Adel F Al Alam
email: adelalalam@usek.edu.lb

Samir F Matar

Naïm Ouaini

Ab initio study of MgH2: destabilizing effects of selective substitutions by transition metals

Keywords: A, intermetallics, B, bonding, C, interstitial content, E, electronic structure calculation

The strong iconicity of H within rutile MgH2 is reduced by selective substitution of Mg by T (= Fe, Co, Ni, Pd, Pt) using trirutile super-structure host TMg2H6. These novel model systems, as computed in the quantum mechanical framework of density functional theory, showed a gradual decrease of the charges carried by H down to -0.02e improving the use of MgH2 for applications.

Introduction

Hydrogen storage materials such as hydrides are leading candidates for clean energy in the future. Archetype hydride MgH2 has been studied intensively owing to its large gravimetric density ~7.6 wt.%. However, its high thermodynamic stability prevents hydrogen absorption/desorption at mild conditions, whence the difficulty of its ad hoc use in applications. Experimental and theoretical efforts have culminated over decades to overcome the latter intricacy. The kinetics of hydrogenation were improved experimentally either by the addition of catalysts [1,2,3] or by the introduction of nickel as an adjoined metal such as in Mg2NiH4 [4]. Recent theoretical investigations suggested the insertion of light elements such as carbon and boron which decreased the largely ionic character of hydrogen in (B,C)0.167MgH2 [5].

The aim of the present study is to remedy the situation prohibiting the use of MgH2 in devices by selective substitution of Mg with transition metals (T = Fe, Co, Ni, Pd, Pt) in a trirutile host super-structure using first-principles density functional theory (DFT) calculations [6,7].

Structural details

As illustrated in Fig. 1, ordered trirutile TMg2H6 crystallizes as rutile with the tetragonal structure in space group P42/mnm (No. 136). Given in Wyckoff letter, T atoms occupy 2a sites at coordinates (0, 0, 0), and Mg atoms are found in 4e sites at (0, 0, z~1/3). There are two hydrogen sub-lattices, namely H1 at 4f (x, x, 0) and H2 at 8j (x, x, z). Both Mg and T species are surrounded by irregular H octahedra. Successive T-H planes (at z = 0 and z = 1/2) are separated by two Mg-H planes (at z~1/6 and z~1/3). Archetype MgH2 crystallizes with the tetragonal rutile structure in space group P42/mnm (No. 136). The latter order can be compared to the trirutile structure by substituting T species by Mg at 2a sites, whereby H atoms are located exclusively at 4f sites.

Computational methodology

Geometry optimization and total energy calculations were performed with the Vienna ab initio simulation package (VASP) [8,9]. The ion-electron interactions were described using the projector augmented wave (PAW) method [9,10]. Electron exchangecorrelation functionals were built within the generalized gradient approximation (GGA) scheme following the nonlocal correction of Perdew, Burke and Ernzerhof (PBE) [11]. It is important to mention that semi-core p states where accounted for PAW potentials of Mg in order to obtain the correct physical bulk properties and electronic structures for TMg2H6 models. The conjugate-gradient algorithm [START_REF] Press | Numerical Recipes[END_REF] is used in this computational scheme to relax the atoms and to optimize the structural parameters until the forces on all the unconstrained atoms were less than 0.02 eV/Å and all stress components were less than 0.003 eV/Å 3 . The tetrahedron method with Blöchl corrections [10] and a Methfessel-Paxton [START_REF] Methfessel | [END_REF] Gaussian smearing scheme were applied for both geometry relaxation and to accelerate the total energy calculations. Brillouin-zone (BZ) integrals were approximated using the special k-point sampling. The calculations are converged at an energy cut-off of 404 eV for the plane-wave basis set with respect to the k-point integration with a starting mesh of 444 up to 888 for best convergence and relaxation to zero strains.

In this work, the atomic charge of hydrogen is calculated using a Bader charge analysis [14]. The latter approach partitions the continuous electron density into region bounded by the minima of the charge density. Such an analysis can be useful when trends between similar compounds are examined; it does not constitute a tool for evaluating absolute ionizations. Bader's analysis is done using a fast algorithm operating on a charge density grid [15]. The results of computed charges Q are such that they lead to neutrality when the respective multiplicities are accounted for.

Results and discussions

Geometry optimization, cohesive energies and hydrogen charge density

In as far as TMg2H6 models are novel theoretical models chosen herein, geometry optimization was firstly performed. Starting and optimized structural parameters are given in Table 1. Rutile-type MgH2 was also examined to establish trends of stability for the computed TMg2H6 models. The calculated structural parameters for MgH2 are within 2% of the experiment. All TMg2H6 models relaxed in the trirutile structure. The stability of these models can be examined from the computed total electronic energies given in Table 2.

The cohesive energies of various TMg2H6 structures were calculated with the expression

Ecoh. = E(T2Mg4H12) -2E(T) -4E(Mg) -6E(H2)
The energy terms on the right-hand side of the equation represent, in order, trirutile hydride model, pure T metal, pure Mg, and gas-phase hydrogen. The strength of cohesive energy of a model is a measure of the stability of that model. Largely negative Ecoh.

indicate stable binding, whereas positive energies correspond to an unstable model. The energy of the gas-phase hydrogen dimer was calculated with an 8×8×8 cell. The cohesive energy per H2 of MgH2 is calculated within 8% of the experimental value -0.79 eV [START_REF] Yamaguchi | Materials Science and technology[END_REF].

The computed Ecoh. per H2 values in Table 2 clearly indicate that all TMg2H6 models are stable owing to the negative values. Compared to MgH2, all models are less stable. The latter finding meets with the aims of this study in as far as less thermodynamically stable hydrides are sought.

