Structural,dielectric and impedance spectroscopy studies of (Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>)(Zr<Subscript>0.025</Subscript>Ti<Subscript>0.975</Subscript>)O<Subscript>3</Subscript> ceramic

Structural, vibrational, dielectric and electrical properties of (Na_0.5Bi_0.5)(Zr_0.025Ti_0.975)O₃ ceramic synthesized by the solid-state reaction technique have been carried out. The X-ray diffraction analysis was indicated as a pure perovskite phase in the rhombohedral structure. The modes of rhombohedral vibrations were appeared in the experimental Raman spectrum at room temperature. The dielectric and electrical properties of the material were investigated by impedance spectroscopy analysis for a broad range of temperatures (50–560 °C) and frequency domain of 10²?10⁶ Hz. The dielectric measurement exhibit two phase transitions: a ferro-antiferroelectric transition followed by an antiferro-paraelectric transition at higher temperatures. Complex impedance analysis was carried out in order to distinct the contribution of the grains and the grain boundaries to the total electrical conduction. The Nyquist plot was proved to be a non-Debye relaxation mechanism. The combined spectroscopic plots of the imaginary part of electric impedance and modulus confirmed the non-Debye type behavior. The frequency dependent ac conductivity obeys the double power law behavior and shows three types of conduction process. The significant decrease of dc conductivity spectrum followed the Arrhenius relationship. The values of calculated activation energy of the compound implied that the electrical conduction is mostly due the high oxygen mobility.     

Structural,electrical and magneto-electric characteristics of complex multiferroic perovskite Bi<Subscript>0.5</Subscript>Pb<Subscript>0.5</Subscript>Fe<Subscript>0.5</Subscript>Ce<Subscript>0.5</Subscript>O<Subscript>3</Subscript>

The polycrystalline sample of bismuth based-complex multiferroic of a composition Bi_0.5Pb_0.5Fe_0.5Ce_0.5O₃ was prepared by a high-temperature solid-state reaction technique (calcinations temperature = 900 °C, sintering temperature = 960 °C, time = 4 h). Preliminary structural analysis using XRD data exhibits the formation of a single-phase compound. Studies of surface morphology of the ceramic sample of the compound, recorded at room temperature using a scanning electron microscope, show uniform distribution of grains of different size with few voids. Detailed studies of dielectric properties (ε_r, tan δ) supported the existence of multiferroic properties in the above complex system. The analysis of impedance parameters, recorded in a wide frequency (1 kHz–1 MHz) and temperature (room temperature to 450 °C) range of the material provide better understanding of (a) role of grains and grain boundaries in resistive and capacitative characteristics, (c) structure-properties relationship and (b) type of relaxation process occurred in the material. Study of temperature dependence of dc conductivity of the compound shows the existence of negative temperature coefficient of resistance in it. The nature of variation of ac conductivity with temperature of the material follows the Josher’s universal power law. Study of magneto-electric characteristics of the sample at room temperature has provided many useful and new data on magneto-electric coupling coefficient of different orders.     

Dielectric,humidity behavior and conductivity mechanism of Mn<Subscript>0.2</Subscript>Ni<Subscript>0.3</Subscript>Zn<Subscript>0.5</Subscript>Fe<Subscript>2</Subscript>O<Subscript>4</Subscript> ferrite prepared by co-precipitation method

Mn–Ni–Zn ferrite with the chemical formula of Mn_0.2Ni_0.3Zn_0.5Fe₂O₄ was prepared by co-precipitation method. The X-ray diffraction (XRD) results show that the prepared sample crystallizes in the cubic spinel structure with the space group of Fm3m. The morphological analysis of the sample was investigated by scanning electron microscopy (SEM). The dielectric properties of Mn_0.2Ni_0.3Zn_0.5Fe₂O₄ ferrite were studied in a frequency range from 20 Hz to 10 MHz and at a temperature range from 293 to 733 K. The dielectric constant decreases with the increasing frequency for all the temperature values chosen. The AC conductivity mechanism was found the small polaron type of conductivity, and in addition to that, the DC conductivity can be explained by Arrhenius type conductivity. According to the dielectric results, relaxation process fits Cole–Cole model. Finally, the effect of the relative humidity upon the impedance of the sample was discussed for a frequency range between 20 Hz and 10 MHz. It is found that the impedance values decrease almost linearly with the increasing % RH (relative humidity) values at low frequencies, while the impedance of the sample is independent of % RH at high frequencies.     

