Nonergodic State Research Articles

The structural evolution and electric field-induced strain performance of Bi0.5(Na0.41K0.09)TiO3–Ba(Fe0.5Sb0.5)O3 lead-free piezoelectric ceramics

In recent years, lead-free Bi0.5Na0.5TiO3 (BNT) based piezoelectric ceramics with excellent strain properties have gained widespread recognition for their application in high-precision displacement actuators. The (1-x)(0.82Bi0.5Na0.5TiO3-0.18K0.5Bi0.5TiO3)-xBa(Fe0.5Sb0.5)O3 ceramics were fabricated through the die-pressing method in this work. The effect of BFS introduction on the dielectric, ferroelectric and microstructure characteristics of BNKT ceramics was systematically investigated. Among these compositions, the BNKT-0.015BFS ceramics exhibited a piezoelectric strain coefficient (d33*) of 658 pm/V at an electric field of 55 kV/cm, while achieving a strain response of 0.51 % at 85 kV/cm. The observed improvement in strain performance can be attributed to the evolution from non-ergodic relaxor state to ergodic relaxor state caused by BFS substitution. Furthermore, transmission electron microscopy (TEM) explicitly confirmed coexistence of rhombohedral and tetragonal phase and revealed the morphology of nanosized domains. This study adds to a deeper comprehension of the characteristics of strain response enhancement in BNT-based ceramics, opening up avenues for designing novel lead-free piezoelectric ceramics with outstanding electromechanical performance.

Optimized pyroelectric behaviors by constructing the nonergodic-ergodic transition state

Bi0.5Na0.5TiO3 (BNT)-based relaxors are considered as potential candidates for pyroelectric applications due to their excellent pyroelectric performances. However, the excellent pyroelectric response in BNT-based relaxors is generally accompanied by a rapid decrease in the depolarization temperature Td, limiting the operation temperature. Herein, we find that the mixed non-ergodic and ergodic relaxor states (a kind of transition system) can promote polarization rotation and remain the reversibility of polarization transformation simultaneously, thereby improving pyroelectric performances and maintaining the Td . The Li+-doped BNKT-based relaxors which possess such a transition state exhibit excellent room temperature (RT) pyroelectric coefficients (1247 μCm−2K−1), and also, the Td can maintain at 69℃. This work provides a strategy for further insight into the enhanced pyroelectric response, which promotes the development of eco-friendly pyroelectric applications (such as infrared detection, temperature sensors, and pyroelectric energy harvesting).

Arrested states in colloidal fluids with competing interactions: A static replica study.

We present the first systematic application of the integral equation implementation of the replica method to the study of arrested states in fluids with microscopic competing interactions (short-range attractive and long-range repulsive, SALR), as exemplified by the prototype Lennard-Jones-Yukawa model. Using a wide set of potential parameters, we provide as many as 11 different phase diagrams on the density (ρ)-temperature (T) plane, embodying both the cluster-phase boundary, TC(ρ), and the locus below which arrest takes place, TD(ρ). We describe how the interplay between TC and TD-with the former falling on top of the other, or the other way around, depending on thermodynamic conditions and potential parameters-gives rise to a rich variety of non-ergodic states interspersed with ergodic ones, of which both the building blocks are clusters or single particles. In a few cases, we find that the TD locus does not extend all over the density range subtended by the TC envelope; under these conditions, the λ-line is within reach of the cluster fluid, with the ensuing possibility to develop ordered microphases. Whenever a comparison is possible, our predictions favorably agree with previous numerical results. Thereby, we demonstrate the reliability and effectiveness of our scheme to provide a unified theoretical framework for the study of arrested states in SALR fluids, irrespective of their nature.

The thermal depolarization behavior of PMN-PT-BZT relaxor ferroelectric ceramics from the standpoint of domain structure transitions

The thermal depolarization behavior of PMN-PT-5BZT relaxor ferroelectric ceramics was studied, and the depolarization mechanism was discussed from the perspective of domain structure transitions. In addition to the transition from MPB structure at room temperature to cubic phase at high temperature, the structure symmetry of PMN-PT-5BZT ceramics has no obvious change with increasing temperature. However, the ceramic had experienced a transition process from ferroelectric state to nonergodic relaxor state, and then to ergodic relaxor state. The results of temperature dependence of ferroelectric properties showed that the depolarization temperature Td corresponds to the transition temperature TF-NR from ferroelectric state to nonergodic relaxor state, and there is an obvious dielectric abnormal peak at this temperature, which is mainly due to the depolarization behavior caused by the decrease of macrodomain size and the beginning of transition to nanodomains.

