Studies on new systems of BNT-based lead-free piezoelectric ceramics

Several new systems of Bi_0.5Na_0.5TiO₃-based lead-free piezoelectric ceramics were proposed based on the design of the multiple complex in the A-site of ABO₃ compounds. These ceramics were prepared by conventional ceramic techniques. The comparison of the piezo- and ferroelectric properties of these ceramics with those of the best properties of the Bi_0.5Na_0.5TiO₃-based lead-free piezoelectric ceramics published recently shows that these ceramics of the new systems have better ferroelectric and piezoelectric performance, and better temperature characteristic of the properties. Among these materials, Bi_0.5(Na_1?x?y K _x Li _y )_0.5TiO₃ possesses higher piezoelectric constant (d ₃₃?=?230.8 pC/N), higher electromechanical couple factor (k _p?=?0.41), larger remanent polarization (P _r?=?40 μC/cm²) and a better P–E hysteresis loop below 200 °C. Practical devices such as ceramic middle frequency filters and buzzers have been made by using these lead-free piezoelectric ceramics.     

Effects of co-doped CaO/MnO on the piezoelectric/dielectric properties and phase transition of lead-Free (Bi0.5Na0.5)0.94Ba0.06TiO3 piezoelectric ceramics

The piezoelectric properties of (1?x)(Bi_0.5Na_0.5)TiO₃-xBaTiO₃ ceramics were reported and their piezoelectric properties reach extreme values near the MPB (about x?=?0.06). The X-ray analysis of (Bi_0.5Na_0.5)_0.94Ba_0.06TiO₃ ceramics for all compositions exhibited a pure perovskite structure without any secondary phase. Within a certain ratio of contents, the co-doped ceramics enhanced piezoelectric coefficient (d ₃₃ ), lowered the dielectric loss, and increased the sintered density. The temperature dependence of relative dielectric permittivity (K ₃₃ ^T ) reveals that the solid solutions experience two phase transitions, ferroelectric to anti-ferroelectric and anti-ferroelectric to relaxor ferroelectric, which can be proven by P-E hysteresis loops at different temperatures. In addition, the specimen containing 0.04/0.01 wt.% CaO/MnO showed that the coercive field E _c was a minimum value of 26.7 kV/cm, while the remnant polarization P _r was a maximum value of 38.7 μC/cm², corresponding to the enhancement of piezoelectric constant d₃₃ of 179 pC/N, electromechanical coupling factor k _p of 37.3%, and relative dielectric permittivity K ₃₃ ^T of 1137. (Bi_0.5Na_0.5)_0.94Ba_0.06TiO₃ ceramics co-doped with CaO/MnO were considered to be a new and promising candidate for lead-free piezoelectric ceramics owing to their excellent piezoelectric/dielectric properties, which are superior to an un-doped BNBT system.     

Dielectric and piezoelectric properties of (K0.5Na0.5)(Nb0.97Sb0.03)O3 ceramics doped with Bi2O3

In this study, to develop the optimal composition of ceramics for low loss piezoelectric actuator and ultrasonic motor applications, (K_0.5Na_0.5)(Nb_0.97Sb_0.03)O₃?+?0.009 K_5.4Cu_1.3Ta₁₀O₂₉?+?0.1wt%Li₂CO₃?+?xwt%Bi₂O₃(x?=?0?~?0.9) lead-free piezoelectric ceramics with a fixed quantity of 0.009 K_5.4Cu_1.3Ta₁₀O₂₉ (abbreviated as KCT) were manufactured using the conventional solid-state solution processes. The effects of Bi₂O₃ addition on the dielectric and piezoelectric properties were then investigated. From the X-ray diffraction analysis result the specimens demonstrated orthorhombic symmetry when Bi₂O₃ was less 0.6?wt%, a pseudo-cubic phase appeared when Bi₂O₃ was 0.9?wt%. SEM images indicate that a small amount of Bi₂O₃ addition affect the microstructure. The piezoelectric properties of (K_0.5Na_0.5)(Nb_0.97Sb_0.03)O₃ ceramics were greatly improved by a certain amount of Bi₂O₃ addition. Excellent properties of density?=?4.54?g/cm³, relative densities?=?98.5?%, k _p?=?0.468, Q _m?=?1,715 and d ₃₃?=?183 pC/N were obtained with a composition of 0.3?wt% Bi₂O₃     

