Improvement of hydrogen uptake in iron and vanadium matrices by doping with 3d atomic impurities

Journal of Alloys and Compounds 545 (2012) 19–27

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Improvement of hydrogen uptake in iron and vanadium matrices by doping with 3d atomic impurities N.B. Nguyen a, A. Lebon a,⇑, A. Vega a,1, A. Mokrani b a b

Laboratoire de Magnétisme de Bretagne, EA 4522 Université de Bretagne Occidentale, 6 avenue Victor Le Gorgeu, 29285 Brest Cedex, France Institut des Matériaux Jean Rouxel, UMR CNRS 6502, Université de Nantes, 2 rue de la Houssinière, B.P. 44322 Nantes, France

a r t i c l e

i n f o

Article history: Received 18 April 2012 Received in revised form 4 July 2012 Accepted 20 July 2012 Available online 28 July 2012 Keywords: Hydrogen absorbing materials Metals and alloys Transition metal and compounds Computer simulations

a b s t r a c t The insertion of hydrogen in V and Fe has been investigated by means of pseudopotential DFT calculations with localized basis sets. In Fe and V matrices we have replaced the central atom by a transition metal impurity X = Sc, Ti, Cr, Mn, Fe, Co and Ni to study the capacity of the environment to trap hydrogen. The dissolution energy and structural rearrangement upon H uptake at the different sites close to the doping impurity are calculated. Optimal electronic environments for H trapping are also determined through the calculation of the Fukui function. In the V matrix, the insertion of hydrogen is promoted by doping with the two impurities located at the left of V in the Periodical Table, that is, Ti and Sc. In the iron matrix, among the elements at its left in the Periodic Table, only Mn improves the H uptake, whereas doping with V and Ti worsen the capability of absorbing hydrogen. Finally, the H–H interaction is found to be strongly dependent upon the metal–hydrogen interaction. Elements like Mn or Fe which shorten the H–X distance, exhibit a strong 3d TM state–1s hydrogen state hybridization that seems to wash out the repulsive H–H Coulomb interaction below the 2.0 Å limit. Addition of a small percentage of Fe or Mn in binary bcc alloys (V–Ti) is suggested to locally enhance the H storage capacity. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Physics and chemistry of hydrogen in solids cover many current research lines such as insertion and diffusion in membranes [1], heterogeneous catalysis at surface and interface of metals [2], or hydrogen storage in solids [3]. Hydrogen storage is precisely regarded as one of the key issues to be solved in the developing field of hydrogen technology. Different solutions have been envisaged to store a large amount of hydrogen either in gaseous or liquid form as well as in a solid compound. This latter method is thought to provide a good compromise as it offers a safe solution and enable to reach very high density. Many metal-based materials have been studied both experimentally and theoretically, examples of which are the hydrides with alkaline-earth, the borohydrides [4,5] or the Li-amide-imide compounds [6]. They offer promising weight– storage ratios with hydrogen percentage values as high as 20.8% for the Mg(BH4)2 [5]. All these compounds in crystalline form display a complex sequence of phase transitions, the most interesting structure being only accessible under pressure. Many of them desorb hydrogen at high temperature, like in the highly exothermic chemical reaction of H2 absorption in Li-amide-imide which leads ⇑ Corresponding author. E-mail address: [email protected] (A. Lebon). Permanent address: Departamento de Física Teórica, Atómica, y Óptica, Universidad de Valladolid, Spain. 1

0925-8388/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2012.07.100

to a high desorption temperature. Albeit these light-metal hydrides are capable of storing a high density of H, their use is limited by thermodynamical conditions that put in question their suitability for practical applications. In the case of Li-amide-imide host, in order to improve these conditions and performance, doping with transition metal (TM) atoms is proposed as a mechanism to reduce the reaction enthalpy [6,7] and, therefore, the H desorption temperature. TM atoms not only play an important role as impurities in substitution in a variety of hosts, but they can also form interesting alloys or hetero-structures with H storage capability. As far as alloys are concerned, Ti–Cr ones incorporating an homogeneous distribution of V atoms [8], as well as LaNi5 ones, [9] exhibit promising H storage capability. Theoretical studies on this research line are still sparse. Smithson et al. analyzed the formation of hydrides in elemental metals like the alkaline earth or the transition metals and proposed a three step process to account for the formation of the hydride [10]. Three contributions were proposed to explain the capability to insert H and to form hydrides. The first is the energy to convert the crystal structure of the metal in the structure formed by the metal ions within the hydride. The second contribution is the loss of cohesive energy upon expansion of the metal structure to form the hydride. The last contribution to the hydride formation energy is the chemical bonding between the hydrogen and the metal host, this being the only exothermic contribution, and hence, the sole

