Diffusion Constant Of Hydrogen Research Articles

(Digital Presentation) Predicting Hydrogen Diffusivity in Amorphous Titania Using Markov Chain Kinetic Monte Carlo Simulations

Understanding hydrogen transport is vital to industries focused on discovering new materials for energy storage and corrosion mitigation. However, knowledge of the physical nature of hydrogen’s diffusion pathways is often limited, especially for materials that exhibit a multitude of phases/defect classes. These materials typically have three rate-limiting structural domains: (1) bulk (2) grain boundaries, and (3) surfaces. In this work we have chosen to study hydrogen diffusion through titania due to its importance in the aforementioned application spaces. Here, we aim to understand diffusion through titania grain boundaries, which are approximated via the amorphous phase. Density functional theory (DFT) was used to calculate thousands of activation energies of hydrogen diffusion in the amorphous phase via nudged elastic band calculations using an automated hydrogen pathway generation scheme. Amorphous structures, on the order of tens of nanometers, were generated using a machine learning force field via classical molecular dynamics (MD). Markov chains were generated using the MD-derived atomic structures as their reference. Kinetic Monte Carlo (KMC) simulations were then performed over a variety of temperatures and stoichiometries, for system sizes in the tens of nanometers, allowing us to connect directly with experimental measurements. Using our KMC simulations we can directly calculate the hydrogen diffusion constant, as a function of temperature and stoichiometry, and compare these values with those determined via experiments. We also employ a graph-based characterization scheme that can quantify the subtle differences in local hydrogen diffusion networks throughout the KMC simulation, allowing us to link local hydrogen diffusivity with structural differences within the material observed along the diffusion pathway. This work sets the stage for one to perform long time-scale and/or length-scale simulations to understand how temperature and atomic structure affect properties such as diffusivity, solubility, and permeation, and connect these values directly with experiments.

Hydrogen diffusion through Ru thin films

In this paper, an experimental measurement of the diffusion constant of hydrogen in ruthenium is presented. By using a hydrogen indicative Y layer, placed under the Ru layer, the hydrogen flux through Ru was obtained by measuring the optical changes in the Y layer. We use optical transmission measurements to obtain the hydrogenation rate of Y in a temperature range from room temperature to 100 °C. We show that the measured hydrogenation rate is limited mainly by the hydrogen diffusion in Ru. These measurements were used to estimate the diffusion coefficient, D, and activation energy of hydrogen diffusion in Ru thin films to be D = 5.9 × 10−14 m2/s ∙ exp (-0.33 eV/kBτ), with kB the Boltzmann constant and τ the temperature.

Determining the effective hydrogen diffusion coefficient in 100Cr6

AbstractIn the present study, the diffusion constant for hydrogen in hardened 100Cr6 was measured in permeation tests. The tests were conducted on samples of different thicknesses. The diffusivity of hydrogen was also measured in prestrained samples to study the influence of plastic strain on the diffusion rate. A finite element‐based diffusion model was applied to confirm the experimental results by computing the concentrations of diffusible hydrogen and trapped hydrogen due to deformation‐induced defects. The results showed that the concentration of trapped hydrogen remained very low throughout the plastic strain regime under consideration. The average effective diffusion coefficient of hydrogen in 100Cr6 at 30°C was found to be Deff = 4.9 × 10−12 m2/s.

Hydrogen Flux through Size Selected Pd Nanoparticles into Underlying Mg Nanofilms

AbstractThe application of Mg for hydrogen storage is hindered due to the slow absorption of hydrogen in Mg films. Herein, the hydrogenation process is explored theoretically using density functional theory calculations, and energy barriers are compared for hydrogen diffusion through Pd nanoparticle/Mg film interfaces and their variations, i.e., Pd(H)/Mg(O). Decomposing the mechanism into basic steps, it is shown that Pd undergoes a strain‐induced crystallographic phase transformation near the interface, and indicated that hydrogen saturation of Pd nanoparticles enhances their efficiency as nanoportals. Using energetic arguments, it is explained why hydrogen diffusion is practically prohibited through native Mg oxide and seriously suppressed through existing hydride domains. Hydrogen flux is experimentally investigated through the nanoportals in Pd‐nanoparticle decorated Mg films by pressure‐composition isotherm measurements. An r ≈ t1/3 relationship is theoretically calculated for the radial growth of hemispherical hydride domains, and this relationship is confirmed by atomic force microscopy. The diffusion constant of hydrogen in Mg films is estimated as DHfilm ≈ 8 × 10−18 m2 s−1, based on transmission electron microscopy characterization. The unique nanoportal configuration allows direct measurement of hydride domain sizes, thus forming a model system for the experimental investigation of hydrogenation in any material.