Effect of sintering temperature on piezoelectric and dielectric properties of 0.98(Na0.5K0.5)NbO3-0.02Li(Sb0.17Ta0.83)O3+0.01wt%ZnO ceramics

We studied sintering temperature to enhance the piezoelectric and dielectric properties of 0.98(Na_0.5?K_0.5)NbO₃-0.02Li(Sb_0.17Ta_0.83)O₃?+?0.01wt%ZnO (hereafter NKN-LST+ZnO) lead free piezoelectric ceramics. The synthesis and sintering method were the conventional ceramic technique and sintering was executed at 1080?～?1120°C. We found that optimal sintering temperature and NKN-LST+ZnO ceramics showed the highest piezoelectric properties and dielectric properties at the optimal sintering temperature. The NKN-LST+ZnO ceramics sintered at 1090°C show a superior performance with piezoelectric constant d ₃₃?=?185 pC/N, k _p?=?0.36, ε ₃₃ ^T /ε₀?=?491 respectively. These results reveal that NKN-LST+ZnO ceramics are promising candidate materials for lead-free piezoelectric application.     

Effect of BiAlO3 concentration on the dielectric and piezoelectric properties of lead-free (Bi0.5Na0.5)0.94Ba0.06TiO3 piezoelectric ceramics

In this paper, lead-free (1-x)(Bi_0.5Na_0.5)_0.94Ba_0.06TiO₃-xBiAlO₃ (BNBT-BA, x?=?0, 0.010, 0.015, 0.020, 0.025, and 0.030) piezoelectric ceramics were synthesized using a conventional solid-state reaction method. The effect of BiAlO₃ concentration on dielectric, ferroelectric and piezoelectric properties were investigated. The ferroelectric and piezoelectric properties of BNBT ceramics are significantly influenced by the presence of BA. In the composition range studied, X-ray diffraction revealed a perovskite phase with the coexistence of rhombohedral and tetragonal phases. The temperature dependence of dielectric properties showed that the depolarization temperature (T _d) shifted towards lower temperatures and that the degree of diffuseness of the phase transition around T _d and T _m became more obvious with increasing BiAlO₃ content. The remanent polarization increased with increasing BA, and reached a maximum value of 30 μC/cm² at x?=?0.020. As a result, at x?=?0.020, the piezoelectric constant (d ₃₃) and the electromechanical coupling factor (k _p) of the ceramics attained maximum values of 188 pC/N and 34.4 %, respectively. These results indicate that BNBT-BA ceramics is a promising candidate for lead-free piezoelectric materials.     

Phase transition,microstructure and properties of (Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>)<Subscript>1-x</Subscript>Ba<Subscript>x</Subscript>TiO<Subscript>3</Subscript> lead-free piezoelectric ceramics

In this article, (Na_0.5Bi_0.5)_1-xBa_xTiO₃ lead-free piezoelectric ceramics were prepared by solid-state reaction. The influence of Ba contents on phase structures, compositional distribution and electrical properties of (Na_0.5Bi_0.5)_1-xBa_xTiO₃ ceramics were systematically investigated to further understand the nature of phase transition. It was found that the phase structure of (Na_0.5Bi_0.5)_1-xBa_xTiO₃ transforms from rhombohedral to tetragonal symmetry at x = 0.06 ~ 0.07 and Ba²⁺ segregation forms the coexistence of Ba-rich tetragonal and Ba-deficient rhombohedral phases close to MPB. The electrical properties of prepared samples regularly changed with Ba content, which is closely related to the distribution of rhombohedral and tetragonal phases. The prepared sample near MPB exhibited the largest dielectric constant and the excellent piezoelectric properties (the maximal measuring field reached 78 kV/cm and the piezoelectric constant d ₃₃ = 151pC/N).     

