Temperature Dependence Of Dielectric Properties Research Articles

Dielectric, electrical and magnetic characteristics of BST modified BLFO lead free ceramic

A single phase 0.5(Bi0.5La0.5Fe)O3-0.5(Ba0.5Sr0.5Ti)O3 (50BLFO-50BST) is successfully synthesized by incorporating the high-temperature solid-state casting technique. The compound is calcined and sintered respectively at the temperature 1010 °C and 1210 °C. The calcined powder is checked by X-ray diffraction (XRD) and analysed through reitveld analysis. It is found the sample is single phase cubic structure having crystallite size of 54.74 nm. UV-Visible spectroscopic analysis is utilized to study the optical behavior of the material and with the help of Tuc plot optical band gap has been calculated which has been found to be 1.38 eV. The LCR measurements have been analyzed for the frequency and temperature-dependent dielectric, impedance,and modulus properties of the above-prepared ceramic. The impedance study shows the participation of grain and grain boundary in the electrical characteristics of this material. The room temperature ferromagnetic parameters (Mr~0.06 emu/gm and Hc~ 1 kOe) suggest material is a potential candidate for magnetic storage devices.

Investigation on barometric and hydrostatic pressure sensing properties of Pb[(Mg1/3Nb2/3)0.7Ti0.3]O3 electro-ceramics

Two-stage solid-state reaction-based intermediate columbite phase technique has been employed to fabricate the single-phase Pb[(Mg1/3Nb2/3)0.7Ti0.3]O3 (PMN-0.3 PT) electro-ceramics. The Rietveld refinement of XRD data suggests the presence of monoclinic crystal structure with space group ‘Cm’. The bulk ceramics interior looks very flat without voids and well-defined grain boundaries, which confirm the high quality single-phase microstructure. The final elemental compositions of the material are similar to the initial compositions within the instrument's experimental error. We have investigated pressure and temperature-dependent dielectric and impedance properties to test the possible applications as a pressure transducer. A well defined square hysteresis with large polarization confirms the high quality ferroelectric and piezoelectric properties. For the first time, we have studied the pressure sensing properties of PMN-0.3 PT ceramic in the range 25–250 kPa in barometric pressure using dead weights and 10–50 MPa hydraulic pressure (oil medium). The ceramic demonstrates a gradual change in capacitance as well as in capacitive reactance, with % sensitivity of 0.10 MPa−1 in the Hydraulic pressure range (10–50 MPa), and with % sensitivity of 0.02 kPa−1 in the Barometric pressure range (25–250 kPa). These results demonstrate the suitability of PMN-0.3 PT ceramic as a pressure transducer.

Effect of bismuth substitution on piezoelectric coefficients and temperature and pressure-dependent dielectric and impedance properties of lead zirconate titanate ceramics

Basic Physics as well as devices fabrication required in-depth analysis of the effect of temperature, pressure, and other physical parameters on dielectric properties to understand the microstructure-property relation. In this regard, we have thoroughly investigated the temperature and pressure dependent ferroelectric, dielectric, and impedance properties of Bi-substituted Pb1-xBi2x/3(Zr0.52Ti0.48)O3 (PBiZT) (x = 0.10 to 0.40) ceramics. The maximum solubility of Bi was found near x = 0.15, and above this composition, it shows a composite phase of PBiZT and ZrO2. The remanent polarization (Pr) increases with decrease in the Bi concentration with the maximum value obtained for x = 0.15, i.e., 40 μC/cm2. Temperature-dependent dielectric constant and tangent loss were measured as function of composition to check the ferroelectric phase transition temperature (Tc) and the operating temperature limit for the material to make a device. The Tc value increases with decrease in bismuth (Bi) concentration which obtained in the range of 350 ℃ - 375 ℃. The tangent loss was observed to be near about 0.01 to 0.03 below 200 ℃ which suggests its suitability for device applications. The temperature-dependent imaginary part of impedance (Z'') was measured at various temperatures with varying frequency in the range of 100 Hz – 1 MHz. The peaks positions of the Z'' vs. frequency shift towards lower temperature side with increasing the value of x from 0.1 to 0.4 near and above Tc. The pressure-dependent dielectric constant (εr) and capacitive reactance (Xc) were also measured for varying x, and it was observed that maximum change in εr and Xc was observed for x = 0.15 i.e. 13% and 10.5%, respectively. The pressure sensitivity was obtained maximum for the composition near the maximum solubility of Bi in PbZr1-xTixO3 (PZT) matrix. The reason behind getting the highest remanent polarization and pressure sensitivity for x = 0.15 is that of the highest piezoelectric coefficients ∼ 130 pC/N.

