Hydrides of YPd3: Electronic structure and dynamic stability

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e1 2

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Hydrides of YPd3: Electronic structure and dynamic stability Ramesh Sharma a, Shalini Dwivedi b, Yamini Sharma b,* a b

Dept. of Physics, Feroze Gandhi Institute of Engineering and Technology, Raebareli 229001, U.P, India Dept. of Physics, Feroze Gandhi College, Raebareli 229001, U.P, India

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abstract

Article history:

Ternary intermetallic YPd3 is known to exhibit superior hydrogen storage capacity

Received 12 May 2014

compared to pure palladium. To understand the characteristics of YPd3 on hydrogenation,

Received in revised form

the ground state electronic and dynamical properties were computed by two computa-

4 November 2014

tional methods, the full potential linearized plane wave and projector augmented wave

Accepted 6 November 2014

methods within the density functional theory. Hydrogen can be inserted in YPd3 at various

Available online xxx

octahedral sites, giving rise to model structures YPd3H and YPd3H4 which retain the L12 crystal structure. The calculated energy bands confirm the metallic nature of YPd3 and also

Keywords:

exhibit greater dispersion of bands with increase in hydrogen content. Large variations in

Hydrides

the optical constants such as transmittance is observed (by ~40% in the violet region) with

Electronic structure

insertion of hydrogen, YPd3 may have thus have applications as a sensing device for

Optical properties

monitoring hydrogen for using hydrogen safely. The electronic component g obtained from

Transport properties

the temperature dependent specific heats, is related to the density of states at the Fermi

Phonon modes

level which may be co-related to instability of hydrides. The modes at G-point in YPd3H and at X and M-points in YPd3H4 give rise to high peaks in the imaginary frequency regime which could drive the dynamical instabilities. From the formation energies and phonon modes it is found that the monohydride YPd3H is more stable, thus occupation of the octahedral sites at 2Y4Pd by hydrogen atoms results in greater dynamic instability in YPd3. Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Introduction Hydrogen storage is one of the key challenges in the development of hydrogen economy due to its low volumetric energy density. Metal hydrides provide an efficient and safe means of storing hydrogen as solid fuel, with sufficiently high volumetric and gravimetric densities. Such solid state hydrogen storage systems are expected to be ideal for

applications as hydrogen powered fuel cells vehicles (FCVs). Extensive theoretical and experimental studies have been carried out to identify materials with optimum stability and hydrogen storage capacity. The electronic structure and heats of formation were computed by density functional theory to study the stability of 3d and 4d transition-metal hydrides [1,2]. Similarly, the dynamic stability of palladium hydrides and its vacancy ordered defect phase Pd3VacH4 was studied by density functional perturbation theory [3]. The Fermi surface of

* Corresponding author. Tel.: þ91 9415117955. E-mail address: [email protected] (Y. Sharma). http://dx.doi.org/10.1016/j.ijhydene.2014.11.029 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

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dilute hydride of palladium has been determined from de Haas-van-Alphen measurements to study the effect of hydrogenation [4]. The optical properties of Pd films exposed to hydrogen were studied by transmittance and reflectance spectroscopy [5]. Alloying of palladium with other metals is of special importance since metal/alloy-hydrogen systems can be used as hydrogen storage materials in batteries or fuel cells (FCs). In this context the PdePt alloys system along with other binary alloys such as PdeAg, PdeCu etc. have been the subject of numerous studies. The crystal and magnetic structure of ternary alloy PdMn3 which may have good hydrogen storage properties was prepared by Rodic et al. and analysed by neutron powder diffraction method [6]. The position of hydrogen atoms in the metal lattice of binary alloys PdCu and PdAg was determined by neutron scattering studies. Selfconsistent density functional calculations were also performed using Amsterdam density functional band-structure package (ADF-BAND) to calculate the absorption energy as a function of hydrogen content in the alloys of Pd-Ag [7,8]. The absorption energy of hydrogen in the series of ternary alloys Pd3M (M ¼ Cd, Ag, Ag, Cu, Ni, Pt, Pb) was calculated by Ke et al. using ADF-BAND and Vienna ab initio simulation packages (VASP) [9]. Similarly, the role of hydrogen in magnetic and electronic structure of binary YeFe alloys was studied by using the general potential linearized augmented plane wave (LAPW) method [10]. Stability of hydrogen in nickel based binary intermetallics with yttrium (FeB structure) and its hydrides with CrB structure was also studied by ab initio methods such as pseudo potential based VASP and scalar relativistic ASW method [11]. Lukaszewski et al. investigated the electrosorption of hydrogen in some Pd alloys with noble metals. The binary PdePt and ternary PdePteRh alloys were found to be most suitable for electrochemical experiments due to the fact that hydrogen sorption can take place at room temperature without corrosion of electrode materials [12]. It has been shown by electro catalytic analysis that Pt, Pd/Pt and Pd based catalyst structures facilitate formic acid oxidation in silicon based formic acid micro fuel cells [13]. Long et al. have established the uses of Pt, Pt/Pd based bimetallic and multimetallic nanocatalysts for applications in FCs, especially for commercialization in proton-exchange membrane FCs (PEMFCs) and direct methanol FCs (DMFCs), which offer potential applications as portable devices at low temperatures ranges for cell phones, compact computers and automobiles [14,15]. Hydrides of Y or Pd and their alloys have been well studied by a number of workers, whereas fewer studies of the properties of YePd intermetallic are available in literature. The electronic structure of YPd3 and ScPd3 along with x-ray photoemission spectroscopy (XPS), brehmsstrahlung isochromat spectroscopy (BIS) and neutron-diffraction measurements are available [16e19]. Since hydrogen is absorbed in alloys by filling of various interstitial sites in the crystal, the hydrogen concentration is quite high, which makes the hydrides of ternary metal YPd3 attractive hydrogen storage material compared to pure palladium or yttrium or other binary alloys. Transmittance and reflectance of thin films of Y/La coated by Pd were measured with and without hydrogen atmosphere using a double-monochromator spectrophoto meter and crystal structure analysed by x-ray diffraction

