Structural and piezoelectric properties of <001> textured PZT‐PZNN piezoelectric ceramics

Rhombohedral 0.69Pb(Zr_0.47Ti_0.53)‐0.31Pb(Zn_0.6Ni_0.4)NbO₃ (PZT‐PZNN) ceramics were textured using 10.0 vol. % BaTiO₃ (BT) platelets along the <001> direction at 950°C with a high Lotgering factor of 95.3%. BT platelets did not react with the PZT‐PZNN ceramics, and the textured PZT‐PZNN ceramic had a tetragonal structure. The PZT‐PZNN ceramics exhibited a strain of 0.174% with a piezoelectric strain constant (d*₃₃) of 580 pC/N at 3.0 kV/mm. The textured PZT‐PZNN ceramic showed an increased strain of 0.276% and d*₃₃ of 920 pC/N at 3.0 kV/mm, which can be explained by the domain rotation. However, the d₃₃ values of the textured specimens are smaller than those of the untextured specimens because of the small remanent polarization and relative dielectric constant of BT platelets. The textured PZT‐PZNN ceramic synthesized in this work can be used for piezoelectric multilayer actuators because of its large strain and low sintering temperature.     

Temperature dependence of field‐responsive mechanisms in lead zirconate titanate

An electric field loading stage was designed for use in a laboratory diffractometer that enables in situ investigations of the temperature dependence in the field response mechanisms of ferroelectric materials. The stage was demonstrated by measuring PbZr_1?xTi_xO₃ (PZT) based materials—a commercially available PZT and a 1% Nb‐doped PbZr_0.56Ti_0.44O₃ (PZT 56/44)—over a temperature range of 25°C to 250°C. The degree of non‐180° domain alignment (η₀₀₂) of the PZT as a function of temperature was quantified. η₀₀₂ of the commercially available PZT increases exponentially with temperature, and was analyzed as a thermally activated process as described by the Arrhenius law. The activation energy for thermally activated domain wall depinning process in PZT was found to be 0.47 eV. Additionally, a field‐induced rhombohedral to tetragonal phase transition was observed 5°C below the rhombohedral‐tetragonal transition in PZT 56/44 ceramic. The field‐induced tetragonal phase fraction was increased 41.8% after electrical cycling. A large amount of domain switching (η₀₀₂=0.45 at 1.75 kV/mm) was observed in the induced tetragonal phase.     

Oxygen plasma-assisted ultra-low temperature sol-gel-preparation of the PZT thin films

PbTi_1-xZr_xO₃ (PZT) thin films prepared by sol-gel method have paid much attention due to the excellent performances in piezoelectric, dielectric, ferroelectric and electro-optical. However, the high crystallization temperature of the PZT thin films restricts the compatibility with modern COMS technology. In this work, PbZr_0.52Ti_0.48O₃ (PZT) ferroelectric thin films were successfully prepared by sol-gel method at an ultra-low temperature (～450 °C) in an oxygen plasma-assisted environment. A large spontaneous polarization ～30 μC/cm² and a large dielectric breakdown ～2,900 kV/cm were obtained in the sample annealed at 450 °C for 25 h. We believe that the oxygen plasma-assisted ultra-low temperature (OPAULT) annealing process is a promising way for the sol-gel technology applied in the modern COMS devices.     

Microwave enhanced sintering of tape-cast ferroelectric films

Porous Pb(Zr_xTi_1−x)O₃(PZT) thick films that had been prepared by tape casting were densified by microwave energy. The microwave absorption effect is substantially correlated with the film thickness. In microwave-processed PZT thick films, rapid particle necking causes densification with no grain growth nearly in a short treatment time of 20 min at 820 °C. The same porous PZT thick films are difficult to densify in a conventional process. A 30-μm-thick PZT thick film has a pure perovskite structure. Self-supporting PZT thick films with a crack-free and uniform microstructure formed in a microwave process have larger coercive field than conventionally processed bulk PZT. The polarization, 14 μC/cm², of PZT thick films in a microwave process exceeds that, 7 μC/cm², of PZT bulk formed in a conventional process.     

