Oxygen Migration Barrier Research Articles

The spin-state effect on the redox performance of LaCoO3 perovskites

LaCoO3 is well-known for its unique thermally induced transition of Co3+ (3d6) ions from a low spin (LS) state to a higher spin state of intermediate spin (IS) state or high spin (HS) state, due to a delicate balance between crystal-field splitting and Hund’s coupling. In this work, we try to stabilize all possible spin states in the same initial structural model and further investigate the spin-state effect on the redox performance of LaCoO3. We find that an initial model of pseudocubic with R3¯c tilting octahedra was effective in stabilizing all possible spin states. The oxygen vacancy formation values of LS > HS + LS > HS > IS indicate that the IS state is the most optimal spin state in oxygen vacancy formation, which results from a weakened Co-O bonding energy by eg orbital occupation. The oxygen migration barriers of LS > IS > HS + LS > HS show that oxygen migration is easier in the relatively loose structure and thus LS structure is the most unfavorable in oxygen migration. Combining the oxygen vacancy formation and migration results, we conclude that the higher spin states of IS and HS are more beneficial than LS in oxygen conduction. Our results confirm the influence of the spin-state effect on oxygen conduction and show that spin-state regulation is a good strategy for improving the redox performance of perovskites.

Application of lattice expansion effect in SrCoO3 based cathodes by Ba doping with elevated electrochemical performances for low-temperature solid oxide fuel cells

Developing excellent-performance cathode materials is an inevitable and challenging obstacle in the process of developing practical solid oxide fuel cells, especially in low temperature range. In this paper, we introduce barium into the premium SrCoO3-based cathodes and research its consequent effect in the oxygen reduction reaction process. It is observed that the barium dopant could expand the lattice, produce more oxygen vacancies and at some extent reduce the thermal expansion coefficient of parent perovskite, which results from the expanded free space for oxygen migration and weakened Co–O bond by Ba doping. The polarization resistances of single cells with Sr1-xBaxCo0.8Sc0.1Nb0.05Ti0.05O3-δ cathodes (x = 0, 0.2 and 0.5, defined as SCSNTi, SB0.2CSNTi and SB0.5CSNTi, correspondingly) are 0.038, 0.025 and 0.016 Ω cm2 at 600 °C, respectively, and corresponding peak power density of 0.852, 1.054 and 1.217 W cm−2. The SB0.5CSNTi cathode is selected and it stably operates for 200 h at 550 °C. And it also exhibits excellent performance when CH4 is used as fuel and good stability for 100 h at 600 °C. First principle calculations prove that the Ba doping effectively reduces the oxygen vacancy formation energy and oxygen migration barrier. This work proves that the lattice expansion effect is an effective strategy for accelerating the oxygen exchange rate and designing high-performance cathode materials.

Mechanistic insights into the origin of the oxygen migration barrier

Electronic structure signatures of oxygen ion migration highlight new fundamental descriptors of the oxygen migration barrier based on the electronic structure of the local chemical environment.

Ni-doping effects on formation and migration of oxygen vacancies in SrFe1-xNixO3-δ oxygen carriers.

Ni is a promising B-site doping element capable of improving the oxygen carrier performance of SrFeO3 perovskite. In this work, the effect of Ni doping on the formation and migration of oxygen vacancies in SrFe1-xNixO3-δ (x = 0, 0.0625, 0.125, 0.1875, and 0.25) is investigated using density functional theory calculations. Our results show that the oxygen vacancies formed from Ni-O-Fe chains exhibit lower formation energy (Ef) compared to those from Fe-O-Fe chains in each doping system. Additionally, Ef generally decreases with an increase of Ni content. This Ni-promoted formation of VO is attributed to three factors: weakened Ni-O bonding, the closure of O-2p states to the Fermi level by Ni-O hybridization, and Ni3+ decreasing the positive charges to be compensated by VO formation. Due to these multiple advantages, a modest Ni doping of x = 0.25 can induce a higher PO2 and a lower T comparted to the relatively larger Co doping of x = 0.5, thermodynamically. Kinetically, Ni-doping appears to be a disadvantage as it hinders oxygen migration, due to a higher oxygen migration barrier through SrSrNi compared to the SrSrFe pathway. However, the overall oxygen ion conduction would not be significantly influenced by hopping through a nearby pathway of SrSrFe with a low migration barrier in a system doped with a small amount of Ni. In a word, a small amount of Ni doping has an advantage over Co doping in terms of enhancing the oxygen carrier performance of the parent SrFeO3 system.

