Effects of W6+ substitution on crystal structure and microwave dielectric properties of Li3Mg2NbO6 ceramics

Li₃Mg₂(Nb_1-xW_x)O_6+x/2 (0 ≤ x ≤ 0.08) ceramics were synthesized by the solid-state reaction route. The effects of W⁶⁺ substitution on the phase composition, microstructure and microwave dielectric properties of Li₃Mg₂NbO₆ ceramics were investigated systematically. The XRD results showed that all the samples formed a pure solid solution in the whole doping range. The SEM iamges and relative density revealed the dense structure of Li₃Mg₂(Nb_1-xW_x)O_6+x/2 ceramics. The relationship between the crystal structure and dielectric properties of Li₃Mg₂(Nb_1-xW_x)O_6+x/2 ceramics was researched through polarizability, average bond valence, and bond energy. The substitution of W⁶⁺ for Nb⁵⁺ in Li₃Mg₂(Nb_1-xW_x)O_6+x/2 ceramics significantly promoted the Q × f values. In addition, the increase of W⁶⁺ content improved the thermal stability of the Li₃Mg₂(Nb_1-xW_x)O_6+x/2 ceramics. The Li₃Mg₂(Nb_0.94W_0.06)O_6.03 ceramics sintered at 1175 °C for 6h possessed excellent properties: ε_r ~ 15.82, Q × f ~ 124,187 GHz, τ_f ~ −18.28 ppm/°C.     

Correlation between crystal structure and modified microwave dielectric characteristics of Cu2+ substituted Li3Mg2NbO6 ceramics

Structural characteristics exert significant influences on microwave dielectric properties, and ion substitution is widely adopted to modify material performances by adjusting the crystal structure. In this work, low loss Li₃Mg_2-xCu_xNbO₆ (x?=?0–0.04) ceramics were prepared by Cu²⁺ substitution. The impacts of Cu²⁺ substitution for Mg²⁺ sites on the microwave dielectric characteristics and crystal structure were discussed in detail. Rietveld refinement results implied that a single Li₃Mg₂NbO₆ phase was formed. Additionally, a dense and homogeneous microstructure with grain sizes of 7–9?μm could be achieved, and moderate Cu²⁺ substitution could significantly promote the grain growth. The correlation between microwave dielectric characteristics and crystal structure was discussed by calculating some structural parameters. The ε_r was determined by the polarizability. The Q?×?f was influenced by the packing fraction. The τ_f value was dependent on the NbO₆ octahedron distortion, and the τ_f value could be adjusted to near zero for x?=?0.02. Typically, the Li₃Mg_2-xCu_xNbO₆ (x?=?0.02) composition exhibited remarkable microwave dielectric performances: ε_r?=?15.75, Q?×?f?=?92,134?GHz (9.86?GHz) and τ_f?=??2?ppm/°C, making it a promising candidate for temperature-stable millimeter-wave applications.     

Crystal structures and microwave dielectric properties of low-firing Ca5Zn4-xMgxV6O24 ceramics

Ca₅Zn_4-xMg_xV₆O₂₄ (x?=?0–3) microwave dielectric ceramics with low sintering temperature were synthesized via the conventional solid-state reaction. Effects of the substitution of Mg²⁺ for Zn²⁺ on crystal structures and microwave dielectric properties were investigated. XRD and Rietveld refinement showed the solid solution single phase formed when 0?≤?x?≤?2, but a few ZnO was observed when x?=?3. Meanwhile, the lattice parameters were found to decrease monotonously with Mg content increasing. The vibration modes of Raman were confirmed and the relationship with microwave dielectric properties was analyzed. Appropriate substitution of Mg²⁺ improved the packing fraction, the cation ordering degree, and the Y-site bond valence, contributing to high Q×f and low | τ_f |. However, the ε_r reduced with the increasing content of Mg²⁺ due to the decrease of ion polarizability. Finally, the best microwave dielectric properties were achieved at x?=?2 with ε_r =?11.0, Q?×?f?=?66,365?GHz (at 10.0?GHz), and τ_f =??80.4?ppm/°C.     

