Transport Of Hydrogen In Metals Research Articles

Explicit implementation of hydrogen transport in metals

Hydrogen embrittlement prediction demands a numerical framework coupling a damage model with local hydrogen concentration. The inherent nonlinearity in hydrogen-stress-damage interactions challenges convergence in implicit schemes. To address this limitation, we propose a novel chemical potential-based explicit formulation for simulating hydrogen transport in metals. Our approach exploits a heat transfer analogy, linking mechanical and hydrogen transport via inelastic energy as a heat source. By employing chemical potential rather than lattice concentration, our method eliminates the need for user-defined boundary conditions and hydrostatic stress gradient determination. We integrate a VUMATHT subroutine for diffusion modelling and a VUMAT subroutine for material behaviour, coupling stress and strain rates as a heat source for diffusion. Validating against a classical benchmark, we compare our explicit approach with hydrogen concentration-based methods in ABAQUS Standard and Comsol Multiphysics. Stability conditions are assessed for different mesh sizes and mass scaling densities and the capabilities of our approach are showcased for 3D simulations of notched tensile specimens. Our framework offers a novel and efficient pathway for integrating hydrogen transport with user-defined material behaviour, promising advancements in hydrogen-informed damage models.

Reinforcement Learning-Guided Long-Timescale Simulation of Hydrogen Transport in Metals.

Diffusion in alloys is an important class of atomic processes. However, atomistic simulations of diffusion in chemically complex solids are confronted with the timescale problem: the accessible simulation time is usually far shorter than that of experimental interest. In this work, long-timescale simulation methods are developed using reinforcement learning (RL) that extends simulation capability to match the duration of experimental interest. Two special limits, RL transition kinetics simulator (TKS)and RL low-energy states sampler (LSS), are implemented and explained in detail, while the meaning of general RL are also discussed. As a testbed, hydrogen diffusivity is computed using RL TKS in pure metals and a medium entropy alloy, CrCoNi, and compared with experiments. The algorithm can produce counter-intuitive hydrogen-vacancy cooperative motion. Wealso demonstrate that RL LSS can accelerate the sampling of low-energy configurations compared to the Metropolis-Hastings algorithm, using hydrogen migration to copper (111) surface as anexample.

HELIUM AND HYDROGEN EFFECTS IN STRUCTURAL MATERIALS FOR NUCLEAR APPLICATIONS

Displacement cascades produce a variety of defects under reactor conditions, but of particular concern is the simultaneous production of helium (He) and hydrogen (H), which enhances the degradation of structural materials. The overall majority of performed studies on helium and hydrogen interactions with materials were based on ion beam irradiation, which served as a convenient tool for the simulation of neutrons exposure over a variety of temperature and dose regimes due to the ability to widely vary and control the irradiation parameters. Experimental investigations of the hydrogen-defect interaction performed by thermal desorption spectroscopy, and the parameters of this interaction obtained by numerical simulations based on diffusion-trapping codes are debated. In this review, we also summarize previous studies on grain boundaries and nanoprecipitate effects on hydrogen transport in metals, as well as the role of hydrogen in the corrosion and cracking of steels. We discuss here issues of helium bubbles formation and some of the evidence for the synergistic effects of hydrogen and helium in the presence of displacement damage, and their influence on irradiation hardening and swelling. Particular attention was devoted to the features of hydrogen interaction with noble-gas bubbles, which were considered on the basis of most recent published data.

On the use of recombination rate coefficients in hydrogen transport calculations

The commonly accepted picture for the uptake of hydrogen isotopes (HIs) from the gas phase across the surface into a metal with an endothermic heat of solution for HIs is that of dissociation followed by thermalisation in a chemisorbed surface state and finally overcoming a surface barrier to enter the metal bulk where the HIs occupy interstitial solute sites. To leave the metal bulk the HIs first transition to the chemisorbed surface state from which they then enter gas phase by recombining into a diatomic molecule. This model is generally attributed to the work of Pick and Sonnenberg from 1985. They clearly distinguish surface states and subsurface solute sites where the recombination flux is proportional to the square of the concentration of chemisorbed atoms due the diatomic nature of this Langmuir–Hinshelwood process. In an effort to compare their extended model with an earlier surface model by Waelbroeck, which uses an expression for the recombination flux proportional to the square of the sub-surface interstitial solute concentration, they derive an effective recombination coefficient. However, also with the so-derived Pick and Sonnenberg recombination coefficient, the Waelbroeck model is only applicable under certain conditions. But, due to its simplicity, it is often used in boundary conditions of diffusion trapping type calculations, generally ignoring whether or not these conditions are met. This paper will use the full Pick and Sonnenberg model implemented in the TESSIM-X code and in simplified algebraic approximations, to show the limits of applicability of the Waelbroeck–Ansatz in modelling hydrogen transport in metals foreseen for the first wall of magnetic confinement fusion devices.