Dielectric and impedance study of lead-free ceramic: (Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>)ZrO<Subscript>3</Subscript>

Polycrystalline sample of (Na_0.5Bi_0.5)ZrO₃ was prepared using a high-temperature solid-state reaction technique. XRD analysis indicated the formation of a single-phase orthorhombic structure. Dielectric study revealed the diffuse phase transition at 425 °C. AC impedance plots were used as tools to analyse the electrical behaviour of the sample as a function of frequency at different temperatures. The ac impedance studies revealed the presence of grain boundary effect at and above 350 °C. Complex impedance analysis indicated non-Debye type dielectric relaxation and negative temperature coefficient of resistance (NTCR) character of (Na_0.5Bi_0.5)ZrO₃. AC conductivity data were used to evaluate the density of states at Fermi level and activation energy of the compound. DC electrical and thermal conductivities of grain and grain boundary have been assessed.     

Investigation of charge transport mechanism in semiconducting La<Subscript>0.5</Subscript>Ca<Subscript>0.5</Subscript>Mn<Subscript>0.5</Subscript>Fe<Subscript>0.5</Subscript>O<Subscript>3</Subscript> manganite prepared by sol–gel method

Here in, we report the charge transport mechanism in semiconducting La_0.5Ca_0.5Mn_0.5Fe_0.5O₃ (LCMFO) polycrystalline material synthesized via sol–gel auto combustion route. X-ray diffraction (XRD) analysis confirmed the orthorhombic phase of the prepared material. Temperature dependent resistivity and impedance spectroscopy measurements have been carried out to probe the dielectric and electrical conduction mechanism which revealed a change of Mott variable range to the small polaronic hopping conduction mechanism around 303 K. The complex impedance and modulus spectra undoubtedly showed the contribution of both grain and grain boundary effect on the conduction properties of LCMFO. An equivalent circuit [(R_gbQ_gb) (R_gQ_g)] model has been used to address the electrical parameters associated with the different phases (grains and grain boundaries) having different relaxation times. The values of resistances of two phases obtained after fitting the equivalent circuit in the nyquist plot have been analyzed which confirmed the change of conduction mechanism around 303 K. The resultant change in conduction mechanism is also supported by the conductivity plots.     

Structural and electric properties of (Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>)<Subscript>0.88</Subscript>Ba<Subscript>0.12</Subscript>TiO<Subscript>3</Subscript>

Lead-free (Na_0.5Bi_0.5)_0.88Ba_0.12TiO₃ ceramics have been prepared and studied by X-ray diffraction and by the complex dielectric response as a function of temperature, frequency and a.c. field intensity. Relaxor-like dielectric behaviour were induced by barium Ba dopping to Na_0.5Bi_0.5TiO₃. It was shown, that relaxor-like characteristics can be enhanced by the increase of the a.c. field intensity. A sharp increase in the electric permittivity and dielectric loss on heating near 230 °C has been observed. This sharp increase in dielectric responses indicates a transformation between classical and relaxor ferroelectric phases. The X-ray diffraction study shows that this transformation corresponds to the first order phase transition from tetragonal to cubic. The use of (Na_0.5Bi_0.5)_0.88Ba_0.12TiO₃ ceramics for device applications has been indicated.     

Frequency and temperature dependence of electrical properties of barium and gadolinium substituted SrBi<Subscript>2</Subscript>Nb<Subscript>2</Subscript>O<Subscript>9</Subscript> ceramics