Realization of the Giant Pyroelectric Response via Modulated Polar Structures.

Among pyroelectric materials, Bi0.5Na0.5TiO3 (BNT)-based relaxors are particularly noteworthy due to their significant polarization fluctuation near the depolarization temperature (Td), resulting in a large pyroelectric response. What has been overlooked is the dynamic behavior of inherent polar structures, particularly the temperature-dependent evolution of polar nanoregions (PNRs), which significantly impacts the pyroelectric behavior. Herein, based on the large pyroelectric response origination (the ferroelectric-relaxor phase transition), the mixed nonergodic and ergodic relaxor (NR+ER) critical state is constructed, which is believed to trigger the easily fluctuating polarization state with excellent pyroelectric response. Composition engineering (with Li+, Sr2+, and Ta5+) strategically controls the relaxor process and modulates the dynamic behavior of inherent polar structures by the random field effect. The pyroelectric coefficient of more than 1441 µCm-2K-1 at room temperature (RT), more than 9221 µCm-2K-1 (RT), and ≈107911 µCm-2K-1 (Td) are achieved in the Li+-doped sample, the Sr2+-doped sample, and the (Li++Ta5+) co-doped sample, respectively. This work earns the highest RT pyroelectric coefficient in BNT-based relaxors, which is suitable for pyroelectric applications. Furthermore, it provides a strategy for modulating the pyroelectric performance of BNT-based relaxors.

High-Temperature Energy Storage Properties of Bi0.5Na0.5TiO3-0.06BaTiO3 Thin Films

Bi0.5Na0.5TiO3-0.06BaTiO3 (BNT-BT) thin films were prepared via both chemical solution (CSD) and pulsed laser deposition (PLD). The structural, dielectric, and ferroelectric properties were investigated. High stability of the dielectric permittivity or TCC (∆ε/ε (150 °C) ≤ ±15%) over a wide temperature range from room temperature to 300 °C was obtained. Distinctly, the CSD film showed high TCC stability with variation of ±5% up to 250 °C. Furthermore, the CSD film showed an unsaturated ferroelectric hysteresis loop characteristic of the ergodic relaxor phase. However, the PLD one exhibited an almost saturated loop characteristic of the coexistence of both ergodic and non-ergodic states. The energy storage properties of the prepared films were determined using P–E loops obtained at different temperatures. The results show that these films exhibited a stable and improved energy storage density comparable to ceramic capacitors. Moreover, the CSD film exhibited more rigidity and better energy storage density, which exceeded 1.3 J/cm3 under a weak applied field of 317 kV/cm, as well as interesting efficiency in a large temperature range. The obtained results are very promising for energy storage capacitors operating at high temperatures.

Entanglement dynamics of multi-parametric random states: a single parametric formulation

A non-ergodic quantum state of a complex system is in general random as well as multi-parametric, former due to a lack of exact information due to complexity and latter reflecting its varied behavior in different parts of the Hilbert space. An appropriate representation for the reduced density matrix of such a state is a generalized, multi-parametric Wishart ensemble with unit trace. Our theoretical analysis of these ensembles not only resolves the controversy about the growth rates of the average information entropies of the generic states but also leads to new insights in their entanglement dynamics. While the state itself is multi-parametric, we find that the growth of the average measures can be described in terms of an information-theoretic function, referred as the complexity parameter. The latter in turn leads to a common mathematical formulation of the measures for a wide range of states; it could also act as a possible tool for hierarchical arrangement of the entangled states of different systems.

Subharmonic fidelity revival in a driven PXP model

The PXP model hosts a special set of nonergodic states, referred to as quantum many-body scars. One of the consequences of quantum scarring is the periodic revival of the wave function fidelity. It has been reported that quantum fidelity revival occurs in the PXP model for certain product states, and periodic driving of the chemical potential can enhance the magnitude of quantum revival and can even change the frequencies of revival showing the subharmonic response. Although the effect of the periodic driving in the PXP model has been studied in the limit of certain perturbative regimes, the general mechanism of such enhanced revival and frequency change has been barely studied. In this paper, we investigate how periodic driving in the PXP model can systematically control the fidelity revival. Particularly, focusing on a product state called the N\'eel state, we analyze the condition of driving to enhance the magnitude of revival or change the frequencies of revival. To clarify the reason for such control, we consider the similarities between the PXP model and the free spin-$1/2$ model in graph theoretical analysis and show that the quantum fidelity feature in the PXP model is well explained by the free spin-$1/2$ model. In addition, under a certain limit of the driving parameters, an analytic approach to explain the main features of the fidelity revival is also applied. Our results give insight into the scarring nature of the periodically driven PXP model and pave the way to understand the (sub)harmonic responses in these models and controls thereof.

