Hydrogen Diffusion In Metals Research Articles

Review and theoretical analysis of ac–av methods for the investigation of hydrogen insertion I. Diffusion formalism

The formalism related to hydrogen diffusion in metals is reviewed and completed, under alternating conditions, considering membranes in permeation cells and electrodes with impermeable boundary conditions. The theoretical expressions for the concentration transfer function, flux transfer function and concentration/flux transfer functions defined on the entry side or through the membranes are derived for linear diffusion, depending on the electrode or membrane type and the boundary conditions. The theoretical problems encountered when the diffusion coefficient depends on the hydrogen concentration are finally pointed out and discussed, depending on the boundary conditions.

Electric field control of the rapid diffusion of K atoms into a graphite surface

We show that the steady-state diffusion rate of potassium atoms into a graphite surface in the temperature range 1100–1500 K is increased strongly if the electric field outside the surface is directed so that no positive ions can leave the surface. This means that the thermal process of removing K atoms from a basal graphite surface is changed by the direction of the external electric field. If ions are allowed to leave the surface, most K atoms leave in the form of ions or easily ionizable Rydberg species, but if the electric field is reversed the K atoms disappear from the surface by diffusion into the material, not by desorption. The mechanism is not yet understood in its details, but the thermal barrier for this process is the same as that required to form a Rydberg state, as shown in recent kinetic studies. We speculate that the rate of diffusion into a metal surface may be increased by a graphite layer, which could greatly increase the hydrogen diffusion in metals used for hydrogen storage.

High-temperature hydrogen permeability of vanadium and niobium

We develop a technique for measuring the coefficient of hydrogen diffusion in metals of group V based on an electricaly conductivity method. By using this technique, we measured the coefficient of hydrogen diffusion in vanadium and niobium in the temperature range 573 – 1373 K and calculated the hydrogen permeability of metals of group V. A high-temperature phase transition caused by hydrogen dissolution was discovered in this work for the first time.

Gorsky effect consequences of lattice expansive strain gradients in diffusion of hydrogen in metals

Among transition metals forming hydrides of a metallic type, palladium and certain palladium alloys have been preferentially utilised as membranes for hydrogen purification — in view of their relative resistances to embrittlement, high solubilities for hydrogen, as derivable from quite comprehensive p - c (n) - T relationships, and accompanying high values of hydrogen diffusion coefficients. As fairly recent points of interest, uphill effects corresponding to temporary localised hydrogen permeation against overall hydrogen concentration gradients have been observed in studies with membranes of Pd, Pd 77Ag 23 and Pd 81Pt 19. These uphill effects have been associated with hydrogen migrations induced by Gorsky Effects resulting from developments of gradients of lattice strain produced by the expansive effects of the permeating hydrogen interstitials. An outline is presented of experimental methods and results of measurements together with some theoretical and technological correlations.

A Mathematical Model for Metal Hydride Electrodes

A mathematical model describing the discharge process of a metal hydride electrode is developed. The model is used to predict the polarization behavior of a metal hydride electrode which can be used as an anode in different types of electrochemical cells. The electrode studied in the model is cylindrical, consisting of spherical metal hydride particles. The model takes into account the ohmic losses in the electrolyte and in the metal hydride powder, the diffusion of hydrogen in metal, and the charge transfer reaction at the surface of metal hydride particles. The model is used to analyze how changes in parameters affect the performance of the electrode.

Effect of cold drawing on susceptibility to hydrogen embrittlement of prestressing steel

This paper compares the behaviour under aggressive environmental conditions of a prestressing steel in two forms (bar and wire) of different yield strengths, to investigate the influence of this material parameter on their susceptibility to hydrogen-assisted cracking in aqueous environments. Slow strain-rate tests using pre-cracked, specimens were performed under various environment conditions. Different fatigue pre-cracking loads were used to analyse the influence of the stress state in the vicinity of the crack tip on the hydrogen-assisted cracking process. The results confirm the well-known fact that the highest-strength steel is the most susceptible to hydrogen embrittlement. A model of hydrogen diffusion in metals— including the effects of both hydrogen concentration and hydrostatic stress distribution—is proposed to explain these results on the basis of the stress-strain curve of the material. Consideration is given to compressive residual stresses induced in the vicinity of the crack tip during the fatigue pre-cracking process. The model is able to explain the different susceptibility to hydrogen embrittlement of the two steels.

