YBCO Research Articles

Yttrium cuprates modification in linear generator application for power generation

Abstract Yttrium barium copper oxide (YBCO) is used for special applications in linear generators because of its excitation loss, lower weight, and higher efficiency. These qualities enable the compound to operate better than the conventional copper wire coil in the stator unit of the linear generator. However, the continuous use of YBCO in linear generators has a fundamental challenge that affects industrial production and material stability after prolonged use. This paper seeks to sustain the adoption of YBCO by improving its quality for linear generator applications. The yttrium cuprates modification (YBYbCO) was synthesized using the solid-state reaction technique by doping YBCO with ytterbium. The crystalline structure, microstructural pattern, and stability of the new sample were adequately measured and found to be structurally stable to ensure durability. It was reported that applying YBYbCO in the linear generator would lead to a 200% increase in energy generation. The higher number of particles and lower individual particulate resistance enable it to withstand chemical pressure, thereby prolonging the lifespan of the linear generator.

Interfacial stability and electronic properties of YBCO/ABO3 heterostructures: A comparative DFT study

In this study, we utilized density functional theory (DFT) to analyze the interfacial properties of YBa2Cu3O7 (YBCO) with perovskite metal oxides LaAlO3 (LAO), KTaO3 (KTO), and SrTiO3 (STO). We focused on surface energies, lattice mismatches, strain energies, and adhesion energies to gauge the stability and compatibility of these interfaces. Our findings indicate that KTO exhibits the highest surface preference due to its lowest surface energy (0.054 eV/Å 2), suggesting superior surface stability. Moreover, LAO and STO show minor lattice mismatches with YBCO, implying effective interface integration, while YBCO/KTO interfaces experience significant strain due to extensive lattice mismatches. STO is distinguished by the lowest strain energy (0.07 eV), indicating minimal energy requirement for lattice mismatch accommodation, unlike KTO, which demonstrates high strain energy (0.42 eV) and potential structural distortions. The strongest interfacial bond, as indicated by an adhesion energy of −2.16 eV, was observed at YBCO/LAO, while the weakest was found at the YBCO/KTO interface, with an adhesion energy of −0.56 eV. Additionally, charge density difference (CDD) analysis highlighted electron density redistribution at the interfaces, predominantly around interfacial oxygen atoms, indicating a mix of ionic and covalent bonding. This study provides comparative insights into the interfacial characteristics of YBCO/ABO3 heterostructures, suggesting pathways for optimizing their design and performance.

The flux pinning effect of different doping element combinations on metal-organic deposition-derived YBa2Cu3O7−δ nanocomposite films

Elemental doping has been proven effective in improving the flux pinning of yttrium barium copper oxide (YBa2Cu3O7−δ, YBCO) nanocomposite thin films. In the present work, we increased the number of doping elements to five to investigate the flux pinning effect of YBCO. The Zr-doped, Zr, Hf and Sn co-doped, Zr, Hf, Sn and Ta co-doped, and Zr, Hf, Sn, Ta and Mn co-doped YBCO films deposited on LaMnO3/MgO/Y2O3/Al2O3/ Hastelloy substrate were systematically studied. The samples were prepared by low-fluorine metal-organic deposition method, with a total dopant of 8 mol%. All films exhibit good c-axis growth and the multi-doping helps refining the surface particles, resulting in a smoother surface. The in-field properties of the films increase with the increase of co-doped element numbers, especially at a low temperature of 30 K. The pinning force density (Fp) and critical current density (Jc) are significantly improved by five-element Zr, Hf, Sn, Ta and Mn co-doped, which is about 3 times and 1.6 times higher, respectively, than that of the undoped film at 30 K and 1 T.

