Hydrogen Diffusion In Palladium Research Articles

Impact of host phonons on interstitial diffusion

The net effect of host phonons on interstitial diffusion has remained as a fundamental knowledge gap in our current theories since the motions of the host atoms and interstitials were coupled in these theories. Here we study this effect through molecular dynamics simulations of hydrogen diffusion in palladium, in which the motions can be decoupled through pinning the host atoms. Mathematically this decoupling corresponds to expanding the total diffusion coefficient into a Taylor series, which separates the phonon contribution from the intrinsic interstitial jumping. Our results clearly show that palladium phonons significantly promote hydrogen diffusion. The phonon contribution, being linear with temperature at high temperatures and exponential at low temperatures, is fitted with Brownian motion model. The total diffusion of interstitials can be understood as the intrinsic interstitial jumping in a pinned host plus phonon-induced Brownian diffusion. The generality of our findings is validated by examining the motion of lithium in manganese oxide and carbon in iron.

Mechanism of fast lattice diffusion of hydrogen in palladium: Interplay of quantum fluctuations and lattice strain

Understanding the underlying mechanism of the nanostructure-mediated high diffusivity of H in Pd is of recent scientific interest and also crucial for industrial applications. Here, we present a decisive scenario explaining the emergence of the fast lattice-diffusion mode of interstitial H in face-centered cubic Pd, based on the quantum mechanical natures of both electrons and nuclei under finite strains. Ab initio path-integral molecular dynamics was applied to predict the temperature- and strain-dependent free energy profiles for H migration in Pd over a temperature range of 150--600 K and under hydrostatic tensile strains of 0.0%--2.4%; such strain conditions are likely to occur in real systems, especially around the elastic fields induced by nanostructured defects. The simulated results revealed that, for preferential H location at octahedral sites, as in unstrained Pd, the activation barrier for H migration ($Q$) was drastically increased with decreasing temperature owing to nuclear quantum effects. In contrast, as tetrahedral sites increased in stability with lattice expansion, nuclear quantum effects became less prominent and ceased impeding H migration. This implies that the nature of the diffusion mechanism gradually changes from quantum- to classical-like as the strain is increased. For H atoms in Pd at the hydrostatic strain of $\ensuremath{\sim}2.4%$, we determined that the mechanism promoted fast lattice diffusion ($Q=0.11$ eV) of approximately 20 times the rate of conventional H diffusion ($Q=0.23$ eV) in unstrained Pd at a room temperature of 300 K.

Temperature control algorithms in dual control volume grand canonical molecular dynamics simulations of hydrogen diffusion in palladium

The effectiveness of five temperature control algorithms for dual control volume grand canonical molecular dynamics is investigated in the study of hydrogen atom diffusion in a palladium bulk. The five algorithms, namely, Gaussian, generalized Gaussian moment thermostat (GGMT), velocity scaling, Nosé-Hoover (NH), and its enhanced version Nosé-Hoover chain (NHC) are examined in both equilibrium and nonequilibrium simulation studies. Our numerical results show that Gaussian yields the most inaccurate solutions for the hydrogen-palladium system due to the high friction coefficient generated from the large velocity fluctuation of hydrogen, while NHC, NH, and GGMT produce the most accurate temperature and density profiles in both equilibrium and nonequilibrium cases with their feedback control mechanisms. However, this feedback control also overestimates the self-diffusion coefficients in equilibrium systems and the diffusion coefficient in nonequilibrium systems. Velocity scaling thermostat produces slight inhomogeneities in the temperature and density profiles, but due to the dissipated heat accumulated in the control volumes it still yields accurate self-diffusion coefficients that are in good agreement with the experimental data at a wide range of temperatures while others tend to deviate.

Hydrogen isotope separation by permeation through palladium membranes

An inverse isotope effect is observed for both the solubility and the diffusivity of hydrogen in palladium, i.e., the lightest isotope has the highest solubility and lowest diffusivity. For permeation of hydrogen isotopes through palladium alloy membranes when diffusion is the rate determining step tritium is the least permeating isotope. Since the absolute values of hydrogen, deuterium and tritium permeabilities in palladium differ considerably, the effect could be employed as a basis for technical isotope separation. Using an experimentally verified mathematical model, a parametric computational study was performed to show the net isotope effects in permeate and bleed flows when feeding a technical permeator with various hydrogen isotope mixtures under different feed and permeate pressures. The technical feasibility of hydrogen isotope permeation as a method for separation is discussed with regard to the necessary process control for either a single permeator or a cascade.

Electromigration and Diffusion of Hydrogen in Palladium Defected by Cold Rolling

Influence of defects induced by cold rolling on hydrogen electromigration in palladium was investigated. It was found that the obtained results can not be explained by means of the occurrence of only one (interstitial) diffusion mechanism. However, accepting the assumption that in the process of hydrogen electromigration in defected palladium there appear two mechanisms of diffusion, that is interstitial (i) and interstitial-defective (i-d), that describe the experimentally obtained dependences well enough. In order to determine the influence of kinds of defects and their concentration on hydrogen electromigration, examination of changes in positron lifetimes and electric resistance in dependence on the degree of cold working on palladium were additionally conducted.