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which favors the hydride formation. An energetic analysis was conducted by Miwa et al. [11] on transition metals with similar conclusions. More recently, Ouyang and Lee [12] focused on the insertion of H in vanadium and demonstrated the capability of this material to store a large amount of hydrogen in the vicinity of vacancies. So far, most of the studies were devoted to elemental systems while the experimental research effort is clearly oriented towards optimizing the properties of alloys [13,14]. Among the many alloys relevant for the design of fuel cells, those that crystallize in a bcc structure such as the V–Ti alloys or the Fe–Ti alloys, hold a prominent place. The bcc structures of the elemental vanadium and iron exhibit very different behavior under hydrogenation. Bcc vanadium stores hydrogen in a reversible fashion and displays a bcc to fcc phase transition during the formation of the VH2 hydride. On the contrary, bcc iron is not prone to absorb hydrogen. It has even been shown by density functional calculations that H tends to localize on the iron surface [15]. This finding may explain the accumulation of H2 gas at the grain boundaries or near defects that could induce embrittlement in the iron based compounds. The aim of the present work is twofold. On the one hand, for V bcc our purpose is to find optimal doping elements that enhance the hydrogen uptake; on the other hand, for Fe bcc it is to find trapping centers for H avoiding its migration to the surface. To this end, we have considered 65-atoms cluster of Fe or V with a bcc structure. This cluster is formed by three concentric layers or atomic shells (including the central atom), with 1, 14, 50 atoms, respectively. The outer shell comprises the 50 surface atoms. This size suffices to mimic the properties of the bulk material according to photoelectron spectroscopy data [16,17]. In fact, it has been shown that the photo-electron spectra of a Vn [16] or Fen [17] have the essential features of the bcc solid for cluster of 60 and 20 atoms, respectively. We have studied how a 3d atomic impurity in substitution X = Sc, Ti, V, Cr, Mn, Fe, Co and Ni, located at the center of the cluster, affects the structural and electronic properties of the matrix. In a second step, one and two H atoms have been inserted at the vicinity of the 3d impurity to get insight on the structural and energetic aspects related to H loading as well as to H–H interaction in the presence of a variety of possible trapping centers. The essential technical details of the calculations carried out in this work are described in Section 2. In Section 3 we first discuss the effects of X substitution before H loading and then we address the insertion of a single H atom. Section 4 is devoted to the study of the insertion of two H atoms in the pure V and Fe matrices. Section 5 deals with the insertion of two H atoms and their interaction in the doped V or Fe matrices. Finally, Section 6 summarizes our main conclusions.

2. Theory and computational details Our calculations have been performed using the ab initio DFT code SIESTA [18–20] which employs linear combination of pseudo-atomic orbitals as basis sets. We calculated the exchange and correlation potential with the generalized gradient approximation (GGA) as parametrized by Perdew, Burke and Ernzerhof [21]. The nonlinear core corrections [22] are included to account for the significant overlap of the core charge with the valence d orbitals and to avoid spikes which often appear close to the nucleus when the GGA approximation is used. We replaced the atomic core by a non-local norm-conserving Troullier–Martins pseudo-potential [23] which was factorized in the Kleinman–Bylander form [24]. All the data for generating the pseudo-potentials is gathered in Table 1. The 3p semi-core states have been taken out from the cores of Sc, Ti, V and Cr to achieve a more realistic description of the properties of the system [25]. In the case of V atoms, this has been shown, on the one hand, to considerably improve the descrip-

Table 1 Valence configuration and cutoff radii (in Bohr) for the generation of the Troullier– Martins pseudo-potentials used in this work, all within the non-local exchange correlation functional of Perdew–Burke–Erhezenof [21]. The nonlinear core corrections are included at radius rnlcc. Atom

Configuration

s

p

d

rnlcc

Sc [39] Ti V [28] Cr Mn [40] Fe [28] Co [41] Ni [41]

[Ne3s2] 3p63d14s2 [Ne3s2] 3p63d24s2 [Ne3s2] 3p63d34s2 [Ne3s2] 3p63d54s1 [Ar] 3d54s24p0 [Ar] 3d74s14p0 [Ar] 3d84s14p0 [Ar] 3d94s14p0