Integration of High‐Tc Superconductors with High‐Q‐Factor Oxide Mechanical Resonators

AbstractMicro‐mechanical resonators are building blocks of a variety of applications in basic science and consumer electronics. This device technology is mainly based on well‐established and reproducible silicon‐based fabrication processes with outstanding performances in term of mechanical Q‐factor and sensitivity to external perturbations. Broadening the functionalities of micro‐electro‐mechanical systems (MEMS) by the integration of functional materials is a key step for both applied and fundamental science. However, combining functional materials with silicon‐based devices is challenging. An alternative approach is directly fabricating MEMS based on compounds inherently showing non‐trivial functional properties, such as transition metal oxides. Here, a full‐oxide approach is reported, where a high‐ superconductor YBa2Cu3O7 (YBCO) is integrated with high Q‐factor micro‐bridge resonators made of single‐crystal LaAlO3 (LAO) thin films. LAO resonators are tensile strained, with a stress of about 350 MPa, show a Q‐factor above 200k, and have low roughness. YBCO overlayers are grown ex situ by pulsed laser deposition and YBCO/LAO bridges show zero resistance below 78 K and mechanical properties similar to those of bare LAO resonators. These results open new possibilities toward the development of advanced transducers, such as bolometers or magnetic field detectors, as well as experiments in solid state physics, material science, and quantum opto‐mechanics.

Dynamical analysis of the low-temperature phase diagram of a cuprate superconductor

For a cuprate superconductor, specifically the yttrium barium copper oxide system, we analyze the low-temperature phase diagram consisting of the superconducting, pseudogap, and normal phases by using a phonon-mediated attraction and Coulomb repulsion mechanism. Through this analysis, we show this mechanism in the cuprate is quite important for its key dynamics. For the pairing mechanism, a variational method is developed and applied, and a generalized mean field theory is used to calculate the condensate energy and the energy gap of the quasiparticle. We obtain a self-consistent system of equations for these quantities. The superconducting and pseudogap phases, which involve pair-condensates, are assumed to be equilibrium systems of the condensate and normal subphases. The condition for the phase transition point is given by the equal total electronic energy gains. Assuming that the difference in the pairing range of the pair condensate is small between just above and below the transition temperature, computations are performed to solve the self-consistent system of equations. We find solutions compatible with experimental data. Plausible values of the energy gap in the superconducting phase and in the pseudogap phase are obtained. The present analysis shows that the phonon-mediated attraction and Coulomb repulsion mechanism itself is compatible with the experimental data. The importance of the screening effect through one-phonon exchange in the pairing mechanism and of the structure of the valence band is discussed.

Fabrication and properties of nano-CeO<sub>2</sub> doped Y-Ba-Cu-O bulk superconductors

Single-domain Y-Ba-Cu-O (YBCO) bulk superconductors can be widely used in the superconducting maglev, cryomagnets, motors/generators fields. In order to improve the performance of the YBCO bulk superconductors further, in this work, nano-CeO<sub>2</sub> doped YBCO bulk superconductors are fabricated by two infiltration growth techniques (011-IG and 211-IG) respectively, in which two solid pellets of compositions Y<sub>2</sub>O<sub>3</sub>+1.15BaCuO<sub>2</sub>+0.1CuO+1wt.% nano-CeO<sub>2</sub> and Y<sub>2</sub>BaCuO<sub>5</sub> (Y-211)+1 wt.% nano-CeO<sub>2</sub> are employed. And a novel pit-type seeding mode is used to prevent the film seed from moving in the heat treatment process, then the growth morphologies, microstructures and superconducting properties of the samples are investigated. The results show that at a low doping level (1 wt.%), the normal growth of the YBCO crystal is not affected, and fully-grown single-domain YBCO bulk superconductors can be successfully prepared by the two techniques. Furthermore, the positions of the seeds do not move at all, which proves the effectiveness of the new seeding mode. The perpendicular growth sector boundaries on the top surfaces of the samples and clear (00<i>l</i>) series X-ray diffraction (XRD) peaks both prove the high <i>c</i>-axis orientations and high growth quality of the samples. The scanning electron microscopy (SEM) results indicate that the nano-CeO<sub>2</sub> doping can effectively refine the sizes of the Y-211 micro-particles in the bulk superconductors, and this method is applicable to both techniques. Low-temperature magnetization measurement shows that the nano-CeO<sub>2</sub> doped sample prepared by the 011-IG method shows obviously better <i>J</i><sub>c</sub> property than the undoped sample at low fields, indicating that the refined Y-211 particles can effectively enhance the δ<i>l</i>-type pinning. In addition, compared with the 211-IG-processed sample, the 011-IG-processed sample performs better in terms of levitation force, microstructure and <i>J</i><sub>c</sub> property, thus the 011-IG method is a more promising preparation process. The results of this study are important in improving the performance of the YBCO bulk superconductors and optimizing the fabrication technique further.

