Diffusion Of Hydrogen Atoms Research Articles

Molecular Dynamics Analysis of Hydrogen Diffusion Behavior in Alpha-Fe Bi-Crystal Under Bending Deformation

The hydrogen embrittlement (HE) phenomenon occurring in drawn pearlitic steel wires sometimes results in dangerous delayed fracture and has been an important issue for a long time. HE is very sensitive to the amount of plastic deformation applied in the drawing process. Hydrogen (H) atom diffusion is affected by ambient thermal and mechanical conditions such as stress, pressure, and temperature. In addition, the influence of stress gradient (SG) on atomic diffusion is supposed to be crucial but is still unclear. Metallic materials undergoing plastic deformation naturally have SG, such as residual stresses, especially in inhomogeneous regions (e.g., surface or grain boundary). In this study, we performed molecular dynamics (MD) simulation using EAM potentials for Fe and H atoms and investigated the behavior of H atoms diffusing in pure iron (α-Fe) with the SG condition. Two types of SG conditions were investigated: an overall gradient established by a bending deformation of the specimen and an atomic-scale local gradient caused by the grain boundary (GB) structure. A bi-crystal model with H atoms and a GB structure was subjected to bending deformation. For a moderate flexure, bending stress is distributed linearly along the thickness of the specimen. The diffusion coefficient of H atoms in the bulk region increased with an increase in the SG value. In addition, it was clearly observed that the direction of diffusion was affected by the existence of the SG. It was found that diffusivity of the H atom is promoted by the reduction in its cohesive energy. From these MD results, we recognize an exponential relationship between the amount of H atom diffusion and the intensity of the SG in nano-sized bending deformation.

Mathematical Modelling of the Impact of IR Laser Radiation on an Oncoming Flow of Nanoparticles with Methane

Introduction. The study is devoted to the numerical investigation of laser radiation’s effect on an oncoming two-phase flow of nanoparticles and multicomponent hydrocarbon gases. Under such exposure, the hydrogen content in the products increases, and methane is bound into more complex hydrocarbons on the surface of catalytic nanoparticles and in the gas phase. The hot walls of the tube serve as the primary source of heat for the reactive two-phase medium containing catalytic nanoparticles. Materials and Methods. The main method used is mathematical modelling, which includes the numerical solution of a system of equations for a viscous gas-dust two-phase medium, taking into account chemical reactions and laser radiation. The model accounts for the two-phase gas-dust medium’s multicomponent and multi-temperature nature, ordinary differential equations (ODEs) for the temperature of catalytic nanoparticles, ODEs of chemical kinetics, endothermic effects of radical chain reactions, diffusion of light methyl radicals CH3 and hydrogen atoms H, which initiate methaneconversion, as well as absorption of laser radiation by ethylene and particles. Results. The distributions of parameters characterizing laminar subsonic flows of the gas-dust medium in an axisymmetric tube with chemical reactions have been obtained. It is shown that the absorption of laser radiation by ethylene in the oncoming flow leads to a sharp increase in methane conversion and a predominance of aromatic compounds in the product output. Discussion and Conclusion. Numerical modelling of the dynamics of reactive two-phase media is of interest for the development of theoretical foundations for the processing of methane into valuable products. The results obtained confirm the need for joint use of mathematical modelling and laboratory experiments in the development of new resource-saving and economically viable technologies for natural gas processing.

Modeling and characterization of low frequency noise in self-aligned top-gate coplanar IGZO thin-film transistors

Abstract A modified low-frequency noise (LFN) model was proposed to accurately estimate the quality of the gate dielectric in self-aligned top-gate (SA TG) coplanar structure indium–gallium–zinc oxide (IGZO) thin-film transistors (TFTs). The proposed LFN model was derived by modifying the conventional carrier number with correlated mobility fluctuation model considering the peculiar characteristics of SA TG coplanar IGZO TFTs such as the channel length reduction due to the diffusion of hydrogen atoms or oxygen vacancies from the source/drain to the channel, as well as the relatively large source/drain parasitic resistance. The proposed model was validated by demonstrating that the measured LFN values were in good agreement with the predicted values from the proposed model for all SA TG coplanar IGZO TFTs with SiO2 gate dielectrics deposited under different plasma-enhanced chemical vapor deposition (PECVD) power densities. The near-interface gate dielectric trap densities extracted from each TFT using the proposed LFN model revealed a clear increase as the PECVD power increased, which is considered a major cause of poor positive-bias-temperature-stress stability of the SA TG coplanar IGZO TFT with SiO2 gate dielectric deposited under high PECVD power conditions.