2.57 2.50 2.50 2.33 1.98 2.00 2.00 2.05

1.08 2.20 2.17 1.30 2.18 2.00 2.00 2.05

1.37 2.20 0.90 1.49 1.88 2.00 2.00 2.05

– 1.10 1.20 0.80 0.70 0.70 0.70 0.70

tion of the magnetic trends in semi-infinite systems [26,27], and on the other hand, to improve the inter-atomic distance of the dimer [28]. We also note that the electronic configurations used to generate the Fe, Co and Ni pseudo-potentials correspond to an excited state (see Table 1). These pseudo-potentials are known to reproduce the correct spin state of the Fe, Co or Ni dimers [29]. We have tested that these pseudo-potentials accurately reproduced the eigenvalues of different excited states of the respective isolated atoms. Concerning the basis sets, we have described the valence states using Double f Polarized pseudo-atomic orbitals (DZP). For the V(Fe) clusters, a 350(450) Ry energy cutoff defines the real space grid to compute the exchange and correlation potential and to perform the real-space integrals that yield the Hamiltonian and overlap matrix elements. We also smoothed the Fermi distribution function that enters in the calculation of the density matrix with an electronic temperature of 15 meV(180 K) [28]. A simulation cell of 25 Å was chosen to avoid the overlap of the orbitals between the adjacent replica. A conjugate gradient method was used to relax the atomic positions until the interatomic forces were smaller than 0.005 eV/Å. Both paramagnetic and spin polarized calculation were carried out. For the calculation of the energies we have considered the ghost atom method to correct the basis set superposition error (BSSE) that arises due to the different dimension of the Hilbert spaces associated to the initial and final systems whose energy difference is computed, which otherwise would imply different degrees of freedom in the variational determination of the energy of each system. The ghost atom means additional basis wave functions centered at the atomic position where it is located, but without any atomic potential. Similar correction were applied by some of the authors on a related system [28]. In the following sections we define the dissolution and the insertion energy. To begin, the insertion energy per H atom EðnÞ ! is defined as

EðnÞ ! ¼

1 ðnÞ ðE  ðEð0Þ þ nEH ÞÞ n

ð1Þ

(n)

where E is the energy of the cluster with n inserted H atoms, n being 0, 1 or 2. EH stands for the energy of an isolated hydrogen atom. The binding energy per H atom Eb/at in the H2 molecule is then computed according to the relation:

Eb=at ¼

EH2  2EH 2

ð2Þ

Our computation gives 2.143 eV for the binding energy, a value which reasonably underestimates by 4% the experimental value of ðnÞ 2.239 eV. The dissolution energy Edis is further derived after the subtraction of the binding energy from the insertion energy and the relation given by Jiang and Carter [15] is obtained: ðnÞ

Edis ¼

  EH 1 ðnÞ E  Eð0Þ  n 2 n 2

ð3Þ

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3. H trapping by an impurity in V and Fe matrices 3.1. H free doped V and Fe matrices Prior to H insertion, an X atomic impurity (X = Sc, Ti, V, Cr, Mn, Fe, Co, Ni) is substituted at the center of the V or Fe clusters. Fig. 1 displays the central X atom embedded in a cube of V or Fe atoms, this chemical environment mimics the prototypical B2 environment encountered in FeTi of VTi alloys. Table 2 summarizes the structural and magnetic data (in the case of the Fe matrix). In the V64X clusters, the impurities at the left side of vanadium in the periodic table repel their first and second V neighbors. Beyond the second neighbors the induced displacements become negligible. The expansion caused by Sc and Ti as subsitutional impurity in the V matrix is consistent with the increase of the atomic radius as moving from the right to the left in the 3d row of the periodic table. On the contrary, a contraction of the cell is observed for the impurities at the right side of vanadium in the periodic table. Only the paramagnetic solution was found for V64X cluster. In fact for a low impurity concentration, below 10%, Green function calculations in the coherent potential approximation [30] have shown that V layers doped with TM magnetic impurities (TM = Fe, Co, Cr, Ni) remained in a paramagnetic state. In the Fe64X cluster, an expansion of the cell is obtained when doping with impurities located at the left of iron in the periodic table, while a slight contraction occurs with Co or Ni as doping elements. For the Fe64X system, the magnetic solution was the most stable one, in keep with the theoretical and experimental results of Drittler et al. [31] regarding the magnetic coupling of transition metal impurities within bulk Fe. That is, Fe couples ferromagnetically with the Mn, Fe, Co and Ni atomic impurities and antiferromagnetically with the rest. The charge transfer on each impurity atom has been computed as well with two charge schemes namely the Mulliken population provided as output by SIESTA and the Bader charge analysis extracted from a grid integration method [32]. The Bader method divides the system in atomic volumes which are defined according to the zeroflux regions of the charge density field. The results of the two schemes are at odd. Owing to chemistry consideration, specifically the value of electronegativity in the sense of Pauling, the charge assessed by the Bader method is clearly the better choice. For instance, for an Fe impurity in the vanadium matrix the Mulliken population predicts a loss of 0.28 e of the iron atom towards the vanadium matrix. In return the Bader analysis predicts a charge transfer from the vanadium matrix to the Fe impurity since the Fe impurity gains 1.04 e. Fe atom has a stronger electronegativity