Microstructure and electrical properties of the rare-earth doped 0.94Na0.5Bi0.5TiO3-0.06BaTiO3 piezoelectric ceramics

Phase structure, microstructure, piezoelectric and dielectric properties of the 0.4 wt% Ce doped 0.94Bi_0.5Na_0.5TiO₃-0.06BaTiO₃ (Ce-BNT6BT) ceramics sintered at different temperatures have been investigated. The powder X-ray diffraction patterns showed that all of the Ce-BNT6BT ceramics exhibited a single perovskite structure with the co-existence of the rhombohedral and tetragonal phase. The morphologies of inside and outside of the bulk indicated that the different sintering temperatures did not cause the second phase on the inside of bulk. However, the TiO₂ existed on the outside of the bulk due to the Bi₂O₃ and Na₂O volatilizing at higher temperature. The ceramics sintered at 1,200 °C showed a relatively large remnant polarization (P _r) of about 34.2 μC/cm², and a coercive field (E _c) of about 22.6 kV/cm at room temperature. The permittivity ? _r of the ceramics increased with the increasing of sintering temperature in antiferroelectric region, the depolarization temperature (T _d) increased below 1,160 °C then decreased at higher sintering temperature. The resistivity (ρ) of the Ce-BNT6BT ceramics increased linearly as the sintering temperature increased below 1,180 °C, but reduced as the sintering temperature increased further. A maximum value of the ρ was 3.125?×?10¹⁰ ohm m for the Ce-BNT6BT ceramics sintered at 1,180 °C at room temperature.     

Synthesis and piezoelectric properties of [Bi1-z(Na1-x-y-zKxLiy)]0.5BazTiO3 lead-free piezoelectric ceramics

[Bi_1-z(Na_1-x-y-zK_xLi_y)]_0.5Ba_zTiO₃ lead-free piezoelectric ceramics were fabricated by ordinary ceramic technique and the piezoelectric and ferroelectric properties of the ceramics were studied. The ceramics can be well sintered at 1,100–1,150 °C for 2 h. X-ray diffraction (XRD) analysis shows that K⁺, Li⁺ and Ba²⁺ diffuse into the Bi_0.5Na_0.5TiO₃ lattices to form a solid solution with a single-phase perovskite structure. The introduction of K⁺, Li⁺ and Ba²⁺ into Bi_0.5Na_0.5TiO₃ significantly decreases the coercive field E _c but maintains the large remanent polarization P _r of the materials. The ceramics provide piezoelectric constant d ₃₃ of 205 pC/N, electromechanical coupling factor k _p of 0.346, remanent polarization P _r of 31.7–38.5 μC/cm², and coercive field E _c of 3.18–5.16 kV/mm.     

Preparation,characterisation, and electrical properties of (K0.5Na0.5)NbO3 lead-free piezoelectric ceramics

Na_0.5?K_0.5NbO₃ (KNN) ceramics were sintered at different temperatures (970 °C, 1000 °C, 1030 °C, 1060 °C, and 1090 °C) for 3 h by a pressureless sintering method. The powders had been synthesised by sol–gel method, using citric acid as a coordination agent and ethylene glycol as an esterifying agent. The effects of temperature on the phase, microstructure, dielectric, ferroelectric, and piezoelectric properties of the as-prepared ceramics were analysed. The results revealed that all of the ceramics had a pure perovskite phase with orthorhombic symmetry. The piezoelectric constant (d ₃₃), the relative dielectric constant (ε _r), the planar electromechanical coupling coefficient (K _p), and the remnant polarization (P _r) initially increased and then decreased with increasing of temperature in such KNN ceramics. The volatilization of sodium and potassium increased with increasing sintering temperature. Over the range of temperatures studied, those ceramics sintered at 1060 °C had the following optimal properties: (ρ?=?3.97 g/cm³, d ₃₃?=?119 pC/N, ε _r?=?362.46, tan δ?=?0.05, K _p?=?0.23, P _r?=?11.97 μC/cm², E _c?=?10.35 kV/cm, and T _c?=?408 °C).     

Piezoelectric properties of (Na0.465K0.465Bi0.07)(Nb0.93Ti0.07)O3 ceramics with MnO2 addition

In this study, (Na_0.465K_0.465Bi_0.07)(Nb_0.93Ti_0.07)O₃ ceramics with MnO₂ addition were prepared by conventional mixed oxide method. The effects of MnO₂ addition on the structural and electrical properties of the specimens were investigated for the application of piezoelectric devices. As the results of X-ray diffraction analysis, all specimens showed the typical polycrystalline perovskite structure without presence of the second phase. Sintered densities increased with increasing the addition amount of MnO₂ and the specimen added with 0.06 mol% of MnO₂ showed the maximum value of 4.87 g/cm³. Average grain size increased and densification increased with an increasing of MnO₂ contents. The electromechanical coupling factor, dielectric constant, dielectric loss, d₃₃ and Curie temperature of the 0.06 mol% of MnO₂ doped (Na_0.465K_0.465Bi_0.07)(Nb_0.93Ti_0.07)O₃ specimens were 0.32, 1309, 0.016, 122 and 465 °C, respectively.     