[20,21]. The hydrogen sensing properties of Pd/Y films could be clearly observed from the enhanced optical properties. In this paper, our aim is to study the effect of hydrogen insertion on the electronic structure of the YPd3 alloy. The results will be useful in guiding us to understand the suitability of YePd alloy for hydrogen storage along with hydrogen sensing characteristics. The ground state electronic properties of YPd3 and its hydrides were computed by full potential linearized augmented planewave (FP-LAPW) method. The projected density of states (DOS) and energy bands provide valuable insight into modification of energy bands due to hydrogenation. We also report the optical and transport properties for the first time to understand the effects of hydrogenation. The thermodynamical properties of the YePd intermetallic were calculated within the quasiharmonic approximation (QHA) by the projector augmented wave (PAW) method which is based on density functional theory. We have reported the phonon calculations for YPd3 for the first time using force constant method, with forces calculated using PAW method.

Methodology In this paper, two computational methods within the density functional theory (DFT) were used in a complementary manner. For calculating the ground state electronic properties, we have adopted the method of full potential linearized augmented plane waves and local orbitals (lo) (Wien2K code) [22], based on the density functional theory (DFT). For the calculations we have used the generalized gradient approximation (GGA) to the exchange-correlation energy proposed by Wu and Cohen [23]. The self-consistent energy and charge distributions were calculated numerically and the electronic and optical properties were derived from the converged configuration. In the Brillouin zone, k-point integration was carried out using the tetrahedron method in the irreducible Brillouin zone (IBZ) to obtain convergence. The RMTKmax was set equal to 7 for the convergence parameter for which the calculation stabilizes and energy convergence was achieved. Here RMT is the smallest muffin-tin radius and Kmax is the cutoff wave vector of the plane-wave. The maximum radial expansion lmax was set to be 10. A mesh with 56 k-points for YPd3 and YPd3H and 84 k-points for YPd3H4 was used in the IBZ. The energy cut-off between the core and valence states was set at 6.0 Ry. The Vienna ab initio simulation package (VASP) [24], has been used to perform the structure optimization and to evaluate the Hellman-Feynmann forces. The projector augmented wave formalism implemented in this package gives very accurate results. The electronic exchange and correlations were treated by using the generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof (PBE) [25]. The 4d electrons of Y and Pd have been included as valence electrons. The electronic wave functions were expanded in a plane wave basis with a cut-off of 250.925 eV and fine FFT grid was chosen with spacing around 0.5 A. The Brillioun zone sampling was done with a Monkhorst-Pack k-point grid of 4  4  4. The Fermi surface was treated by the MethfesselePaxton method with a smearing of 0.2 eV.

Please cite this article in press as: Sharma R, et al., Hydrides of YPd3: Electronic structure and dynamic stability, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/j.ijhydene.2014.11.029

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Table 1 e Electronic and dynamical parameters of YPd3 and its hydrides. Method FPLAPW

PAW

Parameters

YPd3

YPd3H

˚) RMT (A

Pd ¼ 2.5 Y ¼ 2.5

Pd ¼ 2.5 Y ¼ 2.5 H ¼ 1.10

˚) Bond-Length (A

PdePd ¼ 2.87 PdeY ¼ 2.87 YeY ¼ 4.06

PdePd ¼ 2.87 PdeY ¼ 2.87 YeY ¼ 4.06 YeH ¼ 3.52 PdeH ¼ 2.03

˚) Lattice parameter(A ˚ 3) Volume (A Pressure Formation energy (KJ/mol) MESH Density(mg/m3) C(v) (J/Kmol) (Entropy (J/Kmol)) Free Energy (J/Kmol)

4.110 69.44 140 MPa 358.51 444 9.76 96.00 149.0 22.28

4.143 71.121 215 MPa 316.28 444 9.55 117.04 161.06 7.31

The vibrational free energy was obtained by using the phonon software (PHONON) [26] which uses the force constants provided by VASP. Phonon calculations were performed by the super cell approach. The calculations explore the full ˚ , with BZ and accounts for an interaction range of 10.0 A ˚ asymmetric atoms displayed by ± 0.02 A. The supercell contains 32, 40 and 64 atoms in case of YPd3, YPd3H and YPd3H4 respectively. The optimized lattice parameters, pressure, volume etc. along with parameters such as Fermi energy are given in Table 1.

YPd3H3

YPd3H4

4.276 78.19 1.04 GPa 235.98 333 8.73 97.48 162.37 158.61

Pd ¼ 2.5 Y ¼ 2.5 H1 ¼ 1.36 H2 ¼ 1.36 PdeY ¼ 2.92 PdePd ¼ 2.93 YeY ¼ 4.14 YeH1 ¼ 3.58 YeH2 ¼ 2.07 PdeH ¼ 2.07 HeH ¼ 2.92 4.276 78.191 162 MPa 175.87 444 8.75 97.10 155.81 24.71

0.0, 0.0); (0.0, 0.5, 0.0) and (0.0, 0.0, 0.5) [Fig. 1(b)]. The optimized ˚ with the correlattice parameters are 4.143 and 4.276 A sponding cell volume of 71.121 and 78.191 Å3 for YPd3H and YPd3H4 respectively.