Predicting Fast Oxygen Ion Conductors Via Descriptors for Migration Barrier Based on Electronic Structure and Lattice Dynamics

Solid-state oxygen ion conductors are of paramount importance to solid oxide fuel cells and electrolytic cells. However, with the oxygen ion conductors proposed to date, these technologies require too high (close to 800 oC) temperatures to operate, leading to technological challenges and high costs. Therefore, it is of primary importance to design faster oxygen ion conductors at intermediate and low temperatures (below 400 oC) that can enable sustainable energy technologies to mitigate climate change. Descriptors for oxygen ion conduction are highly desirable to identify promising materials, which can be done by leveraging fast-growing statistical and machine learning approaches for screening of material databases [1]. Recently, computational tools combined with experiments have allowed researchers to gain atomistic insights and relate ion transport to features of the lattice dynamics [2] and electronic structure [3] of a given material. In this work, building upon the previous literature, we leverage both the lattice dynamics and electronic structure to predict the migration barrier for oxygen migration in pure and mixed electronic ionic conductors and search for promising oxygen ion conductors.Using density functional theory simulations, we model oxygen migration in perovskite, rutile, fluorite, and Ruddlesden-Popperoxides. We analyze oxygen ion transport in pure and mixed electronic ionic conductors and oxygen vacancies with and without charge. We study changes in the electronic structure during oxygen migration within the solid host lattice in different oxides. By analyzing trends of migration barrier and electronic density of states, we relate the migration barrier to the electronic structure of the transition state. Our results show that the migration barrier depends on the capability that the host lattice has of screening charge associated with the mobile ion in the transition state, which if increased would lower the localization of charge around the mobile ion and in turn the oxygen migration barrier. In pure ionic conductors – where no charge is associated with the mobile ion - the migration barrier is largely dependent on the M-O strength. Based on the mechanistic understanding derived by these initial analyses, we further relate oxygen ion conductivity to the lattice dynamics. We show that in pure ionic conductors, increasing migration barrier follows trends of increasing oxygen vibrational frequency based on phonon-electron coupling, which also relates the prefactor of Arrhenius law with the migration barrier. However, when trying to predict trends of the migration barrier across different crystal structures or mixed ionic conductors, no single descriptor can capture the complex physiochemistry behind oxygen migration. Thus, we leverage statistical learning tools to identify multivariate descriptors and analyze specific features of lattice moieties that improve oxygen ion conduction. The results of this work provide mechanistic understanding of oxygen ion migration and strategies to accelerate the designs of fast oxygen ion conductors.

Suppressing the Dynamic Oxygen Evolution of Sodium Layered Cathodes through Synergistic Surface Dielectric Polarization and Bulk Site-Selective Co-Doping.

Utilizing anionic redox activity within layered oxide cathode materials represents a transformational avenue for enabling high-energy-density rechargeable batteries. However, the anionic oxygen redox reaction is often accompanied with irreversible dynamic oxygen evolution, leading to unfavorable structural distortion and thus severe voltage decay and rapid capacity fading. Herein, it is proposed and validated that the dynamic oxygen evolution can be effectively suppressed through the synergistic surface CaTiO3 dielectric coating and bulk site-selective Ca/Ti co-doping for layered Na2/3 Ni1/3 Mn2/3 O2 . The surface dielectric coating layer not only suppresses the surface oxygen release but more importantly inhibits the bulk oxygen migration by creating a reverse electric field through dielectric polarization. Meanwhile, the site-selective doping of oxygen-affinity Ca into Na layers and Ti into transition metal layers effectively stabilizes the bulk oxygen through modulating the O 2p band center and the oxygen migration barrier. Such a strategy also leads to a reversible structural evolution with a low volume change because of the enhanced structural integrality and improved oxygen rigidity. Because of these synergistic advantages, the designed electrode exhibits greatly suppressed voltage decay and capacity fading upon long-term cycling. This study affords a promising strategy for regulating the dynamic oxygen evolution to achieve high-capacity layered cathode materials.