Theoretical evaluation of diffusivity of hydrogen in palladium and rhodium

A formulation is developed for obtaining diffusivities of hydrogen in f.c.c. metals from cluster calculations of activation energies. Results for palladium compare reasonably well with medium temperature experimental values. A theoretical diffusivity curve is also suggested for hydrogen in rhodium.

Hydrogen diffusion in palladium based f.c.c. alloys

The macroscopic hydrogen diffusion coefficient D in homogeneous Pd 1− x Ag x alloys obtained by electrochemical current pulse time-lag measurements shows for small hydrogen concentrations a strong dependence on the alloy composition. For small silver concentrations up to 25% the diffusion coefficient remains nearly constant. Then it falls off drastically by about three orders of magnitude reaching a minimum value at 60% silver content before increasing again with rising silver content directly towards the value for pure silver, which is nearly the same as for Pd. The results could be fitted satisfactorily for the complete range of alloy composition by Monte Carlo simulations on the basis of a simplified model. In this model two different octahedral sites are assumed to exist showing different hydrogen occupation probabilities (i.e. different hydrogen solubilities). At smaller silver contents the silver atoms partly block the energetically favored diffusion paths in the Pd matrix leading to a round-about way diffusion. At high silver concentrations, Pd atoms act as traps for hydrogen in a silver matrix. The interplay of the hydrogen transport via two kinds of occupation sites with different hydrogen solubilities determines the shape of the curve for the macroscopic diffusion coefficient as a function of the alloy composition. If Ag is substituted by Ni or Cu an analogous behavior is observed for the f.c.c. phase region. When alloying V or Nb to Pd — both metals have a higher hydrogen solubility compared to Pd — these metals act as traps for hydrogen in the Pd matrix similar to Pd in a silver matrix.

Influence of the external stretching on hydrogen electromigration in palladium

Electromigration and diffusion of hydrogen in palladium depending on unit elongation were investigated. It was found that the obtained experimental results cannot be described by means of a single flux of hydrogen, which diffuses in a gradient of electric field. In order to effectively explain the obtained results, a theoretical model was elaborated. It assumed the existence of the following two fluxes of hydrogen in the stretched metal: • J i—of migration, according to the interstitial mechanism, and • J i-d—of migration, according to the interstitial-defective mechanism. Dependence of effective valences and diffusion coefficients for both mechanisms of transportation were determined in relation to the degree of deformation.

Influence of crystal defects on the electromigration of the hydrogen in palladium

Electromigration and diffusion of hydrogen in palladium defected through quenching to liquid nitrogen temperature were investigated. It was found that the obtained experimental results cannot be described by means of a single flux of hydrogen which diffuses in a gradient of electric field. In order to effectively explain the obtained results, a theoretical model was elaborated. It assumed the existence of the following two fluxes of hydrogen in the quenched metal: • J i—of migration, according to the interstitial mechanism, and • J i–d—of migration, according to the interstitial-defective mechanism. Dependence of effective valences and diffusion coefficients for both mechanisms of transportation was determined in relation to the initial temperature of the quenching.

Important Gorsky effect influences on diffusion coefficients in metal–hydrogen systems

Gorsky effect involvements in regard to the diffusion of hydrogen in metallic solids has meant that, in addition to operations of concentration gradients, expansion effects of interstitials themselves can promote a reverse direction diffusion flux component. In cases where concentrations of Hydrogen interstitials have already been present in diffusion membranes, such strain gradients can produce experimentally observable overall long range uphill effects. Specific quantitative evidence of this behaviour has been recorded in the case of hydrogen diffusion in Palladium, Palladium⧸Platinum and Palladium⧸Silver, and has been shown to influence calculations of hydrogen diffusion coefficients [1, 2]. There now also seem strong possibilities that such strain gradient production can have important influences in phase transition and other solid state processes.

Investigation of Electromigration and Diffusion of Hydrogen in Palladium and PdAg Alloy

Investigation of Electromigration and Diffusion of Hydrogen in Palladium and PdAg Alloy

Visualization and analysis of forced diffusion of hydrogen in palladium by electrotransport

This study analyzes electrotransported hydrogen in palladium hydride by the neutron radiographic technique. Electrotransport was utilized to densify hydrogen in palladium metal. The effectiveness of electrotransport on hydrogen densification was verified by neutron radiographic visualization. The concentration was enhanced up to 0.75 ± 0.05 of the (H/Pd) ratio at 395 K, which was equivalent to hydrogen equilibrium pressure of 100 MPa. From the hydrogen profile in electrotransported PdH x , the effective number of the electric charge of hydrogen in PdH 0.75( Z H *) was determined to be 0.38 ± 0.08.