that amounts to 1.83 against 1.63 for vanadium, that is a power to attract the electronic density of the surrounding vanadium atoms. From the aforementioned argument it is reasonable to use the Bader charge analysis. Additionally this analysis relies on the charge density and thus is less sensitive to the choice of the basis set. Electronic effects should also play a role on the stability of H inside the nanoparticles. Electronic bonding of H with its nearest neighborhood is expected to be more or less favorable according to different chemical environments and corresponding electronic redistribution. To determine the best chemical environment according to electronic arguments, we have computed the Fukui functions f+ that is associated with the lowest unoccupied molecular orbital (LUMO) and is an indicator of reactivity toward a donor reagent. In fact, atomic hydrogen has been demonstrated to behave as an electron donor in vanadium matrix by a coupled theoretical and experimental study due to Duda et al. [33]. This f+ function has been chosen to get a qualitative idea of what should be expected for the H insertion according to the impurity. The f+ function has been assessed in the H-free nanoalloys for the tetrahedral and the octahedral sites sketched in Fig. 1. The f+ Fukui function is defined as [34–36].

f þ ð~ rÞ ¼

@ qð~ rÞ @N

ð4Þ

where qð~ rÞ is the spatial charge density and N is the number of electrons. f+ gives a measure of the local fluctuations of electronic charge and, more specifically, it can be used as an index of electronic reactivity of the different spatial regions of the system. As we are using a localized basis set, we can define fiþ as the variation of the charge deduced from the Bader analysis for the atom i [34]. To calculate this derivative we have converged the electronic structure of the different nanostructures with an excess of electronic charge ranging from 0 to 4 e, the net charge of the cluster accordingly was varied from 0 to 4 by step of one half of an electronic charge. Further on we have fitted our results with a linear regression as the correlation coefficient turned out to give value comprised between 0.9 and 1.0, suggesting a linear variation of the function with the increase of the number of electrons. The Fukui function f+ for H absorption on tetrahedral and octahedral sites are obtained after averaging environment of 4 and 6 atoms surrounding the H atom (see Fig. 1). A larger value of this function should correlate with more reactivity of the corresponding environment within the nanoparticle. Fig. 2 plots the f+ Fukui function for the tetrahedral and octahedral environments of the V64X and

9

(0,1/2,3/4) (1/2,1/4,1)

8 (1/2,0,3/4)

6

7 (0,1/4,1/2)

X

(0,3/4,1/2)

5

(0,1/2,1/2)

(0,1/2,1/4)

4

(0,0,1/2)

(1/2,0,1/4)

2

(1/2,3/4,0)

3

(0,1/2,0)

1 (1/2,1/4,0)

z

X

3

4

2

1 (1/2,1/2,0)

y x

V/Fe

V/Fe

Fig. 1. Tetrahedral and octahedral sites of the H atoms inserted in the clusters. The atomic positions are given in fractional coordinate, the central cubic unit has its origin on the V/Fe atom. The black ball is the central atom of the cluster that is substituted by an X element. White balls are V or Fe. The metallic structure is similar to the prototypical CsCl (B2) structure. The small dark blue (dark gray) balls are the reference position for a single H atom. The small light blue (light gray) balls are additional position tested when a second H atom is added (see Table 3). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Table 2 Changes induced by X substitution of the V(Fe) central atom in the V(Fe) matrix. Left side of the table corresponds to the V based compounds, right side to the Fe based compounds. d1 is the first neighbor distance to the central atom and d2 the second neighbor distance to the same central atom. dQMul and dQBad express the charge transfer on the impurity atom computed with the Mulliken and Bader schemes, respectively. All distances are expressed in Å. The charge transfer is expressed as a number of electron, i.e. a negative sign indicates a loss of electronic charge of the impurity. l, the moment of the impurity in the Fe cluster is given in unit of Bohr magneton lB. Parallel and anti-parallel coupling (negative sign) of the X impurity embedded in the Fe matrix are also listed. X

d1

d2

dQMul (dQBad)

d1

d2

dQMul (dQBad)

lMul (lBad)