Results and discussion Crystal structure The ternary alloy YPd3 has the AuCu3 type structure with the space group Pm3m (221) [17]. In the unit cell shown in Fig. 1(a), Y atoms are positioned at 1a (0, 0, 0) and are sitting at the corners of the conventional unit cell. The Pd atoms are located at 3c (1/2, 1/2, 0) and occupy face centres. Fig. 1(b) shows the location of the two octahedral sites (interstitials) for hydrogen insertion. We have performed the structure optimization of YPd3 under minimum conditions of total energy and force acting on the atoms using the PAW method. The experimental lattice ˚ ) for YPd3 was taken from Ref. 16 and the constant (a ¼ 4.07 A equilibrium value of the lattice constant obtained on structure ˚ with a corresponding cell volume of optimization is 4.110 A 3 69.44 Å . Since we are interested in insertion of hydrogen in the ternary metal alloy YPd3, hydrogen is allowed to occupy the various interstitials. It is found that the L12 type crystal structure is preserved in YPd3Hx (x ¼ 1, 3, 4) for different H contents. In YPd3H, the hydrogen atom occupies octahedral interstitial site with coordinates (0.5, 0.5, 0.5) and is surrounded by 6 Pd atoms, called the 6Pd site. In YPd3H4, the hydrogen atom is surrounded by two Y and 4 Pd atoms, this octahedral site is labelled as 2Y4Pd site with coordinates (0.5,

Fig. 1 e Crystal structure of (a) YPd3 (b) Interstitial positions in YPd3.

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From the calculated bond lengths of YPd3 and its hydrides, it is observed that with addition of hydrogen, the PdePd, YeY, PdeY bond lengths as well as the YeH and PdeH bond lengths show a systematic increase of about 1.6e2 % [Table 1]. The corresponding cell volumes also increase with increasing H content; volume of the YPd3H unit cell increases by 2.3% compared to volume of unit cell of YPd3 and by ~11% on formation of the YPd3H4 unit cell.

Energy bands and density of states Yttrium was selected out of the rare-earth metals as a material with hydrogen detecting properties and palladium which is known to have outstanding hydrogen sorption properties has been used as a layer of catalyst on the Y-layer. The Y/Pd alloy may have technological applications as optical sensor for hydrogen with high sensitivity [20]. From our earlier studies (unpublished results), we have observed that palladium forms a number of hydrides such as PdH (NaCl structure), PdH (CsCl structure), PdH2, PdH4, Pd3H and PdH3, out of which PdH is the most stable in terms of formation energy. Similarly, the mono and di-hydrides of yttrium, YH and YH2 were also found to be stable. However, the characteristics of YePd alloy have not yet been investigated from the point of view of hydrogen sensing. From the suggestions available in literature that palladium can be used as a layer of catalyst on the yttrium layer for enhanced hydrogenation [20,21], we have calculated the electronic structure to study the effects of insertion of hydrogen in bulk YPd3. The electronic band structure of YPd3, YPd3H and YPd3H4 has been calculated along the high symmetry directions R-G-X-M-G in the 1st Brillioun zone (IBZ). To interpret the band structure and to understand the various properties such as optical and transport properties at a fundamental level, we have also calculated the total and partial density of states (PDOS and TDOS). The energy bands of YPd3 and its hydrides in the vicinity of Fermi energy level EF (3.0 to 3.0 eV) are shown in Fig. 2. (Inset shows the band structures of YPd3 and YPd3H). The effect of insertion of hydrogen is clearly seen on the group of energy bands in conduction band (CB) of YPd3. The bands (between 0.5 and 2 eV) are pulled down to the Fermi level (EF coincides with 0 eV in Wien2k) in YPd3H, and are found below EF in the valence band (VB) at 1.5 eV in the tetrahydride YPd3H4. The band structure of YPd3 and its hydrides show similar structures, although there is greater dispersion of bands in the hydrides due to YeH and PdeH interactions. The energy bands can be interpreted from the density of states which are considered in energy window - 10.0 to 10.0 eV [Fig. 3(aec)]. In YPd3, the VB is dominated by Pd 4d-states below EF, whereas CB is composed of Y 4d-states which have unfilled d-states. Hybridization of Y and Pd s- and d-states leads to formation of itinerant states in VB. The Fermi level lies in the d-states of Pd which occurs at 0.553 eV. The calculated DOS is in good agreement with the DOS calculated by the LMTO method [16]. The main feature (peak) in the calculated DOS at 2.0 eV is found to be in good agreement with the main peak in the XPS data, which is mainly contributed by Pd dstates and is followed by smaller peaks at lower energies in the VB region. The main peak in the BIS data at ~3.0 eV, coincides with the peaks due to Y d-states found in the CB region

Fig. 2 e Selected energy bands along high symmetry direction of 1st Brillioun zone (BZ) using FP-LAPW method for YPd3 and its hydrides from - 3.5 to 3.5 eV. Here, R (1/2, 1/ 2, 1/2), G (0, 0, 0), X (1/2, 0, 0) and M (1/2,1/2, 0) are featured k-point in the BZ. Inset shows energy bands of (a) YPd3 (b) YPd3H.

[19]. From the PDOS of the monohydride YPd3H, it is observed that the hydrogen s-states are present deep down at low energies between 7.5 and 10.0 eV (Fig. 3b). Insertion of hydrogen in YPd3 thus leads to electroneelectron interactions which repel the d-states of Pd to lower energies (2.0 to 7.02 eV). The Y d-states which contributed from 1.95 eV in CB region in YPd3, now appear at the EF. The Fermi level is also raised (0.83 eV) due to additional H s-states. With further increase in the hydrogen content leading to formation of YPd3H4, the hydrogen s-states hybridize with dstates of Pd forming a bonding band which occurs at lower energy in the VB i.e. from 5.6 to 8.82 eV. A narrowing of states of Y and Pd is observed along with appearance of diffused states throughout the band manifold. Both the kinds of hydrogen, H sstates at 6Pd site (H1) and at 2Y4Pd (H2) octahedral sites contribute along with Pd-states at the Fermi level which is lowered slightly to 0.786 eV compared to Fermi energy of YPd3H. From the increase in number of states in the projected DOS, we observe that as we move from mono to tetra hydrides of YPd3, the weight of H s-states at the 2Y4Pd sites is added to H s-states at 6Pd site. Hydriding also puts extra charge in dstates of both Y and Pd, as can be seen from the increase in number of states in the valence band of Pd and Y. The states of Y and Pd also become more localized due to the s-s* bonding of Pd with H. The new hybridized states of H-and Pd atoms appear at Fermi level. There is opening up of bandgap in the density of states in the monohydride YPd3H, whereas there is a smeared DOS with no gap as seen in YPd3H4. On the basis of X-ray diffraction studies, Imai et al. [21] concluded that on hydrogenation of Y/Pd films, yttrium losses its metallic character and palladium efficiently catalyses