Thermal stability of dielectric and energy storage performances of Ca-substituted BNTZ ferroelectric ceramics

In this study, we synthesized [Cax(Bi0.5Na0.5)1−x](Ti085Zr0.15)O3 (Ca-substituted BNTZ) ferroelectric ceramics with x = 0–0.15 using a solid-state reaction technique. The structural evolution of Ca-substituted BNTZ was revealed by X-ray diffraction combined with Rietveld crystal structure refinement. A pseudocubic structure with P4bm symmetry is suggested for all Ca-substituted BNTZ samples. Temperature-dependent dielectric properties show a clear and broad dielectric peak of approximately 340 °C. The dielectric peak becomes even wider, and the thermal stability of the permittivity is dramatically improved when x gradually increases. In the x = 0.10 composition, the permittivity at 25–450 °C varies between +5% and −14.5%. A recoverable energy storage density (Wrec) of 2.79 J/cm3 with an energy storage efficiency (η) of 76% was achieved in the x = 0.07 composition, which suggests superior properties over other BNT-based systems. In addition, the compositions of x = 0.07, 0.10 and 0.15 show excellent thermal stability of Wrec and η. This work proves that the thermal stability of dielectric and energy storage performances in BNT-based ferroelectric ceramics can be achieved by introducing ions without contributing to the polarization.

Impact of Sm-substitution and microwave sintering on dielectric and mechanical properties of SrBi4Ti4O15 ceramics

In quest of finding an alternative for lead-based materials, ferroelectric materials with Bi-layered structure have attracted great attention due to their potential applications in non-volatile memory, electro-optic devices, and microelectromechanical systems. In this work, samarium (Sm)-substituted SrBi4Ti4O15 (SBTi) ceramics have been prepared by solid-state reaction method and sintered using microwave, as well as conventional heating. XRD phase analysis reveals the formation of single phase compound, and there is no effect of Sm-substitution on basic crystal structure. SEM micrographs showed the plate-like structure of grains both in microwave and conventional furnace. Temperature-dependent dielectric properties were investigated in the temperature range 40–600 °C and frequency range 10 kHz–1 MHz. Sm-substitution increases dielectric constant upto Sm ~ 0.75 and also introduces small relaxor behavior. Hardness and Young’s modulus of SrBi4-xSmxTi4O15 ceramics were measured by nanoindentation. The structural, morphology, dielectric, and mechanical properties of pure and substituted SrBi4Ti4O15 ceramics along with sintering methods have been investigated in detail.

Dielectric relaxation behavior and overlapping large polaron tunneling conduction mechanism in NiO–PbO μ-cauliflower composites

The NiO–PbO μ-cauliflower composites was synthesized via glycine assisted self-ignition techniques with an objective to investigate its temperature evolving distinct dielectric relaxor behavior and alternating current conduction mechanism, for exploring its application as high energy storage devices. The x-ray diffraction and Raman spectroscopy was utilized to characterize exquisite phase formation of the composites. The temperature dependent dielectric properties was performed in a broad range from 100 Hz to 1 MHz and it exhibits a diffuse phase transition in high temperature region. The Non-Debye type dielectric relaxation with grain and grain boundary contribution of different activation energy was confirmed by Nyquist plot (Z′−Z′′) of impedance spectra. Broad dielectric relaxation plateau was observed in the low temperature and high frequency region and electronic hopping motion with interfacial polarization is the underlying mechanism of it, instead of dipolar relaxation and internal barrier effect. The real ac conductivity was fitted by well-known Almond-west equation and the temperature dependent frequency exponent (S) confirmed double overlapping large polaron tunneling model (OLPT) model of electrical conduction mechanism from room temperature (298 K) to 533 K. The ac activation energies varries from 0.39 eV to 0.21 eV with high frequency dispersion and variable range hoppping (VRH) model is introduced to correlate the dc conductivity.