Hydrogen transport in metals: Integration of permeation, thermal desorption and degassing

A modelling suite for hydrogen transport during electrochemical permeation, degassing and thermal desorption spectroscopy is presented. The approach is based on Fick's diffusion laws, where the initial concentration and diffusion coefficients depend on microstructure and charging conditions. The evolution equations are shown to reduce to classical models for hydrogen diffusion and thermal desorption spectroscopy. The number density of trapping sites is found to be proportional to the mean spacing of each microstructural feature, including dislocations, grain boundaries and various precipitates. The model is validated with several steel grades and polycrystalline nickel for a wide range of processing conditions and microstructures. A systematic study of the factors affecting hydrogen mobility in martensitic steels showed that dislocations control the effective diffusion coefficient of hydrogen. However, they also release hydrogen into the lattice more rapidly than other kind of traps. It is suggested that these effects contribute to the increased susceptibility to hydrogen embrittlement in martensitic and other high-strength steels. These results show that the methodology can be employed as a tool for alloy and process design, and that dislocation kinematics play a crucial role in such design.

Hydrogen Diffusion and Trapping in Fluoride Salt Melts and Graphite Electrodes

This paper presents an approach currently under development at University of Wisconsin Madison to study tritium transport in high temperature fluoride salt systems and absorption in graphite. This work has applicability to tritium management in Fluoride Salt Cooled High Temperature Nuclear Reactors (FHRs). The applicability of the Double Potential Step Method (DSPM) and Electrochemical Impendence Spectroscopy (EIS) originally developed for the study of hydrogen transport in metals from water solutions is discussed for the salt-graphite system. Mechanistic models for hydrogen transport and trapping in graphite are reviewed. The experimental setup and electrochemical cell used with 2LiF-BeF2 (flibe) salt at 500-700°C is described. The design and preliminary characterization data for a Ni/Ni(II) flibe thermodynamic reference electrode are presented.

Transport of hydrogen in metals with occupancy dependent trap energies

Common diffusion trapping models for modeling hydrogen transport in metals are limited to traps with single de-trapping energies and a saturation occupancy of one. While they are successful in predicting typical mono isotopic ion implantation and thermal degassing experiments, they fail at describing recent experiments on isotope exchange at low temperatures. This paper presents a new modified diffusion trapping model with fill level dependent de-trapping energies that can also explain these new isotope exchange experiments. Density function theory (DFT) calculations predict that even mono vacancies can store between 6 and 12 H atoms with de-trapping energies that depend on the fill level of the mono vacancy. The new fill level dependent diffusion trapping model allows to test these DFT results by bridging the gap in length and time scale between DFT calculations and experiment.

Thermodynamics of Gaseous Hydrogen and Hydrogen Transport in Metals

AbstractThe thermodynamics and kinetics of hydrogen dissolved in structural metals is often not addressed when assessing phenomena associated with hydrogen-assisted fracture. Understanding the behavior of hydrogen atoms in a metal lattice, however, is important for interpreting materials properties measured in hydrogen environments, and for designing structurally efficient components with extended lifecycles. The assessment of equilibrium hydrogen contents and hydrogen transport in steels is motivated by questions raised in the safety, codes and standards community about mixtures of gases containing hydrogen as well as the effects of stress and hydrogen trapping on the transport of hydrogen in metals. More broadly, these questions are important for enabling a comprehensive understanding of hydrogen-assisted fracture. We start by providing a framework for understanding the thermodynamics of pure gaseous hydrogen and then we extend this to treat mixtures of gases containing hydrogen. An understanding of the thermodynamics of gas mixtures is necessary for analyzing concepts for transitioning to a hydrogen-based economy that incorporate the addition of gaseous hydrogen to existing energy carrier systems such as natural gas distribution. We show that, at equilibrium, a mixture of gases containing hydrogen will increase the fugacity of the hydrogen gas, but that this increase is small for practical systems and will generally be insufficient to substantially impact hydrogen-assisted fracture. Further, the effects of stress and hydrogen trapping on the transport of atomic hydrogen in metals are considered. Tensile stress increases the amount of hydrogen dissolved in a metal and slightly increases hydrogen diffusivity. In some materials, hydrogen trapping has very little impact on hydrogen content and transport, while other materials show orders of magnitude increases of hydrogen content and reductions of hydrogen diffusivity.

