## No full-text available

To read the full-text of this research,

you can request a copy directly from the authors.

The partial atomic volume of hydrogen, vH, is a fundamentally important thermodynamic parameter of interstitial metal hydrides in which dissociated H occupies interstices in the metal lattice. Such an important property should be able to be reliably calculated by a suitable theory or model in order to explain and understand its origin. In practice, vH is typically obtained by means of ab initio calculations founded on density functional theory (DFT), where the equilibrium lattice constant at zero temperature is found by minimising the Born-Oppenheimer energy. While the absolute lattice constants calculated in this way depend quite strongly on the DFT scheme employed, the present work showed that vH is rather robust against differing calculational approaches, thus making a meaningful comparison of theory and experiment possible. Comparing vH for PdnH (0 < n < 8) calculated with DFT and obtained from in-situ neutron diffraction measurements revealed a significant discrepancy when octahedral-only interstitial occupancy was assumed. Calculations for PdH with mixed octahedral and tetrahedral occupancy gave a value for vH in agreement with experiment assuming that PdH contains 15–20% tetrahedral H.

To read the full-text of this research,

you can request a copy directly from the authors.

... Even more fundamentally, it was reported recently that the atomic volume of H in Pd, as calculated employing six common "standard" DFT schemes, disagreed very significantly with experiment [28], suggesting that even the total Born-Oppenheimer energy is not reliable, in consequence of which the phonon properties also cannot be relied on. ...

... In the oct case the spread of Tc values between DFT schemes exceeded 2 to 1 for the same isotope: e.g. for PdH 45.5 K for PBE/PAW versus 19.9 K for PBEsol/PAW. In comparison, the values obtained by Errea et al. [16] after accounting for anharmonicity within one DFT scheme (LDA/USPP, predicting 5.0 K for PdH and 6.5 K for PdD) differ by a smaller factor from the This study has thus exposed a serious consequence of the basic problem of "standard" DFT applied to PdH uncovered by Setayandeh et al. [28], which is that not only are absolute lattice constants variably predicted between DFT schemes, the predicted atomic volume of H in Pd is in strong disagreement with experiment. Because phonon frequencies depend strongly on the absolute lattice constant, all predicted phonon-related properties must also vary depending on the particular DFT scheme employed. ...

Realistic prediction of the superconducting transition temperature (Tc) for PdH is a long-standing challenge, because it depends on robust calculations of the electron and phonon band structures to obtain the electron-phonon scattering matrix element. To date, first-principles calculations employing density functional theory (DFT) have been based on selected exchange-correlation and core-electron approximations. Incorporating anharmonicity produced a more realistic value of Tc that nevertheless still disagreed strongly with experiment unless adjustable parameters were introduced. Here we consider how the value of Tc predicted using DFT in the harmonic approximation depends on the DFT scheme employed. The rationale for this work is that unless the calculation of Tc within the harmonic approximation is robust, albeit incorrect, there is not a solid foundation for incorporating anharmonicity meaningfully. Six combinations of exchange-correlation approximation (LDA, PBE, PBEsol) and core-electron approximation (PAW, USPP) were tested. Following a carefully systematic methodology, the calculated Tc was found to vary by a factor exceeding two across the tested DFT schemes. This suggests strongly that "standard" DFT, even including anharmonicity, is not reliable for PdH, implying that a higher-rung method will be needed to calculate a realistic lattice constant and phonon band structure, and so predict Tc accurately.

... Concerning the use of DFT in the context under consideration or similar contexts, we can add that the DFT studies focused on hydrogen absorption by metals are now numerous (briefly reviewed in [22]; for Pd and Pd hydride, see e.g. a recent review by Setayandeh et al. [28]). Referring to more recent studies, we may notice that Setayandeh et al. [29,30] have articulated the challenge of accurate description of electron and phonon band structures of the Pd hydrides including PdH and Pd 3 VacH 4 (the superabundant vacancy phase) [28]. Borgschulte et al. [31] have analyzed vibrational frequencies in the hydride (ZrV 2 H 2 ) where the distance between nearest-neighbour H atoms is appreciable shorter than in the conventional hydrides. ...

At temperatures below 600 K, the isotherms of hydrogen absorption by Pd exhibit hysteresis loops related to the first-order phase transition or, more specifically, to separation of a diluted phase and hydride. According to the experiments, addition of even small amount of the second metal, e.g. Au or Ta, can appreciably suppress hysteresis. This interesting effect is important in various applications, e.g., in the context of fabrication of efficient hydrogen sensors. To clarify its physical background, we present statistical calculations of the hydrogen absorption isotherms for a series of binary alloys of Pd with Mg, Cu, Ag, Ta, Pt, or Au by using the values of the H-metal interaction provided by the density functional theory (DFT). Aiming at the situations with small amount (≤15%) of the second metal, the metal atoms in an alloy are considered to be located at random or with short-range correlations. In the random alloy approximation, appreciable suppression of hysteresis is predicted for all the additives under consideration except Cu. Concerning the correlations, we show that the tendency of metals to mixing (as, e.g., predicted for the Pd-Au or Pd-Ta alloy) is in favour of additional suppression of hysteresis whereas the tendency to segregation (as, e.g., predicted for the Pd-Ag alloy) makes the hysteresis loops wider. For Au and Ta, our findings are in good agreement with available experimental data.

... Interestingly, for chlorine adatoms when occupying the sulfur-poisoned surface, the local hydrogen adsorption gets stabilized. Setyandeh et al. 338 investigated the atomic volume of hydrogen in Pd using DFT. The first-principle's results were obtained in quite good agreement with the experimental outcomes in terms of partial atomic volume. ...