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Fig. 3 e Partial density of states (PDOS) and total density of states (TDOS) of YPd3 and its hydrides from ¡10.0 to 10.0 eV (a) YPd3 (b) YPd3H (c) YPd3H4.

hydrogen dissociation and easily absorbs hydrogen. They also observed that both the Pd and Y-films absorbed hydrogen since the Y and Pd peaks in YPd3 disappeared in the x-ray spectra with appearance of a PdH0.7 peak. The FPLAPW calculated density of states qualitatively verifies the findings of the X-ray diffraction spectra. This may be understood from the PDOS which shows disappearance of individual contributions of Y and Pd states, with the appearance of peaks of hybridized Pd dand H s-orbitals in the VB in the hydrides YPd3Hx. Similarly, the formation of YH3d peak in the X-ray spectra with increasing H content in YPd3 can again be interpreted from the mixing of Y s, p-orbitals with H s-orbitals in the CB. Another important verification of our DFT calculations is that the PdH peak in the x-ray spectra shifts to a lower angle compared to the Pd peak. This shift was justified by the increase in interplaner lattice spacing of the Pd film due to absorption of hydrogen. Such an increase in lattice parameter is observed on structure optimization of YPd3 on insertion of hydrogen (Table 1). Based on the analysis of chemical bonds between hydrogen and metal atoms, it was found that in the hydrides of early transition-metal yttrium, some charge is transferred to hydrogen, whereas in late metals such as palladium, electron is transferred from lower band to the Fermi energy level on formation of hydrides [1]. From a similar analysis of charge distribution in YPd3, it is found that net charge in Y is reduced and charge on Pd increases on alloy formation. In YPd3H, it is found that charge is reduced in Y, implying charge transfer from yttrium atom, a slight reduction in charge of H is also seen, whereas some charge is added to Pd atoms which results in upward shift in Fermi level. In YPd3H4, yttrium losses

charge and palladium gains charge. Both kinds of H (H1 and H2) show loss of charge i.e. charge is transferred to palladium atom and there is upward shift in Fermi level. The potential energy due to position as seen from (PDOS and TDOS) density of states clearly shows that hydrogen states are localized at lower energies in monohydrides, but are dispersed in the VB in tetra hydrides. The opening up of bandgap in the electronic density of states may be associated with ordered state, whereas the smeared DOS with no gap as seen in YPd3H4 may be associated with disordered state.

Optical properties Palladium has applications as hydrogen sensing material in a broad range of devices such as schottky diodes; photopyroelectric effect based sensors etc. and is known to induce substantive changes in optical properties of these materials [4]. We have seen in section Crystal structure, that YPd3 allows easy insertion of hydrogen at the various interstitial sites, it is thus important to study the optical properties of the hydrides, since the YePd alloy may have better hydrogen sensing capabilities. The frequency dependent dielectric function ε(u) ¼ ε1 (u) þ iε2(u), is used to describe the linear optical properties [27]. The dielectric function ε2 (u) is strongly correlated to the joint density of states (DOS) and transition momentum matrix elements. The equation of the frequency dependent imaginary part of a dielectric function ε2 (u) is given by the relation; ε2 ðuÞ ¼

8 X dSk 2 jPn ðkÞj 2pu2 Vun ðkÞ

(1)

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Here Pn(k) is the outer band transition dipole momentum matrix. The real part of the dielectric function ε1(u) can be obtained from ε2(u) by KramerseKronig relation, ε1 ðuÞ ¼

2 P p

Z∞ 0

uε2 ðuÞ du u02  u2

(2)

Hydrogen absorption in YPd3 lattice does not change the crystal structure but brings about a change in the optimized lattice parameter of YPd3 (Table 1). There is a change in the optical parameters of Pd films exposed to hydrogen, which is associated mainly with change in lattice constants [3], and a corresponding behaviour is expected in YPd3 on absorption of hydrogen. To study the evolution of optical constants on hydrogenation of YPd3, the dispersion of optical parameters such as refractive indices, reflectivity, optical conductivities etc., was calculated from the real and imaginary parts of dielectric functions. The optical parameters show a strong wavelength/energy dependence as seen in Fig. 4(aec). The refractive index is found to increase with increasing hydrogen content, YPd3H4 has the highest refractive index value of 13.019, which falls to a value of 6.2 at 0.79 eV and continues to decrease thereafter. The refractive index for YPd3 and YPd3H is 9.703 and 11.35 respectively and falls beyond 2.505 eV. The refractive index increases by ~25% on hydrogenation, which is much greater than the 5% change observed on hydrogenation of Pd-film [5]. The imaginary part of refractive index, the extinction function k of YPd3H4, has a sharp peak at 0.416 eV in the infrared region which is about 90% higher than the extinction function for YPd3. The value of k decreases to its lowest value at 1.21 eV in the red region and thereafter has nearly constant value in the entire optical region. The extinction function of YPd3 and YPd3H increases steadily with increasing energy and has a maximum value at 2.78 eV in the visible region. Both the refractive index and extinction functions decrease beyond visible region at energies >3 eV.