Improved non-ohmic and dielectric properties of Cr3+ doped CaCu3Ti4O12 ceramics prepared by a polymer pyrolysis solution route

CaCu_3-xCr_xTi₄O₁₂ (x?=?0.00–0.20) ceramics were prepared via a polymer pyrolysis solution route. Their dielectric properties were improved by Cr³⁺ doping resulting in an optimal dielectric constant value of 7156 and a low tanδ?value of 0.092 in a sample with x?=?0.08. This might have resulted from a decrease in oxygen vacancies at grain boundaries. XANES spectra confirmed the presence of Cu⁺ ions in all ceramic samples with a decreasing Cu⁺/Cu²⁺ ratio due to an increased content of Cr³⁺ ions. All CaCu_3-xCr_xTi₄O₁₂ ceramics showed nonlinear characteristic with improvement in both the breakdown field (E_b) and its nonlinear coefficient (α). Interestingly, the highest values of α, ～ 114.4, and that of E_b, ～8455.0?±?123.6?V?cm^?1, were obtained in a CaCu_3-xCr_xTi₄O₁₂ sample with x?=?0.08. The improvement of dielectric and nonlinear properties suggests that they originate from a reduction of oxygen vacancies at grain boundaries.     

Correlations between the structural characteristics and enhanced microwave dielectric properties of V–modified Li3Mg2NbO6 ceramics

Novel low-temperature fired Li₃Mg₂Nb_1-xV_xO₆ (x?=?0.02??0.08) microwave dielectric ceramics were synthetized by the partial substitution of V⁵⁺ ions on the Nb⁵⁺ sites. The effects of V⁵⁺ substitution on structure and microwave dielectric properties were investigated in detail. XRD patterns and Rietveld refinement demonstrated that all of the samples exhibited a single orthorhombic structure. The structural characteristics such as the polarizability, packing fraction and NbO₆ octahedron distortion were determined to establish the correlations between the structure and the microwave dielectric characteristics. The ?_r values presented a tendency similar to that of the polarizability. The high Q×f values were mainly attributed to the effects of the grain sizes and density rather than the packing fraction. The variation in the τ_f values was attributed to NbO₆ octahedron distortion. Notably, the Li₃Mg₂Nb_1-xV_xO₆ (x?=?0.02) ceramics sintered at 900?°C had outstanding microwave dielectric properties: ε_r=?16, Q×f=?131,000?GHz (9.63?GHz), and τ_f=???26?ppm/°C, making these ceramics promising ultralow loss candidates for low temperature co-fired ceramics (LTCC) applications.     

Phase composition,Raman spectra,infrared spectra and dielectric properties of Li2MgTi1-x(Mg1/3Nb2/3)xO4 ceramics at microwave frequency

The Li₂MgTi_1-x(Mg_1/3Nb_2/3)_xO₄ (0?≤x?≤?0.5) ceramics were prepared by the conventional solid-state method. The relationship among phase composition, substitution amount and microwave dielectric properties of the ceramics was symmetrically investigated. All the samples possess the rock salt structure with the space group of Fm-3m. As the x value increases from 0 to 0.5, the dielectric constant linearly decreases from 16.75 to 15.56, which can be explained by the variation of Raman spectra and infrared spectra. The Q·f value shows an upward tendency in the range of 0?≤x?≤?0.3, but it then decreases when x?>?0.3. In addition, the temperature coefficient of resonant frequency (τ_f) is shifted toward zero with the increasing (Mg_1/3Nb_2/3)⁴⁺ addition. By comparison, the Li₂MgTi_0.7(Mg_1/3Nb_2/3)_0.3O₄ ceramics sintered at 1400?°C can achieve an excellent combination of microwave dielectric properties: ε_r=?16.19, Q·f =?160,000?GHz and τ_f =??3.14?ppm/°C.     

Dielectric and microwave absorption properties of divalent-doped Na3Zr2Si2PO12 ceramics

The work attempted to develop a new kind of high temperature microwave absorption material. Dense Na₃Zr_1.9M_0.1Si₂PO_11.9 (M?=?Ca²⁺, Ni²⁺, Mg²⁺, Co²⁺, Zn²⁺) and Na₃Zr_2-xZn_xSi₂PO_12-x (x?=?0.1, 0.2, 0.3, 0.4) ceramics were prepared by solid-state reactions for phase, microstructure characterization and dielectric properties, microwave absorption properties analysis. Results show that the complex permittivity increases in all the divalent-doped Na₃Zr₂Si₂PO₁₂ ceramics. Na₃Zr_1.8Zn_0.2Si₂PO_11.8 ceramic exhibits the highest complex permittivity and optimum microwave absorption performance. The lowest reflection loss is -28.1?dB at 9.88?GHz and the bandwidth is 4.14?GHz (8.26–12.4?GHz) with a thickness of 2.1?mm. It indicates that Na₃Zr₂Si₂PO₁₂ ceramic can be chosen as a potential candidate of microwave absorption material and the performance can be enhanced by divalent doping strategy.     

