Morphotropic Phase Boundary Region Research Articles

Performance enhancement of Pb(In1/2Nb1/2)O3-PbTiO3 ferroelectric single crystals using pulse poling

The regular domain structure is beneficial to the enhancement of piezoelectric properties of relaxor-PbTiO3 ferroelectric crystals after alternating current poling (ACP). However, one shortcoming of ACP is that there are some non-rotational domains. Another is that ACP has no effect on polar axis-oriented crystals. Therefore, ACP is not very satisfactory for the morphotropic phase boundary (MPB) composition. Here, we demonstrate a pulse poling (PP) method that can lead to substantially increase the piezoelectric coefficient d33 of MPB region Pb(In1/2Nb1/2)O3-PbTiO3 (PIN-PT) single crystals. The d33 and free dielectric permittivity εT33/ε0 of ACP [001]c-oriented 0.65PIN-0.35PT single crystals are 1490 pC/N and 3360, which are smaller than DCP sample (1640 pC/N and 3620). The d33 and εT33/ε0 after PP method are 2400 pC/N and 5390, having 61% and 60% improvement compared with ACP method. This work presents a new domain engineering method for achieving high piezoelectricity of these MPB region ferroelectric crystals.

High Piezoelectric Performance in Pb(Ni1/3Nb2/3)O3-Pb(Sc1/2Nb1/2)O3-PbTiO3 Ternary System Featuring Small Structural Distortion and Heterogeneous Domain Configuration.

Ternary/polynary perovskite solid solutions based on binary systems are well-known for their high piezoelectric performance. In this work, a series of Pb(Ni1/3Nb2/3)O3-Pb(Sc1/2Nb1/2)O3-PbTiO3 compositions with the particularly high piezoelectric coefficient of d33* > 1000 pm/V and d33 > 700 pC/N have been developed. The optimal performance was achieved in the 0.52PNN-0.14PSN-0.34PT composition (d33* = 1120 pm/V, d33 = 804 pC/N, and Tm = 109 °C). The high piezoelectric performance of this system is reported and is superior to those of most lead-based ternary/polynary ceramics. By a combination of in situ high-energy synchrotron diffraction with transmission electron microscopy (TEM), the origin of the high piezoelectric response has been unambiguously revealed. Upon application of an external electric field, synchrotron diffraction profiles show no splitting but prominent shifting, indicating that the large intrinsic lattice strain arising from the reduced crystal anisotropy and facilitated polarization variation is associated with the high piezoelectric response. Furthermore, microscopic studies by TEM highlight a heterogeneous ferroelectric domain configuration generated by a small local structural distortion, which is also beneficial for the high piezoelectric performance in the proposed ternary piezoelectric systems. The design process of ternary perovskite solid solutions with a wide morphotropic phase boundary region and small structural distortion may be enlightening for the exploration of other high-performance polynary piezoelectrics.

Enhanced piezoelectric properties in low-temperature sintering PZN-PZT ceramics by adjusting Zr/Ti ratio

[Formula: see text][Formula: see text]([Formula: see text]Ti)[Formula: see text]([Formula: see text][Formula: see text]O3 (PZN–PZT) piezoceramics with various Zr/Ti ratios and Li2CO3 sintering aid were sintered at 900∘C by the solid-state reaction route. The samples with different Zr/Ti ratios were compared according to microstructure, phase structure, piezoelectricity, ferroelectricity, and dielectric relaxation. The Zr/Ti ratio in the PZN–PZT ceramics greatly affects the electrical properties. The Zr/Ti ratio affects the proportion between the rhombohedral and tetragonal phases and also affects the grain size. The PZN–PZT ceramics with the Zr/Ti ratio of 53:47 have the largest grain size and have optimized piezoelectric properties ([Formula: see text] = 0.58, [Formula: see text] = 540 pC/N, and [Formula: see text] = 250∘C). The larger the grain size, the lesser the grain boundary, the easier the domain wall motion, and the better the piezoelectric properties. The PZT ceramic with Zr/Ti ratio of 53:47 locates the morphotropic phase boundary (MPB) region which is one of the key factors for the high piezoelectric properties of the PZT.