A highly efficient method for characterizing the kinetics of hydrogen evolution reaction

PurposeThe purpose of this study is to provide a highly efficient method to obtain the kinetics of the hydrogen evolution reaction (HER) on metal electrodes in an alkaline solution and to analyze the effect of thiourea addition on HER under the same cathodic overpotential.Design/methodology/approachA novel method based on hydrogen permeation tests, potentiodynamic polarization tests and electrochemical impedance spectroscopy was put forward to characterize the HER kinetics on metal electrode.FindingsThe study found that adding thiourea accelerated the Volmer, Heyrovsky and Tafel reactions associated with HER. In addition, it reduced the hydrogen surface coverage and increased the hydrogen permeation steady-state current density. As a result, thiourea facilitated HER, promoted the diffusion of hydrogen atoms into iron and reduced the number of hydrogen atoms in the adsorbed state.Originality/valueThis work provides novel insights into the influence of thiourea on HER kinetics, demonstrating that thiourea addition can significantly enhance HER efficiency by altering reaction dynamics and promoting hydrogen atom diffusion into iron. This has implications for hydrogen energy applications, cathodic protection and understanding hydrogen embrittlement mechanisms.

Size-dependent activity modulation of supported Ni nanocatalysts for efficient solid-state hydrogen storage in magnesium

The activity of Nickel (Ni)-based catalysts strongly depends on their particle size and dispersion; however, achieving controllable preparation of uniform particle size with high activity remains a great challenge for Ni-based catalysts to promote efficient hydrogen storage. Here, we employ a facile Carbothermal Shock (CTS) method to obtain carbon fiber-loaded Ni-based nanocatalysts (Ni@CC) with high dispersibility and size-dependent properties, which can exhibit superior catalytic effects for solid-state hydrogen storage in MgH2. It was found that the shorter the CTS duration, the smaller the size of the Ni nanoparticles, and the better the catalytic effect. Among these, the MgH2-Ni@CC with a CTS duration of 30 s showed the best hydrogen storage performance. Its activation energy for hydrogen release was significantly decreased from 158.3 kJ⋅mol−1 for milled MgH2 to 98.6 kJ⋅mol−1. More importantly, the retention rate of hydrogen absorption capacity is 95.1 % after 30 cycles, which far exceeds the 65.5 % retention rate observed in milled MgH2. These property enhancements can be attributed to the presence of nano-sized Ni and its in situ derived Mg2Ni intermediate phases, which create more channels for hydrogen atoms diffusion. Meanwhile, the close contact between nano-Ni and the Mg/MgH2 matrix can provide active catalytic sites and low-energy interfaces for facilitating hydrogen adsorption and desorption. Our study presents a promising approach to significantly improve the hydrogen storage performance of MgH2 by modulating size-dependent catalytic activity.

Circular Economy Opportunity Utilizing Fitness for Service Methodology for Aged HIC Defected Reboiler

The phenomenon of Hydrogen-Induced Cracking (HIC) is a cracking mechanism of carbon steel material as in ASME SA- 516 pressure containing equipment operating in a wet sour H2S environment. Such phenomenon is mainly driven by the diffusion of hydrogen atoms into the carbon steel due to corrosion reaction. The Structural integrity of an in-service equipment that contain a flaw or damage such as HIC could be scrutinised using Fitness For Service (FFS) assessments as quantitative engineering evaluations. The assessments are conducted using methodologies specifically prepared for pressurized equipment. These assessments provide standard procedure that can be used to determine if pressurized equipment containing flaws could continue to operate safely for certain period of time. FFS assessments are recognized and referenced by the API Codes and Standards such as API- 510, 570, & 653, and by National Board-23. Those assessments are considered suitable methodologies for evaluating the structural integrity of pressurized equipment as heat exchangers, pressure vessels, piping systems and storage tanks where inspection has revealed degradation and flaws in the equipment. The objective of this paper isto illustrate API-579 case study of HIC of fifty (50) years operating pressurized equipment, namely reboiler.