Microwave dielectric ceramics in (Mg1/3Sb2/3)O2-ZrO2-TiO2 system with near zero τf and low loss in a very wide range

A series of (ZrTi)_1-x(Mg_1/3Sb_2/3)_2xO₄ (0.04?≤?x?≤?0.36) ceramics were successfully synthesized through the conventional solid-state processing. Appropriate content of CuO was added as sintering aids to promote the density of ceramics. The XRD analysis revealed that the main crystalline phase of ceramics sintered at optimal temperature belonged to α-PbO₂-type structure. Raman spectroscopy and far infrared reflectivity (FIR) spectra were employed to study the phonon modes of ceramics, which explained the relationship between microwave dielectric properties and structure. It is interesting that the τ_f are near-zero (+6.6 ~ ?4.6?ppm/°C) and meanwhile the Q×f are relatively high (29,000–41,800?GHz) for samples with x in a very wide range of 0.10–0.36. In this range, their dielectric constants (ε_r) can be adjustable from 35.4 to 24.4. The results demonstrated this ceramic system is a potential candidate for microwave dielectric applications requiring an adjustable dielectric constants and near zero τ_f.     

Investigation of chemical bonds in the ordered Ba3Zn(Nb2-xMox)O9+x/2 ceramics and its effects on the microwave performance

1:2 ordered Ba₃Zn(Nb_2-xMo_x)O_9+x/2(BZNM) ceramics with space group $\text{P}\overline{3}\text{ml}$ were prepared by solid-state method. The nature of chemical bonds in Ba₃Zn(Nb_2-xMo_x)O_9+x/2(BZNM) ceramics was investigated for the first time. Firstly, the bond energy was closely related to the lattice vibration. High bond energy would lead to weak non-harmonic interactions, which were the main factors of improving Qf. Secondly, polarization of the chemical bond was the principal contributor to the relative permittivity of microwave ceramics. Compared with the traditional method, the calculated result based on the P-V theory reduced the error from 81% to 4.4%. Through the discussion, it was confirmed that the analysis method based on chemical bond was highly feasible and scientific in the microwave ceramics. At last, the system of Ba₃Zn(Nb_1.992Mo_0.008)O_9.004 sintered at 1435?°C for 6?h and annealed at 1300?°C for 10?h had excellent microwave dielectric properties: ε_r?=?38.9, Qf?=?102,931?GHz, τ_f?=?19.2?ppm/°C, which, to our best knowledge, provided a alternative for the application of millimeter-wave communications.     

A novel solid solution (K1-xNax)2Mo2O7 (0.0 ≤ x ≤ 0.3) ceramics with ultra-low sintering temperatures

The (K_1-xNa_x)₂Mo₂O₇ (0.0?≤?x?≤?0.3) ceramics with ultra-low sintering temperatures were prepared by a modified solid-state reaction method. Polyvinyl ethanol (PVA) binder was replaced by ethanol and isostatic pressing technology was used, which improved the density of the ceramics effectively and avoided the side effect of the residual PVA. When x?≤?0.3, the (K_1-xNa_x)₂Mo₂O₇ ceramics are with a triclinic phase and all components can be sintered well at 450?°C. The substitution of Na⁺ at the K-site modified the dielectric properties of K₂Mo₂O₇ ceramic and in particular increased the Q?×?f value. Among all the components, the (K_0.8Na_0.2)₂Mo₂O₇ ceramic exhibited the best microwave dielectric properties with a permittivity of 8.7, a Q?×?f value of 50 300?GHz and a temperature coefficient of ?64?ppm/°C. The (K_1-xNa_x)₂Mo₂O₇ (0.0?≤?x?≤?0.3) ceramics are very potential candidates for ultra-LTCC devices and the modified solid-state reaction method is an excellent substitution for the conventional solid-state method.     