Ultra-high energy storage performance in Bi5Mg0.5Ti3.5O15 film via a low temperature-induced ergodic relaxation state

Good low-temperature energy storage characteristics are conducive to the successful merger of Si-based semiconductor technology with dielectric energy storage films. Due to low maximum polarization intensity and poor crystallinity at low temperatures, however, it is difficult for dielectric energy storage films to attain excellent dielectric energy storage properties. Herein, Bi5Mg0.5Ti3.5O15 films accomplish the shift from a non-ergodic relaxor state to an ergodic relaxation state by lowering the annealing temperature, which simultaneously increases insulating characteristics. The energy loss is reduced while maintaining a high polarization intensity and high breakdown electric field, which results in the ultra-high energy storage density (122.2 J/cm3) and efficiency (77.3 %) of the Bi5Mg0.5Ti3.5O15 film at an annealing temperature of 500 °C. Meanwhile, the Bi5Mg0.5Ti3.5O15 films show excellent stability in terms of temperature (−20 °C to 150 °C), frequency (0.05 kHz–20 kHz), and fatigue resistance (1 ×108). The domain states and insulation properties of temperature-controlled films are used in this work to achieve ultra-high energy storage properties, and a concise and feasible scheme for the application of low temperature energy storage films in semiconductor technology is provided.

Giant dynamic electromechanical response via field driven pseudo-ergodicity in nonergodic relaxors

Enhanced electromechanical response can commonly be found during the crossover from normal to relaxor ferroelectric state, making relaxors to be potential candidates for actuators. In this work, (Pb0.917La0.083)(Zr0.65Ti0.35)0.97925O3 ceramic was taken as a case study, which shows a critical nonergodic state with both double-like P-E loop and irreversible relaxor-normal ferroelectric phase after poling at room temperature. The low-hysteresis linear-like S-P2 loop, in-situ synchrotron X-ray diffraction and transmission electron microscope results suggest that the nonpolar relaxor state acts as a bridge during polarization reorientation process, accompanying which lattice strain contributes to 61.8% of the total strain. In other words, the transformation from normal ferroelectric to nonergodic relaxor state could be triggered by electric field through polarization contraction, which could change to be spontaneously with slightly increasing temperature in the nonergodic relaxor zone. Therefore, pseudo-ergodicity in nonergodic relaxors (i.e. reversible nonergodic-normal ferroelectric phase transition) driven by periodic electric field should be the main mechanism for obtaining large electrostrain close to the nonergodic-ergodic relaxor boundary. This work provides new insights into polarization reorientation process in relaxor ferroelectrics, especially phase instability in nonergodic relaxor zone approaching to freezing temperature.

Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations

We provide real-space and Fock-space (FS) characterizations of ergodic, nonergodic extended (NEE) and many-body localized (MBL) phases in an interacting quasiperiodic system, namely, the generalized Aubry-Andr\'e-Harper model, which possesses a mobility edge in the noninteracting limit. We show that a mobility edge in the single-particle (SP) excitations survives even in the presence of interaction in the NEE phase. In contrast, all single-particle excitations get localized in the MBL phase due to the MBL proximity effect. We give complementary insights into the distinction of the NEE states from the ergodic and MBL states by computing local FS self-energies and decay length associated, respectively, with the local and the nonlocal FS propagators. Based on a finite-size scaling analysis of the typical local self-energy across the NEE to ergodic transition, we show that MBL and NEE states exhibit qualitatively similar multifractal character. However, we find that the NEE and MBL states can be distinguished in terms of the distribution of local self-energy and the decay of the nonlocal propagator in the FS, whereas the typical local FS self-energy cannot tell them apart.

Distinct microstructure and property evolution of 0.76(Bi0.5Na0.5)TiO3-0.24SrTiO3 ferroelectric ceramics synthesized with different TiO2 reactants

Single phase 0.76(Bi0.5Na0.5)TiO3–0.24SrTiO3 ferroelectric ceramics have been synthesized with homogenous anatase and hierarchical rutile TiO2 raw reactants (BNST-A and BNST-R). Either calcined powder persists the microstructure characteristics of raw reactants. As the result, when the sintering temperature increases from 1000 to 1200 °C, the average grain size and density of BNST-A increase from 0.49 to 1.48 μm and 5.02 to 5.61 g/cm3, while those of BNST-R from 0.86 to 1.44 μm and 5.37 to 5.61 g/cm3. BNST-A illustrates a predominant ergodic relaxor state, and BNST-R prefers a non-ergodic relaxor state, as evidenced by the distinct polarization-electric field loops and current-electric field curves. Especially, such a distinct ferroelectric state is independent of sintering temperature. It is believed that the special hierarchical microstructure of rutile TiO2 reactant is beneficial to form denser ceramics with larger grains, and thus suppresses the contributions of polar nanoregions and defect-induced built-in field to ferroelectric property, leading to non-ergodic relaxor state. This work clearly demonstrates the nonnegligible effects of TiO2 reactants on the microstructure and properties of BNST ferroelectric ceramics.