Residual stress and electrical properties of Pb(Zr0.52,Ti0.48)O3 thin films RF sputtered directly on Cu foils

Polycrystalline Pb(Zr_0.52Ti_0.48)O₃ (PZT) thin films between 250 and 1000 nm thick were deposited on Cu foils via RF magnetron sputtering. Samples were crystallized ex situ between 550°C and 750°C in a low oxygen partial pressure atmosphere, pO₂, in order to avoid oxidation of the substrate. These were compared to films made on more common Pt/TiO_x/SiO₂/Si substrates also crystallized under low pO₂ conditions. The mismatch of the coefficients of thermal expansion for Cu and PZT caused large compressive residual stresses to develop in the films, whereas films on Pt‐Si experienced more moderate tensile stresses. Stress was measured using the sin²ψ method. In addition to mechanical implications, i.e., film cracking and delamination, the effect of residual stress on electrical properties is discussed. Dielectric constants of PZT were lower on Cu than on Pt/TiO_x/SiO₂/Si. This could be due either to a dead layer effect or to the residual stress imposed by the substrate. The remanent polarizations for films on Cu were between 18 and 41 μC/cm², while coercive fields were between 37 and 54kV/cm. Rayleigh analysis was used to describe the role of defects affecting domain wall mobility, as they act as pinning centers and decrease the extrinsic polarization response.     

Effect of excess lead on the structural and electrical characteristics of sol-gel synthesized RuO2/Pb(ZrxTi1−x)O3/RuO2

In this study, we investigated the effect of excess lead on the structural and electrical characteristics of lead zirconate titanate [Pb(Zr_xTi_1−x)O₃, PZT] thin films using the sol-gel spin coating method. X-ray diffraction, atomic force microscopy, X-ray photoelectron spectroscopy, and field-emission transmission electron microscopy were used to study the structural, morphological, chemical, and microstructural features, respectively, of these films as functions of the growth conditions (excess lead concentrations of 10, 20, and 25 mol%). The PZT thin film prepared at the 20 mol% condition exhibited the best electrical characteristics including a lower leakage current of 6×10⁻⁷ A/cm² at an electric field of 50 kV/cm, a larger capacitance value of 1.92 μF/cm² at a frequency of 1 kHz, and a higher remanent polarization of 20.1 μC/cm² at a frequency of 5 kHz. We attribute this behavior to the optimal amount of excess lead in this PZT film forming a perovskite structure and suppressing the reaction of PZT film with RuO₂ electrode.     

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

To develop high-performance piezo-/ferroelectric materials, Bi(Zn_½Ti_½)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(Zn_½Ti_½)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 P_r = 33 μC/cm², as well as a relatively high T_C = 286°C, and a high coercive field E_c = 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.     

Lead zirconium titanate thin films prepared by thermal annealing of multilayer structures composed of PbO,ZrO2 and TiO2

Lead zirconium titanate [Pb(Zr_xTi_1?x)O₃ or PZT] thin films were prepared by the thermal annealing of multilayer films composed of binary oxide layers of PbO, ZrO₂ and TiO₂. The binary oxides were deposited by metal organic chemical vapor deposition. An interdiffusion reaction for perovskite PZT thin films was initiated at approximately 550 °C and nearly completed at 750 °C for 1 h under O₂ annealing atmosphere. The composition of Pb/Zr/Ti in perovskite PZT could be controlled by the thickness ratio of PbO/ZrO₂/TiO₂ where the contribution of each binary oxide at the same thickness was 1:0.55:0.94. The electrical properties of PZT (Zr/Ti = 40/60, 300 nm) prepared on a Pt-coated substrate included a dielectric constant ?_r of 475, a coercive field E_c of 320 kV/cm, and remnant polarization P_r of 11 μC/cm² at an applied voltage of 18 V.     