Compressive-Strain-Facilitated Fast Oxygen Migration with Reversible Topotactic Transformation in La0.5Sr0.5CoOx via All-Solid-State Electrolyte Gating

Modifying the crystal structure and corresponding functional properties of complex oxides by regulating their oxygen content has promising applications in energy conversion and chemical looping, where controlling oxygen migration plays an important role. Therefore, finding an efficacious and feasible method to facilitate oxygen migration has become a critical requirement for practical applications. Here, we report a compressive-strain-facilitated oxygen migration with reversible topotactic phase transformation (RTPT) in La0.5Sr0.5CoOx films based on all-solid-state electrolyte gating modulation. With the lattice strain changing from tensile to compressive strain, significant reductions in modulation duration (∼72%) and threshold voltage (∼70%) for the RTPT were observed, indicating great promotion of RTPT by compressive strain. Density functional theory calculations verify that such compressive-strain-facilitated efficient RTPT comes from significant reduction of the oxygen migration barrier in compressive-strained films. Further, ac-STEM, EELS, and sXAS investigations reveal that varying strain from tensile to compressive enhances the Co 3d band filling, thereby suppressing the Co-O hybrid bond in oxygen vacancy channels, elucidating the micro-origin of such compressive-strain-facilitated oxygen migration. Our work suggests that controlling electronic orbital occupation of Co ions in oxygen vacancy channels may help facilitate oxygen migration, providing valuable insights and practical guidance for achieving highly efficient oxygen-migration-related chemical looping and energy conversion with complex oxides.

Systematic studies of the effects of group-III dopants (La, Y, Al, and Gd) in Hf0.5Zr0.5O2 ferroelectrics by ab initio simulations

La-doped Hf0.5Zr0.5O2 (HZO) ferroelectrics have demonstrated great potential to solve the endurance challenge of hafnia-based ferroelectric memory. In this work, we systematically studied the doping effects of La in HZO by ab initio simulations and theoretically compared it with three other commonly used group-III dopants (Al, Y, and Gd). The physical mechanisms behind superior endurance are thoroughly analyzed based on the calculation results regarding phase stability, oxygen vacancy formation energy, migration barrier, and electronic structures. It has been discovered that among the four dopant candidates, La has the strongest stabilization effect of the ferroelectric phase in HZO. Also, under stoichiometric doping conditions, La and other group-III dopants were observed to increase the oxygen vacancy formation energy and make HZO less susceptible to dielectric breakdown. Finally, La, Al, or Y dopants replacing Hf or Zr can getter migrating oxygen vacancies and passivate the associated defect states in the bandgap. Based on these observations, guidelines were proposed for designing the doping method and concentrations to achieve the best endurance.

Theoretical investigation of formation and diffusion mechanisms for point defects in ytterbium and lutetium silicates

AbstractUnderstanding the mechanism of point defects and the oxygen vacancy diffusion in rare earth (RE) silicates is important to evaluate their performance as environmental barrier coatings. In this work, the defect formation energies are calculated and the similar predominant native point defect type, that is, O Frenkel defect, in RE2SiO5 and RE2Si2O7 (RE = Yb and Lu) is uncovered. Furthermore, the nonstoichiometry related defects and phase composition in RE2SiO5 and RE2Si2O7 is also studied. For RE2SiO5, or is the predominate defect complex accompanied with the RE2Si2O7 separation under SiO2‐rich condition, while or is favorable under RE2O3‐rich condition. In the case of RE2Si2O7, or is the favorable defect complex under SiO2‐rich condition while or dominates the defects, accompanied with the formation of RE2SiO5, under RE2O3‐rich case. Finally, the high oxygen migration barriers are revealed for both RE2SiO5 and RE2Si2O7, indicating the low oxygen permeability in these silicates. These results will not only guide the future performance optimization of RE2SiO5 and RE2Si2O7 through tailoring their composition, but also suggest their potential application as oxidation protective coatings.