Hydrogen has a potential to be a clean energy carrier that emits only water after combustion and can be produced from diverse feedstocks. Hydrogen has much better combustion characteristics in conventional combustion systems and higher energy efficiency when used with fuel cells. More than 75 million tons of hydrogen are currently produced primarily using fossil fuels as feedstock via steam methane reforming processes. Steam methane reforming is the mature technology for producing hydrogen and when coupled with CO2 capture can help address climate challenges. Inorganic palladium (Pd) membranes have demonstrated great potential to separate hydrogen due to their stability and high selectivity for hydrogen. In this review, several methods of fabricating Pd-alloy membranes are discussed and compared in terms of membrane stability and selectivity of hydrogen. Such methods include electroless plating (ELP), chemical vapor deposition (CVD), physical vapor deposition (PVD), and electroplating deposition (EPD). The permeability of hydrogen in different Pd-based alloy membranes are presented and compared. Focus has been made, in this review, on Pd-Ag, Pd-Cu, Pd-Au, and Pd-Ru alloys. The effects of impurities (H2S, CO, O2, and CO2) on performance of different Pd-based alloy membranes are also investigated. Moreover, the subject of using Pd-membrane reactors for fuel reforming and H2 production is investigated in detail based on numerous experimental and numerical studies in the literature, considering different membrane reactor designs: axial-flow tubular, radial-flow tubular, axial-flow spherical, packed-bed, fluidized bed, and slurry bubble column. The performance of Pd-membranes in such reactors for hydrogen production is compared, and the effects of temperature, pressure, H2O/CH4 ratio, and residence time on reformer performance are also investigated. Finally, the use of computational methods, particularly, density functional theory (DFT), to complement well-established experimental methods for studying the diffusion of H and its isotopes in different metals is reviewed. The review concludes with some insights into future work to bring Pd-membrane reactors to the level required for hydrogen production at the commercial level.

The thermodynamics of phase transitions between phases that are size-mismatched but coherent differs from conventional stress-free thermodynamics. Most notably, in open systems such phase transitions are always associated with hysteresis. In spite of experimental evidence for the relevance of these effects in technologically important materials such as Pd hydride, a recipe for first-principles-based atomic-scale modeling of coherent, open systems has been lacking. Here, we develop a methodology for quantifying phase boundaries, hysteresis, and coherent interface free energies using density-functional theory, alloy cluster expansions, and Monte Carlo simulations in a constrained ensemble. We apply this approach to Pd–H and show that the phase transition changes character above approximately 400 K, occurring with an at all times spatially homogeneous hydrogen concentration, i.e., without coexistence between the two phases. Our results are consistent with experimental observations but reveal aspects of hydride formation in Pd nanoparticles that have not yet been accessible in experiment.

Two hydrogen-rich materials, H3S and LaH10, synthesized at megabar pressures, have revolutionized the field of condensed matter physics providing the first glimpse to the solution of the hundred-year-old problem of room temperature superconductivity. The mechanism underlying superconductivity in these exceptional compounds is the conventional electron–phonon coupling. Here we describe recent advances in experimental techniques, superconductivity theory and first-principles computational methods which have made possible these discoveries. This work aims to provide an up-to-date compendium of the available results on superconducting hydrides and explain how the synergy of different methodologies led to extraordinary discoveries in the field. Besides, in an attempt to evidence empirical rules governing superconductivity in binary hydrides under pressure, we discuss general trends in the electronic structure and chemical bonding. The last part of the Review introduces possible strategies to optimize pressure and transition temperatures in conventional superconducting materials as well as future directions in theoretical, computational and experimental research.

We present the formation possibility for Pd-hydrides and Pd-Rh hydrides system by density functional theory (DFT) in high pressure upto 50 GPa. Calculation confirmed that PdH2 in face-centered cubic (fcc) structure is not stable under compression that will decomposition to fcc-PdH and H2. But it can be formed under high pressure while the palladium is involved in the reaction. We also indicate a probably reason why PdH2 can not be synthesised in experiment due to PdH is most favourite to be formed in Pd and H2 environment from ambient to higher pressure. With Rh doped, the Pd-Rh dihydrides are stabilized in fcc structure for 25% and 75% doping and in tetragonal structure for 50% doping, and can be formed from Pd, Rh and H2 at high pressure. The electronic structural study on fcc type Pd x Rh1−xH2 indicates the electronic and structural transition from metallic to semi-metallic as Pd increased from x = 0 to 1.

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

Based on density functional theory calculations, we present an {\it ab initio} study of the structural stability of the palladium-hydrogen (Pd-H) system.
Here, we first investigate two ideal stoichiometries: the monohydride Pd$_1$H$_1$
and dihydride Pd$_1$H$_2$. The former was considered in three different structures
which are faces centered cubic {\it fcc}-rocksalt, {\it fcc}-zincblende and
hexagonal wurtzite, while the latter was considered in two cubic ones which are
fluorite and pyrite.
Energy versus volume calculations were carried out in all structures and theoretical
equilibrium properties (lattice constant, bulk modulus ...etc) are thus obtained. By
evaluating and comparing total energies, the ground state crystal structure is found to
be a {\it fcc}-rocksalt, confirming consequently the experimental finding. Furthermore,
the monohydride is energetically more stable than dihydride. In a second step, we have
studied the experimentally synthesized vacancy-defect phase Pd$_3$H$_4$ compound.
The obtained results (equilibrium lattice constant) are in perfect agreement with experimental
data. (ARTICLE IN PRESS AS OF OCT 2014)

Palladium hydrides display the largest isotope effect anomaly known in the literature. Replacement of hydrogen with the heavier isotopes leads to higher superconducting temperatures, a behavior inconsistent with harmonic theory. Solving the self-consistent harmonic approximation by a stochastic approach, we obtain the anharmonic free energy, the thermal expansion, and the superconducting properties fully ab initio. We find that the phonon spectra are strongly renormalized by anharmonicity far beyond the perturbative regime. Superconductivity is phonon mediated, but the harmonic approximation largely overestimates the superconducting critical temperatures. We explain the inverse isotope effect, obtaining a -0.38 value for the isotope coefficient in good agreement with experiments, hydrogen anharmonicity being mainly responsible for the isotope anomaly.