The latter should be comforted further by examining the atomic charge of hydrogen shown as a function of T species in Fig. 2. As expected, hydrogen exhibits a less ionic character near T elements (H1 sub-lattice) compared to H charges near Mg (H2 sublattice). This can be explained by the electronegativity value of the different species given in the Pauling scale:

χ(Mg) = 1.31, χ(Fe) = 1.83, χ(Co) = 1.88, χ(Ni) = 1.91, χ(Pd) = 2.
2, and χ(Pt) = 2.28. All T elements are more electronegative than Mg, whence the less ionic hydrogen in their surroundings. Furthermore, H1 charge near T elements undergoes gradual reduction of its ionic character from H -0.4 for FeMg2H6 model down to H -0.02 for PtMg2H6. The latter value is also due to the large H1-Pt separation dH1-Pt = 1.80 Å. The other hydrogen sub-lattice, namely H2, exhibits a constant evolution around a charge of -6e. Nevertheless the overall changes brought by T are established. This substantial reduction of the carried charge by H predicted theoretically should be an indication of the readiness of H desorption experimentally. It is important to mention that smaller amounts of metal would be needed to strongly modify MgH2 especially with platinum which is an expensive metal. Tests are underway with experimental groups at our Institute.

Further we comment on the relative changes of charges on T using the Bader charge analysis. The values are as follows: Fe+0.71; Co: +0.50: Ni: +0.52: Pd: 0.27; Pt: +0.13. The ionization degree follows closely the electronegativity magnitude with the following trend: the least electronegative is the least charged.

Electronic density of states: DOS analysis

Fig. 3 shows the site projected density of states (PDOS) corresponding to Mg3H6 and TMg2H6. The energy along the abscissa axis is brought to E V , top of the valence band (VB) which is separated from the conduction band (CB) by a band gap of ~3.5 eV for trirutile-Mg 3 H 6 (Figs. 3a andb). This agrees with the insulating character of archetype MgH 2 showing a band gap of ~5.6 eV [START_REF] Moysés Araújo | [END_REF]. The VB is dominated by H (H1 and H2) with prevailing H2 intensities due to their higher multiplicity with respect to H1. Magnesium PDOS are dominating within the CB due to their low filling and electron departure towards H. The DOS's of TMg2H6 show a few similar feature with MgH 2 -like DOS within the 8 eV range from -2 to -10 eV (Figs. 3c,d,e). Similar DOS skylines are also observed within the CB between itinerant T states and the Mg/H states. The band gap has decreased down to ~2.

Conclusion

The use of trirutile host super-structure allowed selective substitution of Mg by T elements. This brought significant effects relevant to the reduction of the strong ionic character of H which prohibited the use of rutile MgH 2 in applications. The introduction of T species tends to narrow down the band gap of MgH 2 leading to total metallization. Then smaller amounts should be introduced in order to preserve the insulating properties of MgH 2 as future works are planned.

Table 1: Optimized and (starting experimental when available) structural parameters for MgH2 and TMg2H6 models. The distance separating H1 sublattice from T element is also given.

  5 eV for Fe due to the covalent character brought in by iron. From Co to Ni and Pt the extra electrons brought by the increasing Z number shifts E F to the states Mg and H formerly found within the CB. However the doping is far too high and leads to closing of the gap. A peculiar feature appears for the localized (sharp) T nd-states PDOS which signals little mixing with the host Mg and H states and could be labeled as non bonding, as shown by the small PDOS magnitude of Mg and H below the Fe(d) PDOS for instance. The insulating character is preserved is as far as the energy is still referred the top of the VB but the gap is much reduced down to ~0.3 eV. Clearly the amount of transition metal is too large (FeMg 2 H 6  Fe 0.333 Mg 0.6667 H 2 ) by experimental standards. Note that some of the other transition elements candidates have shown total metallization, i.e. a closing of the band gap. Then smaller amounts of T elements should be introduced in order to preserve the insulating properties of MgH 2 and future works are planned. Nevertheless, our approach using trirutile host structure has shown relevant effects brought by T substitution on the electronic structure of MgH 2 owing to the use of trirutile super-structure allowing selective substitutions of Mg.

Fig. 1 :

 1 Fig. 1: (Color online) Sketches of the crystal structures of rutile-type MgH2 (left-hand side) and trirutile-type TMg2H6 (right-hand side).

Fig. 2 :

 2 Fig. 2: (Color online) Atomic charge of hydrogen QH as function of T species in all TMg2H6 models for H1 and H2 sub-lattices. All values of QH are given as a multiple of elementary charge (e = 1.6 × 10 -19 C).

Table 2 :

 2 Total electronic energies and cohesive energies in units of eV for all TMg2H6 models.

	Structure	E(T2Mg4H12) E(T)	E(Mg) E(H2) Ecoh.	Ecoh./H2
	MgH2 (rutile) FeMg2H6 CoMg2H6 NiMg2H6 PdMg2H6 PtMg2H6	-17.570 -64.517 -61.742 -57.907 -56.832 -59.140	-7.813 -6.810 -5.725 -5.360 -5.366	-1.487 -6.52 -1.556 -0.778 -1.487 -6.52 -3.823 -0.637 -1.487 -6.52 -3.054 -0.509 -1.487 -6.52 -1.389 -0.232 -1.487 -6.52 -1.044 -0.174 -1.487 -6.52 -3.340 -0.557

Acknowledgement

We acknowledge financial support from French-Lebanese CEDRE project and CSR-USEK.

Part of the calculations where done on MCIA super computers of the University Bordeaux 1. Support from the Conseil Régional d'Aquitaine is gratefully acknowledged.

Structure