Electronic structure and crystal phase stability of palladium hydrides Abdesalem Houari∗ Theoretical Physics Laboratory, Department of Physics, University of Bejaia, Bejaia, Algeria Samir F. Matar† CNRS, ICMCB, Universit´ede Bordeaux, 33600 Pessac, France Volker Eyert‡ Materials Design SARL, 92120 Montrouge, France (Dated: November 4, 2014) The results of electronic structure calculations for a variety of palladium hydrides are presented. The calculations are based on density functional theory and used different local and semilocal approximations. The thermodynamic stability of all structures as well as the electronic and chemical bonding properties are addressed. For the monohydride, taking into account the zero-point energy is important to identify the octahedral Pd-H arrangement with its larger voids and, hence, softer hydrogen vibrational modes as favorable over the tetrahedral arrangement as found in the zincblende and wurtzite structures. Stabilization of the rocksalt structure is due to strong bonding of the 4d and 1s orbitals, which form a characteristic split-off band separated from the main d-band group. Increased filling of the formerly pure d states of the metal causes strong reduction of the density of states at the Fermi energy, which undermines possible long-range ferromagnetic order otherwise favored by strong magnetovolume effects. For the dihydride, octahedral Pd-H arrangement as realized e.g. in the pyrite structure turns out to be unstable against tetrahedral arrangemnt as found in the fluorite structure. Yet, from both heat of formation and chemical bonding considerations the dihydride turns out to be less favorable than the monohydride. Finally, the vacancy ordered defect phase Pd3H4 follows the general trend of favoring the octahedral arrangement of the rocksalt structure for Pd:H ratios less or equal to one. PACS numbers: 61.50.Lt, 71.20.-b, 75.50.Cc, 88.30.rd Keywords: Palladium hydride, electronic structure, phase stability, magnetism I. INTRODUCTION hydrogen atoms was a matter of long dispute. According to neutron diffraction data, hydrogen atoms occupy the octahedral interstices of the face-centered cubic lattice Metal hydrides have attracted a lot of attention in the 13,14,16,17 last decades due to a variety of exciting applications es- of Pd leading to the rocksalt structure . How- pecially with regard to the environmentally friendly stor- ever, depending on temperature a transfer of substantial age and use of energy. In this context, they have proven amounts of hydrogen to the tetrahedral interstices, lead- ing to the zincblende structure, has been inferred from as very promising candidates for hydrogen storage, fuel 18 cells applications1,2, and heat storage for the solar-energy neutron diffraction data . For the palladium-deuterium industry3. These auspicious perspectives are comple- system a partial occupation of the tetrahedral site was also reported and attributed to the lower zero-point en- mented by strong interest from the point of view of fun- 19 damental research inter alia because of their role as possi- ergy of the D interstitial as compared to H . ble candidates for high-temperature superconductivity4. Due to their increased hydrogen content as compared Since hydrogen insertion can act as negative pressure it to the monohydrides, transition metal dihydrides have may also cause a switching between different electronic or also come into focus quite early, see, e.g. the work by magnetic states, as has been found, e.g., in intermetallic Switendick and references therein20,21. In this case, 5 arXiv:1411.0542v1 [cond-mat.mtrl-sci] 3 Nov 2014 cerium compounds . there was agreement on the fluorite structure. More re- Especially the palladium-hydrogen system has been cently, the formation of superabundant vacancy struc- investigated since long6,7 due to the fact that palla- tures was observed at high temperatures and high hy- dium allows to absorb comparatively large amounts of drogen pressures, possibly the most prominent example hydrogen8–16. For this reason, much interest has centered being Pd3H4, which arises from the monohydride on re- 22–24 about the maximum amount of hydrogen to be absorbed moving Pd and forms an ordered structure . This in the metal as well as the possible hydrogen positions in vacancy formation is accompanied by a compression of the parent structure. This has initiated several structural the lattice. characterizations as well as theoretical studies. Many in- Due to the high interest in the palladium-hydrogen vestigations focused on the question, which open voids system, a number of theoretical studies have been per- in the underlying face-centered cubic lattice of palladium formed ranging from simplified non-self-consistent cal- metal are most likely to be occupied by hydrogen. Es- culations using atomic potentials20,21,25,26 to fully self- pecially, for the monohydride the exact position of the consistent relativistic state-of-the-art electronic structure 2 calculations as based on density functional theory and recently devised especially for the improved treatment of (semi-)local