Investigation of the effect of temperature and applied electric field on the aluminum-water reaction by ReaxFF molecular dynamics

Hydrogen energy is gaining attention as a non-polluting source. Aluminum’s reaction with water for propulsion and hydrogen production is widely used, but its nanoscale characteristics are unexplored. This study investigated aluminum hydrolysis in water vapor by ReaxFF-MD, examining effects of temperature and electric field. The oxidation of the aluminum surface is accompanied by aluminum dissolution, hydrogen generation and H3O+ formation, Formed hydrides and oxides were AlH3 and Al2O3. Hydrogen disappearance at 700 K and 900 K was due to conversion to AlH3. The diffusion of hydrogen and oxygen atoms in the Z direction was enhanced at increasing temperatures, Outer aluminum atoms preferentially reacted with oxygen to form Al2O3, while inner atoms reacted with hydrogen to form AlH3, the loosely packed outer oxide layer contains inclusions of AlH3. Studies at room temperature under different electric fields showed −Z field promoted the reaction while + Z field inhibited it, attributed to different electric field strengths’ effect on OH– ion electron-sharing Coulomb equilibrium, resulting in varying rates of hydroxide polar covalent bond cleavage. Our results clarify the atomic-scale effects of temperature and electric field on the aluminum-water reaction, providing guidance for optimizing experimental conditions and enhancing the efficiency of hydrogen production.

Hydrogen diffusion and precipitation influenced by non-uniformly distributed stress in zirconium alloy with different textures

Hydrogen embrittlement is a crucial factor for the performance and life of zirconium alloys in nuclear industry. During service, the residual stress in the materials induces re-distribution of hydrogen, which further affects the fracture behavior. This study is dedicated to investigating the hydrogen diffusion and precipitation under the meso‑scale non-uniform deformation field. The texture effect of hydrogen behavior was examined by considering three different texture scenarios: grains with c-axis deviating from the tensile direction of random angle, 0°and 90° The cases were termed Random, T000, and T0900 respectively. The crystal plasticity finite element method (CPFEM) was employed to simulate the stress-assisted diffusion of hydrogen atoms in the polycrystalline zirconium alloy. It is determined that the T0900 case gets fewer regions with higher hydrostatic stress gradient, which helps relieve the hydrogen concentration. Compared to the T0900 texture, the interaction between soft and hard grains in the Random and T000 texture conditions results in higher stress gradient and severe hydrogen concentration. Statistical analysis was conducted and the hydrogen concentration in the three textures presents a normal distribution. T0900 gets a relatively lower overall hydrogen concentration while the T000 texture gets severe hydrogen concentration larger than 120 wt.ppm. In Random and T000 textures, hydrogen tends to accumulate at grain interior and boundaries, and continuous hydrogen concentration band forms along adjacent GBs. The T0900 scenario is free of large continuous hydrogen concentration zones, which helps reduces the adverse effects of hydrogen diffusion and precipitation. The findings of the work advance the understanding of the hydrogen behavior affected by stress heterogeneity and texture, which is the basis for the exploration of hydrogen embrittlement.

Effect of Adding Al on the Phase Structure and Gettering Performance of TiZrV Non-Evaporable Getter Materials.

Titanium zirconium vanadium (TiZrV) is a widely used non-evaporable getter (NEG) material with the characteristics of a low activation temperature and a large gas absorption capacity. At present, the research on TiZrV getters mainly focuses on the thin-film state, with little research on the bulk state. In this paper, a TiZrV getter was optimized by adding Al, and the phase structure, activation properties, and gettering performance were studied. With the addition of Al, the α-Zr phase and Ti2Zr phase changed into the Ti-Zr phase and Al-Zr, Al-Ti phase. The newly generated phase promoted the diffusion of hydrogen and oxygen atoms. The activation temperature decreased significantly, as shown in the in situ XPS results. The H2 and CO gettering performance of TiZrVAl samples was promoted to 2073 cm3·s-1 and 1912.8 cm3·s-1, increased by 40.7% and 40.3%. This paper provides valuable ideas for optimizing the properties of bulk TiZrV getters.