Pyroelectric energy harvesting using low–TC (1–x)(Ba0.7Ca0.3)TiO3–xBa(Zr0.2Ti0.8)O3 bulk ceramics

Lead‐free ferroelectric ceramics (1–x)(Ba_0.7Ca_0.3)TiO₃–xBa(Zr_0.2Ti_0.8)O₃ (BCTZ100x) with x = 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, and 0.80 were evaluated for their pyroelectric energy harvesting performance, using the Olsen cycle. As the composition ratio x increased, the crystal phase changed to tetragonal, orthorhombic, rhombohedral, and cubic; the phase boundaries crossed each other in the vicinity of BCTZ70. The crossover phase transition behavior between first‐order and diffuse phase transition changed to only the diffusion phase transition with increasing x. A pinching effect occurred because an increase in dielectric constant was also observed. Energy densities N_D of 229 mJ/cm³ and 256 mJ/cm³ for BCTZ50 and BCTZ80 were obtained, respectively, in temperature of 30°C‐100°C and an electric field of 0‐30 kV/cm. These N_D values are over two times higher than that of soft–Pb(Ti,Zr)O₃ (PZT), which exhibits piezoelectric performance equivalent to BCTZ50 at room temperature. Compared with soft–PZT, BCTZ50 and BCTZ80 exhibited larger N_D values owing to their lower Curie temperatures (T_C ~ 50°C‐110°C). We conclude that low–T_C ferroelectrics are useful for pyroelectric energy conversion based on the Olsen cycle even if they are unsuitable for piezoelectric applications at high temperatures.     

Piezoelectric Properties of a Pioneering 3‐1 Type PZT/Epoxy Composites Based on Freeze‐Casting Processing

Lead zirconate titanate (PbZr_1 ? xTi_xO₃, PZT)/epoxy composites with one‐ dimensional epoxy in PZT matrix (called 3‐1 type piezocomposites) have been fabricated by tert‐butyl alcohol (TBA)‐based directional freeze casting of PZT matrix and afterward infiltration of epoxy. The composites with PZT volume fraction ranging from 0.36 to 0.69 were obtained by adjusting initial solid loading in freeze‐casting slurry. The effect of poling voltage on piezoelectric properties of the composites was studied for various volume fraction of PZT phase. With the increasing of PZT volume fraction, relative permittivity (ε_r) increased linearly and piezoelectric coefficient (d₃₃ and d₃₁) increased step by step. The resultant composites with 0.57 PZT volume fraction possessed the highest hydrostatic piezoelectric strain coefficient (d_h) value (184 pC/N), voltage coefficient (g_h) value (13.6 × 10^?3 V/m Pa), and hydrostatic figure of merit (HFOM) value (2168 × 10^?15 Pa^?1).     

Enhanced optical transmittance and energy-storage performance in NaNbO3-modified Bi0.5Na0.5TiO3 ceramics

Dielectric ceramics with both excellent energy storage and optical transmittance have attracted much attention in recent years. However, the transparent Pb-free energy-storage ceramics were rare reported. In this work, we prepared transparent relaxor ferroelectric ceramics (1 − x)Bi_0.5Na_0.5TiO₃–xNaNbO₃ (BNT–xNN) by conventional solid-state reaction method. We find the NN-doping can enhance the polarization and breakdown strength of BNT by suppressing the grain growth and restrained the reduction of Ti⁴⁺ to Ti³⁺. As a result, a high recoverable energy-storage density of 5.14 J/cm³ and its energy efficiency of 79.65% are achieved in BNT–0.5NN ceramic at 286 kV/cm. Furthermore, NN-doping can promote the densification to improve the optical transmittance of BNT, rising from ∼26% (x = 0.2) to ∼32% (x = 0.5) in the visible light region. These characteristics demonstrate the potential application of BNT–xNN as transparent energy-storage dielectric ceramics.     