Exceptional behavior of a high-temperature superconductor in proximity to a ferromagnet in a bilayer film, La0.67Sr0.33MnO3/YBa2Cu3O7.

We studied the electronic properties of a high-temperature superconductor in proximity to a ferromagnetic material in a bilayer film of La0.67Sr0.33MnO3 (LSMO)/YBa2Cu3O7 (YBCO). High-quality single-crystalline films of YBCO and LSMO/YBCO were grown epitaxially on an SrTiO3 (001) surface. Magnetization data of the LSMO/YBCO bilayer exhibit ferromagnetic transition at about 255 K, which is much smaller than the Curie temperature of bulk LSMO. Experimental data show the emergence of magnetic anisotropy with cooling, which becomes significantly stronger in the superconducting phase. The onset temperature of diamagnetism is observed at 86 K in the YBCO sample for the out-of-plane magnetization and at 89 K in the in-plane data. Interestingly, the diamagnetism sets in at about 86 K for both magnetization directions in the LSMO/YBCO film despite the presence of the ferromagnetic LSMO layer underneath. Ba 4d and Y 3d core-level spectra show different surface and bulk electronic structures. Surface contribution is reduced significantly in the LSMO/YBCO sample, suggesting enhanced bulk-like behavior due to an enhancement of electron density near the surface arising from charge transfer across the interface. These results reveal an outstanding platform for on-demand tuning of properties without affecting the superconductivity of the system for the exploration of fundamental science and applications in advanced technology.

THE APPLICATION OF ANALYSIS OF VARIANCE TO DIFFERENT YTTRIUM BARIUM COPPER OXIDE SUPERCONDUCTING TRANSITION TEMPERATURE MODELING

Extensive research has been conducted on a modeling approach that contributes to predicting the critical temperature of Yttrium barium copper oxide (YBCO) materials. Statistical significance of differences in modeling approaches requires studies that can reliably distinguish between systematic approach effects and errors resulting from modeling approach variation. In this work, we introduce analysis of variance (ANOVA) to assess the statistical significance of differences in modeling approach variation. Comparisons of obtained results with YBCO modeling approach variation data of support vector machine (SVM) and linear regression with natural logarithm transformation (LRNLT) were presented.

DC Resistance Measurements in Multi‐Layer Additively Manufactured Yttrium Barium Copper Oxide Components

Additive manufacturing can offer new methods to shape materials that are difficult or too brittle in nature to process traditionally. In this work the optimization of a linseed oil and ICP solvent based solution with 90 wt% solid loading of the high temperature superconducting material yttrium barium copper oxide (YBCO) for additive manufacturing is demonstrated. The post sintered, printed components are analysed using a combination of X‐ray diffraction, scanning electron microscopy (SEM), magnetometry, and DC transport measurements. It is shown for the first time, for multilayer additively manufactured YBCO, direct DC transport measurements that indicate a current carrying percolative path with an upper transition temperature of 86.5 K.