Barium strontium gadolinium bismuth niobate (Ba_0.1Sr_0.81Gd_0.06Bi₂Nb₂O₉, BSGBN) ceramics were prepared by using the conventional solid-state reaction method. The dielectric permittivity, modulus and impedance spectroscopy studies on BSGBN were investigated in the frequency range, 45 Hz–5 MHz and in the temperature range from room temperature (RT) to 570 °C. The dielectric anomaly with a broad peak was observed at 470 °C. Simultaneous substitution of Ba²⁺ and Gd³⁺ increases the transition temperature of SrBi₂Nb₂O₉ (SBN) from 392 to 470 °C. XRD studies in BSGBN revealed an orthorhombic structure with lattice parameters a = 5.4959 Å, b/a = 1.000, c = 25.0954 Å. Impedance and modulus plots were used as tools to analyse the sample behaviour as a function of frequency. Cole-Cole plots showed a non-Debye relaxation. Also, dc and ac conductivity measurements were performed on BSGBN. The electric impedance which describes the dielectric relaxation behaviour is fitted to the Kohlrausch exponential function. Near the phase transition temperature, a stretched exponential parameter β indicating the degree of distribution of the relaxation time has a small value.     

Structural,dielectric, ac conductivity and electromagnetic shielding properties of polyaniline/Ni<Subscript>0.5</Subscript>Zn<Subscript>0.5</Subscript>Fe<Subscript>2</Subscript>O<Subscript>4</Subscript> composites

A conducting polymer, polyaniline (PANI)/Ni_0.5Zn_0.5Fe₂O₄ composites with high dielectric absorbing properties and electromagnetic shielding effectiveness at low frequencies were successfully synthesized through a simple in situ emulsion polymerization. PANI was doped with hydrochloric acid to improve its electrical properties and interactions with ferrite particles. PANI/Ni_0.5Zn_0.5Fe₂O₄ composites were characterized by X-ray diffraction analysis, scanning electron microscopy, transmission electron microscopy, Fourier transform infrared spectroscopy and thermal gravimetric analysis. Frequency dependence of dielectric and ac conductivity (σ_ac) studies have been undertaken on the PANI/Ni_0.5Zn_0.5Fe₂O₄ composites in the frequency range 50 Hz–5 MHz. The electrical conduction mechanism in the PANI/Ni_0.5Zn_0.5Fe₂O₄ is found to be in accordance with the electron hopping model. Further, frequency dependence of electromagnetic interference (EMI) shielding effectiveness (SE) is studied. The EMI shielding effectiveness is found to decrease with an increase in the frequency. The maximum value 55.14 dB of SE at 50 Hz was obtained at room temperature for PANI/Ni_0.5Zn_0.5Fe₂O₄ composites in the 50 Hz–5 MHz frequency range. PANI/Ni_0.5Zn_0.5Fe₂O₄ composites were demonstrated as a promising functional material for the absorbing of electromagnetic waves at low frequencies because of a large amount of dipole polarizations in the polymer backbone and at the interfaces of the Ni–Zn ferrite particles and PANI matrix.     

Relaxor behavior and ferroelectric 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>-KNbO<Subscript>3</Subscript> lead-free ceramics

Lead-free ferroelectric ceramics of (1−x) [0.88Na_0.5Bi_0.5TiO₃-0.12K_0.5Bi_0.5TiO₃]-x KNbO₃(x = 0, 0.02, 0.04, and 0.06) were prepared by the conventional ceramic fabrication technique. The crystal structure, dielectric properties and P-E hysteresis loops were investigated. XRD data showed that all compositions could form pure perovskite structure. Temperature dependence of dielectric constant ε _r and dissipation factor tanδ measurement between room temperature and 500^∘C revealed that the compounds experience phase transitions that from ferroelectric to anti-ferroelectric and anti-ferroelectric to paraelectric in the range of x = 0–0.04. The frequency dependent dielectric constant showed these compounds were relaxor ferroelectric. At low frequency and high temperature, dielectric constant and dissipation factor increased sharply attributed to the superparaelectric clusters after the KNbO₃ doped.     