Ferroelectric domain structure and atomic-scale phase distribution in a Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystal

Lead-based relaxor ferroelectric crystals, such as Pb(Mg1/3Nb2/3)O3-PbTiO3, are promising for functional applications due to their outstanding ferroelectric properties. Revealing ferroelectric domain structure and phase distribution at the nanoscale are important to understand the basic theory of ferroelectricity and promote their practical applications. In this study, the ferroelectric domain structure and atomic-scale phase distribution in a Pb(Mg1/3Nb2/3)O3 - 35 at.% PbTiO3 single crystal in the region of morphotropic phase boundary are systematically investigated by a combination of optical microscopy, scanning electron microscopy, and aberration-corrected transmission electron microscopy. It is found that 90° and 180° coarse domains are formed simultaneously in the ferroelectric single crystal. Moreover, there are tweed-like nano-domains formed inside each coarse single domain. Through careful investigations of distribution of stress and tetragonality, it is revealed that the tweed-like nano-domains are composed of nano-sized rhombohedral (R), monoclinic (M), and tetragonal (T) phases. The nano-scale T, M, R phases have the best, moderate, and lowest ferroelectricity, respectively.

Effects of Composition Segregation in PMN-PT Crystals on Ultrasound Transducer Performance.

This study investigates the relationship between the composition segregation in lead magnesium niobate-lead titanate (PMN-PT; PMN-29%PT, PMN-29.5%PT, PMN-30%PT, PMN-30.5%PT, and PMN-31%PT) single crystals within morphotropic phase boundary (MPB) and the corresponding ultrasonic transducer performance through PiezoCAD modeling and real transducer testing. For five crystals with compositions distributed across the main body of a crystal ingot, the piezoelectric coefficient and free relative permittivity values were measured to vary by over 30%, whereas the transducer bandwidth and center frequency values were modeled to change by less than 10%. For the single-element ultrasonic transducers fabricated using those crystals without matching layers, the variations of -6-dB bandwidth, insertion loss, receiver-free field voltage response, and center frequency were measured to be 9.61%, -15.23%, 9.76%, and 1.41%, respectively, confirming the modeling results. Using the Mason and Krimholtz, Leedom, and Matthaei (KLM) models, it is found that the relatively stable transducer performance can be attributed to the relatively consistent electromechanical coupling coefficient, acoustic impedance, and clamped relative permittivity originated from the stable elastic compliance properties among the crystals of various compositions. It is expected that the relatively stable performance could be extended to multielement transducers with matching layers for the same contributing mechanisms. Our results suggest that it is possible to use crystal plates of different compositions within the MPB region, obtained from one and the same ingot, to fabricate a batch of ultrasonic transducers that will exhibit a similar performance, significantly reducing the cost of materials.

Dielectric behaviour of BZT-BCT nano pseudobinary system near TCP-assisted morphotopic phase boundary

The present study investigates the comparative dielectric studies in nano pseudobinary system synthesized by conventional and hybrid microwave sintering. The material was formed near Tri Critical Point (TCP)-assisted Morphotropic Phase Boundary (MPB) region from equal weight percentage of Lead Zirconate Titanate (BZT) and Barium Calcium Titanate (BCT) employing high energy ball milling. In the temperature dependent LCR study, a diffused phase transition (DPT) behaviour was identified for both conventional and hybrid microwave sintered samples. In each case, modified Currie-Weiss relation indicates an anomaly in the paraelectric state. Further, another approach using macroscopic composition-fluctuation model also exhibits the anomalous behaviour. Universal dielectric response (UDR) demonstrates that such behaviour is created by a temperature assisted relaxation phenomena by the formation of oxygen vacancies. Beyond 260 °C, microwave sintering creates more oxygen vacancies across grain boundary region as compared to the conventional sintering and in turn plays the key role for enhanced dielectric permittivity.