Feeling the strain: Enhancing the thermodynamics characteristics of magnesium nickel hydride Mg2NiH4 for hydrogen storage applications through strain engineering

This work is based on density functional theory (DFT) and studies the structural, electronic, thermodynamic properties and dehydrogenation kinetics of the hydride Mg2NiH4 under different uniaxial and biaxial strain applied to Mg2Ni or Mg2NiH4. structural properties are first studied based on generalized gradient (GGA) and local density (LDA). Thermodynamic and electronic properties and dehydrogenation kinetics are then studied using the GGA method based on the Perdew-Burke-Ernzerhor (PPE) approximation. The results obtained show that uniaxial/biaxial tensile and compressive strains are capable of inducing structural deformation by increasing the value of the strain step on both Mg2Ni and Mg2NiH4, and that these strains applied to Mg2NiH4 are capable of reducing the stability of the system more than strains applied to Mg2Ni, due to the contribution of strain energy. More specifically, it lowers the enthalpy of formation to −40 kJ/mol.H2 under compressive strain ε = −7.5% or biaxial tensile strain ε = +7.8%, which corresponds exactly to the ideal value suggested by the US Department of Energy (DOE) for materials suitable for hydrogen storage. And the decomposition temperature fell within the fuel cell operating range (PEM) of 289–393 K. On the other hand, under uniaxial and biaxial strains, the activation energy of hydrogen atom diffusion in Mg2NiH4 varied between 0.40 eV and 0.22 eV, resulting in a remarkable improvement in dehydrogenation properties. Analysis of the total (TDOS) and partial (PDOS) density curves shows that the Mg2NiH4 system has a metallic characteristic, and that this characteristic is maintained by increasing the strain pitch, with a variation in the energy width of the valence band.

Reconstructing brittle hydrides using pulsed electric current to restore the degraded performance of zirconium alloys

When zirconium alloy undergoes water corrosion reaction during the service process, it absorbs hydrogen to form brittle hydrides, which is one of the main reasons for the deterioration of the mechanical properties of zirconium alloy. There is an urgent need to find an effective method to regulate brittle hydrides to restore the properties of hydrogen-containing zirconium alloys. This study conducted electropulsing treatment on the hydrogen-charged nuclear grade Zr-4 alloy, and the results showed that the electropulsing process caused the hydrides to transform from large-sized brittle stripe-shaped δ-phase to the small-sized ζ-phase. The hydrogen content in the alloy is significantly reduced, which basically restores the mechanical properties of the alloy. However, in the comparative experiment of isothermal heat treatment at 400 °C, brittle hydrides did not dissolve and their mechanical properties did not recover. A mathematical model was established for the characteristics and morphological changes of strip hydrides, and the current density distribution and introduced free energy during the microstructure evolution process were calculated and analyzed. The calculation results indicate that the pulsed current promotes the decomposition of hydrides through the introduction of free energy, reduces the activation energy of hydrogen atom diffusion, accelerates the diffusion and desorption of hydrogen atoms, and realizes the repair of mechanical properties of hydrogen-charged zirconium alloy.

Hydrogen diffusion dynamics on [formula omitted] surface: A mechanism of hydrogen-induced failure

Hydrogen-induced failure (embrittlement as the primary source) is a significant concern for retrofitting existing pipelines to transport hydrogen. One of the major factors associated with hydrogen embrittlement of metals is hydrogen diffusion. Therefore, understanding the modes and dynamics of hydrogen diffusion into metals is critical for understanding better and acting to limit hydrogen-induced damage to metals. It is well established that transition metals catalyze the dissociation of molecular hydrogen into atomic hydrogen even at room temperature. The atomic hydrogen diffuses through the metal surface, and this causes degradation. Understanding atomic hydrogen diffusion dynamics is critical to reducing hydrogen embrittlement. This work presents atomic hydrogen diffusion dynamics along and into Fe(100) surfaces. The results indicated that diffusion of atomic hydrogen along the surface is favored over surface-to-subsurface diffusion. Once hydrogen diffuses to the subsurface layer, the barrier for further hydrogen diffusion into the subsequent layers is relatively lower. The methodology presented here of atomic hydrogen diffusion under dynamic relaxation into metal surface can be used to study the effect of the metal's chemical composition and structure on the hydrogen diffusion rate. This allows for screening various strategies to reduce hydrogen diffusion into metals and guide the design of degradation prevention strategies.

