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Whispering gallery mode resonators (WGMRs) have garnered significant interest due to their potential applications in the fields of electro-optic modulation and microwave to optical photon conversion. In this study, we have leveraged an electro-optic crystal, lead indium niobate-lead magnesium niobate-lead titanate (PIN-PMN-PT), to fabricate a high-quality WGMR. Our investigation revealed that the crystal composition used in this work is 0.24PIN-0.45PMN-0.31PT, and each element of the whole sample is homogeneously distributed. The dielectric properties of the sample revealed the necessity of limiting the temperature and external electric field frequency to below 100 °C and 106 Hz, respectively. The obtained optical quality factor value (Q value) of the resonator is ∼0.7 × 105. Impressively, our resonator could be conveniently tuned by exploiting the enormous inverse piezoelectric effect d31 of the crystal, thereby alleviating the need for precise fabrication. Furthermore, a theoretical analysis of our resonator revealed that a calculated resonance wavelength shift is within a broad range of 2.16 nm. Intriguingly, if the surface roughness of the resonator is reduced tenfold, we can increase the calculated Q value dependent on surface scattering by 104. Our finding showcases the tremendous potential of the PIN-PMN-PT crystal-based WGMR as versatile building blocks for a variety of applications in the burgeoning field of photonic technology.

A simple method of fabricating P b ( M g 1 / 3 N b 2 / 3 ) O 3 − P b T i O 3 (PMN-PT) deep grooves with high aspect ratios using an 800-nm femtosecond laser with chemical-selective etching is demonstrated. The 567-µm-deep grooves with aspect ratios of approximately 35 were obtained with no cracks or thermal affected zone. The morphologies and chemical compositions of grooves were analyzed by a scanning electron microscope with an energy dispersive x-ray spectrometer. The formation mechanism of PMN-PT grooves is attributed to the chemical reactions of hydrochloric acid (HCl) and laser-induced structural changes (LISCs). PMN-PT in LISC became amorphous or mixtures of metal oxide from crystal and all the compounds could react with concentrated HCl and form soluble matter, leaving no precipitation. Furthermore, influences of laser irradiation parameters on depths and aspect ratios of grooves are studied.

In this study, we theoretically proposed a method to achieve an electromagnetically induced transparency (EIT)-like effect in a whispering gallery mode resonator (WGMR) and experimentally validated the method in a lithium niobate (LN) device. Benefitting from the electro-optic and inverse piezoelectric effects of the LN material, two modes of the LN WGMR that are close in frequency can be tuned at different tuning rates, resulting in EIT-like resonance lineshapes. By varying the electric field applied to the LN WGMR, the full dynamic of the EIT-like phenomenon can be precisely controlled. The experimental results agreed well with the calculations based on the coupled mode theory. Moreover, we observed a hysteresis resulting from the photorefractive effect of LN. We believe our proposed method and demonstrated devices offer a way to control an EIT-like effect, which could have potential applications in light storage, quantum information processing, and enhanced sensing techniques.

Domain engineering in relaxor-PT single crystals are attracting much attention both as unique physical phenomena and for potential applications in various devices. Here, the effect of initial domain state on domain switching process was explored. Different domain switching processes were illustrated by in situ observation, and the dynamic processes of domain switching were obtained by using optical current analysis. We found the samples with different initial domain states have different domain switching processes. For the sample with wide stripe 90° domain, the polarization reversal is driven by a-domain nucleation, 90° domain wall movement and c-domain growth. While, in the sample with thin stripe 90° domain, the nucleation and growth of c-domain prevailed. The influences of the initial domain state on the domain structure evolution are discussed by current analysis. Our findings are of great significance in regulating the domain switching process to meet the demand of different devices.

Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT) single crystals exhibit ultrahigh piezoelectric property and have already been applied in various industrial fields. Here, spatial distribution of coexistent phases and corresponding local piezoelectric responses in a morphotropic phase boundary (MPB) PMN-xPT single crystal are thoroughly investigated by confocal Raman spectroscopy coupled with piezo-response force microscopy (PFM). Different from previous studies on MPB crystals, spatial distribution of coexistent phases is exhibited intuitively in an image obtained by confocal Raman mapping. Via in-situ PFM measurements, domain morphology of each coexistent phase is observed. Moreover, local piezoelectric responses of each coexistent phase are obtained by switching spectroscopy PFM measurements, indicating that Ma and Mc phases behave like PNRs and polar matrix in PMN-xPT crystals Our work clarifies the contribution from different phases to the giant piezoelectric performance, which can deepen the understanding on the ultrahigh piezoelectricity in PMN-xPT crystals and provide the key point for developing novel high piezoelectricity materials.