Absorption kinetics and hydride formation in magnesium films: Effect of driving force revisited

Electrochemical hydrogen permeation measurements and in situ gas-loading X-ray diffraction measurements were performed on polycrystalline Mg films. Hydrogen diffusion constants, the hydride volume content and the in-plane stress were determined for different values of driving forces at 300K. For α-Mg–H, a hydrogen diffusion constant of DHMg=7(±2)·10-11m2s−1 was determined. For higher concentrations, different kinetic regimes with reduced apparent diffusion constants DHtot were found, depending on the driving force, decreasing to about DHtot=10−18m2s−1. This lowest measured diffusion constant is two orders of magnitude larger than that of bulk β-MgH2, and the difference is ascribed to a contribution from a fast diffusion along grain boundaries. The different kinetics regimes are attributed to the spatial distribution of hydrides. A heterogeneous hydride nucleation and growth model is suggested that is based on hemispherical hydrides spatially distributed according to the nuclei densities expressed as a function of the driving force. The model allows us to qualitatively explain the complex stress development, the different diffusion regimes and the blocking-layer thickness. As the blocking-layer thickness inversely scales with the driving force, small driving forces allow the hydriding of large film volume fractions. Maximum stress situations occur for hydride distances reaching four times the hydride radius and for hydride distances equaling the film thickness.

Experimental determination of parameters of multichannel hydrogen diffusion in solid probe

The multi-channel diffusion mechanism is modeled by diffusion equations.The method for analysis of experimental dynamical curves of vacuum hot extraction (VHE) is developed, which allows to determine the binding energy and diffusion constants of hydrogen in the probe under study.The experimental data have been obtained using industrial hydrogen analyzer, which allows to carry out the absolute measurements of the dynamical curves vacuum hot extraction of the hydrogen from a solid probe. Experimental verification of mathematical models gives adequate results.The differences of the proposed approach with the method of TDS are discussed.

Hydrogen diffusion and stabilization in single-crystal VO2 micro/nanobeams by direct atomic hydrogenation.

We report measurements of the diffusion of atomic hydrogen in single crystalline VO2 micro/nanobeams by direct exposure to atomic hydrogen, without catalyst. The atomic hydrogen is generated by a hot filament, and the doping process takes place at moderate temperature (373 K). Undoped VO2 has a metal-to-insulator phase transition at ∼340 K between a high-temperature, rutile, metallic phase and a low-temperature, monoclinic, insulating phase with a resistance exhibiting a semiconductor-like temperature dependence. Atomic hydrogenation results in stabilization of the metallic phase of VO2 micro/nanobeams down to 2 K, the lowest point we could reach in our measurement setup. Optical characterization shows that hydrogen atoms prefer to diffuse along the c axis of rutile (a axis of monoclinic) VO2, along the oxygen "channels". Based on observing the movement of the hydrogen diffusion front in single crystalline VO2 beams, we estimate the diffusion constant for hydrogen along the c axis of the rutile phase to be 6.7 × 10(-10) cm(2)/s at approximately 373 K, exceeding the value in isostructural TiO2 by ∼38×. Moreover, we find that the diffusion constant along the c axis of the rutile phase exceeds that along the equivalent a axis of the monoclinic phase by at least 3 orders of magnitude. This remarkable change in kinetics must originate from the distortion of the "channels" when the unit cell doubles along this direction upon cooling into the monoclinic structure. Ab initio calculation results are in good agreement with the experimental trends in the relative kinetics of the two phases. This raises the possibility of a switchable membrane for hydrogen transport.