Trade‐Off Between Data Retention and Switching Speed in Resistive Switching ReRAM Devices

AbstractMemristive switching devices are promising for future data storage and neuromorphic computing applications to overcome the scaling and power dissipation limits of classical CMOS technology. Many groups have engineered bilayer oxide structures to enhance the switching performance especially in terms of retention and device reliability. Here, introducing retention enhancement oxide layers into the memristive stack is shown to result in a reduction of the switching speed not only by changing the voltage and temperature distribution in the cell, but also by influencing the rate‐limiting‐step of the switching kinetics. In particular, it is demonstrated that by introducing a retention enhancement layer into resistive switching SrTiO3 devices, the kinetics are no longer determined by the interface exchange reaction between switching oxide and active electrode, but depend on the oxygen ion migration in the additional interface layer. Thus, the oxygen migration barrier in the additional layer determines the switching speed. This trade‐off between retention and switching speed is of general importance for rational engineering of memristive devices.

Effective Ca2+-doping in Sr1-xCaxFeO3-δ oxygen carriers for chemical looping air separation: A theoretical and experimental investigation

Perovskite iron oxides are promising oxygen carrying materials due to their effectiveness and the low cost of iron. The effect of Ca2+ doping on oxygen ion diffusion in Sr1-xCaxFeO3-δ (x = 0, 0.125, 0.25, 0.375, 0.5) is investigated by combining density functional theory (DFT) calculations and experimental measurements. The oxygen ion diffusion is determined by two key factors of oxygen vacancy formation and migration. The DFT results show that the oxygen vacancy formation energies greatly decrease as Ca2+ content reaches x = 0.125, then gradually decrease with Ca2+ contents up to 0.375, and finally increase as the Ca content reaches x = 0.5. A combination of experimental thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) results corroborate this trend for Ca2+ contents between 0 and 0.4. The Fe-O bonding dominates the effect of Ca2+ doping on the oxygen vacancy formation. Shortened Fe-O bonds cause the decrease in the formation energy at lower Ca2+ contents, while the lengthened bonds by FeO6 octahedron distortion cause the increase in the formation energy at higher Ca2+ contents. Kinetically, the oxygen migration barrier is lowered upon Ca2+ doping through the increasing lattice spacing for oxygen diffusion. Therefore, an appropriate Ca2+ doping of x = 0.125–0.375 promotes the oxygen ion diffusion in Sr1-xCaxFeO3-δ. Our findings provide the effective Ca2+ doping value for Sr1-xCaxFeO3-δ and a material design clue for the isovalent A-site doping system of oxygen carriers.

Native point defects and oxygen migration of rare earth zirconate and stannate pyrochlores

Various excellent properties of rare earth zirconate and stannate pyrochlores are close related with their native point defects. First-principles calculations are performed to systematically investigate the point defect mechanism and the oxygen diffusion behavior of A2B2O7 (A=La, Ce, Pr, Nd, Pm, Sm, Eu, Gd; B=Zr, Sn). The possible defect complexes and their associated reactions under stoichiometric and nonstoichiometric conditions are explored. The O Frenkel pairs are the most stable defect structure in stoichiometric zirconates, whereas the cation antisite defects are the predominant one in stoichiometric stannates. In the case of BO2 excess zirconates and stannates, the BA cation antisite defect with the A vacancy and/or the oxygen interstitial is energetically favorable, whereas the AB antisite defect together with the oxygen vacancy and/or the A interstitial is preferable under the A2O3 excess condition. Meanwhile, the maximum point defect concentrations of zirconates are much higher than those of stannates. Furthermore, the oxygen migration barriers are similar in these compounds, ranging in 0.68 eV∼ 0.80 eV. The predicted point defects and oxygen diffusion mechanisms play the critical role in their engineering applications and are expected to guide the future property improvement of pyrochlores through the control of point defects and/or composition.

∑3 Twin Boundaries in Gd2Ti2O7 Pyrochlore: Pathways for Oxygen Migration

Understanding the chemistry at the twin boundaries is a well-recognized challenge which could enable the capabilities to manipulate the functional properties in complex oxides. The study of this atomic imperfection becomes even more important, as the presence of twin boundaries has been widely observed in materials, regardless of the dimensionalities, due to the complexities in the growth methods. In the present study, we demonstrate the atomic scale insights on an Ʃ3(111 ̅) <11 ̅0> twin boundary present in pyrochlore-structured Gd2Ti2O7 using the atomic-resolution electron microscopy and atomistic modeling. The formation of the observed TB occurs along (111 ̅) with 71o angle between the two symmetrically arranged crystals. We observe distortions (~3-5% strain) in the atomic structure at the TB with an increase in Gd-Gd (0.66± 0.03nm) and Ti-Ti (0.65± 0.02 nm) bondlengths in the (11 ̅0) plane, as compared to 0.63 nm in the ordered structure. Using atomistic modeling, we further calculate the oxygen migration barrier for vacancy hoping at 48f-48f sites in the pyrochlore structure which is the primary diffusion pathway fast oxygen transport. The mean migration barrier is lowered by ~25% to 0.9 eV at the TB as compared to 1.23 eV in the bulk, suggesting the ease in the oxygen transport through the Ʃ3 twin boundaries. Overall, these results offer a critical understanding of the atomic arrangement at the twin boundaries in pyrochlores, leading to control of the interplay between defects and properties.