Cation distribution of high-performance Mn-substituted ZnGa2O4 microwave dielectric ceramics

In current study, only 5?mol% Mn²⁺ was applied to fabricate high performance microwave dielectric ZnGa₂O₄ ceramics, via a traditional solid state method. The crystal structure, cation distribution and microwave dielectric properties of as-fabricated Mn-substituted ZnGa₂O₄ ceramics were systematically investigated. Mn²⁺-substitution led to a continuous lattice expansion. Raman, EPR and crystal structure refinement analysis suggest that Mn²⁺ preferentially occupies the tetrahedral site and the compounds stay normal-spinel structure. The experimental and theoretical dielectric constant of Zn_1-xMn_xGa₂O₄ ceramics fit well. In all, this magnetic ion, Mn²⁺, could effectively adjust the τ_f value to near zero and double the quality factor from 85,824?GHz to 181,000?GHz of Zn_1-xMn_xGa₂O₄ ceramics at the meantime. Zn_1-xMn_xGa₂O₄ (x?=?0.05) ceramics sintered at 1400?°C for 2?h exhibited excellent microwave dielectric properties, with ε_r =?9.7(@9.85?GHz), Q?×?f?=?181,000?GHz, tanδ?=?5.44?×?10^?5,and τ_f =???12?ppm/°C.     

Effect of Mn2+ doping on the lattice and the microwave dielectric properties of MgTa2O6 ceramics

A series of Mn²⁺-doped Mg_1-xMn_xTa₂O₆ (x = 0.02, 0.04, 0.06, 0.08, 0.10, 0.12) ceramics were synthesized by solid-state reaction method. The influence of introducing Mn–O bonds as a partial replacement for Mg–O bonds on the lattice and microwave dielectric properties was systematically investigated. XRD and Rietveld refinement confirm that Mn²⁺ occupies the 2a Wyckoff position and forms a pure trirutile phase. Moreover, based on the chemical bond theory, the dielectric constant is mainly affected by the ionicity of the Ta–O bond. The lattice and dielectric properties remain relatively stable with Mn²⁺ doping below 0.1, but excessive Mn²⁺ doping leads to pronounced distortion of the lattice, which is not beneficial for lattice stability and microwave dielectric properties. Introducing an appropriate amount of Mn–O bonds with high bond dissociation energy facilitates MgO6 octahedron stability, which improves the thermal stability of the lattice. Accordingly, the microwave dielectric properties for 0.06 Mn²⁺-doped MgTa₂O₆ ceramics were determined: ε_r = 28, Q × f = 105,000 GHz (at 7.5 GHz), τ_f = 19.5 ppm/^°C.     

Effects of (Cr0.5Ta0.5)4+ on structure and microwave dielectric properties of Ca0.61Nd0.26TiO3 ceramics

The Ca_0.61Nd_0.26Ti_1-x(Cr_0.5Ta_0.5)_xO₃ (CNT-CTx) ceramics with orthorhombic perovskite structure were prepared using the conventional solid-state method. The X-ray diffraction (XRD), Raman spectra and X-ray photoelectron spectra (XPS) were employed to investigate the correlations between crystal structure and microwave dielectric properties of CNT-CTx ceramics. The XRD results showed that all CNT-CTx samples were crystallized into the orthorhombic perovskite structure. The SEM micrographs indicated that the average grain size of samples depended on the sintering temperature. As (Cr_0.5Ta_0.5)⁴⁺ concentration increased, there was a significant decrease in the average grain size of samples. The short range order (SRO) structure and structural distortion of oxygen octahedra proved to exist in CNT-CTx crystals according to the analysis of Raman spectra results. The microwave dielectric properties highly depended on the full width at half maximum (FWHM) of Raman spectra, oxygen octahedra distortion, reduction of Ti⁴⁺ to Ti³⁺ and bond valence. At last, the CNT-CT0.05 ceramic sintered at 1420?°C for 4?h exhibited the good and stable comprehensive microwave dielectric properties: relative permittivity of 96.5, quality factor of 14,360?GHz, and temperature coefficient of resonant frequency of +153.3?ppm/°C.     