Kinetic Trapping of D2 in MIL-53(Al) Observed Using Neutron Scattering

We have studied gas adsorption effects on the structure of a metal–organic framework, MIL-53(Al), a material well-known because of the controllable framework “breathing” phenomenon. Neutron powder diffraction between 4 and 77 K and up to 4.5 bar pressure D2 confirms that a structural phase transition is responsible for the observed H2/D2 isotherm hysteresis at 77 K. We find two crystallographically distinct D2 adsorption sites in MIL-53(Al) when the pores are fully opened, similar to those reported for D2 in MIL-53(Cr), but in contrast with the previously published cases of CO2 and H2O. Upon desorption of D2 at 77 K, we find strong evidence for the existence of D2 molecules kinetically trapped in the center of the closed pore of MIL-53(Al). This “molecular clamp” appears to be functional until ≈120 K, the temperature at which the D2 eventually desorbs under dynamic vacuum. Hydrogen diffusion constants calculated using quasielastic neutron scattering data collected along the isotherm are also consistent with H2 being trapped in the closed pore structure. Diffraction experiments performed with N2 and He gases under similar conditions show the range of structural response from immediate pore opening at low N2 pressures (<1 bar) to no observable effect at 10 bar He.

Effects of Cu Addition on Hydrogen Absorption and Diffusion Properties of 1470 MPa Grade Thin-walled Steel in a Solution of HCl

Hydrogen embrittlement is caused by the introduction of hydrogen into steel and is critical for high strength steels. To clarify the effects of the addition of Cu on the suppression of hydrogen embrittlement in a solution of HCl, hydrogen permeation tests and dynamic polarization measurements were conducted on TS 1470 MPa grade, low-carbon martensite steels. To this end, steels containing 0.19% C, 0.2% Si, 1.3% Mn, Cr, Ti, Nb and B were prepared with and without 0.16% Cu. For comparison, ferrite and pearlite steels were also examined. The results of hydrogen permeation tests indicated that the steady-state hydrogen permeation current (JH) of steel containing 0.16% Cu was considerably lower than that of basic steel in 0.1 N HCl at the corrosion potential. Moreover, the JH of martensite steel was suppressed by the addition of Cu, and the cathode current, (iC) and the JH/iC were reduced. The results obtained in this study corroborated the hypothesis that the 1 or 2-μm metallic Cu particles precipitated on the surface of the steel in a solution of HCl suppressed the cathodic reaction and the introduction of hydrogen. The hydrogen diffusion constant (Deff) was obtained from hydrogen permeation tests under a potential gradient. Cu addition has only small effect on Deff regardless of microstructure. The occupancy of trap site (nX) was estimated to be greater than 99% independent of Cu content and microstructure.

Hydrogen diffusion constants in stainless steel and Pd60Ag40 alloy, and permeability of diaphragms made of these metals

Hydrogen permeability through diaphragms made of 12X18H12T stainless steel and Pd60Ag40 alloy under electrolytic hydrogen saturation has been studied with an electrolytic cell with a vacuum chamber. Hydrogen diffusion constants DH = 3.86 × 10−10 cm2 s−1 for stainless steel and DH = 4.36 × 10−8 cm2 s−1 for Pd60Ag40 alloy have been determined at a temperature of 40°C using the Berrer relations.

Physical properties of Zr 50Cu 40 − xAl 10Pd x bulk glassy alloys

It was shown recently (Yokoyama et al. [9]) that the addition of a small amount of Pd to the Zr 50Cu 40Al 10 bulk glassy alloy (BGA) has a beneficial effect on fatigue-strength enhancement, where the composition Zr 50Cu 37Al 10Pd 3 behaved in a resonant-like way by showing the highest fatigue limit of 1050 MPa and the minimum Vickers hardness. We performed a study of the magnetic properties, the specific heat, the electrical resistivity and the hydrogen-diffusion constant for a series of compositions Zr 50Cu 40 − x Al 10Pd x ( x = 0–7 at.%), in order to determine their physical properties and to check for the influence of the Pd content on these properties. The Zr 50Cu 40 − x Al 10Pd x BGAs are nonmagnetic, conducting alloys, where the Pauli spin susceptibility of the conduction electrons is the only source of paramagnetism. The low-temperature specific heat indicates an enhancement of the conduction-electron effective mass m* below 5 K, suggesting that the Zr 50Cu 40 − x Al 10Pd x BGAs are not free-electron-like compounds. The electrical resistivities of the Zr 50Cu 40 − x Al 10Pd x BGAs amount to about 200 μΩ cm and show a small, negative temperature coefficient (NTC) with an increase from 300 to 2 K of 4%. The hydrogen self-diffusion constant D in hydrogen-loaded samples shows classical over-barrier-hopping temperature dependence and is of comparable magnitude to the related icosahedral and amorphous Zr 69.5Cu 12Ni 11Al 7.5 hydrogen-storage alloys. No correlation between the investigated physical parameters and the Pd content of the samples could be observed.