Structure and RF performance evolution of polycrystalline silicon charge capture layer for advanced RF-SOI in in-situ annealing process

In this paper, the structures and radio-frequency (RF) properties of high resistivity silicon (HR-Si) wafers with a polycrystalline silicon (Poly-Si) charge capture layer after in-situ annealing were investigated. The thermal treatment significantly improves the wafer warpage and optimize the resistivity of Poly-Si/HR-Si interfaces. By using spreading resistance profiling (SRP), energy dispersive spectrometer (EDS) and secondary ion mass spectrometry (SIMS) technology, the rise of interfacial resistivity may be as results of the pyrolysis of the native oxide and the diffusion of hydrogen atoms. The transmission Kikuchi diffraction (TKD) analysis exhibited that the grains were recrystallized during the annealing, leading to the transformation from the small angle boundaries (SAGBs) into low-Σ coincidence lattice grain boundaries (CSL GBs). The drop of the bulk resistivity of the Poly-Si layer is attributed to the reduction of the total grain boundary (GB) density and the increase of the low electro-activity GB density. Moreover, the microwave losses and non-linearity of the RF-SOI with embedded Poly-Si layer was evaluated by on-chip testing based on CPW. It was determined that the decrease in the Poly-Si resistivity only worsens the microwave losses but not the non-linearity.

Effect of ionic liquids on the corrosion behaviour of X80 pipeline steel

The study encompasses the synthesis of an ionic liquid corrosion inhibitor using the ion exchange method. Its impact on the corrosion and hydrogen permeation behaviour of X80 pipeline steel in a CO2 environment is thoroughly investigated. The findings reveal that the corrosion resistance and hydrogen atom diffusion of X80 pipeline steel exhibit an initial decline, followed by an increase with escalating inhibitor concentration. The nadir values are recorded at an inhibitor concentration of 500 mg·L−1, attaining a remarkable maximum inhibition efficiency of 97%. Following the addition of corrosion inhibitors, the formation of corrosion products notably decreases, indicating a positive inhibition effect on both corrosion and hydrogen permeation. Additionally, a correlation is successfully established between hydrogen permeation parameters and inhibitor concentration.

Fitness-for-Service assessment of a Hydrogen-Induced crack in an inlet gas separator pressure vessel using computational modelling

Hydrogen-induced cracking is the cracking of carbon steel or low-alloy steel in a wet H2S environment, driven by the diffusion of hydrogen atoms into the steel due to corrosion reaction. The formation of blisters and hydrogen-induced cracks in pressurized components in the oil and gas or petrochemical industries imposes a serious risk to personnel safety and production continuity. In this study, a fitness-for-service assessment of a gas separator pressure vessel containing 3.76 % H2S and 3.47 % CO2 was analyzed using finite element analysis as required by level III assessment in API 579–1/ASME FFS-1 2021. Different load scenarios, including internal pressure, static head from liquid, dead weight, and wind loads, were considered using elastic-perfectly plastic stress analysis. The hydrogen-induced affected area, with dimensions of 2650 mm × 900 mm, was shown to sustain an internal pressure of 14.8 MPa, which is above 1.35 times the design pressure (i.e., 12.1 MPa). The assessment of API 579–1/ASME FFS-1 in level I and II failed due to the presence of a hydrogen-induced crack near the weldment. However, the evaluation in level III assessment considered the influence of residual welding stresses on both longitudinal and circumferential cracks in their as-welded state. The findings indicated that the affected area fell within the acceptable region of the failure assessment diagram, thereby confirming the continued safe operation of the HIC damaged pressure vessel while accounting for welding residual stresses.

Spatial Diffusion of Hydrogen Atoms in Normal and Para-Hydrogen Molecular Films at Temperature 0.7 K

Spatial Diffusion of Hydrogen Atoms in Normal and Para-Hydrogen Molecular Films at Temperature 0.7 K

The influence of hydrogen and oxygen vacancy concentrations on diffusion coefficients of oxide and hydride ions in reduced barium titanate oxyhydride using molecular dynamics simulation

A molecular dynamics method with a reax force field has been employed to investigate the effect of hydrogen and oxygen vacancy concentrations on the diffusion of oxygen and hydrogen atoms in BaTiO3−xHy□(x-y). The result shows that by using this force field, the BaTiO3−xHy□(x-y) samples are stable under the condition of x < 0.18. Therefore, the samples have been simulated under conditions of (x-y) <0.15, y < 0.18 and x < 0.18. The results reveal that the dominant diffusion dynamics of hydrogen atoms is the motion between next-nearest neighboring oxygen vacancies in the form of hydride. The diffusion coefficients and activation energies are evaluated using mean square displacements and Arrhenius plots. The results show that the activation energies of oxide and hydride ions are close together and are in the range of 0.03–0.9 eV and they both decrease by increasing y. The results also show that the pre-exponential factors of hydrogen and oxygen diffusion are in the range of 10−6 to 0.0045 cm2s-1 and 1.7710−6 to 0.0017 respectively.