First principle calculation of electronic structures and hole concentration of YBCO family compounds

Yttrium barium copper oxide (YBCO) family compounds are similar in structure but have different superconducting temperatures. It is well known that superconducting properties arise from the crystal lattice and electronic structure of compounds. This work reveals and discusses the electronic structures of YBCO family compounds (YBa2Cu3O6, YBa2Cu3O6.5, YBa2Cu3O7, and YBa2Cu4O8) based on density functional theory (DFT). The electronic structure results show that Cu–O chains are the trigger components for conduction, and only Cu–O chains and Cu-O2 planes play important roles in electronic and superconducting properties. The results also reveal that additional hole doped will be non-trivially distributed between the Cu–O chains and the Cu-O2 planes, and hence a more comprehensive method is required to calculate the hole concentration in the Cu-O2 plane. This work also demonstrates the calculation of hole concentrations using DFT. By DFT calculation, the Y1236 has hole concentration of 0.5 and the hole doped of Y12365, Y1237 and Y124 are 0.09, 0.16 and 0.10, respectively. The results are consistent with the cuprate-superconductor phase diagram and the bond-valence sum (BVS) calculations.

Controllable spin-triplet superconductivity states and enhanced non-dissipation spin-polarized supercurrents in YBa2Cu3O7/La0.67Sr0.33MnO3 interfaces

The interfaces between superconductors and ferromagnets serve as a nurturing environment for spin-triplet superconducting pairs, where their spins align with the ferromagnetic moments, enabling the conduction of non-dissipative spin-polarized supercurrents that hold immense potential for spintronics applications and scientific advancements. In this study, we explore the spin-triplet superconductivity and the non-dissipative spin-polarized current in the YBa2Cu3O7(YBCO)/La0.67Sr0.33MnO3(LSMO) bilayers with X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD). The induced Cu moment at the interfaces exhibits three distinct alignment states: antiparallel, perpendicular, and parallel to the net moment of the LSMO ferromagnetic layer. Remarkably, the in-plane superconducting critical current experiences a sudden enhancement and displays a slower decaying trend to the applied magnetic field when the Cu-moment undergoes a transition from the antiparallel to the perpendicular state with respect to the LSMO magnetization. These findings shed light on the manipulation of induced Cu moments at interfaces, providing valuable insights for controlling spin-triplet states and enhancing non-dissipative spin-polarized supercurrents.

Design and Numerical Study of Magnetic Energy Storage in Toroidal Superconducting Magnets Made of YBCO and BSCCO

The superconducting magnet energy storage (SMES) has become an increasingly popular device with the development of renewable energy sources. The power fluctuations they produce in energy systems must be compensated with the help of storage devices. A toroidal SMES magnet with large capacity is a tendency for storage energy because it has great energy density and low stray field. A key component in the creation of these superconducting magnets is the material from which they are made. The present work describes a comparative numerical analysis with finite element method, of energy storage in a toroidal modular superconducting coil using two types of superconducting material with different properties bismuth strontium calcium copper oxide (BSCCO) and yttrium barium copper oxide (YBCO). Regarding the design of the modular torus, it was obtained that for a 1.25 times increase of the critical current for the BSCCO superconducting material compared with YBCO, the dimensions of the BSCCO torus were reduced by 7% considering the same stored energy. Also, following a numerical parametric analysis, it resulted that, in order to maximize the amount of energy stored, the thickness of the torus modules must be as small as possible, without exceeding the critical current. Another numerical analysis showed that the energy stored is maximum when the major radius of the torus is minimum, i.e., for a torus as compact as possible.

Manufactured Yttrium Barium Copper Nano Oxide for Medicinal Applications

In light of the considerable interest surrounding the antibacterial properties of nanometal oxides and high-temperature superconductors, this study focuses on the synthesis of YBa2Cu3O7 (YBCO) using the Sol-Gel method. The research delves into the experimental aspects of nanoparticle (NP) synthesis and aims to elucidate the antibacterial potential of YBCO NPs, a high-temperature superconductor, against four distinct bacteria. These bacteria were subjected to varying concentrations of YBCO NPs (0.01 mg/ml, 0.025 mg/ml, 0.05 mg/ml, and 0.1 mg/ml). Comprehensive characterization of the synthesized nanoparticles encompassed techniques such as X-ray diffraction (XRD), scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and thermogravimetric (TG) analysis. Remarkably, the Gram-positive strains, including Staphylococcus epidermidis and Methicillin-resistant Staphylococcus aureus (MRSA), exhibited pronounced susceptibility to the YBCO NPs, while Gram-negative strains displayed minimal response. Intriguingly, even at elevated concentrations of 0.01, 0.025, 0.05, and 0.1 mg/ml, these bacterial strains showcased resilient resistance. This research sheds light on the potential of YBCO NPs as an antibacterial agent against specific pathogens.