A Laser-Based Apparatus for Estimating the Hydrogen Diffusion Constant in Gas Mixtures

A laser-based apparatus for determining the hydrogen diffusion constant in gas mixtures is described. The main units of the apparatus are a diffusion chamber and a computer-based laser system for the selective diagnostics of hydrogen in gas mixtures by coherent anti-Stokes Raman scattering (CARS) in combination with biharmonic pumping based on stimulated Raman scattering. The diffusion constant is estimated by approximating the experimental data that describe changes in the hydrogen concentration with time at a fixed point in the diffusion chamber and comparing them to the exact solution to the diffusion equation for the chosen one-dimensional experimental geometry.

Hydrogen diffusion in Zr-based metallic glasses at high hydrogen contents

Zr-based metallic glasses might be useful for hydrogen storage application: they are known to absorb high amounts of hydrogen, but exhibiting less severe embrittlement than their crystalline counterparts. In order to understand kinetics of hydrogen absorption and desorption, data on hydrogen diffusion are necessary. The aim of this paper is to analyze hydrogen diffusivities in melt-spun amorphous Zr 69.5 Cu 12 Ni 11 Al 7.5 metallic glasses at high hydrogen contents. Zr-Cu-Ni-Al metallic glasses were prepared by melt-spinning; hydrogen charging was performed electrochemically in a 2:1 glycerol-phosphoric acid electrolyte. Hydrogen desorption is hindered by a thin zirconia layer formed immediately at the surface of these Zr-based alloys. Diffusivities were measured at different temperatures by the technique of nuclear magnetic resonance (NMR) diffusion in a static fringe field of a superconducting magnet. The analysis of the echo damping allows a model-independent determination of the hydrogen diffusion constant. For all hydrogen contents studied in this investigation, an Arrhenius-type temperature dependence of the hydrogen diffusion was observed, thus indicating a simple over-barrier-hopping mechanism. Between hydrogen contents of H/M = 0.05 and H/M = 0.2, the hydrogen diffusivity does not change; at higher contents, hydrogen diffusivity was observed to decrease until reaching a constant value at H/M = 1.0. The decrease of the diffusivity can be related to an increased interaction between the hydrogen atoms. At very high concentrations, there might be amorphous phase separation, thus opening new diffusion paths along interfaces and leading to a diffusivity independent of further increase of the hydrogen content. The full text of this work has been published under the title Influence of the hydrogen content on hydrogen diffusion in the Zr 69.5 Cu 12 Ni 11 Al 7.5 metallic glass by T. Apih, M. Bobnar, J. Dolinsek, L. Jastrow, D. Zander. U Koster in Solid State Communications 134 (2005) 337-341.

Hydrogen diffusion in partially quasicrystallineZr69.5Cu12Ni11Al7.5

We report on the direct determination of the hydrogen diffusion constant D in the hydrogen-storage quasicrystalline alloy ZrCuNiAl using the technique of nuclear magnetic resonance diffusion in a static fringe field of a superconducting magnet. The diffusion constant of partially quasicrystalline ${\mathrm{Zr}}_{69.5}{\mathrm{Cu}}_{12}{\mathrm{Ni}}_{11}{\mathrm{Al}}_{7.5}$ exhibits a significant decrease with increasing hydrogen-to-metal ratio $H/M,$ owing to creation of defects in the lattice during hydrogen loading, whereas the actual alloy structure---the amorphous, icosahedral, or approximant---appears to be less important in the hydrogen diffusivity.

Density functional calculations of hydrogen adsorption on palladium–silver alloy surfaces

Palladium–silver alloy surfaces with and without adsorbed hydrogen have been studied through density functional theory within the generalized gradient approximations employing a slab representation of the surface. Our calculated lattice constants are in good agreement with experimental data, but we find a substantially lower surface energy for Ag(111) and Pd(111) than experiments. We have calculated adsorption energies of hydrogen on several sites on various alloy surfaces, and found that threefold hollow sites with as many palladium neighbors as possible are preferred. The difference in adsorption energy is so large that we expect trapping of hydrogen around palladium atoms in the surface, possibly resulting in a lower diffusion constant of hydrogen at low coverage on alloy surfaces than on the pure Pd and Ag surfaces. Assuming that the adsorption energy has contributions from geometric (“ensemble”) and electronic (“ligand”) effects, we found the geometric contribution to dominate. For the geometric contribution it is seen that the binding strength increases as the d-band center moves toward the Fermi level, a result also found by a number of other theoretical studies. However, for the electronic contribution we found that the variation of the adsorption energy as a function of the d-band center was opposite that reported by others: We saw that hydrogen binds less strongly to the surface as the d-band center moves toward the Fermi level. This could possibly be explained by a large variation of the interaction between the metal sp band and hydrogen.

