Theory Of Relaxor-ferroelectricity

Relaxor-ferroelectrics（RFEs）have both novel physical properties and very extensive and important applications.Therefore,the exploration of the mechanism of relaxor-ferroelectricity will not only deepen the understanding of nature,but also give guiding significance for its practical application.Based on the problems that the existing theoretical models of relaxor-ferroelectricity statics lack the ability of quantitative description of the corresponding experimental results,and the existing theoretical model of relaxor-ferroelectricity dynamics is still phenomenological and preliminary,it is undoubtedly one of the most valuable works in the field of RFEs to explore the theoretical model that can quantitatively describe both the statics and dynamics of relaxor-ferroelectricity.According to the following facts that RFEs have periodic crystal lattices,but the distribution of at least two elements on the lattices is disordered or uneven,i.e.structure ordered-component disordered systems,and traditional-and relaxor-ferroelectricity can be transformed into each other,this paper attempts to establish a new theory of statics and dynamics of relaxor-ferroelectricity,i.e.random-site random-field Ising-model of pseudospins（PSs）with Glauber dynamics（RS-RF-IGM）.In order to solve the RS-RF-IGM,this paper presents a new local-mean-field（LMF）method of PS-string（PSS-LMF）,which includes the distributions of PS number and field strength the PSs.Based on the relationship between PSS-LMF and the credible Kramers Wannier mean-field to solve Ising-model,and topological structure of PSs in RS-RF-IGM,it is concluded that PSS-LMF is a credible method to solve this model.Based on the PSS-LMF method,the order-parameter（spontaneous polarization）,local-order-parameter,specific-heat,static-susceptibility and phase diagram of 3-dimensional（3D）-RS-RF-IGM corresponding to 3D-RFEs are calculated,especially the local order parameter changes from high temperature independent polar-nano-regions（PNR）to fractal structures at low temperature.In addition,in view of the problems existing in the existing phenomenological theory of Burns transformation,a new microscopic theory of Burns transformation is proposed based on the coupling of PSs and lattice,and the problems of the existing Burns transformation theory are eliminated.Also based on the PSS-LMF method,it is calculated that the evolution equation of the thermal fluctuation of the local-order-parameter in RS-RF-IGM with time and then the complex susceptibility related to the fluctuation.In particular,the Vogel-Fulcher empirical law,which has always represented the most mysterious feature of relaxor-ferroelectric physics,is given.It originates from the correlation-relaxation of PSs in the subsystem higher than physical-one-dimensional and affected by the effective-interface effect.The comparison between theoretical and experimental results shows that:（1）The predicted order-parameter,specific-heat,high-frequency-high-temperature complex susceptibility and Burns transition are quantitatively consistent with the experimental results of the canonical RFE,PMN;（2）The calculated local-order-parameter is qualitatively consistent with the experimental results of PMN,PMN_1-x-（Pb Ti O₃）_x and Sr_xBa_1-xNb₂O₆;（3）The theoretical phase diagram of 3D-RS-RF-IGM（i.e.the evolution of traditional-ferroelectrics?RFEs?paraelectrics with PS concentration）are also qualitatively consistent with that of Ba Ti_1-xZr_xO₃ with x;（4）According to the results of local-order-parameter and complex susceptibility of our theory in this paper,it is concluded that the intermediate-transformation of RFEs comes of the crossover from the high-temperature individual polar-nanoregions to the low-temperature fractal-structure of local-order-parameter,and its characteristic temperature is the dispersion temperature of the relaxor-ferroelectric phase transition.Aiming at that there is not yet clear definition of canonical-RFEs till now,we try to give a definition of canonical-RFEs according to the theory of this paper.Based on this definition,PMN is very close to canonical-RFEs.In addition,we discuss whether RFEs can be classified into ferroelectrics according to the theory.In order to verify the feasibility of the proposed PSS-LMF method in this paper,the results of this method are compared and discussed with Monte Carlo simulation,and it is concluded that the existing Monte Carlo simulations and PSS-LMF of two-dimensional-random-site-Ising-model are mutually confirmed on the whole.By using Ising-model of statics and Mason theory of dynamics,which are the most successful in describing the traditional-ferroelectricity,as a reference,this paper compares RS-RF-IGM with other representative models of relaxor-ferroelectricity in three aspects of mathematical system,experimental verification and micro-level.Compared with the other models:（1）In terms of the integrity of the mathematical system,the theoretical model in this paper includes dynamic Hamiltonian,and gives more quantitative theoretical predictions that can be verified by experiments;（2）In terms of experimental verification,the theoretical model in this paper not only gives more theoretical prediction parameters,but also quantitatively or qualitatively agrees with the experimental data;（3）In terms of the micro-level,the other representative models of is only at mesoscopic or phenomenological level,while the micro-level of our model that describes the relaxor-ferroelectricity statics is the same as Ising model,and RS-RF-IGM is more micro than Mason theory of traditional-ferroelectricity dynamics.