Structural,dielectric and electrical properties of CaBa<Subscript>4</Subscript>SmTi<Subscript>3</Subscript>Nb<Subscript>7</Subscript>O<Subscript>30</Subscript> ferroelectric ceramic

The polycrystalline sample of CaBa₄SmTi₃Nb₇O₃₀, a member of tungsten bronze family, was prepared by solid-state reaction method. X-ray diffraction analysis shows the formation of single-phase compound with an orthorhombic structure at room temperature. Scanning electron micrograph of the material shows uniform distribution of grains. Detailed studies of dielectric properties of the compound as a function of temperature at different frequencies suggest that the compound has a dielectric anomaly of ferroelectric to paraelectric type at 198°C, and exhibits non-relaxor kind of diffuse phase transition. The ferroelectric nature of the compound has been confirmed by recording polarization-electric field hysteresis loop. Piezoelectric and pyroelectric studies of the compound have been discussed in this paper. Electrical properties of the material have been analyzed using complex impedance technique. The Nyquist plots manifest the contribution of grain boundaries (at higher temperature), in addition to granular contribution (at all temperatures) to the overall impedance. The temperature dependence of dc conductivity suggests that the compound has negative temperature coefficient of resistance (NTCR) behaviour. The frequency dependence of ac conductivity is found to obey Jonscher’s universal power law. The observed properties have been compared with calcium free Ba₅SmTi₃Nb₇O₃₀ compound.     

Effect of neodymium doping on structural,electrical and magnetic properties of multiferroic GdMn<Subscript>2</Subscript>O<Subscript>5</Subscript>

Neodymium doped gadolinium manganate with general composition (Nd_0.1Gd_0.9Mn₂O₅) was prepared by co-precipitation method. Microstructural and compositional analysis has been carried out by X-ray diffraction and scanning electron microscopy. The optical studies have been carried out by Raman and FTIR. The electrical properties studied include dielectric constant, dielectric loss, ac conductivity and activation energy in the temperature range 20–400 ?°C. The shift in the dielectric peak towards higher temperature side with increasing frequency indicates frequency dispersion and suggesting the relaxational behaviour of the material. Frequency dependence of ac conductivity obeys the universal power law. The value of activation energy depends on increase in frequency. The room temperature magnetic behaviour has been analyzed from the magnetic field dependent magnetization curve. The grown material exhibits the paramagnetic behavior at room temperature.     

Structural and electrical properties of Ba(Fe<Subscript>1/3</Subscript>Nb<Subscript>1/3</Subscript>Ta<Subscript>1/3</Subscript>)O<Subscript>3</Subscript> perovskite

Ba(Fe_1/3Nb_1/3Ta_1/3)O₃ (BFNT) perovskite compound (phase purity>99%) was synthesized by conventional ceramic preparation method. XRD, microstructure, impedance spectroscopy and ac conductivity properties were analyzed in this study. BFNT compound has a cubic crystal structure, having grain size of 0.31 μm. This compound has shown normal ferroelectric behaviour but not obeying Curie-Weiss law. The impedance and electrical studies have been performed as a function of frequency and temperature. Impedance as a function of frequency revealed single relaxation process. The impedance spectroscopic plots exhibit the major response due to grains with partial contribution from the grain boundary and negligible electrode effect. Complex impedance plot showed data points lying on a single semicircle, implying the response originated from a single capacitive element corresponding to the bulk grains. Also, the centre of semicircle lies below the real axis indicating non-Debye type relaxation. Relaxation time was calculated from Z″_max of Cole–Cole plots. It is observed that conduction is due to hopping of charge carriers. Activation energies were computed from the Arrhenius plots of the sample.     

Impedance spectroscopy analysis of double perovskite Ho<Subscript>2</Subscript>NiTiO<Subscript>6</Subscript>

The electrical properties of double perovskite Ho₂NiTiO₆ (HNT) are investigated by impedance spectroscopy in the temperature range 30–420 °C and frequency range 100 Hz to 1 MHz. The X-ray diffraction analysis reveals that the compound crystallizes in monoclinic phase. The imaginary part of impedance (Z″) as a function of frequency shows Debye type relaxation. The frequency dependence of Z″ peak is found to obey an Arrhenius law with an activation energy of 0.129 eV. Impedance data presented in the Nyquist plot (Z″ vs. Z′) are used to identify an equivalent circuit and to know the bulk and interface contributions. The complex impedance analysis of HNT exhibits the appearance of both the grain and grain-boundary contribution. The results of bulk ac conductivity as a function of temperature and frequency are presented. The activation energy (0.129 eV), calculated from the slope of log τ versus 10³/T plot, is found to be the nearly same as calculated (0.130 eV) from dc conductivity. The frequency dependent conductivity spectra obey the power law.     