In situ comparison of diffusivities for hydrogen and deuterium in palladium

An electrochemical permeation method was employed to study the diffusion behaviour of hydrogen and deuterium in palladium. Solutions of 0.1 m LiOD (in D2O) and 0.1 m LiOH (in H2O) and their mixtures were used as the catholytes. More than one hundred diffusivity data from 20 palladium membranes were collected. Statistical analysis of these data was made to examine the validity of the reversed isotope dependence for hydrogen diffusion in palladium. It was concluded that the effective diffusivities increased with the concentration of deuterium in the electrolyte. In addition, an in situ experiment was also performed by adding to the cathodic cell an equivalent amount of LiOD solution to the original LiOH solution, or vice versa. Graphical comparison of the corresponding permeation transients showed that the permeation rate increased when deuterium was added to the solution of H2O, and the rate decreased when hydrogen was added to the solution of D2O. This constitutes direct evidence for the higher diffusivity of deuterium than that of hydrogen in palladium.

Some tests of basic assumptions in transition state theory for hydrogen diffusion in FCC-metals

Transition state theory is frequently used to describe interstitial diffusion in solids. A basic assumption in this theory is that equilibrium statistical mechanics can be used to characterize the different configurations in the transition state, the region in configuration space which acts as a bottleneck for the motion of the interstitial. The authors have performed a detailed test of this assumption for hydrogen diffusion in palladium by combining the molecular dynamics and the Monte Carlo techniques. The study clearly confirms that equilibrium statistical mechanics can be used to characterize the different transition state configurations even though the presence of the hydrogen atom in the transition state strongly influences the fluctuations in the system and despite the fact that the time-scales for the motion of the H atom and the Pd atoms differ considerably.

Two-channel mechanism for diffusion of hydrogen in palladium and Pd77Ag23-alloy

Galvanostatic measurements of hydrogen permeation across Pd sheets systematically exibit an asymmetry between the charging and discharging cycles, namely the time necessary to reach the stationary state is always shorter than the depletion one. This asymmetry is enhanced by increasing the dislocation density in the sheets and appears to be caused by the difference between the capture and the release rate of hydrogen atoms at the sites located within the dislocation array. It has been assumed these sites should act as strong traps and their effect always precedes the appearance of the transient permeation current during the charging cycle and does not interfere with that [1,3].

Observations of “Uphill” Diffusion of Hydrogen in Palladium and Nickel Membranes by an Electrochemical Permeation Method*

Article Observations of “Uphill” Diffusion of Hydrogen in Palladium and Nickel Membranes by an Electrochemical Permeation Method* was published on January 1, 1993 in the journal Zeitschrift für Physikalische Chemie (volume 181, issue 1-2).

Strain gradient-induced diffusion of hydrogen in palladium and nickel membranes

The “uphill” diffusion of hydrogen during permeation through flat sheets of palladium and nickel has been studied by an electrochemical permeation method at 303 K. For both annealed and “as cold rolled” Pd samples, uphill diffusion effects on hydrogen absorption and desorption have been observed over a range of initial hydrogen contents from about H/Pd = 0.01, i.e. near or slightly less than the α max composition, up to H/Pd = 0.25–0.3. The occurrence of a non-Fickian component of permeation flux has been associated with temporary formation of lattice volume differences across the (α + β) β and (α + β) α interfaces during absorptions and desorptions, respectively. Influences of the magnitudes of galvanostatic hydrogen fluxes and of the membrane thickness on the uphill effects were examined. Analogous uphill effects were observed in similar studies with nickel membranes also in both annealed and “as cold rolled” states, which were much larger than those observed for palladium.

Reaction probability for exchange of hydrogen isotopes on palladium.

Surface conductances measured for the diffusion of hydrogen in palladium have been used to calculate the probability, as a function of temperature, pressure, and hydrogen isotope, that a H, D, or T atom will enter bulk Pd as a result of a collision of a ${\mathrm{H}}_{2}$, ${\mathrm{D}}_{2}$, or ${\mathrm{T}}_{2}$ molecule with the Pd surface. This low probability is attributed to hydrogen penetrating a surface hydride phase under the driving force of the chemical potential of the gas consistent with the process having the exchange coefficient of the bulk material. These results were in good agreement with published experimental observations near 300 K and 100 kPa hydrogen pressure for D-H and H-D exchange. These exchange-probability calculations predict an isotope effect that inverts at elevated temperatures and, with decreasing temperature and increasing pressure, a marked decrease in the exchange probability.

Observations of “Uphill” Diffusion of Hydrogen in Palladium and Nickel Membranes by an Electrochemical Permeation Method*

Observations of “Uphill” Diffusion of Hydrogen in Palladium and Nickel Membranes by an Electrochemical Permeation Method*

Solubility and diffusivity of hydrogen in palladium and Pd77Ag23 containing lattice defects

The energy of interstitial sites in a palladium alloy depends considerably on the nature and concentration of the alloying substituent. However, the microstructure of the sample (e.g. grain boundaries, dislocations) may also contribute to a certain extent to these alterations. In some cases it is expected that the effect of these defects may be opposite to that of the substituent, while in other cases both contributions have similar directional influences. In either circumstance the strength of the interaction of hydrogen atoms with the interstitial sites will be affected. The aim of this paper is to investigate the contribution of defects to the solubility and diffusivity of hydrogen in Pd77Ag23 alloy. The measurements have been carried out on samples with and without defects, in the Sieverts domain (293–335 K) using a computer-assisted electrochemical method. The results are discussed in terms of Oriani's two-state model and compared with similar data obtained with palladium samples.