Generalized Survival Probability.

Survival probability measures the probability that a system taken out of equilibrium has not yet transitioned from its initial state. Inspired by the generalized entropies used to analyze nonergodic states, we introduce a generalized version of the survival probability and discuss how it can assist in studies of the structure of eigenstates and ergodicity.

Electrostatic energy storage performances of La(Ni2/3Ta1/3)O3‐modified Na0.5Bi0.5TiO3 lead‐free ceramics

AbstractCeramic capacitors with high electrostatic energy storage performances have captured much research interest in latest years. Sodium bismuth titanate (Na0.5Bi0.5TiO3)‐based ferroelectric ceramics show great potential due to their environment‐friendly composition, high polarization, and excellent relaxor properties. However, the nonergodic relaxor state of Na0.5Bi0.5TiO3‐based ceramics hampers the decrement of remanent polarization, leading to poor energy storage performance. Herein, the (1 − x)Na0.5Bi0.5TiO3–xLa(Ni2/3Ta1/3)O3 ceramics were designed to generate the transformation between nonergodic and ergodic relaxor state. As a result, the ceramics exhibit improved dielectric relaxation, slim polarization–electric field loops, and flattened current–electric field curves due to highly dynamic polar nanoregions. Particularly, the 0.85Na0.5Bi0.5TiO3–0.15La(Ni2/3Ta1/3)O3 ceramics show large breakdown electric field Eb (345 kV/cm), high recoverable energy density Wrec (3.6 J/cm3), and efficiency η (80.6%), revealing potential applications in electrostatic energy storage.

Quasielastic Light Scattering in the Broadband Brillouin Spectra of Relaxor Ferroelectric PbMg1/3Nb2/3O3

In this paper, the behavior of quasielastic light scattering (QELS) in a PbMg1/3Nb2/3O3 (PMN) crystal under broadband Brillouin light scattering in a temperature range from 750 K to 80 K was studied. It was shown that QELS consists of two components: narrow (0.9 GHz to 11 GHz) and wide (80 GHz to 600 GHz). The dependencies of the intensity, I, of these components on the frequency, ν, are well described by the power law I ~ eνα, with different α, and are determined by the distribution of the relaxation times. The analysis of the Brillouin spectra showed that the behavior of the relaxation time of both the components of QELS with temperature change is well described by the Arrhenius law. Additionally, in the vicinity of the intermediate temperature T* ≈ 380 K, a critical relaxation time behavior for the narrow component of QELS was detected. In the vicinity of the same temperature, a maximum in the integral intensity of both the components of QELS was observed, which is adjacent to another maximum in the region of the Vogel-Fulcher temperature TVF ≈ 250 K corresponding to the transformation of the crystal to a nonergodic state.

Optimizing strain response in lead-free (Bi0.5Na0.5)TiO3-BaTiO3-NaNbO3 solid solutions via ferroelectric / (non-)ergodic relaxor phase boundary engineering

Lead-free bismuth sodium titanate (Bi0.5Na0.5)TiO3 (BNT) and related solid solutions are potential piezoelectric materials for such applications as actuators and transducers if their excellent strain responses and piezoelectric properties can be optimized. In this work, a large strain response of 0.61% is achieved in lead-free (0.94-x%)(Bi0.5Na0.5)TiO3-0.06BaTiO3-x%NaNbO3 (x = 0 –6, BNT-6BT-xNN) ceramics with the composition of x = 3.5 in a pseudo-cubic structure. Coexistence of ferroelectric (FE) and relaxor (RE) domain structures is observed in all the unpoled ceramics and the enhanced strain response is believed to be related to the evolution of the ergodic relaxor (ER) and non-ergodic (NR) states thanks to the substitution of antiferroelectric NN. BNT-6BT-3.5NN is a critical composition near the FE/NR/ER phase boundary close to room temperature (RT) and its high strain response arises from a synergistic combination of a reversible electric-field-induced phase transition and an active domain switching in the mixed NR/ER state. This work provides new insights into the dynamic interplay between mesoscopic domains and macroscopic electrical properties in the BNT-based piezoceramics.