Dielectric properties of Na<Subscript>1-<Emphasis Type="Italic">x</Emphasis></Subscript>K<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>NbO<Subscript>3</Subscript> in orthorhombic phase

Pellets of ceramic Na_1−xK_xNbO₃ (x = 0, 0.2 and 0.5), were prepared by conventional solid-state reaction method. Prepared samples were characterized using XRD and SEM. The frequency and temperature variation of dielectric constant, loss tangent and dielectric conductivity of prepared samples were measured in the frequency range from 10 KHz-1 MHz, and in the temperature range from 50–250°C for x = 0.2 and 0.5, and between 50 and 480°C for x = 0 compositions. It was observed that the dielectric constant and loss tangent decrease, and conductivity increases with increasing frequency. Near the transition temperature the material shows anomalous behaviour for the observed properties, and the peaks of dielectric constant and loss tangent were observed shifting towards lower temperature with increasing frequency.     

Structural and electrical properties of Ba(Sb<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>)O<Subscript>3</Subscript> ceramic

Lead-free perovskite Ba(Sb_1/2Nb_1/2)O₃ was prepared by conventional ceramic fabrication technique at 1200 °C/5 h in air atmosphere. The crystal symmetry, space group and unit cell dimensions were determined from the experimental results using FullProf software whereas crystallite size and lattice strain were estimated from Williamson–Hall approach. XRD analysis of the compound indicated the formation of a single-phase monoclinic structure with the space group P2/m. EDAX and SEM studies were carried out to evaluate the quality and purity of the compound. Dielectric study revealed the frequency-dependent dielectric anomaly. To find a correlation between the response of the real system and idealized model circuit composed of discrete electrical components, the model fittings were presented using the impedance data. Complex impedance analyses suggested the dielectric relaxation to be of non-Debye type. The correlated barrier hopping model was employed to successfully explain the mechanism of charge transport in Ba(Sb_1/2Nb_1/2)O₃. The ac conductivity data were used to evaluate the density of states at Fermi level, minimum hopping length and apparent activation energy of the compound.     

Modulus spectroscopy of lead potassium titanium niobate (Pb<Subscript>0.95</Subscript>K<Subscript>0.1</Subscript>Ti<Subscript>0.25</Subscript>Nb<Subscript>1.8</Subscript>O<Subscript>6</Subscript>) ceramics

The modulus Spectroscopy of Lead Potassium Titanium Niobate (Pb_0.95K_0.1Ti_0.25Nb_1.8O₆, PKTN) Ceramics was investigated in the frequency range from 45 Hz to 5 MHz and the temperature, from 30 to 600 °C. XRD analysis in PKTN indicated a orthorhombic structure with lattice parameters a = 18.0809 Å, b = 18.1909 Å and c = 3.6002 Å. The dielectric anomaly with a peak was observed at 510 °C. Variation of ε^I and ε^II with frequency at different temperatures exhibit high values, which reflects the effect of space charge polarization and/or conduction ion motion. The electrical relaxation in ionically conducting PKTN ceramic analyzed in terms of Impedance and Modulus formalism. The Cole–Cole plots of impedance were drawn at different temperatures. The dielectric modulus, which describes the dielectric relaxation behaviour is fitted to the Kohlrausch exponential function. Near the phase transition temperature, a stretched exponential parameter β indicating the degree of distribution of the relaxation time has a small value. From the AC conductivity measurements the activation energy near phase transition temperature (T _C°C) has been found to different from that of the above and below T _C. The temperature dependence of electrical modulus has been studied and results are discussed.     