Electrocaloric refrigeration utilizing ferroelectrics has recently gained tremendous attention because of the urgent demand for solid-state cooling devices. However, the low room-temperature electrocaloric effect and narrow operation temperature window hinder the implementation of lead-free ferroelectrics in high-efficiency cooling applications. In this work, chemical engineering and thick-film architecture design strategies were integrated into a BaTiO

The (Nb + In) co-doped rutile TiO2 ceramics were synthesized by spark plasma sintering (SPS) and traditional solid-state sintering (TS) techniques, respectively. Highly-density co-doped rutile TiO2 ceramics are prepared with the SPS method by 20 min, whereas it takes nearly 30 h with the TS method. It is observed that SPS ceramics showed smaller and uniform grain size, and better densification than TS counterparts. Both sets of the co-doped TiO2 ceramics showed single rutile phase according to X-ray diffraction (XRD) results. X-ray photoelectron spectroscopy (XPS) is adopted to detect and compare the element-valence-state of both sets of the co-doped TiO2 ceramics. The dielectric response, impedance spectroscopy (IS), and the effects of annealing treatment are systematically investigated, which could not only be helpful for optimizing their dielectric properties, but also shed the light on the colossal dielectric mechanism.

Transmission spectrum and refractive index of (1−x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 (PMN-xPT) single crystals were studied and second-harmonic generation signal of the crystal powder was measured i...

Ag(Nb0.8Ta0.2)O3 is used here as a model system to shed light on the nature of the low temperature phase behavior of the unsubstituted parent compound AgNbO3, which is an important material for high-power energy storage applications.

A new type of electro-optic crystal (PIN-PMN-PT) has been discovered. It has similar transmission wavelength range and transmittance with the traditional lithium niobate crystal. It has higher electro-optic coefficient and refractive index than lithium niobate crystal. We used this material to make a disk-shaped whispering gallery structure and studied it.

We demonstrated a monolithic optical whispering-gallery-mode (WGM) resonator made of lithium niobate (LN) single crystal. The effect of WGM resonator side roughness on the quality factor (Q-factor) of resonator was simulated by finite-difference time-domain (FDTD) method. WGM resonators were annealed at high temperature(1050 °C) to improve the Q-factor, and measured the side roughness of the WGM resonator before and after annealing with a white light interference microscope. It found that Q-factor of WGM resonator can be increased by more than 2 orders of magnitude by thermal treatment at 1050 °C.

The effect of compositional segregation on the properties of relaxor ferroelectric single crystal are attracting increasing attention for its serious limitation on the application field. In this paper, the composition, phase structure, optical properties and electric properties of Mn-doped Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIN-PMN-PT) single crystal were investigated. The real composition of the single crystal fluctuated around the original ratio, except for MnO2. The single crystal contained less Mn element after removing inclusions compared with the starting ratio. The single crystal samples exhibited rhombohedral phase (R phase), orthorhombic phase (O phase) and tetragonal phase (T phase) structures with different composition due to the segregation. The rhombohedral to tetragonal phase transition temperature (TR-T) shifted to a lower value along the growth direction, while the Curie Temperature (TC) shifted to a higher value instead. The relaxation level of the single crystal went down to a lower level when the crystal structure changed from R phase to T and O phase. The coercive field (EC) with [001] poling in R phase remained stable before a rise in O phase and T phase. However, the composition segregation didn't obviously affected the internal bias field and kept around 0.2 kV/cm. The piezoelectric coefficient d33 and unipolar strain with poling direction along [001] had the same trend along growth direction. The curves of them both took a rapid fall at the top of the single crystal boule, which related to the T phase.