Sc Ti V Cr Mn Fe Co Ni

2.67 2.64 2.59 2.56 2.54 2.56 2.57 2.59

2.97 2.95 2.94 2.95 2.93 2.92 2.92 2.92

0.80 (0.88) 0.30 (0.65) 0.00 (0.00) 0.10 (0.51) 0.49 (0.97) 0.28 (1.04) 0.26 (1.16) 0.08 (1.19)

2.61 2.55 2.53 2.56 2.56 2.52 2.51 2.53

2.94 2.93 2.93 2.93 2.93 2.92 2.92 2.91

0.04 (1.18) 0.24 (0.74) 0.23 (0.20) 0.51 (0.01) 0.30 (0.74) 0.00 (0.00) 0.04 (0.40) 0.13 (0.56)

0.64 (0.48) 1.41 (1.47) 2.28 (2.72) 3.19 (3.74) 3.04 (4.08) 2.57 (2.49) 1.59 (1.29) 0.67 (0.30)

0.004

d HX-d HV (Å)

0.2

0.0

(a)

-0.1 0.000

-0.2 200

+

f Fukui finction

0.002

0.1

100 0

1

-0.002

E dis (meV)

T site (V64 X) O site (V64 X) T site (Fe64 X) O site (Fe64 X)

(b)

-100 -0.004 Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Fig. 2. Evolution of the f+ Fukui function at tetrahedral (T) and octahedral (O) sites tested around the impurity. The black line stands for the f+ Fukui function associated with the X impurity in the V matrices whereas the red line (light gray) corresponds to f+ of the X impurity in the Fe matrices. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fe64X clusters. As to the V matrix, the Fukui function is positive for all the X impurity except Mn. Thus the environment can trap atomic hydrogen that yields parts of its electronic charge. The f+ Fukui function has also been computed in Fe matrices with different X doping impurities; in this case the values are always smaller than in the vanadium matrix. The sign of f+ oscillates around the zero value suggesting that these Fe based matrices are less reactive towards H insertion than vanadium based matrices. We note however an exception for Mn. This f+ function does not exhibit significant difference of values between the tetrahedral and octahedral interstice. Therefore from this data there is no electronic argument for H to prefer one site from the other. Anticipating a bit on the forthcoming findings, the overall results derived from the Fukui function have some common features with the evolution of the dissolution energies like a maximum for X = Mn for the Fe64X cluster a larger value of f+ in V based matrices than in Fe based matrices. For X = Ti and V in the V64X clusters the highest f+ values are reported. 3.2. H loaded doped V and Fe matrices Let us turn to the possible sites of H insertion within the local environment of the doping impurity. There is one tetrahedral site and two possible octahedral sites that are distinguished because of their respective distances to the central X atom. These insertion

-200

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Fig. 3. Structural and energetic characteristics of the insertion of one H atom in the X doped V compounds. Panel (a) gives the evolution of the H–X distance compared to the distance of H with the central V atom of the pure V cluster. Lower panel (b) plots the variation of the H atom dissolution energy as a function of the X doping element.

sites are sketched in Fig. 1 as small dark blue (gray) balls. Additional octahedral and tetrahedral sites are displayed in this figure and will be considered in the following sections. In our V64X and Fe64X clusters, the tetrahedral and the two octahedral sites were tested. In most cases the tetrahedral site was the most stable site. Only for V64Ni, an octahedral site appeared as the most stable position. In Fig. 3, we plot the difference between the H–X distance and the reference H–V distance measured in the non-doped V65 matrix. The dissolution energy of an H atom is also given as a function of X or in other words as a function of the d-band filling of the doping impurity. For elements like scandium or titanium, the H–X distance is larger than the H–V distance in non-doped V65 cluster. In return, for impurities at the right side of vanadium in the periodic table, the H–X distance is smaller than the reference H–V distance in the non-doped V matrix. The H–X separation decreases as the impurity band filling increases. As to the energetic aspects, the dissolution energy changes abruptly when the d-band is more than half filled. Thus, from X = Mn to Ni, the dissolution energy is positive while it is negative from X = Sc to Cr. This latter result is consistent with the high storage capability of V–Ti alloys and explains the interest for this alloy [8,13]. In all the V64X clusters except X = Ni, the H atom sits in a tetrahedral interstice. In its tetrahedron of coordination, the H atom is nearest neighbor of the impurity