High piezoelectricity after field cooling AC poling in temperature stable ternary single crystals manufactured by continuous-feeding Bridgman method

After field cooling (FC) alternating current poling (ACP), we investigated the dielectric and piezoelectric properties of [001]pc-oriented 0.24Pb(In1/2Nb1/2)O3 (PIN)-0.46Pb(Mg1/3Nb2/3)O3 (PMN)-0.30PbTiO3 (PT) (PIMN-0.30PT) single crystals (SCs), which were manufactured by continuous-feeding Bridgman (CF BM) within morphotropic phase boundary (MPB) region. By ACP with 4 kVrms/cm from 100 to 70 °C, the PIMN-0.30PT SC attained high dielectric permittivity (ε33T/ε0) of 8330, piezoelectric coefficient (d33) of 2750 pC/N, bar mode electromechanical coupling factor k33 of 0.96 with higher phase change temperature (Tpc) of 103 °C, and high Curie temperature (TC) of 180 °C. These values are the highest ever reported as PIMN-xPT SC system with Tpc > 100 °C. The enhancement of these properties is attributed to the induced low symmetry multi-phase supported by phase analysis. This work indicates that FC ACP is a smart and promising method to enhance piezoelectric properties of relaxor-PT ferroelectric SCs including PIMN-xPT, and provides a route to a wide range of piezoelectric device applications.

Enhanced ferroelectric and piezoelectric properties of BCT-BZT at the morphotropic phase boundary driven by the coexistence of phases with different symmetries

The discovery of lead-free piezoelectric materials is crucial for future information and energy storage applications. Enhanced piezoelectric and other physical properties are commonly observed near the morphotropic phase boundary (MPB) composition of ferroelectric solid solutions. The $(1\ensuremath{-}x)\mathrm{Ba}({\mathrm{Zr}}_{0.2}{\mathrm{Ti}}_{0.8}){\mathrm{O}}_{3}\text{\ensuremath{-}}x({\mathrm{Ba}}_{0.7}{\mathrm{Ca}}_{0.3}){\mathrm{TiO}}_{3}$ $(\mathrm{BZT}\text{\ensuremath{-}}x\mathrm{BCT})$ system exhibits a large electromechanical response around its MPB region at $x=0.5$. We report experimental and theoretical results of $\mathrm{BZT}\text{\ensuremath{-}}x\mathrm{BCT}$ over a wide composition range $(0.3\ensuremath{\le}x\ensuremath{\le}1.0)$. X-ray diffraction and Raman spectroscopy studies indicate a composition-induced structural phase transition from a rhombohedral $(R3m)$ phase at $x\ensuremath{\le}0.4$ to a tetragonal $(P4mm)$ phase at $x\ensuremath{\ge}0.6$ through a multiphase coexistence region at 0.45 \ensuremath{\le} $x\ensuremath{\le}0.55$ involving orthorhombic + tetragonal (Amm2 + $P4mm$) phases. First-principles calculations elucidate the phase competition in the coexistence region. The critical composition $(x=0.5)$ displays enhanced dielectric, ferroelectric, and piezoelectric properties, where notably ${d}_{33}\ensuremath{\sim}320$ pC/N. This paper provides clear evidence of Amm2 + $P4mm$ crystallographic phases in the MPB region, which is responsible for the improved functional properties.

Pressure induced phase transitions in Sm-doped BiFeO3 in the morphotropic phase boundary

Sm-doped BiFeO3 compacted powders with composition across the morphotropic phase boundary region were prepared by sol-gel method. Crystal structure, morphology and magnetic state of the compounds were analyzed as a function of dopant concentration, temperature and external pressure using synchrotron and laboratory X-ray diffraction, electron microscopy, Raman and Mössbauer spectroscopy. Application of external pressure shifts the phase transition from the rhombohedral structure to the nonpolar orthorhombic structure towards lower concentration of the dopant content, wherein the amount of the anti-polar orthorhombic phase notably decreases. Raman and Mössbauer spectroscopy data provides additional information about the structural distortion on local scale level which testifies faster formation of nonpolar orthorhombic phase and associated modification in the magnetic state in the compounds subjected to high pressure. Temperature increase leads to the structural transition to the nonpolar orthorhombic phase regardless the structural state at room temperature; furthermore, application of external pressure decreases the phase transition temperature.