For a long lime, the fragility of ceramic nanofibers is a key issue for their application in wearable nano devices. BaTiO3 (BTO) flexible nanofibers with excellent elastic modulus of 1.33 GPa and high morphology integrity have been successfully obtained by electrospinning. The BTO flexible nanofibers with diameter around 100 nm have pure perovskite structure at room temperature and no secondary phase. Further analysis shows the prepared BTO flexible nanofibers to have core-shell structure, which are thought to be responsible to its improved elastic response. In addition, the comparative experiments show the oxygen vacancies to play an important role in the formation of core-shell structure. This work provides an effective approach for designing advanced mechanical properties of BTO nanofibers. The BTO nanofibers after being calcined in nitrogen atmosphere show better surface morphology and crystallinity than the nanofibers calcined in other atmospheres. The results reveal that the nitrogen atmosphere will effectively modify the mechanical properties of the BTO nanofibers.

Mechanisms of the dielectric relaxation and electric field induced dipole re-orientation process in the 0.6BaTiO 3 -0.4Bi(Mg 1/2 Ti 1/2 )O 3 ceramic have been investigated by a combination of experiments and simulations. Using the modified Debye relaxation theory, the observed strong relaxation is related to the evolution of the distribution of relaxation times with increasing temperatures. The increased freezing temperature under dc bias electric fields indicates that the nonlinear dielectric behavior has positive contributions to the total polarization. In relaxor state, the dielectric response of the 0.6BaTiO 3 -0.4Bi(Mg 1/2 Ti 1/2 )O 3 ceramic shows a maximum value with the increasing external fields, which is attributed to two main polarization mechanisms, lattice phonon polarization and re-orientation of polar clusters. The contribution of these two polarization mechanisms is separated by the multi-polarization model, indicating that the re-orientation of polar clusters is responsible for the increase of the dielectric constant. At last, Monte Carlo method is performed to simulate the dipole re-orientation process, and the simulated results are consistent with experimental findings. This study provides a different perspective to investigate the relaxor materials with isolated polar clusters.

In this paper, the relaxation behavior and electrical inhomogeneity of the 0.9BaTiO 3 - 0.1Bi(Mg 1/2 Ti 1/2 )O 3 ceramic which exhibits outstanding temperature stable dielectric and energy storage properties are investigated. The relaxation process is well described by the empirical Vogel-Fulcher law, also indicating a freezing process in the system simultaneously. Such a freezing process is also observed in the “Vogel-Fulcher” shaped temperature dependence of the universal relaxation exponent n. Furthermore, the electrical inhomogeneity, showing up as two dielectric anomalies in the temperature dependence of the dielectric constant, is ascribed to the compositional inhomogeneity between grains and grain boundaries. The grain and grain boundary contributions to the total polarization are separated by analyzing the complex impedance spectroscopy with equivalent circuit model. Finally, the compositional inhomogeneity is manifested by the confocal Raman microscopy, indicating that the grain is rich in BaTiO 3 , whereas the grain boundary has Bi(Mg 1/2 Ti 1/2 )O 3 concentrations.

Polarization reversal process has been studied in [001]-cut lead magnesium niobate-lead titanate single crystals with 30% lead titanate by in situ visualization of domain kinetics and switching current analysis. It has been shown by high-resolution methods that the sample poling leads to partial decay of as-grown domain structure and decrease of the domain width down to 200 nm. Analysis of the switching current by modified Kolmogorov-Avrami approach has shown that the field dependence of the characteristic time follows activation law with activation field value 1040±50 V/mm. In situ visualization has allowed revealing the main stages of domain structure evolution.

Flexible piezoelectric energy harvesting devices based on inorganic piezoelectric materials have attracted wide attention for their outstanding physical properties and potential applications. Different strategies, such as adding ductile elements, increasing sintering time, sintering in various atmospheres, mixing with organic compounds which usually is not only for piezoelectric materials, are also used to fabricate highly flexible devices. However, these methods always accompanied by a sharp reduction in piezoelectric performance, and then the sensitivity of the device will be reduced. Here, The flexible piezoelectric energy harvesting device by mixing Ce-doped barium titanate (BaTiO3, BTO) nanofibers with poly (vinylidene fluoride-trifluorethylene) [P(VDF-TrFE)] nanofibers is studied. Due to the introduction of P(VDF-TrFE) nanofibers, the device show high flexibility. The device with high output signal is obtained, since both fillers are piezoelectric materials. The results show that the output power density of the device fabricated by Ce-BTO/P(VDF-TrFE) composite nanofibers is about six times larger than the device obtained by P(VDF-TrFE) nanofibers. This proposed method is expected to provide reference for the development of future nanoscale piezoelectric-based energy harvesting devices and sensors.