Effect of the biphase TiO2 nanoparticles on the dielectric and polaronic transport properties of PVA nanocomposite: Structure analysis and conduction mechanism

Polymeric composite films with tunable electrical and dielectric performance have several uses in electronics based on organic materials. This paper reports the fabrication and the role of TiO2 NPS (nanoparticles) on the dielectric and nanocomposites' conduction of pristine polyvinyl alcohol (PVA). The nanopowder of biphase TiO2 and the nanocomposites of different NPS weight percentages have been fabricated via the sol-gel and casting methods. Structure of the synthesized NPS and nanocomposites were analyzed via PXRD (Powder X-ray diffraction), HR-TEM (High-resolution microscopy of transmission electron), and FTIR (Fourier transform-IR). The average size of the biphase TiO2NPS crystallite is around 52 nm, as calculated from Scherer law. Frequency and temperature dependence of dielectric properties have been studied in a wide range. The dielectric constant of the host matrix has been enhanced by adding TiO2NPS. AC conductivity increases with the further addition of TiO2NPS contents, and its frequency dependence follows the universal power law. The nanocomposite with 6.6 wt% of TiO2NPS shows higher conductivity as compared to other concentrations. The exponent power (s) has values in the range of 0.2–0.9, indicating that the conduction mechanism is correlated with barrier hopping (CBH). The dependence of the DC conductivity on absolute temperature has been studied and obeys Arrhenius relation. Three discrete sections were recognized from the AC conductivity spectra. In light of polaronic hopping conduction models, the electrical conductivity data were analyzed. The analysis shows that the high-temperature conductivity is well explained by the polaronic model, while at an intermediate temperature, the Greaves VRH (variable-range hopping) model is appropriate. Also, the non-adiabatic conduction was established in the nanocomposite system via the application of different suggestions. The values of the decay constant and the density of states confirmed the presence of the localized states. Finally, a small polaron coupling constant (γp) is more significant than four, which indicates a strong electron-phonon interaction.

Dielectric-based temperature sensing of nanoliter water samples with a post-processing tuned matching network

Microfluidic devices present new opportunities for a wide range of applicationsin which the temperature control of nanoliter droplets is required. Due to the inherent size of the employed miniature volumes, several challenges exist, related to temperature measurements. In this work, we present a non-contact and label-free dielectric-based temperature measurement technique. A capacitive sensor transduces the temperature-dependent dielectric properties into a capacitive value. With a post-processing tuned matching network, the reflection coefficient of the capacitive sensor is minimized at a specific frequency, directly related to the sample temperature. The system is calibrated via a water-only calibration method, using two calibration values. A measurement accuracy of ± 0.24 °C is achieved, with an offset of −0.19 °C, over a temperature range from 20 °C to 55 °C. The potential for simultaneous use of the proposed sensor as a microwave heater, gives us a dual-purpose device that minimizes the footprint of the chip, and thus its cost, while also reducing the number of electrical connections to the chip.

Influence of Zn2+ doping towards the structural, magnetic, and dielectric properties of NiFe2O4 composite

The present work is aimed to study the changes in characteristics of nickel ferrites followed by the zinc doping and for that, the nanocrystalline Ni–Zn ferrites (Ni1−xZnxFe2O4: x = 0, x = 0.2 and x = 0.4) were prepared via sol–gel auto combustion method and by annealing at subsequent temperature. The physical characterization studies of the final composite provided that the lattice structure of Zn2+ substituted at Ni sites confirms for the single-phase ferrite with spinel structure got investigated at room temperature (RT) with functional, morphological as well as temperature-dependent magnetic and dielectric properties. The magnetic properties imply that the distribution of cations at the lattice sites suggests that the magnetization is getting increased with a decrease of temperature from RT to lower temperature in a field cooling process and is due to the strong dipolar magnetostatic interactions between the individual magnetic moments, which also affirms that the magnetization decreases with a decrease of Ni concentration. The coercively extracted from isothermal magnetization curves attributed to the single domain nature at RT. Further, the dielectric constant (e′) and dielectric loss (tan δ) are also examined and found to be strongly dependent on the function of frequency and temperature. The change in e′ and tan δ demonstrated that the dispersion due to the Maxwell–Wagner interfacial polarization and is in a good agreement with Koop’s theory.