Hydrogen permeation in stressed and strained membranes of palladium alloys

In experimental studies of hydrogen permeation through a Pd 77Ag 23 membrane at 25 and 50°C, forms of the time-dependent changes of hydrogen pressure within the membrane have been found to be clearly dependent on the catalytic activities of the membrane surface, initial hydrogen content of the membrane and conditions of lattice strain due to different processes of generation of lattice stress. This strongly supports the appreciation that hydrogen diffusion in metals involves non-Fickian features which are associated with Gorsky Effect phenomena. Correlations have been made between these effects and the forms of isothermal hydrogen pressure( p)-hydrogen content( n) relationships for the Pd 77Ag 23H n system.

Nonadiabatic effects in hydrogen diffusion in metals.

Molecular dynamic simulations for hydrogen diffusion in Pd are performed, using a potential based on the embedded-atom method. It is found that a single adiabatic Born-Oppenheimer potential energy surface cannot reproduce the wave-vector dependence of the quasielastic peak obtained in neutron scattering studies. By incorporating coupling to low-lying electron-hole-pair excitations among the conduction electrons close agreement with the experimental result is obtained. This shows that in some cases one has to go beyond the Born-Oppenheimer approximation in order to characterize correctly the diffusive motion of hydrogen in metals.

Quantum transition state theory and the diffusion of hydrogen in metals

The diffusion of hydrogen in metals is dominated at low temperatures by transitions between vibrational quantum ground states, but at high temperatures quantum effects are expected to be small. These ideas are illustrated by the behaviour of simple barrier-crossing models. The recently developed quantum transition state theory is outlined. Its ability to span both the quantum and the classical regimes is noted, and it is shown how simulation techniques allow it to be used to calculate diffusion coefficients. New simulation results for the diffusion coefficient of hydrogen and deuterium in niobium indicate that the observed change in activation energy at T ≈ 250 K signals a cross-over between quantum and classical regimes. The close relation between this and previous interpretations is stressed.

Theory of hydrogen diffusion in metals. Quantum isotope effects

A statistical mechanical theory of hydrogen diffusion in metals is developed. The mystery of why heavier deuterons can diffuse faster than hydrogens in Pd is resolved by computing the quantum mechanical zero-point energy associated with the confining potential perpendicular to the interstitial channel. An excellent quantitative agreement between theory and experiment is obtained for fcc and bcc host metals.

Experimental studies of grain boundary diffusion of hydrogen in metals

Electrochemical permeation tests and silver decoration tests were performed in polycrystalline nickle with different grain sizes. Comparison of experimental results with theoretical predictions of a newly proposed grain boundary diffusion model indicates that grain boundaries are not high diffusivity paths for hydrogen. The sominant role played by grain boundaries during mass transport of hydrogen is retardation due to the trapping effect. The grain boundary diffusivity of hydrogen is concentration dependent. When the hydrogen concentration is extremely low, the grain boundary diffusion of hydrogen is virtually stopped. It is postulated that the low energy sites within grain boundaries are responsible for such retardation.

Quantum transition state theory and the diffusion of hydrogen in metals

Quantum transition state theory and the diffusion of hydrogen in metals

Non‐Local Non‐Fickian Diffusion of Hydrogen in Metals

AbstractStudies of the permeation of hydrogen through the walls of a tubular membrane of a Pd81Pt19 alloy have provided clear examples of evidence of the occurrence of non‐local, non‐Fickian diffusion of absorbed hydrogen from the inner regions of the wall, against overall gradients of hydrogen content — as a consequence of strain gradients produced by the lattice‐expanding effects of the permeating hydrogen.