Low‐Cost,Damage‐Free Patterning of Lead Zirconate Titanate Films

The ability to pattern piezoelectric thin films without damage is crucial for the development of microelectromechanical systems. Direct patterning of complex oxides through microcontact printing was explored as an alternative to subtractive patterning. This process utilized an elastomeric stamp to transfer a chemical solution precursor of a piezoelectric material onto a substrate in a desired pattern. Polyurethane‐based stamps improved wetting of polar solutions on the stamp. This allowed for high‐fidelity patterning over multiple stamping cycles. Microcontact printing deposited patterned PbZr_0.52Ti_0.48O₃ layers from 0.1 to 1 μm in thickness. The lateral feature sizes attained varied from 5 to 500 μm. Upon crystallization at 700°C, the features formed phase‐pure perovskite PZT. The printed features had comparable electrical and electromechanical properties to those of continuous PZT films of similar thicknesses. For example, 1 μm thick PZT features had a permittivity of 1050 and a loss tangent of 0.02 at 10 kHz. The remanent polarization was 30 μC/cm², and the coercive field was 45 kV/cm. The piezoelectric coefficient e_31,f was ?7 C/m². These values indicated that the microcontact printing process did not adversely affect the PZT crystallization or properties for the thicknesses explored in this work.     

Structure and microwave dielectric characteristics of Sr2[Ti1−x(Al0.5Nb0.5)x]O4 (x ≤ 0.50) ceramics

Sr₂[Ti_1−x(Al_0.5Nb_0.5)_x]O₄ (x = 0, 0.10, 0.25, 0.30, 0.5) ceramics were synthesized by a standard solid-state reaction process. Sr₂[Ti_1−x(Al_0.5Nb_0.5)_x]O₄ solid solutions with tetragonal Ruddlesdon-Popper (R-P) structure in space group I4/mmm were obtained within x ≤ 0.50, and only minor amount (1-2 wt%) of Sr₃Ti₂O₇ secondary phase was detected for the compositions x ≥ 0.25. The temperature coefficient of resonant frequency τ_f of Sr₂[Ti_1−x(Al_0.5Nb_0.5)_x]O₄ ceramics was significantly improved from 132 to 14 ppm/°C correlated with the increase in degree of covalency (%) with increasing x. The dielectric constant ɛ_r decreased linearly with increasing x, while high Qf value was maintained though it decreased firstly. The variation tendency of Qf value was dependent on the trend of packing fraction combined with the microstructure. Good combination of microwave dielectric properties was achieved for x = 0.50: ɛ_r = 25.1, Qf = 77 580 GHz, τ_f = 14 ppm/°C. The present ceramics could be expected as new candidates of ultra-high Q microwave dielectric materials without noble element such as Ta.     

Ultrahigh energy storage density and charge-discharge performance in novel sodium bismuth titanate-based ceramics

Lead-free ferroelectric ceramics are very suitable for electrostatic energy storage capacitors due to their outstanding characteristics of high charge-discharge speed, high power density, and environmental friendliness. Herein, a novel material system as (1−x)Na_0.5Bi_0.5TiO₃-xCaZr_0.5Ti_0.5O₃ (NBT-CZT, x = 0, 0.05, 0.10, 0.12, 0.15, and 0.20) was designed and prepared for dielectric energy storage ceramics. It demonstrated that the CZT additives induced a phase transition for the NBT ceramics, from ferroelectric to relaxor ferroelectric. In particular, extremely high stored energy storage density (6.92 and 5.37 J/cm³), high recoverable energy storage density (4.77 and 4.37 J/cm³), and moderate efficiency (69.0% and 81.4%) were achieved in both the samples of x = 0.12 and x = 0.15, respectively. The ceramics exhibited excellent stability of energy storage performance covering a wide temperature (25°C–200°C) and frequency (0.5–50 Hz) range, and also fatigue cycles up to 10⁵. Additionally, the NBT-CZT ceramics had a fast discharge speed (t_0.9 < 100 ns) and high power density (24.2 MW/cm³, E = 100 kV/cm, x = 0.15), and the charge-discharge process remained stable even when the measured temperature was up to 160°C. Therefore, the NBT-CZT ceramics have the potential to be utilized in electrostatic energy storage applications.     