Hydrogen Diffusion in Quasicrystalline ZrCuNiA1

ABSTRACTThe hydrogen diffusion constant D in the hydrogenated quasicrystalline alloy ZrCuNiAl has been determined using the technique of NMR diffusion in a static fringe field of a superconducting magnet. The diffusion constant of partially quasicrystalline Zr69.5Cu12Ni11Al7.5 exhibits a significant decrease with increasing hydrogen-to-metal ratio H/M, owing to creation of defects in the lattice during hydrogen loading, which dominates over the site-blocking effect. The actual alloy structure—the amorphous, icosahedral or approximant—appears to be less important for the hydrogen diffusivity.

Hydrogen embrittlement of nickel-titanium alloy in biological environment

A nickel-titanium superelastic alloy is susceptible to environmental embrittlement in a corrosive atmosphere. Because a delayed fracture of the alloy is associated with hydrogen absorption and subsequent formation of brittle hydride phases, the diffusion rate of hydrogen is thought to be one of the factors determining its service life. The Ni-Ti alloys subjected to hydrogen charging of 1 or 10 A/m2 for 24 or 120 hours, respectively, were arranged using an electrochemical system. Both the hardness numbers in the cross-sectional area of the alloy and the amount of evolved hydrogen were determined. The fracture surface of the alloys, under tension, was observed using a scanning electron microscope (SEM). Theoretical distributions of the hydrogen concentration were computed for an infinite cylinder model using the differential equation of diffusion. The diffusion constant of hydrogen through the alloy is estimated to be 9×10−15 m2/s, assuming that the hardness is proportional to the concentration of hydride and/or hydrogen. Experimental results of the hardness measurements and fractography support the estimated diffusion constant. The process of fracture formation in a biological corrosive environment was discussed. It was concluded that galvanic currents and fretting corrosion of the alloy might be effective factors in fracture formation during function.

Dissociation Energy of the Passivating Hydrogen-Aluminum Complex in 4H-SiC

The thermal stability of the passivating hydrogen-aluminum complex ((HAl)-H-2) in 4H-silicon carbide has been studied by determining the effective diffusion constant for hydrogen in an AI-doped epitaxial layer. Assuming a complex comprised of one H-2 and one AI acceptor ion, the extracted diffusivities provide the dissociation frequency of the complex. The extracted frequencies cover three orders of magnitude and yield a close to perfect fit to an Arrhenius equation with the extracted dissociation energy for the (HAl)-H-2-complex equal to 1.66 (+/-0.05) eV and a pre-exponential attempt frequency nu (0) = 1.7x10(13) s(-1) in good agreement with the expected value for a first order dissociation process.

Molecular Hydrogen Production in the Radiolysis of High-Density Polyethylene

The production of molecular hydrogen in the radiolysis of high-density polyethylene by γ rays and heavy ion beams has been investigated. Only the slightest increase in the radiation chemical yield of 3.1 molecules/100 eV was found from γ rays to protons of 5−15 MeV. A gradual increase in yield was observed on further increasing the linear energy transfer of the incident particles. This increase amounted to almost a doubling in the hydrogen yield from 10 eV/nm protons to about 800 eV/nm carbon ions. The exact reason for the increase in molecular hydrogen yield is uncertain, but it may involve reactions of excited states or enhanced combination reactions of carbon-centered radicals, thereby allowing more hydrogen to escape the particle tracks. Diffusion from the bulk material was found to have a dominant role on the observed dynamic profiles of hydrogen gas. A simple one-dimensional diffusion model was used to estimate the diffusion constant of hydrogen in polyethylene to be 2.2 × 10-6 cm2/s.

Quantum diffusion of hydrogen and deuterium on nickel (100)

The diffusion constants of hydrogen and deuterium at low temperature were calculated using the surrogate Hamiltonian method and an embedded atom potential. A comparison with previous experimental and theoretical results is made. A crossover to temperature-independent tunneling occurs at 69K for hydrogen and at 46K for deuterium. An inverse isotope effect at intermediate temperatures is found, consistent with experiment. Deviations are found at low temperature where a large isotope effect is calculated.