Investigation of the oxidation behavior and high oxidation-resistant mechanism of Ti(C,N)-based cermets

The oxidation kinetics and mechanisms of Ti(C,N)-based cermets have been studied systematically in this work. The continuously stable NiCo2O4-spinel and (Co,Ni)WO4 film are the keys to providing essential reassurance for low oxidation rates in conventional cermets. After the addition of alloyed Cr, the oxidation weight gain of the cermet significantly decreased. The superior oxidation-resistant performance of Cr-doped cermet was a result of the formation of Cr(W,Mo)O4, which showed high stability and a high oxygen migration barrier energy. The distribution of Cr(W,Mo)O4 in the intermediate oxide layer reduced the ions mobility during the oxidation process.

Heterointerface Engineered Oxygen Electrode for High Performance Reversible Solid Oxide Fuel Cells (R-SOFCs)

Solid oxide fuel cells (SOFCs) are promising alternatives to combustion technology for electric energy production due to no emission and high efficiency in chemical to electric energy conversion. Despite such advantages, the commercialization of SOFCs is hindered by the high operating temperature, resulting in a few problems, such as expensive system cost and short lifetime. Thus, while reduced-temperature SOFCs have been a long-lasting interest in the SOFC community, the sluggish oxygen reduction reaction (ORR) occurring at the oxygen electrode at intermediate temperature is the most critical challenge for the enhanced overall performance of SOFCs. As a promising strategy to achieve higher catalytic activity of oxygen electrode, the infiltration method has been employed due to not only extended active site for ORR by electrode surface decoration with active nanoparticle catalysts, but enriched oxygen vacancies additionally formed on the surface of infiltrates. Furthermore, heterointerface engineering in the infiltrated oxygen electrode has, more recently, emerged as a promising approach to optimize oxygen electrode performance. The lattice strain, induced by lattice parameter mismatch in heterostructured materials, can significantly influence the ORR/OER (oxygen evolution reaction) kinetics by changing oxygen defect formation energy and migration barrier. We report the enhancement in the electrochemical performance of the La0.6Sr0.4Co0.2Fe0.8O3 (LSCF) based heterostructured oxygen electrode, when infiltrated with aliovalent cation doped La2-xAxNi1-yByO4 (Ruddlesden-Popper, RP), leading to different intrinsic catalytic ability according to dopant; Sr and Co for A and B site, respectively, to generate oxygen defect (e.g., oxygen vacancy or interstitial O2-). This study demonstrates the impact of the oxygen defect in the infiltrates on the heterointerface, dominating ORR & OER kinetics in the heterostructured oxygen electrode, and investigate the primary oxygen defect for RP structured infiltrate to realize high ORR & OER activity. To characterize the morphology of infiltrates anchored on the oxygen electrode surface and the heterointerface synthesized between infiltrated layers and backbones, scanning electron microscope (SEM) and transmission electron microscopy (TEM) are performed. The electrochemical performances of the infiltrated SOFCs were examined by electrochemical impedance spectroscopy and analyzed in terms of the distribution of relaxation time (DRT) from impedance data. Thermogravimetric analysis (TGA) and iodometric titration are conducted to understand the correlation between oxygen defect produced by aliovalent doping and electrochemical ORR activity.

Improved oxidation performance of TiAl alloy by a novel Al–Si composite coating

A novel Al–Si composite coating was fabricated on γ-TiAl by the combination of magnetron sputtered Al coating and subsequently electrodeposited SiO2 coating. The oxidation performance of the specimens was evaluated in static air at 900 °C. Results shown that the Al–Si composite coating can act as an efficient oxygen migration barrier and provide good oxidation resistance. During the oxidation process, an Al2O3 enriched layer formed beneath the composite coating. The interfacial reaction between the composite coating and alloy resulted in the generation of Al2O3 and Ti5Si3.