Modeling of hydrogen diffusion in metals

The study of the diffusion of hydrogen in metals is very important to further understand the hydrogen embrittlement of metals. To describe the diffusion of hydrogen in metals the diffusion equation deduced from Fick's law under an ideal condition has been generally used and the effect of hydrogen trapping in metals has been neglected. In the process of hydrogen diffusion through a metal, hydrogen fills the traps continuously and the fraction of the traps filled by hydrogen, which have only little effect on the diffusion of hydrogen, may be different at different places because the distribution of hydrogen concentration may be different at different places. Thus the hydrogen diffusion coefficient in the metal may also be different at different positions, i.e., the diffusion coefficient should be affected by time in a dynamic process of hydrogen diffusion through a metal. But in the previous analyses, the above fact is not considered and the hydrogen diffusion coefficient is generally taken as a constant. In the present paper a new model of hydrogen diffusion in metals in which the effect of time is taken into account is developed.

Two-atom hydrogen clusters and diffusion of hydrogen in metal

Two-atom hydrogen clusters and diffusion of hydrogen in metal

Defect Migration in Sollids: Microscopic Calculation of Diffusion Rates

Diffusion includes some of the commonest processes on an atomic scale, in which uncorrelated atomic jumps bring about changes in solids. The many predictions of activation energies characterising the temperature dependence of diffusion have high accuracy when good interatomic potentials are known, and a continually improving accuracy from direct quantal calculations. Much more is needed to find the absolute rate at some temperatures. Recent work for both classical and quantum diffusion shows that rates too can be estimated with respectable accuracy. Such calculations highlight basic problems of solid-state defect physics. They alsow offer predictions of techonogical value for diffusion rates in cases where the timescale or physical conditions are too hard for direct experiment. This talk will discuss (a) various ways of obtaining absolute rates, (b) rates of cation diffusion in oxides and their for the so-called Compensation rule (c) issues of charge state in oxides and semiconductors or the motion of shortlived species, and (e) quantum diffusion of hydrogen in metals.

Monte Carlo simulation of hydrogen diffusion in metal and alloys

Monte Carlo simulations of diffusion in a lattice gas with both long-range (mean-field) and short-range interactions are presented. Deviations from the conventional site-blocking model are observed, in agreement with experimental data for hydrogen diffusion in Pd. Simulations of multi-site lattice gases, with site-dependent jump frequencies, are also presented and compared with a generalised site-blocking model. It is found that this model can be applied for hydrogen diffusion in metallic alloys up to a concentration of about c=0.3 (i.e. 30% of the sites are occupied).

Quantum-classical crossover of the transition rate in the damped double well

The author studies the barrier-crossing rate Gamma for a particle in a symmetric double well coupled to a sluggish bath; the aim is to justify the quantum simulation procedure used in related work on the diffusion of hydrogen in metals. He uses path-integral methods to discuss the transition between the low-temperature tunnelling and the high-temperature barrier-jumping regimes, and suggests a unifying formula valid for both, which relates Gamma to the probability of finding the centroid of the quantum path at the barrier top. Numerical results for Gamma are presented for the case of the quartic double well.

Tunnelling of hydrogen in metals

Abstract It is argued that the old equation τ -1 Tn =(ΔE Tn / h )exp(-E n /k B T) for the tunnelling rate from interference between the tunnel-split excited states E n is correct for hydrogen diffusion in metals. Most of the self-trapping effects can be neglected in calculating the tunnelling rate since the self-trapping energy is shown to be constant during the tunnelling.

Detection of trapping and diffusion of very diluted nuclei by nuclear double resonance techniques. Application to hydrogen diffusion in metals

The temperature dependence of the quadrupole spectra measured by nuclear double resonance techniques at the matrix atoms in the neighbourhood of diluted lattice defects or foreign atoms can be used to study diffusion and trapping properties. The experimental possibilities are demonstrated by hydrogen diffusion in lithium metal.