Model-based analysis of the ferroelectric response of multiferroic (1-x)BiFeO3-xPbTiO3 solid solution thin films around morphotropic phase boundary

It is a challenging task to deposit single phase multiferroic (1-x)BiFeO3-xPbTiO3 (BF-xPT) solid solution thin films on Fluorine-doped tin oxide (FTO) coated glass substrate due to its high crystallization temperature. This study presents the preparation of BF-xPT solid solution thin films covering the morphotropic phase boundary (MPB) region. Films were prepared in ambient conditions via solution processing method on FTO coated glass substrate. Optical absorption in the visible region has been observed for intermediate compositions, promising for optoelectronic applications. The presence of multiple phases, strain, and finite-size effects results in structural complexities that have been discussed in detail. In addition to that, due to the presence of defects such as grain boundaries and porosity, considerable leakage in hysteresis loops has been observed. Linear capacitive and ferroelectric responses have also been observed, indicating that the films are composed of induced dipoles and ferroelectric domains, respectively. The origin of each mechanism has been discussed in detail. Model-based analysis was carried out to separate intrinsic ferroelectric switching by identifying MPB compositions exhibiting optimum results. Based on the intrinsic response MPB compositions are found to lie in the 0.35 < x < 0.45.

Phase Diagram of Sub‐GHz Electric‐Field‐Induced Polarization Oscillation

Polarization oscillation under GHz electric field stimuli is a key issue for the future development of ultrafast sensor devices. An ultrafast phase‐field model is developed to study the phase diagram of polarization oscillation under sub‐GHz electric field for Pb(Zr,Ti)O3. At the morphotropic phase boundary region, the polarization and strain oscillation show maximum amplitude (electric field stimuli frequency &lt;0.1 GHz). The phase difference of π/2 between the input of electric field and the polarization response, which can be tuned by the frequency of ac electric field stimuli, can lead to a maximum of polarization oscillation amplitude (electric field stimuli frequency &gt;0.1 GHz). Moreover, under this phase difference, the polarization oscillation amplitude can be increased furthermore with the increasing ac electric field strength. With the absence of a phase transition, it is found that the polarization component along the z‐direction has a maximum oscillation amplitude of 0.2, and the strain has a maximum oscillation amplitude of 0.35%. The results provide useful guidance to explore and manipulate dynamic functionalities of ferroelectric sensing materials.

Structure and properties of Bi(Zn½Ti½)O3‐modified Pb(Zr,Ti)O3 piezo‐/ferroelectric ceramics around the ternary morphotropic phase boundary

AbstractTo develop high‐performance piezo‐/ferroelectric materials, Bi(Zn½Ti½)O3–PbZrO3–PbTiO3 (BZT–PZ–PT) ternary solid solution with compositions around the morphotropic phase boundary (MPB) is synthesized by solid‐state reaction. The crystal structure and electric properties are investigated systematically by X‐ray powder diffraction (XRD), dielectric spectroscopy, and ferroelectric and piezoelectric measurements. On the basis of the results of the XRD, dielectric and ferroelectric measurements, the pseudo‐binary phase diagram of the yBi(Zn½Ti½)O3–(1 − y)[(1 − x)PbZrO3–xPbTiO3] system has been constructed for three series, namely, y = 0.05, 0.10, and 0.15. It is found that the introduction of BZT into the PZT system makes the paraelectric to ferroelectric phase transition more diffuse, brings the MPB to a lower PT content, and enlarges the MPB region. The best properties with an improved dielectric constant ε' = 1248, and a large remnant polarization Pr = 33 μC/cm2, as well as a relatively high TC = 286°C, and a high coercive field Ec = 23 kV/cm was achieved in the y = 0.15 series with MPB composition x = 0.425, making it a promising material for high‐power piezoelectric applications.

AC Conductivity and Dielectric Properties of BiScO3–PbTiO3 Piezoelectric Ceramics

Bi-based BiMeO3 (where Me is a transition metal) has been extensively studied owing to its outstanding ferroelectric properties. The dielectric and electrical properties of piezoelectric ceramics can be enhanced by the addition of Bi-based materials such as BiAlO3, BiScO3 , and Bi(Mg, Ti)O3. Among them, BiScO3–PbTiO3 ceramics have shown excellent piezoelectric properties and temperature stability near the morphotropic phase boundary (MPB) region. Meanwhile, it is important to study the electrical properties of piezoelectric materials such as dielectric permittivity, conductivity of ferroelectric compounds, since dielectric and conductivities are related to pyroelectricity and piezoelectricity. In this study, the AC conductivity and dielectric properties of BiScO3–PbTiO3 ceramics were investigated with a wide range of frequencies and temperatures. Especially,the effect of PbTiO3 content on dielectric behavior of the BiScO3–PbTiO3 system was intensively studied by impedance spectroscopy.