We present an ab initio density-functional theory study of PdH x systems. We evaluated the total energy of PdH x systems with the H atoms occupying interstitial (octahedral and tetrahedral) sites of a Pd supercell, allowing for the relaxation of the coordinates and supercell dimensions. The majority of our calculations were based on supercells consisting of four Pd atoms, and up to four H atoms, covering the range from x = 0.25 to x = 1. In addition some larger calculations are reported. In order to compare the relative stability of systems at different values of x (at fixed pressure and temperature T = P = 0), we computed the enthalpy of formation ΔH f (x) of the (non)stoichiometric systems. In the regime x = 0 → 1, the ΔH f (x) decrease in a manner indicative of the existence of attractive interactions between the dissolved H atoms. Ideal-solution theory cannot be applied to this system. Furthermore, we find that tetrahedral occupation is favoured over octahedral occupation at high x, leading to the formation of a zincblende structure at x = 1. A preliminary vibrational analysis of normal modes has been performed. Inclusion of vibrational zero-point energies in a harmonic approximation leads us to conclude, tentatively, that the observed stability of octahedral site occupation is due to more favourable zero-point energies of the H atoms in those sites. The results indicate that a proper understanding of this system must take into account the quantum nature of the dissolved hydrogen.

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s$-${}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

Popular modern generalized gradient approximations are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of density gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approximation that improves equilibrium properties of densely packed solids and their surfaces.

Palladium hydride alloys are superconductors and hydrogen storage materials. One synthesis route is compression of Pd to high pressure in a hydrogen-rich environment. Here we report the evolution of the unit cell volume of PdHx synthesized by compressing Pd in a pure H2 medium to pressures from 0.2 to 8 GPa in a diamond anvil cell at room temperature. The volume of the face-centered cubic unit cell changes nonmonotonically with pressure, increasing upon compression from 0.2 to 1 GPa and decreasing upon compression from 1 to 8 GPa. Volume is reversible upon decompression and is independent of whether the sample was heated to 600 K at low pressure (P<2 GPa). The x-ray diffraction data show no evidence for a phase transition between 0.2 and 8 GPa. The volume maximum at 1 GPa must be caused by progressive hydrogenation from 0 to 1 GPa. Assuming a pressure-volume-composition equation of state derived from previously published data, the [H]:[Pd] ratio in this study increases to a maximum value of x=1±0.02 at 2±0.5 GPa and remains stable upon further compression to and from 8 GPa. These results add to a mounting body of evidence that PdH1±ε is in thermodynamic equilibrium with pure H2 at room temperature from 2 GPa to at least 8 GPa. The simplest interpretation is that H atoms occupy all octahedral sites and no tetrahedral sites in face-centered cubic PdH1.0.

Density functional theory is increasingly used to predict and understand the properties of hydrogen storage materials. Many such calculations have been performed for various real and hypothetical palladium hydrides, yet despite excellent agreement on electron band structures, significant disparities persist in relation to phonon band structures and critical matters such as dynamic stability of alternative structures. Some disparities may arise because of differing computation approaches between researchers. Therefore in this work a systematic approach was followed to compare calculated electron and phonon band structures for four palladium hydrides: PdH and Pd3VacH4 (the superabundant vacancy phase) assuming that octahedral (oct) or tetrahedral (tet) lattice interstices are occupied by H, with six commonly used calculation schemes based on the local density approximation and the generalised gradient approximation, within the harmonic approximation. Of the twenty-four combinations tested, seven are new to the literature. Excellent agreement was found between the calculation schemes for the electron band structures of all four crystal structures. The position regarding phonons is much less satisfactory, however, and highlights the sensitivity of phonon properties to the calculated lattice constants. None of the calculation schemes could reproduce the measured phonon energy gap of PdH(oct) and it is necessary to include anharmonicity of the H potential to obtain realistic results. The calculated lattice constants of PdH(tet) were larger than any observed in experiments, although the structure is dynamically stable. All six calculation schemes predicted dynamic instability for Pd3VacH4(oct), although the calculated lattice constant agreed with the estimated zero-temperature experimental value. This structure requires new calculations accounting for anharmonicity. The calculated lattice constant for Pd3VacH4(tet) was larger than any experimental value, so this alternative, while dynamically stable, is certainly not observed.

