O3 Relaxor Ferroelectric Ceramics Research Articles

High-performance electric energy storage in BiFeO3–Ba(Ti0.8Zr0.2)O3 relaxor ferroelectric ceramics

Perovskite relaxor ferroelectrics have been widely developed for energy storage applications due to their exceptional dielectric properties. This work explores the energy storage performance, thermal stability, and structural evolution in (1-x)BiFeO3–x Ba(Ti0.8Zr0.2)O3 ceramics (x = 0.3, 0.4, 0.5, and 0.6) via modulating Ba(Ti0.8Zr0.2)O3 (BZT) concentration. An enhancement of breakdown electric field from 120 kV/cm at x = 0.3–220 kV/cm at x = 0.5 can be attributed to increased grain boundaries and nanodomains as electric barriers to inhibit charge mobility. A high recoverable energy density of 5.9 J/cm3 and a high energy efficiency of 86.2 % were achieved at x = 0.5 and 0.6, respectively. The structure shifts from ferroelectric rhombohedral R3c symmetry toward a coexistence of nonpolar symmetries (including tetragonal P4/mmm, cubic Pm-3m, and orthorhombic Pbnm) with increasing BZT. The integration of BZT in BiFeO3 demonstrates to break the long-range order and promote the formation of polar nanoregions and nanodomains, leading to a high-efficiency energy storage.

Advanced energy storage properties and multi-scale regulation mechanism in (1-x)(Bi0.5Na0.5)0.7Sr0.3TiO3-xCa(Nb0.5Al0.5)O3 relaxor ferroelectric ceramics

Since recently, lead-free dielectric ceramics have garnered significant interest for their high-power density and rapid charge-discharge capabilities. Nonetheless, their practical application is still limited by relatively low energy storage density and efficiency. To address this issue, a new class of relaxor ferroelectric ceramics ((1-x)(Bi0.5Na0.5)0.7Sr0.3TiO3-xCa(Nb0.5Al0.5)O3, with x from 0.00 to 0.16) was formulated and synthesized in the present work using a solid-state reaction method. Special attention was paid to the effect of multiscale structure regulation on the energy storage properties of the ceramics. All ceramics exhibited the relaxor characteristics, which increased with the added content of Ca(Nb0.5Al0.5)O3 (CNA). Significant achievements have been made in multi-scale regulation of energy storage characteristics of these ceramics. In particular, the ultrahigh energy storage density and efficiency (10.15 J/cm3 and 86.2 %, respectively) were realized in the ceramic with x = 0.14. This optimized composition also displayed good temperature stability at 20–140 °C and excellent frequency stability in the range of 1–200 Hz. Furthermore, the outstanding charge and discharge characteristics (current density CD, power density PD, and discharge time t0.9 of 1257 A/cm2, 377 MW/cm3, and 45.8 ns, respectively) were obtained. The experimental study, finite element analysis, and first-principles calculations confirmed that the multiscale features, such as nano-scale domains, large band gap, and small grain size, promoted by the addition of CNA, are all beneficial for the improvement of energy storage performance, opening up new prospects in the application of advanced dielectric capacitors.

Domain engineered lead-free Bi0.5Na0.5TiO3-Bi(Ni0.5Hf0.5)O3 relaxor ferroelectric ceramics for energy storage with low electric field applications

Lead-free materials for energy storage are increasingly receiving attention due to their exceptional properties of high charging and discharging rates, high power density, and eco-friendliness. In this work, (1−x)Bi0.5Na0.5TiO3-xBi(Ni0.5Hf0.5)O3 (BNT-BNH, x = 0.05, 0.10, 0.15 and 0.20) ceramics were prepared for electrostatic energy storage. P-E loops results show that the introduction of Ni2+ and Hf4+ induces the formation of polar nanoregions (PNRs) and the phase transition from ferroelectric to relaxor ferroelectric in BNT ceramics. Transmission Electron Microscopy directly confirm the increase of crystal plane spacing implies a good solid solution of BNT-BNH, and the number of spherical PNRs increases significantly with increasing the BNH content. Herein, a recoverable energy storage density of 2.68 J/cm3 and relative efficiency of 72.1 % are achieved for 0.8BNT-0.2BNH ceramics under 210 kV/cm. The 0.8BNT-0.2BNH ceramics also exhibit a fast discharge rate (t0.9 = 76 ns), high current density (403.1 A/cm2), and high power density (12.85 MW/cm3), which illustrates that BNT-BNH material systems have good application potential in electrostatic energy storage.