Microwave field: Temperature-dependent dielectric properties and heating characteristics during the synthesis of alpha-tellurium dioxide

The temperature-dependent dielectric properties of the precursor can provide theoretical support for microwave synthesis related materials. Herein, temperature-dependent dielectric properties and microwave heating characteristics were researched in detail during the synthesis of alpha-tellurium dioxide (α-TeO2) by a microwave removal of hydrogen from orthotelluric acid (H6TeO6). The results showed that the dielectric constant (εr′) and the dielectric loss (εr″) values of H6TeO6 were divided into six stages due to the evolution of the structure with increasing temperature. And the loss tangent coefficient (tanδ) values had two distinct wave crests: 200–400 °C, and 450–600 °C, which corresponded to maximum tanδ values of 0.044 (F/m) at 350 °C and 0.028 (F/m) at 550 °C, respectively. In addition, TG-DSC, XRD, FT-IR, SEM were employed to track the as-synthesized evolution of structure and morphology during calcination. The results indicated that the fine and uniform α-TeO2 particles could be obtained by the microwave treatment at 600 °C for 10 min. The work not only provides a stable and high-quality precursor for the application of α-TeO2, but also offers theoretical data support for microwave preparation and design of tellurium oxide-based materials.

Effect of Precursor on the Dielectric Properties of Diamond-Like Silicon–Carbon Films

We report results on frequency and temperature dependences of dielectric properties (dielectric permittivity and dielectric loss tangent) of amorphous silicon–carbon films produced using different precursors: poly(phenylmethylsiloxane) (PPMS) and poly(methylsiloxane) (PMS). It has been shown that the PPMS-based films consist of a well-defined polar dielectric, whereas the PMS-based films consist of a weakly polar dielectric. At the same time, their high-frequency dielectric permittivities differ relatively little (4.9 and 4.4, respectively, at 300 K and 1 MHz). We analyze the dielectric properties of the films as functions of frequency and temperature and in relation to the nature of the precursor.

Dielectric, piezoelectric and dc bias characteristics of Bi-doped PZT multilayer ceramic actuator

In this study, the microstructure, dielectric, piezoelectric and dc bias properties of the Bi-doped PZT (PZTB) multilayer piezoelectric actuators, have been discussed. The thickness of the dielectric monolayer was about 70 μm, and a relatively uniform distribution of the grain size was developed. The application of a large dc bias field resulted in a decrease in the dielectric constant and dielectric loss of the multilayer piezoelectric ceramics. The shift of the Curie temperature (Tc) towards a higher value and stabilized temperature-dependent dielectric properties were observed under the dc bias field. The increase in parameter γ suggested the enhancement of the degree of diffuseness of the phase transition. The large displacement reached 0.11% of the thickness of the multilayer piezoelectric ceramic under a low driving voltage of 150 V, indicating the potential of commercial applications of the studied multilayer piezoelectric actuators. This study provides specific experimental data to evaluate the practical application of the Bi-doped PZT multilayer piezoelectric actuators.

Piezoelectric and pyroelectric properties of Mn-doped 0.36Pb(In1/2Nb1/2)O3–0.36Pb(Mg1/3Nb2/3)O3–0.28PbTiO3 ceramics

0.5 mol% Mn-doped 0.36Pb(In1/2Nb1/2)O3–0.36Pb(Mg1/3Nb2/3)O3–0.28PbTiO3 (Mn-PIMNT) ceramics were fabricated by a two-step precursor method. The phase structure, morphologies, and temperature-dependent dielectric, ferroelectric, piezoelectric, and pyroelectric properties were studied. The results indicated that the Mn-PIMNT ceramics had pure perovskite phase and uniform grain distribution. Meanwhile, it exhibited ultrahigh piezoelectric coefficient d33 of 235 pC/N, high-power figure of merit (FOM) of 60,160 pC/N, large remnant polarization Pr of 34.57 µC cm−2 and coercive field EC of 12.97 kV cm−1, which were much better than that of binary Mn-PMNT ceramics. Moreover, by Mn ions-doping, giant pyroelectric coefficient p up to 4.8 × 10–4 C m−2 K−1 was obtained and the figure of merits for the detectivity Fd reached 2.317 × 10–5 Pa−1/2, higher than PIMNT ceramics. Combined with the outstanding piezoelectric and pyroelectric properties as well as high ferroelectric rhombohedral to tetragonal phase transition temperature Trt (up to 146 ℃) and ferroelectric tetragonal to cubic phase transition TC of 188 ℃, it is suggested that the Mn-PIMNT ceramics are an excellent candidate for piezoelectric and pyroelectric devices.