Avila et al. have observed that the optical resistivity of palladium films increases on hydrogenation and it is expected that YPd3 will also exhibit a corresponding change in optical resistivity [5]. The optical conductivity for YPd3 and its hydrides was computed in the energy range 0e14 eV [Fig. 4(c)]. It was observed that maximum optical conductivity (22701.89 1/ Ucm) was observed in YPd3 at 2.69 eV in the blue region, followed by a smaller conductivity peak around 4.23 eV in UV region. The optical conductivity of YPd3H does not show appreciable change except for slight shift in the peak positions. In YPd3H4, a small peak of height 3558 1/Ucm at 0.38 eV in infrared (IR) region is observed. The high conductivity at 2.69 eV observed in YPd3 falls to 7560.13 1/Ucm i.e. ~60% rise in optical resistivity is observed. The reduced conductivity or increased optical resistivity may be due to impurity scattering by large number of hydrogen atoms in YPd3H4 at the octahedral sites. The reflectance as a function of photon energy is plotted in Fig. 5. The tetrahydride is initially highly reflective and falls to a value of 0.62 at 0.96 eV (1291.5 nm) in the infrared region, and exhibits high reflectance of 0.7e0.8 in the visible and UV regions. The reflectance of YPd3 and YPd3H is lower than YPd3H4 in the IR region and has value of 0.86 and 0.995 respectively. YPd3H4 shows ~40% decrease in reflectance at 2.85 eV (427.5 nm) in violet region compared to YPd3. The optical transmittance spectra over the spectral range 300e2500 nm (0.496e4.133 eV) up to the violet region are also shown in Fig. 5. The enhancement in transmittance of YPd3 on absorption of hydrogen is clearly seen throughout the optical region. It is observed that the increase in transmittance of the PdeY alloy on hydrogenation is considerably greater than the change in transmittance due to hydrogenation of Pd monolayer film [5,21]. From the calculations of optical properties it is seen that hydrogen insertion in YPd3 produces large variations in the optical constants similar to response of palladium films, and it would be useful to take into consideration the specific optical

Fig. 4 e Optical properties of YPd3 and its hydrides (a) Refractive index (b) extinction coefficient (c) Optical conductivity s (hy). Please cite this article in press as: Sharma R, et al., Hydrides of YPd3: Electronic structure and dynamic stability, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/j.ijhydene.2014.11.029

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Fig. 5 e (a) Transmittance vs. wavelength in optical region (b) Reflectivity function R(u) of YPd3 and its hydrides.

region to be used for hydrogen sensing. Thus, YPd3 has potential applications as optically readable hydrogen sensor.

Transport properties In section Optical properties, we have observed that the YePd alloy exhibits interesting optical response in the visible region. Similarly, computation of transport parameters such as specific heats, thermal and electrical conductivity etc. will be very

useful for understanding the response of YPd3 to temperature variations. Some interesting physical parameters such as Fermi energy and no. of charge carriers can also be derived from the Seebeck and Hall coefficients [28]. In the semi-classical approach, the relaxation time approximation is used to calculate the solution of the Boltzmann equation. The electrical current j, may be due to contributions from both the electrical and thermal currents in the material and also due to both kinds of carriers (electrons and

Fig. 6 e Variation of (a) Thermal conductivities (b) specific heats (c) Magnetic susceptibility (d) Electrical conductivity with temperature of YPd3 and its hydrides. Please cite this article in press as: Sharma R, et al., Hydrides of YPd3: Electronic structure and dynamic stability, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/j.ijhydene.2014.11.029

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holes). The local relations between the electric field E and temperature gradient VT will be given as a combination of electric and heat currents. In addition to the electronic contributions to the thermal conductivity, there would be lattice contributions which would add further terms to the current ji. Considering only the electronic part of the thermal conductivity and neglecting lattice contributions, the electric current, j, can be written in terms of the conductivity tensors, ji ¼ sij Ej þ sijk Ej Bk þ vij Vj T þ ::::::::

(3)

The conductivity tensors can be obtained using       sab i; k ¼ e2 ti;k va i; k vb i; k

(4)

Where, t is the relaxation time which depends on the band index i and k vector direction, and nk is the group velocity. The group velocity nk which is a derivative of the band energy εk with respect to the wave vector, is rewritten to include the momentum operator p, which is called the optical matrix element and is implemented in the Wien2k code within the optic package. The semi classic transport coefficients are calculated using program Boltztrap [28] interfaced with Wien2k. The plots for thermal conductivity vs. temperature for YPd3 and its hydrides are shown in Fig. 6(a). At room temperature the thermal conductivity values are 33.40, 9.13 and 25.2 W/mK for YPd3, YPd3H and YPd3H4 respectively. Thermal conductivity of hydrides is lower than conductivity of YPd3 in the entire temperature, YPd3H shows smallest thermal conductivity, whereas YPd3H4 shows values comparable to YPd3 in the entire temperature range from 0 to 400 K (Table 2). The observed lowering of thermal conductivity in hydrides is in accordance with the fact that atomic substitution at the interstitial sites scatters phonons, thereby significantly reducing the thermal conductivity in the crystalline solids. In the monohydride YPd3H, the thermal conductivity is greatly reduced compared to YPd3, which implies that there is reduction in scattering due to presence of H atom at 6Pd interstitial site. The filling up of all the interstitial sites increases scattering, thereby raising the thermal conductivity in YPd3H4 compared to YPd3H. Another important parameter to consider in thermal properties is the thermal diffusivity, which can be obtained from the relation k ¼ scpd, where k is thermal conductivity, s is the electrical conductivity, cp is the specific heat and d is the density of the material (Table 1). The

Table 2 e Transport properties of YPd3 and its hydrides (at 300 K). Parameters r (Um) k (W/K) S (V/K) RH (m3/C) cp (J/mol K) g (mJ/mol K2) Calculated DOS at (εf) No. of states/eV unit cell From DOS curve (Fig. 3) at (εf) No. of states/eV unit cell