Preeminent energy storage properties and superior stability of (Ba(1–x)Bix)(Ti(1–x)Mg2x/3Tax/3)O3 relaxor ferroelectric ceramics via elongated rod-shaped grains and domain structural regulation

(Ba(1–x)Bix)(Ti(1–x)Mg2x/3Tax/3)O3 (BBTMT-x, x = 0.075, 0.1, 0.125, and 0.15) ceramics were manufactured via a solid-phase reaction method. The pseudo-cubic BaTiO3 (BT) as the primary phase and Ba4MgTi11O27 as the secondary phase were detected in BBTMT-x ceramics. The elongated rod-shaped grains therein became numerous as x increased. The introduction of Bi/Mg/Ta (BMT) elements transformed BT ceramics from ferroelectrics to relaxor ferroelectrics and induced the formation of short-range order polar nanoregions (PNRs), which were beneficial for the preeminent energy storage properties (ESPs). The highest ESPs (a giant recoverable energy-storage density Wrec of 5.97 J cm–3 with a high-efficiency η of 87.4%) were achieved in BBTMT-0.1 ceramics at 710 kV cm–1. BBTMT-0.1 ceramics also possessed excellent frequency (1–500 Hz), temperature (30–150 °C), and fatigue (cycle number of 1–100,000) stabilities. Finite element simulations (FES) demonstrated that elongated rod-shaped grains had stronger obstacles to the development of electrical branches, which was beneficial to improving the comprehensive ESPs.

Enhanced energy storage properties and good stability of novel (1–x)Na0.5Bi0.5TiO3–xCa(Mg1/3Nb2/3)O3 relaxor ferroelectric ceramics prepared by chemical modification

The increase in energy consumption and its collateral damage on the environment has encouraged the development of environment-friendly ceramic materials with good energy storage properties. In this work, (1–x)Na0.5Bi0.5TiO3-xCa(Mg1/3Nb2/3)O3 ceramics were synthesized by the solid-state reaction method. The 0.88Na0.5Bi0.5TiO3-0.12Ca(Mg1/3Nb2/3)O3 ceramic exhibited a high recoverable energy storage density of 8.1 J/cm3 and energy storage efficiency of 82.4% at 550 kV/cm. The introduction of Ca(Mg1/3Nb2/3)O3 reduced the grain size and increased the band gap, thereby enhancing the breakdown field strength of the ceramic materials. The method also resulted in good temperature stability (20–140 °C), frequency stability (1–200 Hz), and fatigue stability over 106 cycles. In addition, an ultrahigh power density of 187 MW/cm3 and a fast charge-discharge rate (t0.9 = 57.2 ns) can be obtained simultaneously. Finite element method analysis revealed that the decrease of grain size was beneficial to the increase of breakdown field strength. Therefore, the 0.88Na0.5Bi0.5TiO3-0.12Ca(Mg1/3Nb2/3)O3 ceramics resulted in high energy storage properties with good stability and were promising environment-friendly materials for advanced pulsed power systems applications.

Achieving ultrahigh energy storage properties with superior stability in novel (Ba(1-x)Bix)(Ti(1-x)Zn0.5xSn0.5x)O3 relaxor ferroelectric ceramics via chemical modification

Relaxor ferroelectrics are receiving widespread attention due to their excellent energy storage properties (ESPs). In this study, (Ba(1-x)Bix)(Ti(1-x)Zn0.5xSn0.5x)O3 (abbreviated as BBTZS-x, x = 0.08, 0.10, 0.12, 0.14, 0.16, 0.18) ceramics were synthesized via a solid-state reaction route, and the effects of chemical modification on their structure and properties were investigated in detail. The introduction of Bi/Zn/Sn (BZS) elements into BaTiO3 (BT) systems induced the change from normal to relaxor ferroelectric behavior, which caused the enhancement of comprehensive ESPs. Significantly, BBTZS-0.12 ceramics acquired the preeminent total energy density (Wtot = 5.8 J/cm3), recoverable energy density (Wrec = 4.99 J/cm3) and efficiency (η = 86.1%) at high field strength of 550 kV/cm because of the existence of polar nanoregions (PNRs) therein. The dynamic response of PNRs to the external field was found to be propitious to the enhancement of energy-storage performance. In particular, excellent current density (CD = 721.5 A/cm2), power density (PD = 151.5 MW/cm3) and the time of release of up to 90% of the discharge energy density value (t0.9 = 53 ns) were simultaneously achieved in BBTZS-0.12 ceramics at 420 kV/cm. Moreover, BBTZS-0.12 ceramics were found to be the most optimal for the long-term applications under different environmental conditions because of their outstanding temperature (30–150 °C), frequency (1–500 Hz), and fatigue cycle (cycle numbers: 1–100000) stabilities. Therefore, exceptional ESPs make BBTZS-x ceramics promising for advanced pulsed power capacitors and energy storage applications.