approximations to the exchange-correlation solids42. The single-particle equations were solved using functional27–33. Nevertheless, even the early work by the projector-augmented wave (PAW) method43,44 with Switendick revealed considerable distortions of the Pd a plane-wave basis with a cutoff of 326.203 eV. The Bril- band structure on hydrogenation and allowed to rule out louin zone was sampled using a Monkhorst-Pack mesh previous rigid-band considerations20,21. In particular, with a spacing below 0.1 A˚−1 leading to 27 × 27 × 27 k- based on his finding of only a partial charge transfer from points for the rocksalt and zincblende structures as well hydrogen to the metal, Switendick was the first to aban- as 26×26×13 k-points for the wurtzite structure45. Fur- don the then popular anion and proton models, which thermore, 25×25×25 and 16×16×16 k-points were used were based on an ionic picture. These findings were lat- for the dihydride and Pd3H4, respectively. Phonon spec- eron confirmed by more refined calculations25–27,29. More tra were calculated using the Phonon software46, which is recent theoretical work centered about the issue of the likewise part of the MedeA R computational environment hydrogen site in PdH, which was motivated by the afore and used the forces evaluated with the VASP code. mentioned disputes31–33. As is well known from a number of studies, hydro- gen insertion in metals may induce long-range magnetic order via strong magnetovolume effects. This is espe- cially relevant for paramagnetic palladium, which is at Once the optimized structures were known, calcula- the verge of a ferromagnetic instability. Yet, in general tions of the electronic structure and the chemical bond- there is a strong competition between the magnetovol- ing properties were carried out using the full-potential ume effects enhancing magnetization and the effects of augmented spherical wave (ASW) method in its scalar- 47,48 hydrogen bonding to the underlying metal substructure relativistic implementation . Exchange and correla- leading to the suppression of the magnetic order34,35. tion effects were considered using the GGA parametriza- 49 The present work employed electronic structure calcu- tion of Wu and Cohen . In the ASW method, the wave lations as based on density functional theory and focusses function is expanded in atom-centered augmented spher- on the structure-property relationships of several palla- ical waves, which are Hankel functions and numerical so- dium hydrides. We thus follow two main goals: First, lutions of Schr¨odinger’s equation, respectively, outside emphasis is on the thermodynamic stability of a vari- and inside the so-called augmentation spheres. In order ety of palladium hydrides with perfect stoichiometry and to optimize the basis set and enhance the variational free- different crystal structures. This includes three possible dom, additional augmented spherical waves were placed structures of the monohydride PdH: the observed rock- at carefully selected interstitial sites. The choice of these salt structure, the zincblende structure, and the hexag- sites as well as the augmentation radii were automat- onal wurtzite structure. In addition, the hydrogen over- ically determined using the sphere-geometry optimiza- tion algorithm50. Self-consistency was achieved by a stoichiometric palladium dihydride PdH2 is considered 51 in both the fluorite and the related pyrite structure. Fi- highly efficient algorithm for convergence acceleration nally, the above mentioned recent experiments suggested until the variation of the atomic charges was smaller than 10−8 electrons and the variation of the total energy to investigate the new ordered Pd-defect phase Pd3H4. was smaller than 10−8 Ryd. Brillouin zone integrations The second goal of this work centers about the calcu- 52 lation of the electronic and magnetic properties as well were performed using the linear tetrahedron method k as chemical bonding indicators, which lead to a deeper with 27 × 27 × 27 -points for face-centered cubic Pd, k understanding of the various phases. 26×26×26 -points for the rocksalt structure, 25×25×25 k-points for the zincblende structure, and 24×24×12 k- points for the wurtzite structure. In addition, 24×24×24 k II. COMPUTATIONAL METHODS and 15×15×15 -points were used for the dihydride and Pd3H4, respectively. The first principles calculations were based on density functional theory36,37 with exchange-correlation effects accounted for by both the local and semilocal approxi- mation. Two complementary tools were employed: In the present work, a new full-potential version of the In a first step, the Vienna ab-initio simulation program ASW method was employed48. In this version, the elec- (VASP) as implemented in the MedeA R computational tron density and related quantities are given by spherical environment of Materials Design was used to perform harmonics expansions inside the muffin-tin spheres while, total-energy and force calculations aiming at an opti- in the remaining interstitial region, a representation in mization of the structures38,39.