Large enhancement of piezoelectric properties and resistivity in Cu/Ta co-doped Bi4Ti3O12 high-temperature piezoceramics

In this study, the electrical properties of Bi₄Ti₃O₁₂-based Aurivillius-type ceramics were tailored by a B-site co-doping strategy combining high valence Ta⁵⁺ and low valence Cu²⁺. A series of Bi₄Ti_3−x(Cu_1/3Ta_2/3)_xO₁₂ (BTCT) (x = 0, 0.005, 0.01, 0.015, 0.02, 0.025, and 0.03) ceramics were prepared by the conventional solid-state reaction method. The effect of Cu/Ta co-doping on the crystal structure, microstructure, dielectric properties, piezoelectric properties, ferroelectric properties, and electrical conductivity of these ceramics was systematically investigated. Co-doping significantly enhanced the piezoelectric properties and DC electrical resistivity of the resulting composites. The optimized comprehensive performances were obtained at x = 0.015 with a large piezoelectric coefficient (34 pC/N) and a relatively high resistivity of 9.02 × 10⁶ Ω cm at 500°C. Furthermore, the ceramic also exhibited stable thermal annealing behaviors and excellent fatigue resistance. The results of this study demonstrated great potential of the Cu/Ta co-doped Bi₄Ti₃O₁₂ ceramics for high-temperature piezoelectric device applications.     

Submicron crystalline buildup and size‐dependent energy harvesting characteristic in PZN–PZT ternary ferroelectrics

Piezoelectric energy harvester converts low‐frequency vibrational energy in the environment into electrical energy, enabling the purpose of self‐supplying power for low‐energy consumption devices. The key to miniaturizing energy harvester is the buildup of the submicron‐grained ceramic with a high transduction coefficient (d×g), which is still a big challenge from a technical point of view. In this work, the popular ternary system of Pb(Zn_1/3Nb_2/3)O₃–Pb(Zr_0.5Ti_0.5)O₃ (PZN–PZT) has been selected as objective compound, and the submicron‐grained ceramics were prepared by a combination of high‐energy ball milling and pressureless sintering technology. The results revealed that nanocrystalline PZN–PZT powders can be synthesized by one step mechanochemical route without the calcination stage. Using these nanopowders as precursors, dense ceramics with different grain size have been prepared through tailoring the sintering temperature. The study of size‐dependent energy harvesting characteristic evidenced an optimum transduction coefficient of 7980×10^?15 m²/N was obtained for 950°C sintered specimen, which has uniform microstructure with mean grain size of 0.33 μm. In the mode of the cantilever‐type energy harvester constructed by this material, the output power at low frequency of 89 Hz was as high as 69 μW at an acceleration of 10 m/s², showing the suitability for piezoelectric generators harvesting environmental vibrational energy.     

Dielectric and structural studies of ferroelectric phase evolution in dipole-pair substituted barium titanate ceramics

Ba{[Ga_x,Ta_x]Ti_(1−2x)}O₃ ceramics with x equal to 0, 0.0025, 0.005, 0.01, 0.025, and 0.05 have been prepared by conventional solid-state reaction. Structural and dielectric characterization have been performed to investigate the effect of dipole-pair substitution concentration on the macroscopic dielectric properties. Ba{[Ga_x,Ta_x]Ti_(1−2x)}O₃ evolves from a classic ferroelectric to a diffuse phase transition (DPT) as x increases. Ba{[Ga_x,Ta_x]Ti_(1−2x)}O₃ for x ≥ 0.01 possesses diffuseness parameters comparable to Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (PMN-PT) and recently reported (Ba_0.97Pr_0.03)(Ti_0.9425Ce_0.05)O₃ (BPTC), yet it lacks the frequency and temperature dependence of T_m necessary to be a strictly defined relaxor ferroelectric. Additionally, Ba{[Ga_0.05,Ta_0.05]Ti_0.9}O₃ possesses a relative permittivity, ɛ_r, of 700 ± 16% and dissipation factor less than 0.05 at 10 kHz within the temperature range [−75°C, 120°C]. In comparison to BaTiO₃, Ba{[Ga_x,Ta_x]Ti_(1−2x)}O₃ possesses enhanced electrical resistivity at and above room temperature. In situ XRD, including Rietveld refinement, have been performed to determine the lattice parameter, coefficient of thermal expansion, and phase transition temperature (T_c) of each composition within the temperature range [RT, 1000°C], thus linking the dielectric properties with the material's structure. These studies have been corroborated by temperature-dependent Raman spectroscopy to compare the T_c determined by electrical and structural characterization. The properties of Ba{[Ga_x,Ta_x]Ti_(1−2x)}O₃ are discussed in context with available models that describe donor and acceptor dopants spatially separated in the parent matrix, inter-relating lattice parameter, Curie temperature, and other material properties.     