Palladium hydride was discovered more than 150 years ago and remains one of the most-studied interstitial metal hydrides because of the richness of its physical behaviours, which include ordered phases and anomalous properties at temperatures below 100 K, a superabundant-vacancy (SAV) phase with stoichiometry Pd3H4 formed at high temperature and pressure, and quenching of the enhanced Pauli paramagnetism of palladium. One of the most fascinating properties of palladium hydride is superconductivity at about 10 K without external pressure, in contrast to the newly-discovered polyhydride room-temperature superconductors that require megabar pressures. Moreover, the superconductivity exhibits an inverse isotope effect. Remarkably, modern first-principles approaches are unable to accurately predict the superconducting transition temperature by calculating the electron–phonon coupling constant within Migdal-Eliashberg theory. Anharmonicity of the hydrogen site potential is a key factor and poses a great challenge, since most theoretical approaches are based on the harmonic approximation. This review focuses on the electron and phonon band structures that underpin all such calculations, with palladium as a reference point. While the electron band structures of palladium and its monohydride are uncontroversial, the phonon band structure of palladium hydride in particular is problematic, with a realistic treatment of anharmonicity required – and largely yet to be achieved – to reproduce the results of inelastic neutron scattering experiments. In addition to the monohydride and SAV phases, possible higher hydrides are surveyed and the origin of the famous “50-K” anomaly in specific heat and other physical properties is critically reviewed.

The stable forms of palladium hydrides up to 100GPa were investigated using the direct reaction of palladium with hydrogen (deuterium) in a laser-heated diamond anvil cell. The structure and volume of PdH(D)x were measured using synchrotron x-ray diffraction. The Pd atoms remain on a fcc lattice. The stoichiometry of the hydride is inferred from the volume expansion due to the hydrogen solubility in the Pd lattice. No evidence for hydrogen to palladium ratio greater than 1 is observed for both isotopes. An inverse isotope effect on the formation enthalpy of the stoichiometric Pd hydride is disclosed by measuring the equilibrium formation pressure of PdH and of PdD, 1.9GPa and 2.7GPa, respectively. An isotopic shift between the compression curves of PdH and of PdD is also measured, in good agreement with ab initio calculations quantifying the contribution of the hydrogen zero-point vibrational energy.

Superstoichiometric hydrides PdHx have been synthesized by the electrochemical method. The H concentrations, x = H/Pd = 1.13~1.97, have been determined directly by thermal desorption. From X-ray diffraction, the structure is found to be face-centered cubic, with the lattice parameter changing smoothly over the concentration range, x = 0.7 ~ 2.0. Surprisingly, however, the lattice parameter goes through a maximum at x ~ 1.0 and decreases at higher concentrations. It is suggested from electronic and Monte Carlo calculations that these unique features of the structure and formation process should be the consequence of partial replacement of Pd atoms with H2, namely, the formation of superabundant vacancies filled with H2 molecules.

An isobar x(T) of deuterium solubility in iron is constructed at P=6.3GPa and 100≤T≤800∘C based on the results of thermal desorption analysis of FeDx samples produced by quenching under high D2 pressure to the temperature of liquid nitrogen. The experiment confirms the value of x=0.64 at T=715∘C proposed previously in a neutron diffraction work [Machida et al., Nature Commun. 5, 5063 (2014)] for γ iron deuteride under the assumption that deuterium atoms occupy both octa- and tetrahedral interstices in its fcc metal lattice. An estimate of ΔV/x=2.2Å3/atom D made in that work for the deuterium-induced volume expansion ΔV(x) of fcc iron is also confirmed. To prove that the absorption of protium leads to a similar volume expansion, we constructed an isotherm x(P) of hydrogen solubility in fcc iron at T=600∘C and H2 pressures from 4.3 to 7.4 GPa. The available ΔV(P,T) data of in situ x-ray diffraction studies of iron hydrides [T. Hiroi et al., J. Alloys Compd. 404–406, 252 (2005); H. Saitoh et al., J. Alloys Compd. 706, 520 (2017)] agree with this isotherm under the assumption that ΔV/x=2.2Å3/atom H. The transformation between the high-temperature fcc (γ) and low-temperature dhcp (ε′) deuterides of iron is shown to occur at 260 °C, which is approximately 100 °C lower than the temperature of the γ ↔ ε′ transformation in the Fe-H system at the same pressure of 6.3 GPa.

Absorption of hydrogen by palladium causes PdH to become superconducting below [Formula: see text]. Due to the presence of one octapore and two tetrapores per each Pd atom, it is believed that [Formula: see text] of PdH[Formula: see text] should increase further. Here, using ab initio calculation we show that (i) H placed in tetrapores of PdH[Formula: see text] induces a wide optical gap in the phonon density of states, which significantly reduces the electron-phonon coupling, and that (ii) the energetically preferable octapores filled by H enable the 9 K superconductivity only. This scenario may close a long-standing problem of the high-[Formula: see text] palladium hydrides. Moreover, simulating the pore population by H and D, within ab initio molecular dynamics, we are able to explain the inverse isotope effect in the framework of the Bardeen-Cooper-Schrieffer theory.

We calculate the formation enthalpies of PdHx (x = 0–3) by cluster expansion (CE) and calculations based on density functional theory. CE predicts the stable palladium hydride structures PdH, PdH2.67, and PdH2.75. The band structures and density of states indicate that the amount of hydrogen in the palladium lattice does not alter the metallic character of the palladium significantly. However, all PdHx structures with x > 1 have greater formation enthalpies than that of the given reaction path 4PdH2=2PdH+2Pd+3H2 and thus they are thermodynamically unstable. The shorter bond length of Pd–H and the smaller bond angle of Pd–H–Pd imply a higher cohesive energy in zincblende (ZB) PdH than that in rocksalt (RS) PdH. Bader charge analysis shows a stronger electronegativity of H atoms in ZB-PdH than that in RS-PdH. This results in a stronger Pd–H bond in ZB-PdH than that in RS-PdH. Thus ZB-PdH has lower formation enthalpy than that of RS-PdH. However, regarding the dynamic stability, we conclude that hydrogen atoms prefer to occupy the octahedral sites of the palladium lattice because of the lower zero-point energy and vibration free energy than that of occupying the tetrahedral sites.