Ion dynamics in a highly compressed solution of tetra-ethylammonium – tetra-fluoroborate salt in propylene carbonate: A study in the equilibrium and glassy states

Electrical conductivity of a solution of (Et4N+,BF4−) in propylene carbonate is measured by varying the pressure and temperature along different thermodynamic paths: pressure is increased from a low value in the liquid state up to ̴ 3.6 GPa well above the glass-transition pressure PG, along isotherms at temperatures between ̴ 295 K and ̴ 326 K. Up to a crossover pressure Pcross ̴ 1 GPa, the dc-conductivity decreases and obeys the Walden rule. Above Pcross, an anomalous pressure-dependence of the conductivity spectra is observed, leading to an increase in dc-conductivity up to PG. The dc-conductivity obeys density scaling, showing in the glassy state an exponential decrease against the scaling variable, independently of the thermobaric history of the sample. The conductivity spectra obey the time-temperature-pressure-superposition principle, therefore, the ion dynamics is not affected by the transition from the liquid state to the non-ergodic glassy state.

Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity

We explore the role of non-ergodicity in the relationship between income inequality, the extent of concentration in the income distribution, and income mobility, the feasibility of an individual to change their position in the income rankings. For this purpose, we use the properties of an established model for income growth that includes 'resetting' as a stabilizing force to ensure stationary dynamics. We find that the dynamics of inequality is regime-dependent: it may range from a strictly non-ergodic state where this phenomenon has an increasing trend, up to a stable regime where inequality is steady and the system efficiently mimics ergodicity. Mobility measures, conversely, are always stable over time, but suggest that economies become less mobile in non-ergodic regimes. By fitting the model to empirical data for the income share of the top earners in the USA, we provide evidence that the income dynamics in this country is consistently in a regime in which non-ergodicity characterizes inequality and immobility. Our results can serve as a simple rationale for the observed real-world income dynamics and as such aid in addressing non-ergodicity in various empirical settings across the globe. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

Quantum transitions, ergodicity, and quantum scars in the coupled top model.

We consider an interacting collective spin model known as coupled top (CT), exhibiting a rich variety of phenomena related to quantum transitions, ergodicity, and formation of quantum scars, discussed in our previous work [Mondal, Sinha, and Sinha, Phys. Rev. E 102, 020101(R) (2020)2470-004510.1103/PhysRevE.102.020101]. In this work, we present a detailed analysis of the different type of transitions in the CT model, and find their connection with the underlying collective spin dynamics. Apart from the quantum scarring phenomena, we also identify another source of deviation from ergodicity due to the presence of nonergodic multifractal states. The degree of ergodicity of the eigenstates across the energy band is quantified from the relative entanglement entropy as well as multifractal dimensions, which can be probed from nonequilibrium dynamics. Finally, we discuss the detection of nonergodic behavior and different types of quantum scars using "out-of-time-order correlators," which has relevance in the recent experiments.

Lead-free Bi0.5(Na1-xKx)0.5TiO3 relaxor ferroelectric ceramics for a wearable energy harvester

We fabricated Bi0.5(Na1-xKx)0.5TiO3 (BNKT) [x = 0.16–0.24] relaxor ferroelectric ceramics that undergo a transition from the non-ergodic state (NR) to the ergodic state (ER) using a conventional solid-state reaction method. Structural analysis was conducted using X-ray diffraction (XRD), and the electrical properties related to the polarization (P) and strain (S) resulting from the external electric field were analyzed. With an increase in the component ratio x, from 0.16 to 0.24, the remnant polarization (Pr) reduced continuously from ∼18 to ∼3 μC/cm2, respectively. Concomitantly, the form of the S-E loops changed from a butterfly-like shape to a sprout shape (in which the negative strain value (Sneg) that approaches 0 appears as a special feature), suggesting that the NR of the BNKT relaxor ferroelectric ceramic at x = 0.16 transitions to the ER as the composition ratio x increases. In particular, for x = 0.20, the inverse piezoelectric coefficient (d33*) achieved a maximum value of 386 pm/V, while the value of the Pr was relatively low at ∼ 6 μC/cm2. To investigate the possible application as a wearable energy harvester, BNKT ceramic powders of various compositions were mixed with polydimethylsiloxane (PDMS) to fabricate flexible generator devices. The change in the output voltage and current as a function of the composition ratio x had a similar tendency as the change in the value of d33*, suggesting that the ER of relaxor ferroelectric ceramics with a large strain value is suitable for application in wearable energy harvesters.