YPd3 7

YPd3H 6

YPd3H4

2.50  10 33.40 2.93  106 1.23  1011 1.54 3.88, 1.46 [19] 2.026

1.56  10 9.13 8.65  105 4.61  109 1.72 5.3 3.08

2.82  107 25.2 3.57  106 5.84  1010 1.46 4.85 2.40

1.65

1.29

2.47

diffusivity of YPd3 was found to be 2.3  105 m2/s, which is close to experimental values in alloys. The WeidmaneFranz relation implies that the electronic contribution kel depends on the electrical conductivity s. At low temperatures, the thermal conductivity of a given metal tends to increase inversely proportional to the electrical resistivity r and follows the simple relation, kel ¼

LT r

(5)

Here, L is the Lorentz coefficient which has a value of 2.45  108 W s1 K2, r is the electrical resistivity and T is the absolute temperature. It is observed that the electrical resistivity [Fig. 6(d)] for YPd3 and its hydrides become nearly constant at temperatures > 100 K, however the thermal conductivity is found to increase continually with increasing temperature. Although, the electrical resistivity of YPd3H is anomalously high at low temperatures and falls off at temperature >150 K, the thermal conductivity of monohydride is found to reduce substantially. In order to understand the cause of this discrepancy, the ktot obtained from the FP-LAPW calculation as well as kel using Eq. (5) are plotted in Fig. 6(a). It is observed that kel < ktot for YPd3 and YPd3H4 in the entire temperature range, whereas kel > ktot for temperatures >350 K for YPd3H. The deviation of ktot from the WiedemaneFranz relation for the YePd alloy may be due to contributions from phonons (kphon) which have not been included here. Experimental measurements of thermal conductivity are required to verify the various contributions kphon and kel in YPd3 and its hydrides. From the electronic structure calculations it has been observed that hydrogen insertion in YPd3 modifies the density of states to a great extent (Fig. 3). It is possible to verify the electronic structure from specific heat measurements, we therefore compute the heat capacity of pure YPd3 and its hydrides as a function of temperature [Fig. 6(b)]. The low temperature specific heat can be expressed as follows, cp ¼ g þ bT2 T

(6)

The coefficients in Eq. (6) are the Sommerfeld electronic term g and the lattice term b which includes the metal vibrational term for acoustic mode and the hydrogen vibrational term for the optical mode. It is seen that there is a fair agreement between calculated and fitted data. From data fitting we obtain the equations of specific heat for YPd3 and its hydrides,

cp ðYPd3 Þ ¼ 0:073 þ 0:00388T þ 3:93  106 T2 1:277  109 T3 cp ðYPd3 HÞ ¼ 0:1636 þ 0:0059T þ 2:582  106 T2 1:536  109 T3 cp ðYPd3 H4 Þ ¼ 0:0152 þ 0:0046Τ þ 9:085  107 T2 þ 2:4  1010 T3 (7) Ambient temperature specific heats are 1.54, 1.72 and 1.46 J/mol K for YPd3, YPd3H and YPd3H4 respectively (Table 2). Specific heat of YPd3H is slightly higher compared to YPd3 for temperatures <400 K, whereas cp of YPd3H4 is slightly lower in the entire temperature range.

Please cite this article in press as: Sharma R, et al., Hydrides of YPd3: Electronic structure and dynamic stability, International Journal of Hydrogen Energy (2014), http://dx.doi.org/10.1016/j.ijhydene.2014.11.029

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e1 2

From the analysis of the electronic structure in Section Energy bands and density of states, we have observed that the hydrogen states in monohydrides are found at low energies, whereas in tetrahydrides of YPd3, the hydrogen states are well dispersed throughout the VB. The position of the Fermi level is quite sensitive to doping and hence is directly connected to the stability of the alloy and its hydrides. It is possible to extract N(EF) from the temperature dependent specific heats using the conventional Sommerfeld theory of a free-electron gas according to the relation given below. The electronic term g can be easily confirmed from experimental specific heat measurements. g¼

p2 k2B NA NðEF Þð1 þ lÞ 3n

(8)

Here NA is the Avogadro number and the parameter l consists of contribution le-ph due to electron-phonon coupling and a contribution lsf due to spin fluctuations. This parameter is difficult to estimate and can be theoretically derived using McMillan's equation by using the value of Debye temperature, for intermetallics l lies in the range 0.4e0.6 [19]. The electronic specific heat terms are extracted from Eq. (7) and have the values 3.88, 5.9 and 4.6 mJ mol1 K2 corresponding to YPd3, YPd3H and YPd3H4 respectively (Table 2). The calculated parameter for YPd3 is overestimated compared to the experimental value of 1.46 mJ mol1 K2 obtained from specific heat measurements by Kuentzler and Loebich [19]. From X-ray photoemission studies and calculated DOS (Fig. 3), contribution to g is mainly due to Pd d-states in YPd3 and the density of states at EF are 2.026 states/eV unit cell. In the case of YPd3H, the Fermi level lies in the vicinity of the gap and the contribution to g is mainly from yttrium states, here N(EF) is 3.08 states/eV unit cell. In the tetrahydride YPd3H4, the Fermi level lies on a peak which contains states from Y, Pd and H atoms. The no. of states obtained from the fitting parameters using Eq. (8) are overestimated compared to those obtained from the projected DOS (Fig. 3), which yield 1.65, 1.29 and 2.47 states/eV unit cell for YPd3, YPd3H and YPd3H4 respectively. The difference between the values may be because the strong correlations due to ded interactions as well as electronphonon interactions have been neglected in calculating N(EF). The calculated magnetic susceptibility for diamagnetic YPd3 is 9.27  1010 m3/mol (7.38  105 emu/g atom) which is greater than experimental value of 2  106 emu/g atom [19]. At very low temperatures the alloy and its hydrides show anomalous high values. The magnetic susceptibility and electrical resistivity vs. temperature for YPd3 and its hydrides are shown in Fig. 7(b,c). The resistivity is of the order of 107 Um and remains nearly constant for temperatures >50 K YPd3H shows anomalous high resistivity at low temperatures below 20 K. The electrical resistivity of YPd3 is quite close to the value of room temperature resistivity of isomorphic CePd3 (3  106 Um) which exhibits metallic resistivity. It appears that presence of hydrogen at one of the interstitial site is responsible for indirect electroneelectron scattering which increases the resistivity in YPd3H. Study of various other transport properties allows a better understanding of the intermetallic YPd3. Transport parameters such as Seebeck coefficient are also derived from electrical conductivity. At room temperature, the value of Seebeck