High pressure x-ray diffraction of PdHx and PdDx demonstrate that these materials remain in a face-centered cubic (fcc, Fm3 ̅m) structure to these pressures at room temperature. The volumes indicate stoichiometric compositions under pressure with x = 1 for both materials. No indications of phase transitions were observed up to the highest pressures reached in the experiments. A third-order Birch-Murnaghan equation of state used to fit the pressure-volume data gives V0 = 10.73 (±0.03) cm³/mol, K0 = 147 (±11) GPa, and K0' = 4.7 (±0.5), whereas a Vinet fit gives V0 = 10.74 (±0.03) cm³/mol, K0 = 143 (±11) GPa, and K0' = 5.1 (±0.5), for both PdHx and PdDx. The results are used to obtain the pressure dependence of the effective volume of H and D atoms in PdHx and PdDx to megabar pressure for comparison with other hydrides, with implications for superconductivity in this class of materials.

The nanometer-sized materials attract much attention since their physical and chemical properties are substantially different from those of bulk materials owing to their size and surface effects. In this work, the neutron powder diffraction experiments on the nanoparticles of palladium hydride, which is the most popular metal hydride, have been performed at 300 K, 150 K and 44 K to investigate the positions of the hydrogen atoms in the fcc lattice of palladium. We used high-quality PdD0.363 nanocrystals with a diameter of 8.0±0.9 nm. The Rietveld analysis revealed that 30% of D atoms are located at the tetrahedral (T) sites and 70% at the octahedral (O) sites. This is in contrast that only the O sites are occupied in bulk palladium hydride and most of fcc metal hydrides. The temperature dependence of the T-site occupancy suggested that the T-sites are occupied only in a limited part, probably subsurface region, of the nanoparticles. This is the first study to determine the hydrogen sites in metal nanoparticles.

Systematic and automatic calculations of the electronic band structure are a crucial component of computationally driven high-throughput materials screening. An algorithm, for any crystal, to derive a unique description of the crystal structure together with a recommended band path is indispensable for this task. The band structure is typically sampled along a path on or within the Brillouin zone in reciprocal space. Some points in reciprocal space have higher site symmetries and/or have higher constraints than other points regarding the band structure and therefore are likely to be more important than other points. This work categorizes points in reciprocal space according to its symmetry and provides recommended band paths that cover all special wavevector (k-vector) points and lines necessarily and sufficiently. Points in reciprocal space are labeled such that there is no conflict with the crystallographic convention. The k-vector coefficients of labeled points, which are located at Brillouin zone face and edge centers as well as vertices, are derived based on a primitive cell compatible with the crystallographic convention, including those with axial ratio-dependent coordinates. The definitions and k-vector coefficients of labeled points and recommended band paths in this study will be useful as a common ground when discussing the band structure.

A new approach to the construction of first-principles pseudopotentials is described. The method allows transferability to be improved systematically while holding the cutoff radius fixed, even for large cutoff radii. Novel features are that the pseudopotential itself becomes charge-state dependent, the usual norm-conservation constraint does not apply, and a generalized eigenproblem is introduced. The potentials have a separable form well suited for plane-wave solid-state calculations, and show promise for application to first-row and transition-metal systems.

The effect of the alloying elements on the distribution of deuterium in Pd-Au has been investigated by total neutron scattering. The data are analyzed by Reverse Monte Carlo modeling in order to assess the type of interstitial sites occupied with deuterium and how this is correlated with the distribution of the Pd and Au atoms on the host metal lattice. The results show that in Pd Au alloys deuterium occupies both octahedral and tetrahedral interstitial sites: the overall occupancy of tetrahedral sites increases with increasing Au content and decreasing overall D content. Short-range ordering (SRO) is identified in the D occupancy of interstitial sites in the sample with higher Au content. Indications of SRO and D-induced reorganization in the metal lattice are discussed.

The interaction potentials of the palladium and hydrogen sublattices at different hydrogen concentrations have been obtained in terms of the density functional theory and ab initio pseudopotentials. It has been shown that the anharmonicity of this interaction depends on the hydrogen concentration. The phonon spectrum of palladium hydride PdH has been calculated in the harmonic approximation and taking into account the anharmonic effects. The temperature-dependent effective potential technique accounting for the anharmonic effects of lattice vibrations has been described.

The crystallographic properties of palladium at temperatures from absolute zero to the freezing point are assessed following a review of the literature published between 1901 to date. However values above 1100 K are considered to be highly tentative since they are based on only one
set of measurements. Selected values of the thermal expansion coefficient and measurements of length change due to thermal expansion have been used to calculate the variation with temperature of the lattice parameter, interatomic distance, atomic and molar volumes and density. The data is
presented in the form of Equations and in Tables whilst a comparison between selected and experimental values is shown in the Figures.

Lattice constants of the β phase of PdHx and
PdDx for the concentration range 0.8<x<0.98 have been
measured at 77 K using a powder x-ray diffraction technique. The lattice
constant a0 of PdHx is slightly larger (~ 0.1%)
than that of PdDx and dlna0dx=0.044 for both
PdHx and PdDx; extrapolated a0 values
for x=1.0 are 4.090 and 4.084 A for PdH and PdD, respectively. This
study shows that the inverse isotope effect in the superconducting
transition temperature is not simply a result of the relative volume of
PdHx and PdDx.