Fabrication of the transparent ferroelectric heterostructures based on KNN-based lead-free films

Transparent and epitaxial 0.95(K0.49Na0.49Li0.02)(Ta0.2Nb0.8)O3-0.05CaZrO3 with 2 wt.% MnO2 addition (KNNLT-CZM) lead-free ferroelectric film heterostructures are fabricated on the La0.07Ba0.93SnO3 (LBSO)-coated SrTiO3 (001) substrates using pulsed laser deposition. The optical measurements show that these film heterostructures exhibit good transmittance with a maximum transmittance of ∼80%. Temperature-dependent dielectric properties demonstrate that the KNNLT-CZM films possess a high Curie temperature (TC) above 420 °C, and exhibit an orthorhombic to tetragonal phase transition at ∼170 °C. Furthermore, these film heterostructures also have a large twice remnant polarization of 29.66 μC cm−2 and well-defined ferroelectric hysteresis loops up to 200 °C. The x-ray photoelectron spectra suggest that partial K elements did not enter in the lattice of the KNNLT-CZM perovskite structure and the Mn dominantly existed in the form of Mn2+. The observed good transmittance, high TC and excellent electrical properties of the LBSO-buffered KNNLT-CZM film heterostructures indicate that these films have great application potential in opto-electronic devices and film transistors.

Enhanced dielectric and ferroelectric properties in lead magnesium niobate-lead titanate ferroelectrics solid solutions by controlling the sintering protocols

Due to requirements for miniaturization and integration of electronic devices, ferroelectric materials with high dielectric permittivity would have potential applications in dielectric capacitors. In this work, (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT) powders with x from 0.10 to 0.30 were obtained on the basis of a transitional columbite precursor method, while sintering processes were carried out under three protocols, i.e., (I) 1230 °C for 2 h, (II) 1230 °C for 16 h and (III) 1250 °C for 2 h. The temperature-dependent dielectric properties measured from 25 °C to 225 °C show that, under protocols II and III, the maximum permittivity (εm) is significantly improved compared to those obtained via protocol I. A maximum εm of 47036 is obtained in x = 0.25 composition under protocol II, and the εm is increased by more than 90% at the same composition. In the ceramics sintered through protocols II and III, the characteristics of both dielectric relaxations and dielectric dispersions are also enhanced. In addition, the ferroelectric and piezoelectric properties also show a marked increase in the composition of x = 0.3. Our results suggest that the dielectric and ferroelectric properties of PMN-xPT solid solutions could be effectively enhanced by controlling the sintering protocols.

Doped ceramics of indium oxides for negative permittivity materials in MHz-kHz frequency regions

Negative permittivity has been widely studied in various metamaterials and percolating composites, of which the anomalous dielectric behavior was attributed to critical structural properties of building blocks. Herein, mono-phase ceramics of indium tin oxides (ITO) were sintered for epsilon-negative materials in MHz-kHz frequency regions. Electrical conductivity and complex permittivity were analyzed with Drude-Lorentz oscillator model. Carriers’ characters were measured based on Hall effect and the magnitude and frequency dispersion of negative permittivity were mainly determined by carrier concentration. Temperature-dependent dielectric properties further proved the epsilon-negative behaviors were closely associated with free carriers’ collective responses. It’s found that negative permittivity of ITO ceramics was mainly caused by plasma oscillations of free carriers, while the dielectric loss was mainly attributed to conduction loss. Negative permittivity realized here was related to materials intrinsic nature and this work preliminarily determined the mechanism of negative permittivity in doped ceramics from the perspective of carriers.