9

coefficient is 2.93, e8.65 and 0.357 mV/K for YPd3, YPd3H and YPd3H4 respectively. YPd3 has positive values which changes sign with slight lowering of temperature. Similarly the Hall coefficients at room temperature are 1.23  1011, 4.61  109 and 5.84  1010 m3/C for YPd3, YPd3H and YPd3H4 respectively. Unfortunately, there are no theoretical and experimental results to compare the calculated transport properties.

Dynamical properties Stability and formation energy The importance of metal hydrides in the field of nuclear energy requires the stability of the YPd3 alloys at high temperatures. It is therefore important to study the temperature dependence of thermal properties such as specific heats, entropy, internal energies etc. The calculations have been performed by the force constant method with forces calculated using VASP. Since the stability of the hydrides of intermetallic structures cannot be judged from the total energy calculations alone, we carry out an analysis of the thermodynamic stability of hydrides by calculating the internal energy, entropy and free energy. Overall, the thermodynamic properties amongst the YPd3 and its hydrides are similar and follow the same trends. The temperature dependence of specific heats (Cv) and vibrational entropy show almost similar trends in both the alloy and its hydrides at low temperatures, however the specific heat (at constant volume) for monohydrides increases rapidly at higher temperatures. The Helmholtz free energy which is obtained using the relation F(V,T) ¼ U(V,T) þ TS(V,T) decreases with increasing temperature for the alloy and its hydrides. The specific heat, entropy and Helmholtz free energy at room temperature are presented in Table 1. To study the stability of the hydrides of YPd3, we apply the model of Jacob et al. [29]. According to this model, the relative occupation number of various interstitial sites in intermetallic hydrides is predicted on the basis of the Boltzmann distribution function and heats of formation between the hydrogen atoms and host metallic atoms forming the interstitial sites. The total energies of YePd ternary alloys were evaluated by the PAW formalism implemented in VASP package. The energy of reactants Y and Pd are 8.33 and 3.22 kJ/mol respectively. Formation energy of YPd3 is - 358.51 kJ/mol, for the monohydride YPd3H the energy is 316.28 kJ/mol, for YPd3H3 the energy is 235.98 kJ/mol and for the tetra hydrides YPd3H4 the formation energy is 175.87 kJ/mol (Table 1). The negative values of formation energies imply exothermic reactions, i.e. the stabilization of hydrides at ambient temperature and pressure. We separately evaluated the formation energies of a few hydrides of yttrium and palladium such as YH (198.78 kJ/ mol) and PdH4 (9.03 kJ/mol). From the calculations it could be concluded that the tetrahydride of pure palladium has the lowest value of energy and hence is most stable. Our calculations also confirm the experimental results that the heats of formation of palladium hydride are small compared to yttrium hydride [1]. The formation energies were obtained from energy differences between the total energy of compound and those of the

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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e1 2

Fig. 7 e Phonon dispersion relations of (a) YPd3 (b) YPd3H (c) YPd3H4.

atomic constituents Y, Pd and H, which were obtained from PAW-GGA calculations. The enthalpy of formation of YPd3 is 0.847 eV/atom, which increases with addition of hydrogen at the octahedral sites. The formation energy follows the trend of. YPd3 (0.847 eV) / YPd3H (0.653 eV) / YPd3H3 (0.323 eV) / YPd3H4 (0.275 eV) From the structural considerations, the lattice expansion on hydrogen insertion can be related to the formation energies which have negative values and indicate stabilization of hydrogen in YPd3. The energy is greatest for hydrogen at the 2Y4Pd octahedral sites, which implies easy retrievability of hydrogen in YPd3H4. Amongst the hydrides, YPd3H has minimum energy i.e. the octahedral interstitial 6Pd site is the most stable site for hydrogen insertion. These inferences from the formation energy that the preferential site for hydrogen insertion appears to be the 6Pd site are in agreement with neutron diffraction results of Yamaguchi et al. [16]. The total formation energy calculations do not predict dynamic instabilities, therefore the phonon spectra of YPd3 hydrides was calculated for the equilibrium lattice parameters and analysed in order to study its dynamic stability.

Phonon spectra and phonon density of states From the formation energies of La and Y hydrides as well as alkali-metal hydrides, it was found that few of the hydrides are not stable [18]. Similarly, from studies of the dynamic stability of PdH and defect phase Pd3VacH4, it was found that positions of hydrogen atoms in the defect phase strongly effects its stability [2]. Since the hydrides of metal Y and Pd are found to be stable, the YPd3 alloy also promises to have good hydrating properties. We therefore calculate the dynamic properties which have not been undertaken so far, to understand the stability of the hydrides of YPd3 due to site occupation. We have calculated the phonon frequency within the harmonic approximation using 4  4  4 super cells. From standard symmetry analysis of crystal point Group O_h (m3m), the phonons show infrared active modes. The calculated phonon spectrum is presented along special symmetry directions R-X-G-M-R-G (Fig. 7). Both the hydrides of YPd3 contain imaginary modes making the hydrides dynamically unstable. It is also seen that both hydrides have states at higher frequencies compared to the alloy YPd3. The zero-point frequencies are collected and presented in Table 3. The “i” represents imaginary modes and the blank positions indicate that the corresponding modes are not present.