Analysis of electrochemical techniques for studying the diffusion of hydrogen in metals

Abstract The electrochemical techniques used nowadays or proposed recently for studying the transport of hydrogen dissolved in metals are critically reviewed. That is preceded by an overview of fundamentals of equilibrium in the metal–hydrogen systems and transport of hydrogen in metals, taking also self-stress into account. As the main example, hydrogen in palladium and some its substitutional alloys is used.

Effects of Self Stress on the Transport of Guest Species in Solids: Transport of Hydrogen in Metals

Influence of self stress on the transport of a guest in a host matrix is studied within the process of hydrogen permeation through a large thin membrane having properties similar to those of palladium or Pd 8 1 Pt 1 9 alloy. The equilibrium in the system is perturbed at one side of the membrane by a sinusoidal signal of hydrogen concentration. At the opposite side, the hydrogen concentration is maintained at its initial value, and the flux of hydrogen is the response. The transport equations are solved numerically for a wide range of frequencies and amplitudes of the perturbing signal. At the periodic steady state, the larger the signal amplitude, the more important become the zero and higher harmonics of the flux, accompanying the fundamental harmonics. The presence of the zero harmonics causes a permanent pumping of hydrogen throughout the membrane. The fundamental harmonics closely reproduces the results obtained by solving the linearized transport equations. This means that, up to the largest amplitudes, the frequency spectrum of the fundamental harmonics allows for obtaining reliable values of the diffusion coefficient of hydrogen and the bulk elastic modulus of the metal matrix.

Analysis of Hydrogen Trapping in Palladium by Modulated Permeation Spectroscopy

The dynamics of transport processes, such as hydrogen transport in metals, can only be obtained from non‐steady‐state techniques. We have derived the relevant expressions for the phase shift and magnitude of the transfer function describing the response to a modulated flux at one surface of a foil. The expressions include the influence of trapping and surface effects. Experimental measurements of the phase shift and magnitude on annealed palladium foils agree with the model taking and no trapping or surface effects. Experiments on palladium foils with poor surface treatment exhibited an increase in the phase shift and decrease in the magnitude across the accessible frequency range, consistent with surface effects. These results demonstrate that modulation permeation spectroscopy can be used to study transport in metallic foils. © 2000 The Electrochemical Society. All rights reserved.

Models for hydrogen permeation in metals

Hydrogen transport in metals is affected by processes occurring in the bulk, the surface/bulk, and gas/surface interfaces. Several models have been proposed to explain the permeation process. Here the development of the various models is discussed and the similarities and differences among them are highlighted. By considering the limiting case of high pressure, it is shown that the dissociative chemisorption model of Wang [Proc. Cambridge Philos. Soc. 32, 657 (1936)] is sufficient to explain the observed experimental results.

The modeling of hydrogen transport in metals and its application to the evaluation of hydrogen permeation and inventories

Hydrogen transport behavior in metals is discussed with a conventional transport model which takes into account diffusion in the bulk and hydrogen recombination at surfaces as principal rate-determining steps. The present model will allow one to evaluate the permeation rate and bulk inventory of hydrogen isotopes at steady state. But, with the application of an appropriate surface-bulk potential energy diagram, the model can be extended to evaluate surface inventories as well. When the recombination process is the rate-determining step, the state of the surface, especially the presence of impurities, plays an important role. It is shown how a change of surface composition due to ion implantation is reflected in an anomalous transient transport behavior known as the “permeation spike”.

Theoretical modeling of gain boundary diffusion of hydrogen and its effect on permeation curves

A new grain boundary model is proposed. The model can be utilized to calculate the contribution of grain boundary diffusion to total mass transport in metals where lattice diffusion occurs interstitially and where the ratio of grain boundary diffusivity to that lattice is expected to be close to unity. The grain boundary segregation factor, small grain sizes and a large range of the ratio of grain boundary to lattice diffusivity can be accommodater. An analytical solution has been obtaine and applied to electrochemical permetion tests to give predictions of permeation rates enhanced by diffusion through grain boundaries. It is concluded that under most circumstances an average grain size of 10 μm can be used to determine if the transport of hydrogen in metals is enhanced by grain boundary diffusion.