Magnetic,optical, dielectric,and sintering properties of nano-crystalline BaFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> synthesized by a polymerization method

A one-pot polymerization method using citric acid and glucose for the synthesis of nano-crystalline BaFe_0.5Nb_0.5O₃ is described. Phase evolution and the development of the crystallite size during decomposition of the (Ba,Fe,Nb)-gel were examined up to 1100 °C. Calcination at 850 °C of the gel leads to a phase-pure nano-crystalline BaFe_0.5Nb_0.5O₃ powder with a crystallite size of 28 nm. The shrinkage of compacted powders starts at 900 °C. Dense ceramic bodies (relative density ≥ 90%) can be obtained either after conventional sintering above 1250 °C for 1 h or after two-step sintering at 1200 °C. Depending on the sintering regime, the ceramics have average grain sizes between 0.3 and 52 µm. The optical band gap of the nano-sized powder is 2.75(4) eV and decreases to 2.59(2) eV after sintering. Magnetic measurements of ceramics reveal a Néel temperature of about 23 K. A weak spontaneous magnetization might be due to the presence of a secondary phase not detectable by XRD. Dielectric measurements show that the permittivity values increase with decreasing frequency and rising temperature. The highest permittivity values of 10.6 × 10⁴ (RT, 1 kHz) were reached after sintering at 1350 °C for 1 h. Tan δ values of all samples show a maximum at 1–2 MHz at RT. The frequency dependence of the impedance can be well described using a single RC-circuit.     

Dielectric and impedance characteristics of Ba(Bi0.5Nb0.5)O3 ceramics

A lead free polycrystalline material Ba(Bi_0.5Nb_0.5)O₃ was prepared using a high-temperature mixed oxide technique using high purity ingredients. The formation of the material in monoclinic crystal structure was confirmed by an X-ray structural analysis at room temperature. The nature and texture of microstructure by scanning electron microscopy show that the compound has well defined grains uniformly distributed throughout the surface of the sample. Detailed studies of dielectric and impedance properties of the material, carried out in the frequency range of (1 kHz–1 MHz) at different temperatures (30 °C to 475 °C), have shown many interesting properties. Dielectric study showed an existence of diffuse phase transition around 317 °C. The temperature dependence of impedance parameters (impedance, modulus etc.) of the material exhibits a strong correlation of its micro-structure (i.e., bulk, grain boundary, etc.) with the electrical parameters. An existence of negative temperature coefficient of resistance (NTCR) type behavior in the material similar to that of semiconductors was also observed. The complex electric modulus analysis indicates the existence of hopping conduction mechanism in the system with non-exponential type of conductivity relaxation. The nature of variation of dc conductivity with temperature confirms the Arrhenius behavior of the material. The ac conductivity spectra show a typical signature of an ionic conducting system, and are found to obey Jonscher’s universal power law. The temperature dependent pre-exponential factor (A) shows peak and frequency exponent (n) possesses a minimum at transition temperature.     

Dielectric and impedance studies of (Pb<Subscript>1−x</Subscript>Ca<Subscript>x</Subscript>)(Fe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>)O<Subscript>3</Subscript> dielectric ceramics

Ceramic samples of (Pb_1?xCa_x)(Fe_0.5Nb_0.5)O₃ with x = 0.20, 0.40, 0.45, 0.50, 0.55 and 0.60 were obtained by columbite precursor method. All the synthesized samples have perovskite structure with pseudo-cubic symmetry. Dielectric properties of all the samples were measured as a function of frequency from room temperature up to 573 K. Two dielectric anomalies were observed in ε_r–T plots at about 400 and 500 K. The impedance analysis depicts a single relaxation process. Activation energies obtained from temperature dependence of relaxation frequency, f₀ and grain resistance, R_g were found to be more or less comparable. The observed relaxation in all the samples seems to be due to electron relaxation associated with oxygen vacancies.     

Structural,electrical and magnetic properties of Mn<Subscript>3</Subscript>O<Subscript>4</Subscript>/MgO nanocomposite

The present paper deals with the synthesis of Mn₃O₄/MgO nanocomposite through a simple sol–gel route and their electrical and magnetic properties are discussed for electrode applications. The grain size and particle morphology of the synthesized nanocomposite are characterized using XRD and HRSEM. The elemental compositions of the synthesized samples were analyzed using EDAX spectra. The dielectric constant, dielectric loss and AC conductivity of the synthesized samples were studied in the frequency range of 100 Hz–5 MHz at different temperatures (303–573 K) using impedance spectra. The activation energy was calculated using Arrhenius plot. The vibrating sample magnetometry (VSM) study shows that the nanocomposites are found to be paramagnetic at room temperature.