Effects of structural characteristics on microwave dielectric properties of low-loss (Zn1-xNix)ZrNbTaO8 ceramics

Low-loss (Zn_1-xNi_x)ZrNbTaO₈ (0.02?≤?x?≤?0.10) ceramics possessing single wolframite structure are initiatively synthesized by solid-state route. Based on the results of Rietveld refinement, complex chemical bond theory is used to establish the correlation between structural characteristics and microwave performance in this ceramic system. A small amount of Ni²⁺ (x?=?0.06) in A-site with the fixed substitution of Ta⁵⁺ in B-site can effectually raise the Q?×?f value of ZnZrNb₂O₈ ceramic, embodying a dense microstructure and high lattice energy. The dielectric constant and τ_f are mainly affected by bond ionicity and the average octahedral distortion. The (Zn_0.94Ni_0.06)ZrNbTaO₈ ceramic sample sintered at 1150?°C for 3?h exhibits an outstanding combination of microwave dielectric properties: ε_r =?27.88, Q?×?f?=?128,951?GHz, τ_f =?–39.9?ppm/°C. Thus, it is considered to be a candidate material for the communication device applications at high frequency.     

Effects of Ti-substitution on the crystal structures,micro-structures and microwave dielectric properties of Li2Mg3Zr1-xTixO6 (0 ≤ x ≤ 1) ceramics

Li₂Mg₃Zr_1?xTi_xO₆ (x = 0, 0.2, 0.4, 0.6, 0.8, 1) ceramics were prepared via a solid-state reaction method. Crystal structures, sintering behaviors, micro-structures and microwave dielectric properties of Li₂Mg₃Zr_1?xTi_xO₆ (0 ≤ x ≤ 1) ceramics were investigated by XRD, SEM and chemical bond theory. XRD results showed that a single phase with the rock-salt structure was formed in all ranges. On the basis of the Rietveld refinement and chemical bond theory, several intrinsic parameters were calculated and connections between intrinsic parameters and microwave dielectric properties were investigated. The substitutions of Ti⁴⁺ for Zr⁴⁺ obviously increased the relative density and improved the quality factors. Variations of ε_r could be explained by changes of the polarizability. Q·f values showed the similar trend with the packing fractions, average bond valences and lattice energy of Zr–O bonds. τ_? values significantly correlated with the bond energy of Zr–O bonds.     

Structural and thermoelectric properties of hydrothermal-processed Ag-doped Fe2O3

Fe_2-xAg_xO₃ (0?≤?x?≤?0.04) nanopowders with various Ag contents were synthesized at different hydrothermal reaction temperatures (150?°C and 180?°C). Their structural properties were fully investigated through an X-ray diffraction, a Fourier transform infrared spectroscopy, and an X-ray photoelectron spectroscopy. The hydrothermal reaction temperature, time, and Ag content remarkably affected the morphological characteristics and crystal structure of the synthesized powders. The Fe_2-xAg_xO₃ (0?≤?x?≤?0.04) powders synthesized at 150?°C for 6?h and the Fe_2-xAg_xO₃ (0.02?≤?x?≤?0.04) powders synthesized at 180?°C for 12?h formed the orthorhombic α-FeOOH phase with a rod-like morphology, whereas the Fe_2-xAg_xO₃ (0?≤?x?≤?0.01) powders synthesized at 180?°C for 12?h formed the rhombohedral α-Fe₂O₃ phase with a spherical-like morphology. The Fe_1.98Ag_0.02O₃ fabricated by utilizing Fe_1.98Ag_0.02O₃ powders synthesized at 180?°C showed the largest power factor (0.64?×10^?5 Wm^?1 K^?2) and dimensionless figure-of-merit (0.0036) at 800?°C.     

Effects of Magnesium–Tungsten co-substitution on crystal structure and microwave dielectric properties of CaTi1-x(Mg1/2W1/2)xO3 ceramics

CaTi_1-x (Mg_1/2W_1/2)_xO₃ (x = 0, 0.02, 0.04, 0.06, 0.08) dielectric ceramics were synthesized via the traditional solid-state reaction method. Crystal structure and microwave dielectric properties of CaTi_1-x (Mg_1/2W_1/2)_xO₃ system were systematically investigated based on chemistry bond theory (P–V-L theory) for the first time. The pure perovskite phase was obtained for all doped samples, as confirmed through the XRD and Rietveld refinement results. The lattice characteristics were closely related to the microwave dielectric properties. The bond ionicity, lattice energy, and bond energy affected the dielectric constant, quality factor, and temperature stability of the ceramic material. Through the use of (Mg_1/2W_1/2)⁴⁺ doped on B-site, the CaTi_1-x (Mg_1/2W_1/2)_xO₃ system can maintain a high dielectric constant (ε_r > 100) while effectively reducing the τ_f value from 800 ppm/^°C to less than 300 ppm/^°C and improving the Q × f value to 9650 GHz (at 3.76 GHz).     