Enrichment of piezoelectric properties in Nb5+doped (0.94) (Na0.5Bi0.5)TiO3–(0.06) BaTiO3 ceramics across morphotropic phase boundary region

Enrichment of piezoelectric properties in Nb5+doped (0.94) (Na0.5Bi0.5)TiO3–(0.06) BaTiO3 ceramics across morphotropic phase boundary region

Piezoelectric Properties of (1 – X)BiScO3 – XPbTiO3 System for Actuator Applications

ABSTRACTIn this research, the crystalline and piezoelectric properties of (1 – X )BiScO3–XPbTiO3 (X = 0.60, 0.62, 0.64, 0.66 and 0.68) ceramics were investigated to determine the optimized composition for energy harvester and sensor applications. BS-PT ceramics have strong merits in terms of their high Curie temperature and piezoelectric charge coefficient. Devices of the (1 – X )BS-XPT ceramics were fabricated by a conventional mixed-oxide sintering process with nano-powders. By employing the X-ray diffraction patterns, the morphotropic phase boundary (MPB) region of the monoclinic and tetragonal phases was identified at X = 0.64. Near the MPB region, the piezoelectric and dielectric properties of BS-PT ceramics were improved compared with those of other composition. By optimizing the compositions of the BS-PT ceramics, the maximum values of the dielectric constant (εr), piezoelectric charge coefficient (d33), electromechanical coupling factor (kp) and remanent polarization (Pr) were obtained, with values of 1387, 417 pC/N, 51.4% and 44.8 µC/cm2, respectively. Moreover, a high Curie temperature of 399.2 °C and inverse piezoelectric charge coefficient of 574 pm/V were observed for the 0.36BS–0.64PT composition, which can be a huge merit for actuator applications. These high piezoelectric charge coefficients and inverse piezoelectric charge coefficients can be the strong merits for energy harvester and actuator applications.

Composition designing and sintering behavior tailoring in [(Ba1−xCax)0.995Eu0.005](Ti1−yHfy)O3 multifunctional piezoceramics

[(Ba1−xCax)0.995Eu0.005](Ti1−yHfy)O3 (B1−xCxT1−yHy-Eu) lead-free ceramics were fabricated by conventional solid-state method, in which the effects of sintering temperature and the ratios of Ba/Ca and Ti/Hf cations around the morphotropic phase boundary (MPB) on the electrical and fluorescent properties were explored. Rather pure perovskite structure B1−xCxT1−yHy-Eu ceramics with densified microstructure and high density are obtained, which locate around the MPB region and show dependency on compositions and sintering conditions. Complex ferroelectric characteristic is confirmed by dielectric performance measurement and dielectric behavior fitting. Enhanced ferroelectric and piezoelectric properties can be attributed to the donor doping characteristic induced by Eu doping, which engenders donor point defects EuBa/Ca•. Extremum piezo-luminescence figure of merit FPC-PLI appears in the sintered B1−xCxT1−yHy-Eu ceramics, in which the 1450 °C sintered [(Ba0.86Ca0.14)0.995Eu0.005](Ti0.9Hf0.1)O3 ceramics exhibit the most outstanding multifunctional performance. The high-temperature conductance mechanism of the B1−xCxT1−yHy-Eu ceramics can be attributed to the oxygen vacancies produced by the evaporation of cations during sintering process.

Effect of Sr doping on the energy storage properties of BNT–BST–KNN anti-ferroelectric ceramics

(1−x)Bi1/2Na1/2TiO3–xBa1/2Sr1/2TiO3–0.05KNaNbO3 (BNT–BST–KN, x = 0.01, 0.03, 0.05, 0.07) lead-free anti-ferroelectric ceramics were synthesized by a conventional solid-state. The hysteresis loop of the ceramic at different temperature under 70 kV/cm electric field was analyzed. In this paper, the energy storage properties of BNT–BST–KNN ceramics are studied. It was found that the addition of Sr element helps to improve the electric field strength tolerance and the breakdown resistance performance the material, so as to improve its energy storage density. At room temperature, the P–E curves of the materials in the system basically show a double hysteresis loop, and with the increase of temperature, the characteristics of the double hysteresis curve are particularly obvious. The ceramics exist in the ferroelectric–antiferroelectric coexistence phase region near 303 K, namely the morphotropic phase boundary region. It shows that the ceramic has anti-ferroelectric characteristics at room temperature, and is a typical anti-ferroelectric material.