Nanocrystalline buildup,relaxor behavior,and polarization characteristic in PZT–PNZN quaternary ferroelectrics

The Pb(Zr_0.47Ti_0.53)O₃–Pb[(Ni_0.6Zn_0.4)_1/3Nb_2/3]O₃ (PZT–PNZN) quaternary ferroelectrics presenting the high piezoelectric coefficients are the active element in a range of piezoelectric devices. However, the buildup of nanoceramics with stable perovskite structure is still a big challenge, which prohibits the miniaturization of piezoelectric devices. In this work, the high dense PZT–PNZN nanoceramics with average grain size of 130 nm were prepared by a combination of high‐energy ball milling (HEBM) and spark plasma sintering (SPS). The domain configuration and relaxor behavior in this nanoceramic are reported for the first time. Although the noncubic crystal structure and dielectric anomaly suggest a ferroelectric behavior, only very slim polarization–electric (P–E) hysteresis loops are observed. The suppression of macroscopic ferroelectric polarization mainly originates from the decrease in crystal tetragonality and the enhanced clamping effect on domain wall motion. The piezoelectric properties, d₃₃=65 pC/N and k_p=17%, raise the possibility of PZT–PNZN nanoceramics for application in multilayer piezoelectric devices.     

Crystal structures and electrical properties of Sr/Fe-modified KNbO3 ferroelectric semiconductors with narrow bandgap

In the process of exploring ferroelectric semiconductors, a new system of (1−x) KNbO₃–xSrFeO_3−δ (x = 0.00-0.20) was successfully synthesized via solid-state reaction. The crystal structures, ferroelectric, dielectric, optical, and electrical properties were systematically characterized. The orthorhombic phase with Amm2 space group is detected in all the ceramics. In addition, the orthorhombic and tetragonal phases coexist in 0.80KNbO₃-0.20SrFeO_3-δ ceramic. The decrease in oxygen octahedron distortion induces a weak ferroelectric polarization. The existence of long-range ferroelectric polarization order in all the ceramics is verified and the bandgap of the ceramics can be tuned to ~2.18 eV. The improved short-circuit photocurrent density (J_sc) and open-circuit voltage (V_oc) of the poled 0.95KNbO₃-0.05SrFeO_3−δ ceramic at 30 kV/cm are ~6.90 nA/cm² and 0.04 V, respectively. The activation energies for electrical conductivity of the grains and grain boundaries from 0.90KN–0.10SF ceramic are 0.67 and 0.77 eV, respectively, which indicate the doubly ionized oxygen vacancies. This work provides a new way to tune the optical bandgap/ferroelectric properties of KNbO₃-based ceramics for potential application in ferroelectric photovoltaic and energy fields.     

Effect of annealing temperature on ferroelectric electron emission of sol–gel PZT films

In this work, the influence of annealing temperature on the ferroelectric electron emission behaviors of 1.3-μm-thick sol–gel PbZr_0.52Ti_0.48O₃ (PZT) thin film emitters was investigated. The results revealed that the PZT films were crack-free in perovskite structure with columnar-like grains. Increasing annealing temperature led to the growth of the grains with improved ferroelectric and dielectric properties. The remnant polarization increased slightly from 35.3 to 39.6 μC/cm² and the coercive field decreased from the 56.4 to 54.6 kV/cm with increasing annealing temperature from 600 to 700 °C. The PZT film emitters exhibited remarkable ferroelectric electron emission behaviors at the threshold voltage above 95 V. The film annealed at 700 °C showed a relatively lower threshold voltage and higher emission current, which is related to the improved ferroelectric and dielectric properties at higher annealing temperature. The highest emission current achieved in this work was around 25 mA at the trigger voltage of 160 V.