Diffraction-based methods offer unique advantages for elucidating the pathways by which materials absorb and desorb hydrogen, especially when a phase change or the formation of new compounds is involved. In this case, the hydriding reaction may be followed via the changing crystallography of the phases involved in response to a change in temperature or hydrogen pressure. By using a fast diffractometer, the reaction kinetics may also be correlated to environmental conditions and the degree of completion of the reaction. In this paper we consider and model quantitatively the essential elements of a successful in-situ diffraction experiment with neutrons or X-rays under hydrogen pressures up to several kilobars: a gas manifold to accurately measure hydrogen uptake; a pressure cell designed for maximum detected intensity; means to exclude scattering arising in the cell as much as possible; methodology to correct for attenuation and subtract background intensity from the cell and environment.

Ground-state properties of palladium-hydrogen systems are investigated in the framework of density functional theory in the local-density approximation. Norm-conserving ab initio pseudopotentials are used to describe the interactions between electrons and ion cores. The crystalline wave functions and the charge densities of the valence electrons are represented by a mixed basis containing plane waves and additionally localized d-like functions for palladium and s-like functions for hydrogen. Total energies are calculated for Pd-H systems with different hydrogen concentrations using PdnH supercells (n = 1,4, 8, 16, 32). We report on the cohesive properties as well as the diffusion potentials and vibrational energies for the interstitial hydrogen. Lattice relaxations are taken into account by calculating atomic forces according to the Hellmann-Feynman theorem and statistically relaxing the atomic positions.

From the viewpoint of electron theory of cohesion, it is shown that anharmonic vibration of H(D) atom in PdHx(PdDx) alloy gives rise to an isotope effect such that φH ≡ mHω2H > φD ≡ mDω2D which is the basis to explain the inverse isotope effect in superconducting transition temperature of these systems in contradiction to the expectation from BCS theory.

The question of whether in the two-phase region of a metal-hydrogen system the desorption branch of the hysteresis loop of an isotherm is nearer to equilibrium than the absorption branch (concept I) or the absorption and the desorption branches both deviate to a similar extent from equilibrium (concept II) is still an open question. After a review of the literature on this problem we try to solve it for the systems Pd-D2 and Pd-H2 as examples by applying a new method based on isothermal measurements of p(n) and χ(n) (p is the pressure of D2 or H2, n is the atomic ratio D:Pd or H:Pd and χ is the magnetic susceptibility) in the field about the critical point. The evaluation of the p(n) isotherms measured in the homogeneous solution phase above the critical temperature Tc yielded a value of the critical concentration nc = 0.257 ± 0.004, equal for Pd-D2 and Pd-H2. On the basis of this nc value the other critical data were redetermined; the values Tc = 556 ± 1 K and pc = 39 ± 0.5 bar obtained for Pd-D2 deviate markedly from those accepted so far.By means of the absorption and the desorption branches of the p(n) and the χ(n) isotherms measured across the two-phase region below Tc the boundaries of this region, i.e. the coexistence curve, could be determined. Different boundary lines for absorption and desorption were obtained in the Tvs. n diagram resulting in nc(abs) = 0.295 ± 0.005 and nc(des) = 0.255 ± 0.005, which were also equal for both isotopes. The coincidence of nc(des) with the nc value from the homogeneous region decides the question in favour of concept I. The shift of the coexistence curve obtained from the absorption measurements relative to that from desorption is interpreted as being a consequence of the constraining pressure on the more voluminous β phase. By means of this shift the hysteretic behaviour of the χ(n) isotherms also becomes understandable.

We present results of our ab initio studies of electronic and dynamic properties of ideal palladium hydride PdH and its vacancy ordered defect phase Pd3VacH4 (“Vac” - vacancy on palladium site) with L12 crystal structure found experimentally and studied theoretically. Quantum and thermodynamic properties of these hydrides, such as phonon dispersion relations and the vacancy formation enthalpies have been studied. Dynamic stability of the defect phase Pd3VacH4 with respect to different site occupation of hydrogen atoms at the equilibrium state and under pressure was analyzed. It was shown that positions of hydrogen atoms in the defect phase strongly affect its stability and may be a reason for further phase transitions in the defect phase.

The optical constants n and k were determined for some transition metals (Ti, V, Cr, Mn, Fe, Co, Ni, Pd) from reflection and transmission measurements on vacuum-evaporated polycrystalline thin films at room temperature, in the spectral range 0.5-6.5 eV. Three optical measurements were inverted to determine the film thickness d as well as n and k. The estimated error in d was ±2 Å and that in n, k was less than ±2% over most of the spectral range. Transmission measurements were made on films in the thickness range 200-500 Å. Many transition metals oxidize rapidly in the air and so measurements on those samples were performed in a nitrogen atmosphere. A detailed analysis of the effect of oxidation on the measured quantities indicates that it is small. The effects on the optical constants of the film thickness and the evaporation rate are discussed. Some recent theoretical calculations of the interband optical conductivity are compared with the results for V, Cr, and Ni. In addition, some other recent experiments are compared with our results.

A detailed investigation of the electronic structure of palladium is presented in terms of two different band models: (1) ab initio calculations using the augmented-plane-wave method, and (2) calculations using the combined interpolation scheme augmented by inclusion of relativistic corrections. The width and position of the d-band complex are found to be particularly sensitive features of the electronic structure of palladium. A highly detailed density-of-states histogram, and estimates for the first and second derivatives of the density of states at the Fermi energy are derived. In addition, detailed comparisons are made with Fermi-surface-static susceptibility, and specific-heat experimental results. Estimates for the effects of manybody enhancements suggest that paramagnons raise the effective mass at the Fermi energy by only about 41%. Owing to the strong s-d hybridization in palladium, the Fermi surface is made up almost entirely of d-like states. Because the Fermi energy in palladium falls near the strongly spin-orbit split levels at X and L, spin quenching reduces the effective g factor at the Fermi energy from 2 to about 1.65. This increases an estimate of the effective Stoner-enhancement factor from 10 to about 15.