Effect of ultrasonic treatment on comprehensive properties of (Ti32.5V27.5Zr7.5Nb32.5)0.91Ni0.09 high entropy hydrogen storage alloy

This study verified the effect of ultrasonic treatment (hereinafter referred to as UST) on the comprehensive properties of (Ti32.5V27.5Zr7.5Nb32.5)0.91Ni0.09 high entropy alloy (HEA). The UST refines the interdendritic of (Ti32.5V27.5Zr7.5Nb32.5)0.91Ni0.09 HEA and reduces the content of C14 Laves phase. The increase of BCC/C14 Laves value has an effect on the diffusion of hydrogen atoms, this factor makes the hydrogen absorption amount appear the law of the sample before UST > the sample after UST at low and medium temperature, and the sample before UST < the sample after UST at high temperature. The UST makes the BCC phase at the dendrite become coarse. This factor prolongs the distance for hydrogen atoms to detach from the BCC phase, making the removal of hydrogen atoms difficult.

Experimental study on the hydrogen diffusion across an individual grain boundary in pure nickel by scanning Kelvin probe force microscopy

There are few existing experimental studies on the controversial diffusion behavior of hydrogen atoms across an individual grain boundary (GB). In this study, by combining Electron Back Scattered Diffraction (EBSD) and scanning Kelvin probe force microscopy (SKPFM) techniques, the transverse diffusion behavior of hydrogen atoms across a random GB with a misorientation of 45° within the directionally solidified high purity nickel was directly observed. The results suggest that the hydrogen atoms diffused perpendicular to the studied GB will be trapped by this GB, resulting in hydrogen segregation at the GB. In addition, the studied GB acts as a two-dimensional barrier that can block the transverse diffusion of hydrogen atoms. This present study reveals the real role played by a specific random GB on the hydrogen transverse diffusion and enriches the existing experimental research for intergranular diffusion.

Modelling deuterated isotopologues of methanol towards the pre-stellar core L1544

Context. In the extremely cold and dark environments of pre-stellar cores, methanol is formed on the surface of interstellar dust grains and released into the gas phase via non-thermal desorption mechanisms. Gaseous methanol constitutes the starting point for the formation of many massive complex organic molecules and is therefore of utmost importance for the build-up of chemical complexity. Aims. We aim to improve upon a previous model for the prediction of column densities and deuterium fractions of non-deuterated and singly deuterated methanol. Thereby, we try to identify crucial chemical and physical parameters for which the study of deuteration could provide valuable additional constraints. Methods. We employed a gas-grain chemical code to devise a model that is in agreement with the observed column density and deuterium fraction profiles of the innermost region of the pre-stellar core L1544. For that purpose, we developed a new treatment of reactive desorption, deriving an individual reactive desorption efficiency for every product species in a chemical reaction that depends on the reaction enthalpy and type of the underlying surface. Furthermore, we explored several options to promote the diffusion of hydrogen and deuterium atoms over the surface of interstellar dust grains in order to increase methanol formation. Results. Our fiducial model employs diffusion via the quantum tunnelling of hydrogen and deuterium atoms, resulting in CH3OH and CH2DOH column densities that are approximately an order of magnitude lower than the observed values, which is an improvement over the results of the previous model by a factor of 10. The N(CH2DOH)/N(CH3OH) ratio is reproduced within a factor of 1.2 for the centre and 1.8 for the position of the methanol peak. Given the large uncertainties that chemical models typically have, we consider our predictions to be in agreement with the observations. In general, we conclude that a diffusion process with a high diffusion rate needs to be employed to obtain methanol column densities that are in accordance with the observed values. Also, we find that the introduction of abstraction reactions into the methanol formation scheme suppresses deuteration when used in combination with a high diffusion rate.