Organic piezoelectric materials exhibit excellent physical properties and potential applications in implantable biological devices. As a result flexible nanoscale piezoelectric sensors based on these materials have been the focus of numerous investigations. Different strategies have been developed as promising approaches to obtain high properties flexible nano devices. Nevertheless, the piezoelectric performance of the materials could not be fully utilized, which in turn leads to a decrease in the sensitivity of the device. Here, the highly efficient utilization of flexible nanoscale piezoelectric sensor is realized through the ingenious design of the interdigital electrode structure. The high flexibility is attributed to the organic materials of P(VDF-TrFE). The output performance of the sensor made by the nanofibers has been greatly improved, since each segment of the nanofibers on the interdigital electrode structure is utilized efficiently. The results show that a maximum voltage of 140 mV and a current of about 0.59 nA for the sensor are generated. The volume power density of the nano device based on P(VDF-TrFE) nanofibers is 5.01 nW cm−3. This proposed method could be a promising strategy to fabricate future nanoscale piezoelectric sensors.

Quantum communication has attracted much attention in recent years, provides an ultimate level of security, and uniquely it is one of the most likely practical quantum technologies at present. In order to realize global coverage of quantum communication networks, not only need the help of satellite to realize wide area quantum communication, need implementation of optical fiber system to realize city to city quantum communication, but also, it is necessary to implement end-to-end quantum communications intercity and wireless quantum communications that can be received by handheld devices. Because of the limitation of application of light in buildings, it needs quantum communication with microwave band to achieve quantum reception of wireless handheld devices. The single microwave photon energy is very low, it is difficult to directly detect, which become a difficulty in microwave quantum detection. This paper summarizes the mode of single microwave photon detection methods and the possibility of application in microwave quantum communication, and promotes the development of quantum communication in microwave band and quantum radar.

The new (Nb+In) co-doped TiO2 ceramics recently stimulated considerable attention due to their colossal permittivity (CP) (~100,000). In this research, the 3 mol% (Nb+In) co-doped TiO2 ceramics were synthesized by an standard solid-state reaction method. Phase structure was studied by XRD and Raman, which showed that all samples were in pure rutile phase. The elements distribution was tested by the SEM–EDS, indicating that the Nb and In ions were homogeneously distributed in the grain and grain boundary. Dielectric properties and I–V behavior analysis demonstrated that the ceramics may compose of semiconducting grains and insulating grain boundaries. The existence of CP and nonlinear I–V behavior in sample had been explained by an internal barrier layer capacitance (IBLC) model, which consists of n-type semiconductor grains and insulating grain boundaries.

K0.5Na0.5NbO3 (KNN) powder was synthesized by a novel sol–gel method and used to fabricate an energy harvesting device. The precursor gel and KNN powder were studied by thermogravimetric analysis (TG), differential scanning calorimetry (DSC), X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The elemental composition of the KNN powder was characterized by energy dispersive X-ray analysis (EDAX). Well crystallized single phase perovskite KNN powder with an average particle size on the order of 450 nm was obtained from the gel after calcining at 750 °C for 2 h. A flexible and implantable energy harvesting device fabricated using the KNN nanopowder exhibited an output power of up to 0.13 μW with a load resistance of 100 MΩ. The Young’s modulus of the device was determined to be 10.4 GPa by atomic force microscopy (AFM).

Ce-doped BaTiO3 (BTO) nanofibers were prepared by sol–gel combined with electrospinning method. The influence of cerium ions concentration on BTO crystal phase, microstructure, piezoelectricity, and elasticity were investigated. The energy harvesting properties of the device based on Ce-doped BTO nanofibers were tested. The piezoelectric property of BTO nanofibers were improved after cerium doping. The elastic property of the fibers changed little after cerium doping. The elastic modulus of the pure BTO nanofibers was about 3.37 GPa. When the Ce/Ba atomic ratio was 0.6%, the elastic modulus dropped to 1.18 GPa. Our analysis of the temperature range of the energy harvesting device indicates that an effective operation can be obtained when the working temperature of the device is below 110 °C. The largest delivered power of the energy harvesting device was 14.37 μW with a load resistance of 100 MΩ, when the Ce/Ba atomic ratio was 0.6%.