Outstanding comprehensive energy storage performance in lead-free BiFeO3-based relaxor ferroelectric ceramics by multiple optimization design

Lead-free ceramic-based dielectric capacitors with high-performance energy storage properties have become an emerging issue recently as a result of the applications in high-power and/or pulsed-power technologies. However, the trade-off between various parameters, such as maximum polarization Pmax, remnant polarization Pr and dielectric breakdown strength Eb, restricts the further improvement of the energy storage properties of dielectric ceramics. Herein, a synergistic optimization strategy via simultaneous enhancement of Pmax and Eb and reduction of Pr is adopted to achieve outstanding energy storage properties for Bi0.9La0.1FeO3-Ba0.7Sr0.3TiO3NaNb0.85Ta0.15O3 relaxor ferroelectric ceramics, characterized by an ultrahigh recoverable energy density Wrec of 15.9 J/cm3 and high efficiency η of 87.7%. The inborn gene of BiFeO3-based materials results in high Pmax and the improved relaxor behavior gives rise to a small Pr value. In Particular, a very large value for Eb is obtained by tailoring multiple intrinsic and extrinsic factors. These results demonstrate the reliability and feasibility of the multiple optimization strategy proposed in this work to develop novel dielectric ceramics for advanced energy storage applications.

Effective strategy to improve energy storage properties in lead-free (Ba0.8Sr0.2)TiO3-Bi(Mg0.5Zr0.5)O3 relaxor ferroelectric ceramics

Although relaxor ferroelectrics (RFEs) have received considerable attention in advanced pulsed power capacitor systems (APPCSs) due to their numerous advantages, it remains difficult to achieve comprehensive outstanding energy storage performance (ESP) owing to the trade-offs among recoverable energy density (Wrec), energy efficiency (η) and thermal stability. In this work, we proposed a collaborative optimization strategy for improving the ESP of (Ba0.8Sr0.2)TiO3 (BST)-based RFE ceramics, i.e., the introduction of Bi(Mg0.5Zr0.5)O3 (BMZ) and the use of viscous polymer process (VPP). The former obstructs the long-range ferroelectric order, induces high dynamic polar nanoregions and broadens temperature stabilized platform, thus alleviating the polarization hysteresis and increasing the energy efficiency. The latter progressively dilute pore concentration and thins the sample to ∼70 μm, which can greatly improve breakdown strength. As a result, exceptional ESP parameters are simultaneously achieved in 0.85BST-0.15BMZ ceramics by VPP (BMZ15VPP), which exhibit ultrahigh Wrec (10.3 J/cm3) and high η (88%) under 720 kV/cm while maintaining stable temperature stability. It is also noteworthy that a superior current density of 800 A/cm2 and a power density of 140 MW/cm3 are obtained. The overall excellent performance implies the competitiveness of BMZ15VPP in APPCSs and the feasibility of this strategy in designing compositive high ESP ceramic systems.

Enhancement of energy storage properties of Bi0.5Na0.5TiO3-based relaxor ferroelectric under moderate electric field

Dielectric capacitors, as one of the important electronic devices, are widely used in various fields. However, most ferroelectric capacitors with high energy storage density require excessively high electric fields. In this work, we have prepared 0.9(Bi0.5Na0.5)0.7Sr0.3TiO3-0.1 Bi(Mg2/3Nb1/3)O3 relaxor ferroelectric ceramics with different BaZrO3 doping levels. A high energy storage (Wr) of 4.07 J/cm3 and efficiency (η) of 91% are simultaneously obtained in 0.94[0.9(Bi0.5Na0.5)0.7Sr0.3TiO3-0.1 Bi(Mg2/3Nb1/3)O3]-0.06BaZrO3 ceramic under a medium electric field of 260 kV/cm. Additionally, the ceramic also exhibits excellent temperature and frequency stability. Furthermore, the phase field simulation is used to simulate the evolution of domain structure and hysteresis loops of the ceramics with different doping levels. The results of phase field simulation explicitly explain the influence of different relaxation degrees on energy storage density and efficiency of the ceramics. We believe that the ceramic prepared in this work is one of the most promising candidate materials for some miniaturized energy storage devices operating under low or medium electric fields.