The purpose of this paper is to explore the possibility of using augmented Slater-type orbitals (STO) as basis functions for electronic-structure calculations. STO's have a radial dependence given by rn-1exp(-ζr) and as a result have a number of important advantages. They are localized about sites and have the same asymptotic form as actual atomic orbitals. They are regular at the origin and possess analytic Fourier transforms. The Fourier transform can be manipulated to yield an addition theorem, that is, a reexpansion formula for an STO about another site which is similar to the one used for spherical Bessel functions. Augmenting the STO's with numerical solutions of the Schrödinger equation within touching spheres leads to a small secular matrix since the numerical functions are orthogonal to all the core states and the STO's are only used in the interstitial region. The method has been applied to copper, silver, and palladium using Chodorow-type potentials and accounting for all relativistic effects except spin-orbit coupling. The results on copper are in good agreement with previous calculations and with experiments. The results on Pd and Ag are in better agreement with photoemission experiments than fully self-consistent local-density calculations.

We report a detailed augmented-plane-wave energy-band study and wave-function analysis of stoichiometric PdH which shows that, even though the Fermi surface of PdH is qualitatively similar to that of silver, the simple "proton model" is not valid. Instead, the screening of the proton in PdH is found to be larger than in an isolated H atom due, in part, to the formation of a H-Pd bonding band below the bottom of the d-band complex. This result, which is in qualitative agreement with Switendick's earlier calculation, is confirmed by ultraviolet photoemission experiments. A partial density-of-states (DOS) analysis in the energy range spanned by the six valence and conduction bands reveals the quantitative details of the bonding mechanism between the Pd and H constituents. At the Fermi energy, the high Pd d to H s DOS ratio ∼ 10.3 is found to be far higher than expected in silver, despite the fact that the Fermi-surface geometry is similar. The field-induced conduction-electron spin density at the proton site is evaluated from the wave functions at the Fermi energy. The calculated value of the spin-lattice relaxation rate arising from the contact term in the hyperfine interaction is found to be in good agreement with the experimental value of Wiley et al.

Calculations of the electronic structure of transition-metal hydrides are applied to the cohesive energy of 3d and 4d monohydrides, and the single-particle lifetime of states in nonstoichiometric Cu and Pd hydrides. A simple formula is presented which delineates the principal contributions to the cohesive energy of the hydrides: (i) the formation of a metal-hydrogen bonding level derived of states of the pure metal band structure which have s symmetry about the site of the added proton, (ii) a slight increase in binding of the metal d bands due to the added attractive potential, and (iii) the addition of an extra electron to the metal electron sea. The calculations, corrected for Coulomb repulsion at the hydrogen sites, qualitatively reproduce the experimental trends of the heats of formation of the transition-metal hydrides. The single-particle lifetime calculations are in quantitative agreement with Dingle-temperature measurements and they correctly predict the existence of essentially undamped states on the hole sheets of the α-phase PdH Fermi surface.

Absorption isotherms (25°) and thermodynamic parameters of absorption of deuterium by several platinum-palladium alloys have been determined. Relationships between the relative resistance of the alloys and their deuterium content have been established (25°). Results have been compared to the previously obtained data on the hydrogen-platinum-palladium system. The experimental differences between the heats of absorption of deuterium and hydrogen in palladium and several platinum-palladium alloys have been compared to predicted values for these differences. Lattice constants of the f.c.c. platinum-palladium alloys have been determined as a function of both the hydrogen and deuterium content of the alloys. Phase boundaries have been established using X-ray diffraction techniques.

On the basis of the local density functional approximation the authors re-derive a local force theorem and, from this, a linearised expression for total energy differences. This can be used to decompose calculated heats of formation into angular momentum contributions constituting a basis for a bond analysis of heats of formation. They demonstrate this by applying the linearised theory to analyse results of augmented spherical wave calculations of the electronic structure and heats of formation of the transition-metal hydrides NiH, PdH, IrH, PtH and AuH.

Hydrides of iron and iron-based alloys are thermodynamically stable only at hydrogen pressures in the gigapascal range and rapidly lose hydrogen under ambient conditions. At low temperatures, however, these hydrides can be retained in a metastable state at atmospheric pressure after being cooled under high pressure to liquid nitrogen temperature. This review will discuss the current state of studies on phase transformations in the Fe–H and related systems and also on the composition, crystal structure and physical properties of the hydrides, both under high hydrogen pressures and in the 'quenched' metastable state at ambient pressure. The studies at ambient pressure include magnetization measurements, x-ray and neutron diffraction, Mössbauer spectroscopy and inelastic neutron scattering. In the sections on Mössbauer and structural investigations of hydrides of Fe–Cr and Ni–Fe alloys new experimental results will be presented.

Interstitial hydrogen contents and their associated volume increments have been determined for a variety of fcc metals and alloys. Using high pressure techniques, hydrogen contents approaching n = 1, where n = H-to-metal (atomic ratio), have been obtained. Despite electronic and initial volume differences amongst the fcc metallic matrices, all data fall onto a common relationship.