Temperature dependent electrical properties of 0.95[(K0.5Na0.5)(1-x)Ag x NbO3]-0.05LiSbO3 ceramics

Lead free 0.95[(K_0.5Na_0.5)_1-x Ag _x NbO₃]-0.05LiSbO₃ (KNAN-LS) ceramics with x?=?0.02, 0.04, 0.06 and 0.08 have been synthesized by conventional solid state reaction route (CSSR). XRD analysis confirmed the presence of a mixed structure for x?=?0.06. The orthorhombic?Ctetragonal polymorphic phase transition (PPT) temperature and the Curie temperature (T_c) decreased with the increase in Ag⁺ ion content in KNAN-LS ceramics. The relationship between the PPT of the ceramics and the temperature dependence of electrical properties of KNAN-LS ceramics were discussed in detail. The KNAN-LS ceramics with x?=?0.06 showed better piezoelectric and electromechanical properties (d₃₃?=?227pC/N and k_p?=?42.5?%).     

SYNTHESIS AND CHARACTERIZATION OF SB-SUBSTITUTED (K0.5Na0.5)NbO3 PIEZOELECTRIC CERAMICS

ABSTRACT

Lead-free piezoelectric ceramics (K_0.5Na_0.5)(Nb_1-xSb_x)O₃+0.5 mol.%MnO₂, where x = 0 ÷ 0.10, with single phase structure and rhombohedral symmetry at room temperature were prepared by conventional ceramic technology. The optimal sintering temperatures of compositions were within 1100°–1140°C. MnO₂ functions as a sintering aid and effectively improves the densification. The samples reached density from 4.26 g/cm³ for undoped (K_0.5Na_0.5)NbO₃ to 4.40 g/cm³ for Mn/Sb⁵⁺ co-doped ceramics. The co-effects of MnO₂ doping and Sb⁵⁺ substitution lead to significant improvement in dielectric and piezoelectric properties: ε at the T_c increased from 6000 (KNN) to 12400 (x = 0.04), d₃₃ = 92 ÷ 192 pC/N, k_p = 0.32 ÷ 0.46, k_t = 0.34 ÷ 0.48.     

Lead-free piezoelectric ceramics of (Bi1/2Na1/2)TiO3–(Bi1/2K1/2)TiO3–(Bi1/2Ag1/2)TiO3 system

The ternary lead-free piezoelectric ceramics system of 0.90[x(Bi_1/2Na_1/2)TiO₃–(1???x)(Bi_1/2K_1/2)TiO₃]–0.10(Bi_1/2Ag_1/2)TiO₃ (x?=?0.77, 0.79, 0.81, 0.83, 0.85) were successfully synthesized by conventional ceramic sintering technique. The samples were studied by X-ray diffraction, dielectric, ferroelectric and piezoelectric measurements. The MPB composition of the system appears to be near BNKA-79 according to the results of the X-ray diffraction and ferroelectric properties. The sample with x?=?0.79 showed the highest piezoelectric constant d ₃₃?=?160 pC/N. The maximum electromechanical coupling factors, k _p and k _t, are 0.30 for BNKA-79 and 0.42 for BNKA-85, respectively.     