Achieving Ultrahigh Energy Storage Properties with Superior Stability in Novel (Ba(1-X)Bix)(Ti(1-X)Zn0.5xsn0.5x)O3 Relaxor Ferroelectric Ceramics Via Chemical Modification

Achieving Ultrahigh Energy Storage Properties with Superior Stability in Novel (Ba(1-X)Bix)(Ti(1-X)Zn0.5xsn0.5x)O3 Relaxor Ferroelectric Ceramics Via Chemical Modification

Simultaneously achieving large energy density and high efficiency in NaNbO3–(Sr,Bi)TiO3–Bi(Mg,Zr)O3 relaxor ferroelectric ceramics for dielectric capacitor applications

A large recoverable energy storage density of 7.59 J cm−3 and high energy storage efficiency of 81.3% are simultaneously achieved in NaNbO3–(Sr,Bi)TiO3–Bi(Mg,Zr)O3 relaxor ferroelectric ceramics.

Enhanced energy storage performance in Na(1-3x)BixNb0.85Ta0.15O3 relaxor ferroelectric ceramics

High-performance lead-free dielectric containers have excellent energy storage performance such as higher power density and energy density. While being eco-friendly materials, lead-free dielectric materials are more suitable for pulse power systems than other dielectric materials. In this study, Ta 5+ and Bi 3+ ions were introduced into the A site and B site of the NaNbO 3 matrix. The introduction of Bi 3+ ions induced the formation of a vacancy in the A site, yielding Na (1-3 x ) Bi x Nb 0.85 Ta 0.15 O 3 (NBNT, x = 0.05, 0.08, 0.11, 0.14) ceramics. The recoverable energy density ( W rec ) and the energy storage efficiency ( η ) were highest for the Na 0.67 Bi 0.11 Nb 0.85 Ta 0.15 O 3 ceramic, with values of 3.37 J/cm 3 and 89% respectively. Batteries employing the Na 0.67 Bi 0.11 Nb 0.85 Ta 0.15 O 3 ceramic achieved a current density of 830.4 A/cm 2 , an energy density of 49.8 MW/cm 3 and 60.2 ns discharge time. These results show that the Na 0.67 Bi 0.11 Nb 0.85 Ta 0.15 O 3 ceramic is an effective energy storage material with broad application prospects.

Achieve ultrahigh energy storage performance in BaTiO3–Bi(Mg1/2Ti1/2)O3 relaxor ferroelectric ceramics via nano-scale polarization mismatch and reconstruction

Development of lead-free dielectric ceramics with large recoverable energy storage density (Wrec), high energy storage efficiency (η) and wide usage temperature range is of great significance to improve the overall performance of power electronic devices. Despite the numerous research efforts, performance of existing lead-free dielectric ceramics is barely satisfactory. Herein, an effective strategy to achieve ultrahigh energy storage performance via nano-scale polarization mismatch and reconstruction is proposed. By developing solid solutions of A-site coupling and B-site coupling ferroelectrics, polarization mismatch and ultrahigh energy storage performance can be realized in intermediated compositions. It is demonstrated that ultrahigh energy storage performance with a η of 93% and a Wrec of 4.49 J/cm3 is achieved in the 0.6BaTiO3-0.4Bi(Mg1/2Ti1/2)O3 (0.6BT-0.4BMT) ceramic, which is a record high energy storage property in lead-free relaxor ferroelectric bulk ceramics. Excellent temperature stability with a variation of Wrec and η less than 5% is also realized in a wide temperature range from 30 °C to 170 °C. Such an ultrahigh energy storage performance not only verifies our strategy, but also makes the 0.6BT-0.4BMT ceramic a promising candidate material for energy storage. Moreover, of particular significance is that this work provides an effective method to design novel high performance dielectric ceramics for future energy storage devices.