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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e1 2

Table 3 e Vibrational modes of YPd3 and its hydrides. Modes

YPd3 (cm1)

YPd3H (cm1)

YPd3H3 (cm1)

YPd3H4 (cm1)

T1u(I) T1u(I) T2u T1u(I) T1u(I) T2u T1u(I) T1u(I) T1u(I)

5.2i* 129.5 137.6 198.3 e e e e e

91.2i 5.2i* 156.6 157 229.9 e e e e

432i* e 429.7i* 2.2i* 113.4 118.3 164.1 1605.9 e

530.4i* e 176.6i* 105.8i* 1.7 157.7 159.4 213.3 1560.1

*

‘i’ represents imaginary modes.

From the partial density of states (PDOS) of each displaced atom, it is found that phonon modes between 0 and 4.2 THz (modes T1u(I) with energy 16.05 meV and T2u with energy 17.06 meV) are essentially dominated by motion of heavy Pd atoms while the Y atoms have low contribution to these phonon modes. The phonon modes between 5 and 7 THz (mode T1u(I) with frequency of 24.59 meV) are essentially dominated by the Y atoms. Insertion of H at octahedral site (6Pd) i.e. in YPd3H, leads to softening of Pd modes which appear at 2.5 THz (negative values imply imaginary modes). The hydrogen states occur at higher frequencies >7.5 THz. In Table 3, the frequency corresponding to T1u(I) with energy 28.5 meV (229.9 cm1) appears to originate from dispersion caused by PdeH interactions whereas the mode at lower energy 19.5 meV (157 cm1) (T1u(I) and T2u) are due to YePd interactions. However with H atoms entering both octahedral sites, YPd3H4 becomes highly unstable with softening of Pd and H modes. Occupancy of hydrogen at all interstitial sites gives rise to very high energy mode T1u(I) at 193.4 meV (1560.1 cm1) which originates from dispersion due to HeH interactions. The T1u(I) modes at 26.4 meV (213.3 cm1) are due to YeH and PeH interactions, while the T2u(I) mode at 19.5 meV (157.7 cm1) once again are the YePd interaction modes. The dispersion relations in the hydrides thus possess in general three distinct regimes. The highest vibrational modes are due to vibrations of H atoms, whereas the vibrations of Y and Pd atoms contribute to the lowest modes. The middle modes form a bridge of vibrations between YeH and PdeH atoms. Optical mode at G (0, 0, 0) point in YPd3H and at X (0.5, 0, 0) and M (0, 0.5, 0.5) points in YPd3H4, which give rise to high peaks in the imaginary frequency regime could drive the dynamical instabilities. Occupation of the octahedral sites at 2Y4Pd by hydrogen atoms results in greater dynamic instability in YPd3. Thus it is seen that the dynamic stability of hydrides is strongly connected to the local environment of hydrogen atoms. For kinetic energy contributions, the vibrational dispersion relations thus give a good picture of stability of YPd3 on hydrogenation. It is also observed that the hydrogen at the 6Pd site gives real modes in YPd3H, whereas H-modes at 2Y4Pd site are imaginary and thus are not stable site for hydrogen occupancy. The intermetallic YPd3 is seen to allow easy

11

hydrogen insertion with marginal distortion in crystal structure.

Conclusions The hydrogen site occupation in ternary YPd3 alloys has been studied by two computational methods. The site preference and stability of an interstitial atom is determined by a combination of potential and kinetic energy considerations. From the PDOS of the monohydride YPd3H, it is observed that the hydrogen s-states are present deep down at low energies between. With further increase in the hydrogen content in YPd3H4, the H and Pd states hybridize and form a bonding band which occurs at lower energy in the VB region. Opening up of bandgap in the density of states in YPd3H states is observed, which may be associated with ordered state, whereas there is a smeared DOS with no gap in YPd3H4 which may be associated with disordered state. The position of the Fermi level is found to be quite sensitive to doping and changes due to presence of hydrogen. The opening of bandgap in monohydride YPd3H can be related to its greater stability compared to and YPd3H4. The formation energies of hydrides of YPd3 are negative (exothermic), which indicates stabilization of hydrogen in YPd3. Amongst the hydrides, YPd3H has minimum energy i.e. the octahedral interstitial 6Pd site is the most stable site for hydrogen insertion. Both the hydrides of YPd3 contain imaginary modes making the hydrides dynamically unstable compared to YePd alloy. In YPd3H, there is softening of Pd modes, although the hydrogen atom gives real modes. However with H atoms entering both octahedral sites, YPd3H4 becomes highly unstable with softening of both Pd and H modes. The optical resistivity is found to increase on hydrogenation. Similarly, reflectivity decreases or transmittance increases by ~40% with insertion of hydrogen, therefore YPd3 may have applications as a sensing device for monitoring hydrogen for using hydrogen safely. The heat capacity of YPd3H is slightly larger than YPd3, whereas cp of YPd3H4 is nearly unchanged. The electronic component of specific heat g ~ N(EF) has a greater value for hydrides compared to YPd3, which may be co-related to instability of hydrides. The thermal conductivity is also strongly temperature dependent and varies with change in hydrogen content. The dynamic and electronic calculations are in complete agreement the neutron diffraction studies. Hydrides with high hydrogen-to-metal ratio are formed in YPd3, but are not too stable, which implies that hydrogen can be released easily. Thus YPd3 can act as optical sensor as well as important potential hydrogen storage material.

Acknowledgements We are thankful to DAE-BRNS 2011/37P/29/BRNS/1782, Mumbai, India and CST CST/5093 (U.P), Lucknow, India for providing financial assistance in form of major research projects. We are grateful to Prof. Blaha and his team for the WIEN2k code and Prof. Kresse and team for VASP code.

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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e1 2

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