Influence of doping mode on phase structure and electrical properties of antiferroelectric ceramics

The ferroelectric, lead-free perovskite sodium bismuth titanate-barium titanate (BNT-BT) has excellent electrical performance and is now recognized as a possible alternative material for lead zirconate titanate (PZT). It can be doped with some active elements to form a solid solution with a morphotropic phase boundary (MPB), where the solid solution has high dielectric properties and high energy storage performance. In this paper, the research results of BNT-BLT, BNT-BLZT, BNT-BSLZT, BNT-BMNLT and BNT-BST-KNN ceramic materials are summarized, and the influence of their doping mode on the phase structure and electrical properties are analyzed. The study found a rhombohedral and tetragonal phase coexistence region, where the tolerance factor value of ceramics is between 0.7530 and 0.7803. Moreover, the energy storage density of antiferroelectric ceramics increases with the expansion of the MPB region and is affected by the dielectric constant.

Pure perovskite BiFeO3–BaTiO3 ceramics prepared by reaction flash sintering of Bi2O3–Fe2O3–BaTiO3 mixed powders

In this work, the 0.67BiFeO3-0.33BaTiO3 ferroelectric ceramic was prepared by Reaction Flash Sintering (RFS). This preparation technique combines synthesis and sintering in a single Flash experiment. The starting oxides reacted during the flash to produce a stoichiometric well-sintered solid solution at a temperature of 858 °C by applying a modest field of 35 V cm−1. The process takes place in a matter of seconds, which allows obtaining a pure perovskite structure without secondary phases. X-ray diffraction (XRD) results show the mixture of rhombohedral and pseudocubic phases expected for a composition that lies within a morphotropic phase boundary (MPB) region, since a significant splitting is observed in the reflections at 2θ values of 39° and 56.5°. The microstructure exhibit a peculiar bimodal grain size distribution that determines the electrical properties. As compared with previous results, flash-prepared 0.67BiFeO3-0.33BaTiO3 evidences smaller grain size, as well as slightly lower remanent polarization (Pr) and smaller coercive field (Ec) under similar electric fields. It is also demonstrated that the preparation by RFS provides benefits regarding electrical energy consumption.

Stabilization of the morphotropic phase boundary in (1−x)BNT-xBCTS ceramics prepared by the solid-state combustion technique

Producing lead-free Bi0.5Na0.5TiO3 (BNT)-based ceramics with a composition near the morphotropic phase boundary (MPB) region is highly important to optimize the piezoelectric properties. Therefore, a range of the ceramic compositions, designed to be near the MPB region were attempted and investigated to confirm the phase was at MPB for the lead-free BNT-based ceramics, which is needed to improve the piezoelectric performance. The aim of this work is to study the design of (1-x)Bi0.5Na0.5TiO3-x(Ba0.945Ca0.055)(Ti0.91Sn0.09)O3 ((1-x)BNT-xBCTS)) ceramics by forming ceramics with compositions around the MPB region (x = 0.03–0.09), synthesized via the solid-state combustion technique using glycine as the fuel. The influence of the x content on phase formation, local structure, microstructure, and electrical properties of (1-x)BNT-xBCTS ceramics was investigated. The X-ray diffraction (XRD) patterns exhibited coexisting phases between the rhombohedral (R) and tetragonal (T) phases in all compositions and the T phase increased with increasing x content. Rietveld analysis of the XRD data and the X-ray absorption spectroscopy (XAS) with the EXAFS technique confirmed the stable formation of a coexisting R + T perovskite phase for all ceramics and the ratio of R:T phases was obtained for both techniques with nearly identical values. The ceramic with x = 0.07 exhibited a MPB region with a coexisting R + T perovskite phase at room temperature (with ratio of R and T phases close to 50:50), this composition showed the highest density and the highest electrical parameters (εr ≅ 1998, εm ≅ 6995, Pr ≅ 32.67 μC/cm2, Ec ≅ 17.54 kV/cm, Smax ≅ 0.199% d33∗ ≅ 308 pm/V and d33 ≅ 202 pC/N). These findings make the (1-x)BNT–xBCTS lead-free ceramics produced with a composition near the MPB zone are very promising as candidates for lead free piezoelectric materials.