Composition‐induced non‐ergodic–ergodic transition and electrocaloric evolution in Pb 1−1.5 x La x Zr 0.8 Ti 0.2 O 3 relaxor ferroelectric ceramics

Relaxor ferroelectrics, with polar nanoregions (PNRs), are good candidates for electrocaloric (EC) refrigeration. This study investigates the EC performance of the Pb1−1.5x La x Zr0.8Ti0.2O3 relaxor ferroelectric ceramics by the direct measurement using a modified differential scanning calorimeter. All the ceramics exhibit pure perovskite phase with a dense microstructure. The results indicate that the increasing La substitution strengthens the relaxor behaviour, promotes the transition from non-ergodic to ergodic state, and enhances the thermal stability of EC property (instability η < 16% within 0–140°C for x = 0.09). While the EC peak widens and shifts to lower temperatures, the peak value decreases from ΔT max = 0.98 K (@140°C) for x = 0.06 to ΔT max = 0.25 K (@40°C) for x = 0.09 under an electric field of 40 kV/cm. Moreover, the ceramics with x = 0.07, near the non-ergodic–ergodic state boundary, show the optimised room temperature EC performance, i.e. ΔT = 0.41 K (@20°C) and η < 20% within a wide temperature range of 0–80°C. This work provides an effective material design approach for EC refrigeration in different application conditions.

Enhanced energy storage and fast charge-discharge properties of (1-x)BaTiO3-xBi(Ni1/2Sn1/2)O3 relaxor ferroelectric ceramics

Abstract In this work, we designed novel lead-free relaxor ferroelectric ceramics of (1-x)BaTiO3-xBi(Ni1/2Sn1/2)O3 (abbreviated as (1-x)BT-xBNS, with x = 0–0.20). With an increasing concentration of BNS, (1-x)BT-xBNS solid solutions displayed a phase transition from tetragonal symmetry to pseudocubic symmetry with highly diffusive and frequency-dependent relaxor ferroelectric behavior. Modified by BNS, (1-x)BT-xBNS ceramics yielded slim polarization-electric field (P-E) loops and improved energy-storage performances. The optimal energy storage properties can be achieved at x = 0.10, and samples showed a high recoverable energy density of 2.526 J/cm3 and a remarkably high energy efficiency of 93.89% under 240 kV/cm simultaneously at ambient temperature, which represent enhancements by 925% and 286%, respectively, over pure BaTiO3. The energy storage characteristics of the 0.9BT-0.1BNS ceramic manifested good thermal stability (−55–150 °C) and frequency stability (10 Hz-1 kHz), with a variation in recoverable energy density of less than 10%. Meanwhile, the pulsed charging-discharging measurement showed that the 0.9BT-0.1BNS ceramic had a fast discharge period of 67 ns and a large power density of 19 MW/cm3. Due to the outstanding characteristics, there is potential for this new and environmentally friendly BT-based ceramic to be used in high-power pulse capacitor applications.

High Energy Storage Properties and Electrical Field Stability of Energy Efficiency of (Pb0.89La0.11)(Zr0.70Ti0.30)0.9725O3 Relaxor Ferroelectric Ceramics

In this study, electric energy storage properties of (Pb0.89La0.11)(Zr0.70Ti0.30)0.9725O3 (PLZT 11/70/30) relaxor ceramics were investigated. XRD pattern and SEM image confirms the perovskite phase and dense structure without any secondary phases and pores, respectively. Room temperature dielectric constant was found to be high (~ 3520) with low dielectric loss (~ 0.03). Dielectric constant changes with temperature confirm the relaxor ferroelectric behaviour of PLZT ceramics. Different parameters such as degree of deviation (ΔTm) from the Curie–Weiss law, the diffuseness of the phase transition (ΔTdiff) and degree of diffuseness (γ), which are related to the relaxor nature of ferroelectrics were calculated. With the remarkably slim polarization versus electric field hysteresis loops even at high applied electric field, high energy storage of 0.85 J/cm3 and very high energy storage efficiency of 92.9% were obtained from the PLZT ceramics. These values suggest that the PLZT 11/70/30 composition can be used for the pulse driving energy storage applications.