Fabrication of C-Band High-Temperature Superconducting Microstrip Triplexer with High Accuracy

This article presents a miniaturized C-band triplexer fabricated with high-temperature superconducting (HTS) microstrip lines and to be applied to quantum computers. The triplexer consists of three bandpass filters and branch lines. In the design of the bandpass filters, folded step impedance resonators (SIRs) are firstly used to achieve good stopband performances by harmonic suppression. Secondly, cross-coupling structures are also utilized to further improve the passband edge steepness of the bandpass filters. Finally, the parasitic transmission zeros originating from the assembling box sizes are employed to achieve a deeper out-of-band rejection. Three bandpass filters are designed and connected to the common input port of the triplexer. After that, the triplexer is coarsely optimized by advanced design system (ADS) for time-saving and is finely optimized by Sonnet for better accuracy. The optimized layout of the triplexer is fabricated on a 2-inch diameter and 0.5 mm thickness MgO wafer; here, the MgO wafer is double-sided coated with HTS YBa2Cu3O7 (YBCO) thin films. The measured passband bandwidths (return loss greater than 12 dB) of the triplexer are 6.420-6.680 GHz, 6.780-7.030 GHz, and 7.110-7.380 GHz, respectively, which satisfy the required design specifications.

Defining optimal thickness for maximal self-field in YBCO/CeO2 multilayers grown on buffered metal

The effect of multilayering YBa2Cu3O (YBCO) thin films with sequentially deposited CeO2 layers between YBCO layers grown on buffered metallic template is investigated to optimize the self-field critical current density . We have obtained that the improvement in clearly depends on the YBCO layer thickness and temperature, where at high temperature can be increased even 50% when compared with the single layer YBCO films. Based on our experimental results and theoretical approach to the growth mechanism during multilayer deposition, we have defined a critical thickness for the YBCO layer, where the maximal self-field is strongly related to the competing issues between the uniform and nonuniform strain relaxation and the formation of dislocations and other defects during the film growth. Our results can be directly utilized in the future coated conductor technology, when maximizing the overall in-field by combining both the optimal crystalline quality and flux pinning properties typically in bilayer film structures.

Synthesis and Characterization of 15N‐Labeled Poly(sulfur nitride) in Bulk and in Superconductor Composites

Abstract15N‐labeled tetrasulfur tetranitride (S415N4) was synthesized by reacting S2Cl2 with 15NH3. The reaction was finalized with 14NH3. The successful labeling was confirmed by solution 15N nuclear magnetic resonance (NMR) spectroscopy. S415N4 was used for the synthesis of poly(sulfur nitride) S15Nx via the intermediate species of S2N2. It was a topochemical polymerization in the solid state. The isotope ratio in the labeled polymer was obtained by laser deposition ionization time‐of‐flight mass spectroscopy. Solid‐state 15N NMR spectroscopy of S15Nx indicates that at least three different chemical environments for 15N atoms are present in the crystals. Finally, SNx was polymerized in the presence of two other superconductors, MgB2 and yttrium barium copper oxide (YBCO), which demonstrates the capability of SNx for grain boundary engineering.

High-Tc Josephson Junction Arrays for THz Applications

High-T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> superconductors (HTS) like yttrium barium copper oxide (YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-x</sub> ) pave the way towards readily available and precise voltage standards at liquid nitrogen temperatures. They can be driven by terahertz radiation, thus achieving higher output voltages with a significantly reduced junction count. The reduced effort in cooling also simplifies the overall application. The use of a gallium focused ion beam (Ga-FIB) represents a promising method to tailor the geometry of Josephson junctions after conventional patterning of an array to tune the junction parameters individually. In this work, we present a Josephson junction array made from the HTS YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-x</sub> based on grain-boundary Josephson junctions. The junction parameters are investigated and afterwards the influence of the Ga-FIB on the junctions is examined. This serves as an important step to show the suitability of this process for HTS voltage standards. Furthermore, the high frequency properties of the array and the associated Shapiro steps are characterized in the terahertz range. This technique represents an important step towards versatile HTS voltage standards.