Frequency and temperature dependence of dielectric properties and capacitance–voltage in GO/TiO2/n-Si MOS device

Dielectric properties and capacitance–voltage of GO/TiO2/n-Si junction were investigated in frequency range 10–2 × 107 Hz and temperature (233–363 K). Reliance of $$\varepsilon^{\prime}$$ , $$\varepsilon^{\prime\prime}$$ , tanδ, Mʹ, Mʺ, impedance, and ac conductivity on frequency and temperature were studied. From results, it is found that $$\varepsilon^{\prime}$$ increases with increasing frequency at low-frequency region, while that it decreases at high frequencies. $$\varepsilon^{\prime\prime}$$ decreases with frequency (f) increment in the range 10–56 Hz and 1619–12195 Hz. It is observed the decrement of tanδ with increasing frequency in higher range 1,355,210–2 × 107 Hz. Real part of electric modulus (Mʹ) reduces with increment frequency. Conductivity rises with rising temperature. Moreover, activation energy (Ea) values decrease with increasing f then increase at higher f. Different parameters, such as carrier density, built-in potential, and barrier height, were derived from the reverse bias C−2–V curves. It is found that, built-in-voltage (Vbi), barrier height (φb), and Fermi energy (EF) increase with increasing temperature. Moreover, donor concentration (ND) and image force barrier lowering (∆φb) decrease with temperature increment. In addition, series resistance (Rs) decreases with temperature and frequency increment. In addition, this MOS structure GO/TiO2/n-Si works as a device, and by controlling the temperature, frequency, and voltage, the required properties from this device can be adjusted to make it suitable for any required applications; this is obvious from investigated dielectric properties.

Doping-induced dielectric and transport properties of Ni1−xZnxO

Ni1−xZnxO (with 0 ≤ x ≤ 0.05) nanoparticles are synthesized by chemical precipitation method in order to investigate the effect of Zn doping on the dielectric and transport properties of NiO. Prepared samples are characterized by means of X-ray diffraction (XRD) method, scanning electron microscope (SEM), and Transmission electron microscope (TEM). The size of the nanoparticles is calculated and found to be 26 nm and 22 nm for x = 0.0 and 0.05, respectively. Regular increase of the optical band gap with increase in doping concentration (x) is observed which is consistent with the variation of particle size. Frequency (f) dependence of AC (σac) conductivity, dielectric constant (er), and dielectric loss (tanδ) of Ni1−xZnxO (0 ≤ x ≤ 0.05) has been studied. It is observed that the dielectric constant (er) increases gradually with x at high frequency (2 MHz). The dc conductivity (σdc) is found to decrease with Zn doping at room temperature which may be attributed to the reduction of oxygen vacancy. The temperature dependence of dielectric properties for x = 0.00, 0.05 are also investigated as a function of f. Cross over of dc conductivity of Ni0.95Zn0.05O to that of NiO observed around ~ 365 K indicates the lowering of activation energy of conductivity for x = 0.05 with increase in temperature.

Temperature field simulation of polyolefin-absorber mixture by FDTD-FDM model during microwave heating

Abstract This work has performed a numerical simulation of the temperature field during microwave heating of polyolefin-absorber mixture by means of a combined electric and thermal model. A finite difference time domain was used to model the electric field distribution within the cavity, while the finite difference method was used to calculate the temperature field distribution in different reactors. This study has focused only on the process from room temperature to 500 K for reducing heating time and energy consumption. This temperature range is a process with high energy consumption, difficult to control and great influence on the follow-up reaction. Temperature dependence of dielectric properties and thermal properties of heated materials are fully considered and simulated through an iterative process. The simulation results show that input power, the size and location of the heated materials, the position of the waveguide, and the kinds of microwave absorbers are important factors affecting the heating process. As a result, the uniform temperature distribution (the temperature difference Td

Temperature-dependent dielectric and structural properties of Li-doped (Na, K) NbO3 near the morphotropic phase region

In this study, pellet samples of (Na0.5K0.5)1-yLiyNbO3, (NKLN) y ≤ 0.06, were prepared using a conventional solid-state reaction method with double sintering. The temperature-dependent dielectric constant and high-temperature X-ray diffraction characteristics of the prepared compositions were observed. Four consistent distinct phases were determined according to the observations as follows. For the compositions where y ≤ 0.02, the phases exhibited monoclinic symmetry between room temperature and about 200 °C, tetragonal between about 200 °C and 400 °C, tetragonal with different symmetry between about 400 °C and 460 °C (the so-called X phase), and cubic symmetry above about 460 °C. For the compositions with higher Li concentrations (y) between 0.03 ≤ y ≤ 0.06, the X phase was not observed and two distinct phase transitions were observed from monoclinic to tetragonal at around 200 °C, and from tetragonal to cubic at around 460 °C.