Effects of MnO<Subscript>2</Subscript> addition on microstructure and electrical properties of (Bi<Subscript>0.5</Subscript>Na<Subscript>0.5</Subscript>) <Subscript>0.94</Subscript>Ba<Subscript>0.06</Subscript>TiO<Subscript>3</Subscript> ceramics

In this letter, MnO₂-doped (Bi_0.5Na_0.5)_0.94Ba_0.06TiO₃ (BNBT-6) lead-free piezoelectric ceramics were synthesized by solid state reaction, and the microstructure and electrical properties of the ceramics were investigated. X-ray diffraction (XRD) reveals that all specimens take on single perovskite type structure, and the diffraction peaks shift to a large angle as the MnO₂ addition increases. Scanning electron microscopy shows that the grain sizes increases, and then decreases with increasing the MnO₂ content. The experiment results indicate that the electrical properties of ceramics are significantly influenced by the MnO₂ content, and the ceramics with homogeneous microstructure and excellent electrical properties are obtained with addition of 0.3 wt% MnO₂ and sintered at 1160°C. The piezoelectric constant (d₃₃), the electromechanical coupling factor (k _p ), the dissipation factor (tan δ) and the dielectric constant (ɛ _r ) reach 160 pC/N, 0.29, 0.026 and 879, respectively. These excellent properties indicate that the MnO₂-doped BNBT-6 ceramics can be used for actuators.     

Structure and electrical properties of (Na0.5Bi0.5)1−x Ba x TiO3 ceramics made by a citrate method

(Na_0.5Bi_0.5)_1?x Ba _x TiO₃ (x?=?0–0.12) powders were synthesized by a citrate method, and the structure and electrical properties of the resulting ceramics were investigated. A gradual change of crystal structure with the increase of BaTiO₃ concentration was detected together with a significant evolution in grain size and shape. A rhombohedral-tetragonal morphotropic phase boundary (MPB) near x?=?0.06 at room temperature was ascertained for the ceramics. The dielectric constant (? _r) and dissipation factor (tanδ) attain maximum values at x?=?0.08 and x?=?0.06, respectively. The specimen of x?=?0.06 provides the maximum piezoelectric constant (d ₃₃?=?180 pC/N) and electromechanical coupling factor (k _p?=?0.28), accompanied by a large remanent polarization of P _r?=?37.1 μC/cm² and a low coercive field of E _c ?=?42.7 kV/cm.     

The effect of Bi4Ti3O12 particles addition in lead-free Bi0.5(Na0.75K0.25)0.5TiO3 ceramics

We studied the effect of Bi₄Ti₃O₁₂ (BiT) platelet addition in Bi_0.5(Na_0.75K_0.25)_0.5TiO₃ (BNKT) ceramics by preparing two kinds of BNKT ceramics. One type of BNKT ceramic was fabricated by a conventional solid state reaction method (normal sample), while the other by addition of 15 wt% BiT platelets to BNKT powders (BiT-added sample). In the case of BiT-added BNKT ceramics, plate like grains were formed by the reaction of BiT platelets with Na₂CO₃, K₂CO₃, and TiO₂ during the sintering process. The grain size of BiT-added BNKT ceramics was 10 times larger than that of normal BNKT ceramic. The piezoelectric strain and d₃₃ values of BiT-added BNKT ceramics were 0.135% and 225 pm/V, respectively. These values were 35% higher than those of normal BNKT ceramics. The piezoelectric properties of BiT-added BNKT ceramics were enhanced by the higher domain activity due to a decrease in domain density at larger grain sizes.     

ABS-064: Grain oriented (Na0.5Bi0.5)0.94Ba0.06TiO3 piezoceramics prepared by the screen-printing multilayer grain growth technique

The texture control of polycrystalline ceramics is an important and effective way to improve the piezoelectric properties of lead-free ceramics without drastically changing the composition of the ceramics. The screen-printing multilayer grain growth (MLGG) technique is now successfully applied to perovskite-structured lead-free piezoelectric ceramics. Grain oriented (Na_0.5Bi_0.5)_0.94Ba_0.06TiO₃ (NBBT) ceramics with (100) orientation were fabricated. The influences of sintering time, heating rate, and pre-reaction at low temperature on grain orientation were studied. Highly textured NBBT ceramics (f?~?92%) were obtained with a high heating rate. The interface between adjacent layers, which was formed by screen-printing, was the main mechanism for the texture development in MLGG technique. Compared with other grain orientation techniques, screen-printing is a simple and effective method to fabricate grain oriented lead-free piezoelectric ceramics.     