First-principles study of oxygen reduction reaction on Pd-doped LaxSr1-xCoyFe1-yO3-δ cathodes of solid oxide fuel cells

Surface adsorption, adissociation and bulk migration behaviors of oxygen species on Pd-doped LSCF (LSCF-Pd) cathode are investigated with first-principle method. Results show that Pd-doping reduces largely the formation energy of oxygen vacancy on LSCF-Pd surface. Oxygen adsorption abilities on LSCF and LSCF-Pd surfaces are comparable (1.30 vs 1.32 eV) with oxygen vacancies, while on perfect LSCF surface that is weakened by Pd-doping. The minimum dissociation energy barriers of oxygen molecules on LSCF and LSCF-Pd surface are 0.48 and 0.34 eV, respectively, which indicates that Pd-doping improves oxygen dissociation behaviors. Also, migration barriers of oxygen vacancy in LSCF-Pd bulk is comparable to that in LSCF bulk. The improved mechanisms can be attributed to the lowered formation energy of oxygen vacancy, oxygen dissiciation barriers of innate oxygen defect and migration barriers of oxygen vacancy in the bulk by Pd-doping.

First-Principles Study of Anisotropic Oxygen Diffusion in PrBaCo2O5.5.

We address the anisotropic oxygen diffusion in PrBaCo2O5.5 using first-principles calculations based on the density functional theory. First, the experimentally observed magnetic properties such as ferromagnetic, ferrimagnetic, and paramagnetic phases are examined through systematic consideration of cobalt spin ordering and oxygen vacancy position. Then, the diffusion mechanism of an oxygen atom, assumed to be externally supplied, is explored by evaluating the oxygen migration barriers with the formation of one-dimensional oxygen-vacancy channel.

First-principles calculations of the oxygen-diffusion mechanism in mixed Fe/Ti perovskites for solid-oxide fuel cells

Abstract The ionic conductivity of transition-metal (TM) oxide perovskites plays an essential role in their applications in solid-oxide fuel cells. The conductivity of oxygen ions can increase the reaction rate on the electrode surface and improve the performance of fuel-cell devices. Herein, the oxygen-diffusion mechanism in a series of Fe/Ti oxide perovskites, especially oxygen-vacancy formation and migration, was investigated using density functional theory calculations. By simulating various vacant sites, we found that the oxygen vacancy adjacent to the Fe cation has lower formation energy than that between two Ti cation sites. Analysis of differential charge densities demonstrated that electrons originating from oxygen vacancies are reorganized at the d -state of Fe through the weak covalency of TM–O bonds, resulting in the low formation energy of these vacancies. The energy profiles of oxygen migration around Fe and Ti cations were calculated in the rocksalt supercell of SrFe0.5Ti0.5O3 through the nudged-elastic-band method. The oxygen migration barrier around Ti cations was lower than that of Fe cations, which suggests that Ti cations also play an important role in oxygen diffusion in the perovskites. Overall, our study elucidated the oxygen-diffusion mechanism in the B-sites of mixed Fe/Ti oxide perovskites and provides a theoretical basis for the design of TM oxide perovskites with mixed ionic and electronic conductivity for solid-state fuel cells.

Electronic Origin of Oxygen Transport Behavior in La-Based Perovskites: A Density Functional Theory Study

Understanding the oxygen transport behavior in perovskites is of central importance for tailoring their physical and chemical properties to various practical applications. In this contribution, periodic DFT+U calculations have been performed to unravel the electronic origin of the oxygen mobility difference in La-based perovskites involving 3d-block transition metals from Sc through Cu. Calculated results indicate that the perovskites generally exhibit an increased reducibility on going from LaScO3 to LaCuO3, and the exceptionally high oxygen vacancy formation energy in LaFeO3 is due to the significant lowering of the electron exchange stabilization upon reduction. The oxygen migration barrier in the first four perovskites varies from 1.2 to 2.1 eV while that for the later five materials is much lower and lies between 0.4 and 0.9 eV. Electronic structure analysis indicates this abrupt change in the migration barrier can be attributed to the different degrees of charge redistribution on the central transit...