Dielectric and energy storage properties of BaTiO3–Bi(Mg1/2Ti1/2)O3 ceramic: Influence of glass addition and biasing electric field

B2O3-SiO2 glass added 0.88BaTiO3–0.12Bi(Mg1/2Ti1/2)O3 relaxor-ferroelectric ceramics were successfully prepared and characterized by means of X-ray diffraction, dielectric and ferroelectric measurements. Effects of glass contents on the properties of the ceramics are discussed. The pure 0.88BaTiO3–0.12Bi(Mg1/2Ti1/2)O3 ceramic displays a good temperature stability of the dielectric constant from −75°C to 100°C. And this temperature stable dielectric behavior gradually disappears with increasing glass content. The energy storage density increases from 1.641J/cm3 to 1.971J/cm3 by glass additives. Influences of biasing electric fields on dielectric properties are also discussed. The long range ordered phase can be extended to higher temperatures by biasing electric fields. A slight increase of the permittivity under the biasing field is obtained. These results indicate that a weak polar phase existed in the 0.88BaTiO3–0.12Bi(Mg1/2Ti1/2)O3 ceramic and the B2O3–SiO2 glass addition is an effective method to improve energy storage properties.

Suppressed ferroelectric relaxor behavior of Mn‐modified Ba(Zr0.3Ti0.7)O3 relaxor ceramics

MnCO3‐modified Ba(Zr0.3Ti0.7)O3 relaxor ferroelectric ceramics were fabricated by using the solid‐state reaction method. The temperature dependences of electrical and dielectric properties of the ceramics were systematically investigated over the range −140 to 400 °C. The typical ferroelectric relaxor behavior of the Ba(Zr0.3Ti0.7)O3 ceramics was greatly suppressed by adding a proper amount of MnCO3. The suppressed relaxor behavior can be restored by annealing the samples in air, which is attributed to the presence of oxygen vacancies in the samples. In the paraelectric phase region, the low‐frequency dielectric relaxations associated with oxygen vacancies are observed above room temperature, and increase with increasing of Mn content. Compared to the undoped Ba(Zr0.3Ti0.7)O3 ceramic, Mn‐doped samples display excellent temperature stability in a wide temperature. The critical composition of x = 0.05 (MnCO3) not only exhibits a lower degree of ferroelectric relaxor behavior (ΔTm = 5.6 K), but also maintains a relatively higher tunability (66.9%@30 kV cm−1) than that of pure Ba(Zr0.3Ti0.7)O3 (ΔTm = 16.5 K, 49.6%@30 kV cm−1).

Morphotropic phase boundary and electrical properties of lead-free (K0.5Bi0.5)TiO3–Bi(Ni0.5Ti0.5)O3 relaxor ferroelectric ceramics

Lead-free relaxor ferroelectric ceramics (1−x)(K0.5Bi0.5)TiO3–xBi(Ni0.5Ti0.5)O3 were prepared by a conventional solid-state route, the phase transition behavior and corresponding electrical properties were investigated. A typical morphotropic phase boundary (MPB) between rhombohedral and tetragonal ferroelectric phases was identified to be in the range of 0.05<x<0.07 where the optimum piezoelectric and electromechanical properties of d33=126 pC/N and kP=18% were achieved. Most importantly, a high Curie temperature ~320 °C, around which the material shows a typical relaxor ferroelectric behavior characterized by the presence of diffuse phase transition and frequency dispersion, was obtained in MPB compositions, significantly higher than those of some existing MPB lead-free titanate systems. These results demonstrate a tremendous potential of the studied system for device applications.

Acoustic emission and dielectric studies of phase transitions within the morphotropic phase boundary of xPb(Zr1/2Ti1/2)O3-(1−x)Pb(Ni1/3Nb2/3)O3 relaxor ferroelectrics

We have carried out a combined acoustic emission (AE) and dielectric permittivity study of the xPb(Zr1/2Ti1/2)O3-(1−x)Pb(Ni1/3Nb2/3)O3 relaxor ferroelectric ceramics with compositions x=0.7–0.9 corresponding to its morphotropic phase boundary. Temperatures of all phase transitions occurring on heating are identified accurately by AE, and a direct transition between the low-temperature (rhombohedral) and high-temperature (pseudocubic) relaxor phases is found. The AE peak intensity is generally proportional to the temperature derivative of the dielectric permittivity, in agreement with a model proposed for a thermally cycled small elastic dipole.