BaTiO3 (BTO) nanofibers were fabricated by sol–gel combined with electrospinning method. The effects of the concentration of acetic acid and sintering temperatures on the crystal phase and microstructure of the samples were investigated by scanning electron microscopy, X-ray diffraction, and transmission electron microscopy (TEM). BTO nanofibers with improved surface morphology were obtained as the ethanol to acetic acid ratio (E/A) was 8:3. The fibers calcined at 750°C for 2 h exhibited good morphology and crystallization. TEM studies revealed that the BTO nanofibers were polycrystalline, with diameters being on the order of hundreds nanometer, where the existence of domains offered proof of ferroelectric structure. The ferroelectric domains and piezoresponse of BTO nanofibers were characterized by piezoresponse force microscopy. The calculated d33 was 20 pm/V at maximum strain amplitude.

The surface plasmon polaritons (SPPs) have many potential application due to their local field enhancement and sub-wavelength characteristics. Recently, the gradient metasurface is introduced to couple the spoof SPPs in microwave frequency band. One of the most important issue which should be solved is the narrowband of spoof SPPs coupling on the gradient metasurface. Here, the metasurface is proposed to achieve the wideband helicity dependent directional spoof SPPs coupling for circular polarized light. Our research show that the coupling frequency of spoof SPPs on the gradient metasurface is determined by the dispersion of the metasurface, so the coupling frequency can be controlled by dispersion design. The careful design of each cell geometric parameters has provided many appropriate dispersion relations possessed by just one metasurface. The wave vector matching between the propagating wave and the spoof SPPs has been achieved at several frequencies for certain wave vector provided by the metasurface, which leads to wideband spoof SPPs coupling. This work has shown that wideband helicity dependent directional spoof SPPs coupling has been achieved with a high efficiency. Hence, the proposed wideband spoof SPPs coupling presents the improvement in practice applications.

An electro-optic (EO) modulator is one of the most important optical devices and has been widely used in the photonic industry. Performance of EO modulators mainly depends on the property of EO materials. Here, the EO property of the (111)-oriented single domain rhombohedra phase (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT) single crystal is investigated. Due to the light scattering by domain walls, a single domain crystal is essential and has been well prepared here by a thermal annealing and high temperature poling process. It is found that domains become irregular with significantly decreased dimension after annealing, which indicates that the ferroelastic domain walls are eliminated. A crack-free single domain crystal shows excellent optical quality, with a high transmittance of approximately 70% in near-infrared regions. Finally, the effective EO coefficient of the (111)-oriented rhombohedral phase PMN-PT crystal is measured by a Senarmont compensator amplitude modulator. An effective EO coefficient of 112 pm/V is obtained in the (111)-oriented rhombohedral phase PMN-PT crystal, which is much higher than that of the commercial LiNbO3 crystal, indicating the potential for use in compact and low driving voltage EO devices.An electro-optic (EO) modulator is one of the most important optical devices and has been widely used in the photonic industry. Performance of EO modulators mainly depends on the property of EO materials. Here, the EO property of the (111)-oriented single domain rhombohedra phase (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT) single crystal is investigated. Due to the light scattering by domain walls, a single domain crystal is essential and has been well prepared here by a thermal annealing and high temperature poling process. It is found that domains become irregular with significantly decreased dimension after annealing, which indicates that the ferroelastic domain walls are eliminated. A crack-free single domain crystal shows excellent optical quality, with a high transmittance of approximately 70% in near-infrared regions. Finally, the effective EO coefficient of the (111)-oriented rhombohedral phase PMN-PT crystal is measured by a Senarmont compensator amplitude modulator. An effective EO coefficient of 112...

Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN–PT) single crystals have attracted increasing attention in electro-optic and nonlinear optical applications. In this paper, it was found that the domain configuration of PMN–PT single crystals was influenced by machining and electric process, such as cutting, grinding, polishing, and electrical field poling. The ordered herringbone/stripe domain pattern can be changed into an unexpected disordered domain state in tetragonal PMN–PT crystals which was observed in some crystal samples. Those chaotic structures can decrease transmittance and increase possibility of cracking during poling. However, the disordered domain pattern can be eliminated by a temperature cycling process. Crack-free single-domain crystals were successfully obtained by electric field poling, exhibiting complete optical extinction in an orthogonal polarized light microscope. The results suggest that the domain configuration of PMN–PT single crystals is sensitive to machining process and can be controlled by proper temperature and electric field.Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN–PT) single crystals have attracted increasing attention in electro-optic and nonlinear optical applications. In this paper, it was found that the domain configuration of PMN–PT single crystals was influenced by machining and electric process, such as cutting, grinding, polishing, and electrical field poling. The ordered herringbone/stripe domain pattern can be changed into an unexpected disordered domain state in tetragonal PMN–PT crystals which was observed in some crystal samples. Those chaotic structures can decrease transmittance and increase possibility of cracking during poling. However, the disordered domain pattern can be eliminated by a temperature cycling process. Crack-free single-domain crystals were successfully obtained by electric field poling, exhibiting complete optical extinction in an orthogonal polarized light microscope. The results suggest that the domain configuration of PMN–PT single crystals is sensitive to machining process and can be controlled by pr...

The relaxor–PbTiO3 single crystal has attracted extensive attention in ultrasound transducers, sensors, actuators, and optoelectronics devices due to its excellent piezoelectric response and electro–optic properties. Preparation of a single–domain crystal as a critical process for application in electro–optic and non–linear optical devices suffers from serious and inevitable cracking. Therefore, a pre-poling thermal annealing process was suggested to release residual stress from crystal growth and the ferroelectric–paraelectric phase transition, which significantly reduced the chance of cracking. The effect of thermal annealing on dielectric properties, strain behavior, and domain structure were investigated. As a result, a significant increase of the dielectric constant near room temperature was obtained after annealing, which is close to the dielectric constant of the a-oriented domain. The annealed single crystal showed a lower and sharper strain peak at the coercive electric field compared with the un...

The performance of a robotic hand is severely limited by the tactile feedback information similar to a human hand. Hence, a novel and robust tactile sensor has been developed to cope with the challenge of robotic hand technology. Piezoelectric material is proposed as a suitable candidate for a new efficient tactile sensor due to its excellent piezoelectric properties. In this paper, a novel flexible tactile sensor based on Ce-doped BTO nanofibers was developed. The doping mechanism of cerium ions and the working process of the sensor were analysed. The results showed that sheer stress had no contribution to the sensor, this indicated that the sensor was easy to control according to the individual's wish. The output voltage of the sensor could reach up to 0.078 V which showed great potential for the future of intelligent robot skin application.

The (Nb + In) co-doped TiO2 ceramics recently attracted considerable attention due to their colossal dielectric permittivity (CP) (∼100,000) and low dielectric loss (∼0.05). In this research, the 0.5 mol. % In-only, 0.5 mol. % Nb-only, and 0.5–7 mol. % (Nb + In) co-doped TiO2 ceramics were synthesized by standard conventional solid-state reaction method. Microstructure studies showed that all samples were in pure rutile phase. The Nb and In ions were homogeneously distributed in the grain and grain boundary. Impedance spectroscopy and I-V behavior analysis demonstrated that the ceramics may compose of semiconducting grains and insulating grain boundaries. The high conductivity of grain was associated with the reduction of Ti4+ ions to Ti3+ ions, while the migration of oxygen vacancy may account for the conductivity of grain boundary. The effects of annealing treatment and bias filed on electrical properties were investigated for co-doped TiO2 ceramics, where the electric behaviors of samples were found to be susceptible to the annealing treatment and bias field. The internal-barrier-layer-capacitance mechanism was used to explain the CP phenomenon, the effect of annealing treatment and nonlinear I-V behavior for co-doped rutile TiO2 ceramics. Compared with CaCu3Ti4O12 ceramics, the high activation energy of co-doped rutile TiO2 (3.05 eV for grain boundary) was thought to be responsible for the low dielectric loss.