Dielectric and Piezoelectric Properties of Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript>-K<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript>-NaNbO<Subscript>3</Subscript>Lead-Free Ceramics

The ternary lead-free piezoelectric ceramics system of (1 – x) [0.88Na_0.5Bi_0.5TiO₃-0.12K_0.5Bi_0.5TiO₃] – xNaNbO₃(x = 0, 0.02, 0.04, 0.06, 0.08, 0.10) were synthesized by conventional solid state reaction method. The crystal structure, dielectric, piezoelectric properties and P-E hysteresis loops were investigated. The crystalline structure of all compositions is mono-perovskite phase ascertained by XRD, and the lattice constant was calculated from the XRD data. Temperature dependence of dielectric constant _r and dissipation factor tan measurement revealed that all compositions experienced two phase transitions: from ferroelectric to anti-ferroelectric and from anti-ferroelectric to paraelectric, and these two phase transitions have relaxor characteristics. Both transition temperatures T_d and T_m are lowered due to introduction of NaNbO₃. P-E hysteresis loops show that 0.88Na_0.5Bi_0.5TiO₃-0.12K_0.5Bi_0.5TiO₃ ceramics has the maximum P_r and E_c corresponding to the maximum values of electromechanical coupling factor K_p and piezoelectric constant d_33. The piezoelectric constant d₃₃ and electromechanical coupling factor K_p decrease a little, while the dielectric constant ₃₃^T/₀ improves much more when the concentration of NaNbO₃ is 8 mol%.     

Dielectric,ferroelectric and bipolar electric field induced strain properties of MPB composition of NBT-xKNN system

(1-x) (Na_0.5Bi_0.5TiO₃)-xK_0.5Na_0.5NbO₃/NBT-xKNN [x?=?0.07, 0.06, 0.05] ferroelectric ceramics were prepared by solid state synthesis route (SSSR). The effects of KNN contents on the microstructure, dielectric, piezoelectric and ferroelectric properties of the NBT-xKNN system were investigated in detail. For single perovskite phase formation, the calcination temperature was optimized at 800 °C for 6 h. From the XRD study, the morphotropic phase boundary (MPB) was confirmed for x?=?0.07 composition. For better densification, the sintering temperature was optimized for 1150 °C for 4 h. SEM micrographs illustrate the closely packed and non-uniform distribution of grains. Diffusive type of behaviour was observed in all the ceramics. Polarization (P) vs. electric field (E) study confirmed the ferroelectric nature of the NBT-xKNN ceramics. The bipolar field-induced strain measurement for all the ceramic samples showed butterfly-shaped loops indicating their piezoelectric nature. Among all the different compositions in MPB region, high dielectric constant (ε_r) of?~?3011, high remnant polarization (P _r ) of 17.88μC/cm² and high strain % of 0.41, were obtained in NBT-xKNN system with x?=?0.07 confirming the existence of MPB at this composition.     

High-temperature stable dielectrics in Mn-modified (1-x) Bi0.5Na0.5TiO3-xCaTiO3 ceramics

In the current work, the bulk (1-x) Bi_0.5Na_0.5TiO₃-xCaTiO₃ [BNCT100x] system was synthesized via solid-state route. CaTiO₃ in solid solution with Bi_0.5Na_0.5TiO₃ was observed to decrease the dielectric constant at higher temperature and raise the dielectric constant at lower temperature. Polarization hysteresis measurements indicated that the ferroelectricity of Bi_0.5Na_0.5TiO₃ was weakened with an increase of CaTiO₃, resulted in the shift of the depolarization temperature (T _d) toward lower temperatures. X-ray diffraction analysis revealed that TiO₂ was produced as a secondary phase due to the losses of Bi and Na during milling and sintering processes. Moreover, the addition of Ca promoted the segregation of Ti out of BNT grains. Dielectric properties of BNCT12 ceramics with different dopant levels of Mn were characterized as a function of temperature for potential use of high-temperature capacitors. Modification of BNCT12 materials with Mn improved the temperature characteristic of capacitance (?55°C to 250°C, △C/C_25°C ≤ ±15%). Finally, by doping 1.5 wt% Mn, the dielectric constant at room temperature could reach over 900, with a low dielectric loss below 1% and a high insulation resistivity about 10¹² Ω?cm. Furthermore, a small amount of Mn influenced the microstructure in the way to inhibit the long grains and grain growth of BNCT solution ceramics. However, excess Mn caused abnormal grain growth, and therefore, rectangle grains appeared again.