimum, the variation of the orientation of every thermodynamic force with location causes the variation of the orientation of the corresponding thermodynamic flux with location. Thisleads to the occurrence of domain structure in ferroics."Molecular field" is a concept that companies with ferroic phase transitions. It was introduced by Weiss in 1907, explaining the spontaneous magnetization. To describe ferroic phase transitions using thermodynamics of irreversible processes, molecular field is also a useful concept. If molecular field has been not introduced, the theory would disagree with facts. This appears as being puzzled by the necessity of discussing the sign of the applied electric potential. In view of thermodynamics of irreversible processes, molecular field should be regarded as an embodyment of the inhomogeneity of the interactions in a system. If ferroelectric phase transitions is regarded as a kind of thermal-electric coupling transport processes, the Onsager relations can be applied to first order ferroelectric phase transitions and second order ferroelectric phase transitions for some new explanations. What's more, for molecular field is a kind of "internal field", molecular field energy, which is one part of the system's inner energy, should be dealt with carefully for avoiding to obtain wrong results. Molecular field is an embodyment of a kind of mechanical-thermal-electric coupling in multiparticle systems. In order to characterize it well, the two-component molecular field was introduced, and the influences of stress on ferroelectric phase transitions was analyzed.There is a boundary between the ferroelectric phase and the paraelectric phase in a system of coexisting two phases in the course of a ferroelectric phase transition. Bringing the relations to light, which arebetween the width of boundary, velocity of interface motion and the temperature, pressure and concentration, is the job of dynamics of ferroelectric phase transitions. In the last part of the work, the research of complexity of ferroic phase transitions was reviewed and summarized comprehensively from the points of view of thermodynamics of irreversible processes, dynamics and non-equilibrium statistical physics.The main results were summarized as the following The entropy flux density vector and the rate of local entropyproduction for a ferroelectric phase transition have been obtained asrespectively, where Js is the entropy flux, Jq is the heat flux, JP is the polarization current, T is the temperature, crs is the rate of local entropy production, Jn is the material flow, // is the chemical potential, ^ is the applied electric potential and can be regarded as a random positive constant if the electric field is not applied. It can be seen from above equations that heat hysteresis is not an intrinsic property of first order ferroelectric phase transition systems, though hysteresis is related to the discontinuity of spontaneous polarization P at phase transition temperature, the finiteness of a system surface is another factor that causes heat hysteresis. Also, stress, which occurs in the course of ferroelectric phase transitions, is another factor that causes heathysteresis. The entropy flux density vector and the rate of local entropyproduction are similar for ferromagnetic phase transitions.? For ferroelastic phase transitions, those was obtained as thefollowingwhere J$ is the entropy flux density, JqV is the conductive heat flux density, v is the velocity, s is the entropy density, T is the temperature, crs is the local entropy production, P' can be regarded as the self-drive factor of spontaneous strain i.e. molecular field. A ferroelastic phase transition is a transition accompanied with a change of point group. Domain structure in ferroics is an embodyment of the disappeared symmetric operations in the course of a transition. In the treatment of domain occurrence in ferroics, the finiteness of the system (existence of surface) and the irreversibility of the process (asymmetry of time) were taken into account. Finiteness of the system make the thermodynamic forces have almost infinite space symmetry. This almost infinite space symmetry, combined with the asymmetry of time, reproducse the symmetry operations lost at the phase transition in the ferroic phase. ? Molecular field is an embodiment of the inhomogeneity of the interactions in a ferroic phase transition. We applied the Onsager relations to ferroelectric phase transitions. For a first order ferroelectricphase transition, there are complete differences between the transformed region, the transforming region and the un-transformed region. The gradient of temperature and spontaneous polarization in transformed region keep constant. Spontaneous polarization is changed abruptly in the transforming region where lies a source or sink of heat exists. The un-transformed region can be regarded as a equilibrium system basically. Second order ferroelectric phase transitions can be described well by equilibrium thermodynamics. All ferroic phase transitions must have volume-shape effect because charge is a fundamental attribute of matter. Mechanical-thermal-electric coupling is the nature of multiparticle systems.? The effect of stress was taken into account and the corresponding entropy flux density vector and rate of local entropy production obtained as the followingwhere Js is the entropy flux density, JqX is the conductive heat flux density, v is the velocity, JP is the polarization current, Je2 is the convective electric flux, T is the temperature, as is the local entropy production, and P' is the internal potential and "stress" and, can be regarded as two components of the binary molecular field and related by the following equationThe above equation reveals the mechanical-thermal-electric coupling of ferroelectric phase transitions. The influences of stress on ferroelectric phase transitions were described by using "superposition" the real stress and the self-drive factor of spontaneous strain. Usually, the strain of a system surface occurs at phase transition hinders the internal part of phase transition.
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