Low-temperature sintering and microwave dielectric properties of B2O3-added ZnO-deficient Zn2GeO4 ceramics for advanced substrate application

ZnO-deficient Zn_2-xGeO_4-x ceramics with 0.05?≤?x?≤?0.15 were synthesized because a ZnO secondary phase is formed in the stoichiometric Zn₂GeO₄ ceramics synthesized using micrometer-sized ZnO and GeO₂ powders. The Zn_1.9GeO_3.9 ceramic sintered at 1000?°C showed a homogeneous Zn₂GeO₄ phase with good microwave dielectric properties: ε_r of 6.8, Q?×?f of 49,000?GHz, and τ_f of ?16.7?ppm/°C. However, its sintering temperature was still too high for it to be used as an advanced substrate for low-temperature co-fired ceramic devices. Therefore, various amounts of B₂O₃ were added to the Zn_1.9GeO_3.9 ceramics to reduce their sintering temperature. Owing to the formation of a B₂O₃-GeO₂ liquid phase, these ceramics were well sintered at low temperatures between 925?°C and 950?°C. In particular, 15?mol% B₂O₃-added Zn_1.9GeO_3.9 ceramic sintered at 950?°C showed promising microwave dielectric properties for advanced substrates without the reaction with an Ag electrode: ε_r?=?6.9, Q?×?f?=?79,000?GHz, and τ_f?=??15?ppm/°C.     

Crystal structure,Raman spectra and microwave dielectric properties of Li2Mg3Ti1-x(Mg1/3Nb2/3)xO6 (0 ≤x ≤ 0.25) ceramics

Li₂Mg₃Ti_1-X(Mg_1/3Nb_2/3)_XO₆ (0?≤x?≤?0.25) ceramics were prepared by a conventional solid-state reaction process. Their crystal structures, sintering characteristics, Raman spectra and microwave dielectric properties were then investigated. XRD patterns of the sintered samples indicated that all compositions showed a single phase and the rock-salt structure. As the (Mg_1/3Nb_2/3)⁴⁺ contents increase, the variations of ε_r values showed a downward trend, which could be explained by the changes of polarizabilities and the shift of Raman vibration modes. Q·f values initially increased to a maximum value and then decreased with increasing of x values. In addition, τ_f values decreased almost linearly with the x values, which significantly correlated with the thermal expansion coefficient. Excellent combined microwave dielectric properties with ε_r =?14.79, Q·f?=?204,900?GHz and τ_f =??18.43?ppm/°C were obtained for Li₂Mg₃Ti_.95(Mg_1/3Nb_2/3)_.05O₆ ceramic sintered at 1550?°C.     

Colossal permittivity and dielectric relaxations in Tl + Nb co-doped TiO2 ceramics

A series of Tl?+?Nb co-doped TiO₂ ceramics ((Tl_0.5Nb_0.5)_x%Ti_1-x%O₂ 0.5?≤?x?≤?10.0) were prepared by a solid-state reaction method under N₂ atmosphere. The evolution of their microstructures, and dielectric properties were systematically studied. The co-doped ceramics exhibited a tetragonal rutile structure wherein the Nb and Tl elements were homogeneously distributed. The cell volumes, grain size, and permittivity increased with doping x, whereas the impedance values of the grain and grain boundary decreased with an increasing x. The optimum dielectric performance (ε_r >?10⁴, tanδ?<?0.05) in the range of 10–10⁶ Hz was obtained for x?=?1.5 with a corresponding grain boundary active energy of 0.86?eV. Four types of dielectric relaxation were observed at different temperature ranges: 10–30?K, 30–200?K, 200–350?K and 350–475?K; those dielectric relaxtions were respectively caused by electron-pinned defect-dipoles, electron hopping, oxygen vacancy hopping, and Maxwell–Wagner polarization. The colossal permittivity is primarily a result of the electron-pinned defect-dipole polarization.