Design Rules for Resistors, Capacitors and Inductors Fabricated From Single Layer Y-Ba-Cu-O Thin Films With Focused Helium Ion Beam Irradiation

Yttrium barium copper oxide (YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-<inline-formula><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula></sub> or YBCO) Josephson junctions fabricated using focused helium gas field ion sources show great promise for high transition temperature superconducting electronics. A unique feature of this technology is that it can also be utilized for the fabrication of resistors, capacitors and inductors in the same material and process step. The key to this method is that the electrical resistivity of high critical temperature superconductors is very sensitive to ion irradiation. The ions introduce disorder into the material which causes it to undergo a metal-to-insulator transition. By carefully controlling the position of the beam and ion dose delivered to the material, insulating pathways and reduced critical temperature metallic regions can be fabricated to construct the aforementioned passive components. We have prepared this manuscript to serve as a guide for circuit designers utilizing this process. We discuss the capabilities and limitations of helium ion beam lithographic patterning of YBCO and estimate the practical ranges of the values that can be obtained for resistors, capacitors and inductors in single layer thin films. Estimates are provided for two processes: one with the highest resolution with the smallest beam diameter (0.5 nm) and another based on the highest source current (100 pA) for fastest write time.

Experimental Study on Quench Protection Method for HTS Coil That Uses Cu Tape Co-Wound With HTS Tape

The authors previously proposed a quench protection method for a high-temperature superconducting (HTS) coil that uses Cu tape co-wound with HTS tape (Cu-CW method). In this method, when a quench occurs in the HTS coil, part of the current in the HTS coil is quickly transferred to the co-wound Cu tape coil by shorting the Cu coil with a resistor due to the tight magnetic coupling of both coils, and the hot-spot temperature of the HTS coil is reduced due to the quick reduction of the HTS coil current. The previous work showed by a numerical simulation that the method is effective to improve the quench protection performance compared with a commonly used detect and dump method (D&D method). In this work, the effectiveness of the method was studied by an experiment using small-scale test coils wound with yttrium barium copper oxide (YBCO) coated tapes to experimentally simulate quench behaviours of HTS coils of significant scale.

THz Microscopy With Josephson Cantilevers for Characterization of Additive Manufactured Spiral Phase Plates

Josephson cantilevers from high-temperature superconductors are versatile sensors to measure frequency and power of microwave and terahertz radiation in the range of 1 GHz to about 5 THz. They consist of at least one Josephson junction, which is fabricated from the high-temperature superconductor yttrium barium copper oxide (YBCO). The Josephson cantilever is mounted on a positioning system inside a vacuum chamber to perform three-dimensional scanning measurements in the THz microscope. The frequency and the power of external radiation can be determined from the recorded data by evaluating the occurring Shapiro steps. In this work, spiral phase plates (SPPs) optimized for the terahertz regime were additively manufactured with a fused filament fabrication 3D printer. Multiple SPPs were investigated and the results of two of them are shown, each made of a different thermoplastic. The SPPs are designed to transform Gaussian light beams into twisted light beams with an orbital angular momentum. An optically pumped molecular gas far-infrared laser system with difluoromethane as lasing medium can be employed as radiation source to generate frequencies between 1 THz and 1.6 THz with powers up to 125 mW. The beam is coupled into the THz microscope via quasi-optical windows and an evacuated optical path. The SPP is placed near the far-infrared laser to measure the far-field distribution. In this work, measurement results based on superconducting Josephson cantilevers are obtained with our unique THz microscope setup to characterize SPPs. The results present an important contribution for the evaluation of the design and the fabrication process of SPPs and showcase one of the multiple measurement modes of the THz microscope.