An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way. The method allows high-quality first-principles molecular-dynamics calculations to be performed using the original fictitious Lagrangian approach of Car and Parrinello. Like the LAPW method it can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function. The augmentation procedure is generalized in that partial-wave expansions are not determined by the value and the derivative of the envelope function at some muffin-tin radius, but rather by the overlap with localized projector functions. The pseudopotential approach based on generalized separable pseudopotentials can be regained by a simple approximation.

Previous calculations for Group IIIB transition metal and rare earth compounds with hydrogen showed that for the dihydrides a new band is added below the Fermi energy. This bond corresponds to the antibonding combination of the two hydrogen 1s-orbitals in the unit cell. The original transition metal s-band hybridizes with the bonding combination of the two hydrogens, the implications being that for compounds with only one hydrogen per unit cell no new band is formed and the additional electron goes into host metal states. This result has now been verified by calculations for YH and PdH. Previous conclusions about the relative stability of the trivalent trihydrides have been extended to Groups IVB, VB, and VIB dihydrides. The relative position of the added hydrogen bands below the Fermi energy determines the relative stability of a structure. This position depends primarily on interatomic distance. Thus the trihydride forms only for yttrium and the rare earths and not for scandium. The dihydride only forms for transition metals and rare earths for which the metal ion radius (which determines the metal spacing but not the structure) is greater than 1.25 Å. The monohydride forms only when the dihydride is relatively unstable and the density of states in the d-band is high, e.g. VH, NbH, TaH, NiH, and PdH. Quantitative substantiation of these ideas from band structure calculations will be presented.

The limits nmax and nβmin of the two-phase region of PdHn can only roughly be estimated from the shape of the equilibrium isotherms pH2(n). Other methods applied so far do not yield more accurate results. More precise values can be obtained, however, from measurements of the magnetic susceptibility x as a function of the hydrogen content n at various temperatures.Such x(n) isotherms have been measured at temperatures between 20 and 300°C and H2 pressures up to 140 atm (0 · n · 0.8), using samples of Pd wire (1 mm) and Pd foil (33 μm). In the homogeneity range isotherms for adsorption and desorption were identical, in the two-phase region, however, hysteresis was always observed. Here the desorption curve was taken as the equilibrium isotherm, and was applied to determine the values of nmax and nβmin by extrapolation.Measurements on Pd black in the same region of pressure and temperature showed a number of peculiarities, for instance smaller values of susceptibility and smaller hysteresis loops as compared with bulk Pd. These can be attributed to the large specific surface area of Pd black as well as to its strongly distorted lattice structure.By means of the measurements on bulk Pd the position of the critical point of the palladium-hydrogen system could be redetermined with rather high precision: Tc = 291 ± 2°C; nc = 0.250 ± 0.005 mol H/mol Pd; Pc = 19.7 ± 0.2 atm H2.The measurements on Pd-black yielded within the limits of error the same values for the critical temperature and the critical pressure, whereas the value of the H/Pd ratio, properly corrected, was found to be a bit higher, namely nc = 0.260 ± 0.005.Die Grenzen nmax und nβmin des Zweiphasengebietes von PdHn können aus der Form der Gleichgewichtsisothermen pH2(n) nur grob abgeschtzt werden. Andere bisher angewandte Methoden liefern keine genaueren Ergebnisse. Przisere Werte können dagegen erhalten werden aus Messungen der magnetischen Suszeptibilitt x als Funktion des Wasserstoff-Gehaltes n bei verschiedenen Temperaturen.Solche x(n)-Isothermen sind im Temperaturbereich 20 bis 300°C und mit H2-Drücken bis zu 140 atm gemessen worden (0 · n · 0,8), und zwar an Proben aus Pd-Draht (1 mm) und Pd-Folie (33 μm). Im Homogenittsbereich waren die Isothermen für Absorption und Desorption identisch,im Zweiphasengebiet wurde dagegen stets Hysterese beobachtet. Hier wurde jeweils die Desorptionskurve als Gleichgewichtsisotherme angesehen und zur Bestimmung von nmax und nβmin durch Extrapolation herangezogen.Messungen an Pd-Mohr im gleichen Druck- und Temperaturbereich zeigten eine Reihe von Besonderheiten, z. B. kleinere Suszeptibilitt und schmalere Hysterese im Vergleich zum kompakten Pd. Diese können auf die große spezifische Oberflche des Pd-Mohrs zurückgeführt werden sowie auf seine stark gestörte Gitterstruktur.Die Lage des kritischen Punktes im Palladium-Wasserstoff-System konnte mit Hilfe der an kompaktem Pd durchgeführten Messungen mit verhltnismßig großer Genauigkeit neu bestimmt werden: Tc = 291 ± 2°C; nc = 0,250 ± 0,005 mol H/mol Pd; pc = 19,7 ± 0,2 atm H2.Die Messungen an Pd-Mohr lieferten innerhalb der Fehlerstreubreite dieselben Werte für die kritische Temperatur und den kritischen Druck, whrend für das H/Pd-Verhltnis unter Berücksichtigung erforderlicher Korrekturen ein etwas höherer Wert, nmlich nc = 0,260 ± 0,005 gefunden wurde.

Most conventional work on metal hydrides has been restricted to compositions and temperatures at which they are stable under normal pressure. In this paper we describe some results of our recent high-pressure experiments which have been performed in order to extend our scope to the entire range of metal-hydrogen systems. Thus, general features of phase diagrams of binary metal-hydrogen systems, encompassing the whole composition range and temperatures up to the melting point of constituent phases, are established, and a general compression behavior of hydrogen atoms in metallic environment, including interstitial hydrogen and elemental metallic hydrogen, is inferred.