Theory of relaxor-ferroelectricity

Abstract

Relaxor-ferroelectrics are fascinating and useful materials, but the mechanism of relaxor-ferroelectricity has been puzzling the scientific community for more than 65 years. Here, a theory of relaxorferroelectricity is presented based on 3-dimensional-extended-random-site-Ising-model along with Glauber-dynamics of pseudospins. We propose a new mean-field of pseudospin-strings to solve this kinetic model. The theoretical results show that, with decreasing pseudospin concentration, there are evolutions from normal-ferroelectrics to relaxor-ferroelectrics to paraelectrics, especially indicating by the crossovers from, (a) the sharp to diffuse change at the phase-transition temperature to disappearance in the whole temperature range of order-parameter, and (b) the power-law to Vogel-Fulcher-law to Arrheniusrelation of the average relaxation time. Particularly, the calculated local-order-parameter of the relaxorferroelectrics gives the polar-nano-regions appearing far above the diffuse-phase-transition and shows the quasi-fractal characteristic near and below the transition temperature. We also provide a new mechanism of Burns-transformation which stems from not only the polar-nano-regions but also the correlationfunction between pseudospins, and put forward a definition of the canonical relaxor-ferroelectrics. The theory accounts for the main facts of relaxor-ferroelectricity, and in addition gives a good quantitative agreement with the experimental results of the order-parameter, specific-heat, high-frequency permittivity, and Burns-transformation of lead magnesium niobate, the canonical relaxor-ferroelectric. 65 years after the discovery of so-called relaxor-ferroelectrics (RFEs) 1 , this manuscript promises to deliver the still missing theory of relaxor-ferroelectricity [Supplementary Information (SI) 1] 2-10 . For the existing phase-transition theories of normal-ferroelectrics are based on both structure and component homogeneity [11][12][13] , theoretically, the main difficulty in describing relaxor-ferroelectricity originates from RFEs being component-disordered although structure-ordered, i.e. disordered components on crystal lattices [14][15][16][17][18][19] . In fact, understanding how the component disorder on lattices leads to novel properties is an outstanding scientific challenge for a broad class of materials that include not only RFEs, but also spin glasses 20 , superelastic strain glasses (shape-memory alloys) 21 , colossal magnetoresistance manganites, and some superconductors 22 .The best-known member of the RFE family is the disordered perovskite crystal PbMg 1/3 Nb 2/3 O 3 (PMN), for which 27 years ago a plausible interpretation of its diffuse-phase-transition (DPT) was proposed by Westphal et al. 3 . Fluctuations of random-internal-electric-field (RIEF) emerging from the quenched charge disorder of the RFE are stabilizing the typical disordered polar nanodomain state. This disordering mechanism convinced sceptical experts at the latest thanks to a favorable review of Cowley et al. 16 . The subseq...

No or Diffuse Phase-Transition With Temperature in One-dimensional Ising Model?

“…Obviously, as the scale of the local-order-parameter proposed in Ref. 21 and this paper tends to infinity, it becomes the global-order-parameter. So, local-order-parameter can provide a unified description of 1 st and 2 nd -order phase-transitions as well as diffuse-phase-transition.…”

“…According to the method of reference 21 , the temperature corresponding to the maximum of −  is defined as the characteristic temperature ( ) of diffuse phase-transition in 1D-IM, and it is obtained = 0.32 ⁄ (Fig. 2B).…”

“…Although diffuse phase-transition is common in component-heterogeneous [10][11][12][13][26][27][28][29] and small-size [30][31][32] systems, there is no accurate calculation of the corresponding theoretical model so far 21 . Therefore, the exact results in this paper lay the theoretical foundation of this kind of phase-transition.…”

“…The present and relevant 2,22,23 results show that this theory is valid for IM of all dimensions in judging whether there exists phase-transition, although its predicting phase-transition behaviors, such as the transition temperature and the subtle characteristics of order parameter and heat capacity, are different from the exact solutions 2,22,23 . It also shows that Weiss-type mean-field approximation 21 is an effective and feasible method for Ising-category models of phase-transition which are too complex and difficult to get their exact solutions.…”

Mn Katkılı PIN-PMN-PT Tekil Kristalinin Dielektrik Katsayısı, Relaksiyon Zamanı ve Aktivasyon Enerjisinin Hesaplanması

“…2011). Ancak, relaksör-ferroelektrik malzemelerin gevşeme süresi davranımının doğruluğu, halihazırda ileri teorik ve deneysel çalışmalara ihtiyaç duymaktadır (Zhang and Huang 2020). Bu çalışmada, Mn-0.15PIN-0.55PMN-0.30PT kristal malzemenin her iki Raman modu için gevşeme zamanının sıcaklığa bağlılığı, PS ve EF model için hesaplanan sönümleme sabiti değerleri kullanılarak hesaplanmıştır.…”