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N.B. Nguyen et al. / Journal of Alloys and Compounds 545 (2012) 19–27

(a)

0.5

Table 3 Initial positions between the two H inserted atoms and the H–H distance in Å unit for the V or Fe based compounds. The superscript in the notation of the distance indicates the majority element in the cluster. The labeling of the initial H position is T for tetrahedral sites and O for octahedral sites. For instance in T15, the index 15 corresponds to a first H atom at position 1 and a second H atom at position 5 (see Fig. 1).

dHX-dHFe (Å)

0.4 0.3 0.2 0.1

Initial positions T12

0.0

dH—HFe

-0.1

dH—H

V

400

80

300

60

T15

T16

T17

T18

O12

O13

T 14 Δ E (meV)

1

E dis (meV)

T14

O14

(b)

500

200 100 0

T13

1.05 1.40 1.80 2.08 2.32 2.51 2.71 1.40 2.08 2.51 1.14 1.44 1.81 2.11 2.34 2.56 2.87 1.44 2.11 2.56

Sc

Ti

V

Cr

Mn

Fe

Co

T 18 T 16

40

T 17 20 0

Fig. 4. Structural and energetic characteristics of H atom insertion in the X doped Fe compounds. Panel (a) plots the evolution of the H–X distance compared to the distance of H with the central Fe atom of the pure Fe cluster. Panel (b) gives the variation of the H atom dissolution energy in the Fe cluster when the X atom substitutes to Fe.

4. H–H interaction in pure Fe and V matrices Let us turn now to the addition of a second hydrogen atom in the central cell of the pure V or Fe matrix. In Table 3, we summarize the configurations tested for the two H atoms, indicating the initial distance between the H atoms in each set. A labeling is proposed to identify the position of the H atoms according to Fig. 1, that is, an initial configuration T15 means one H atom at site 1 and the other at site 5. Site 9 is just a translation by a unit cell parameter of position 1. In the same way as in Fig. 2, a numbering

80 60

Δ E (meV)

atom as well as of a V atom located at 1.75 Å, a distance that remains unchanged for the different impurities. The two other V atoms are further apart. The X–H–V angle, where V is the nearest neighbor exhibits a monotonous increase from 110° for X = Sc to 180° for X = Ni. Thus, there is a progressive transition from a distorted tetrahedral environment to an octahedral environment. This transition is made possible by the ease distortion of the V cluster owing to its low bulk modulus so as to fulfill the criterion of the H–V distance. Fig. 4 is the equivalent of Fig. 3 for the doped Fe matrices. The H–X distance compared to the H–Fe reference distance evolves in much the same way as in the doped V matrices. For instance, H– Fe is clearly smaller than H–Ti but larger than H–Ni. The most marked difference is found for the dissolution energy. In the Fe matrix, the element immediately at the left of iron lowers the dissolution energy to a 0.15 eV value that emphasizes the endothermic character of H uptake in Fe matrices [15]. This result clearly reveals that H cannot be trapped in an environment where the Fe atoms are majority and impose an overall magnetization, unless some pressure is added to insert the H atoms. Only when the magnetic couplings are switched off assuming no structural change, the dissolution energy become slightly negative with Cr as doping impurity. As in the V matrices, H atoms sit in tetrahedral interstices. The H atom maintains a constant distance of 1.68 Å to its Fe nearest neighbor. In contrast to the V matrices, the greater rigidity of the Fe matrices, that can be accounted for by the larger bulk modulus of bulk iron, explains the stability of the tetrahedral sites.

V cluster

T 15

Ni

T 14

Fe cluster 40

T 16

20

T 15

T 18 T 17

0 1.75

2.00

2.25

2.50

2.75

d H-H (Å) Fig. 5. Total energy variation as a function of the H–H distance in the pure V or Fe clusters. The energy reference is taken at the most stable site for each matrix. The vertical dashed line at 2.00 Å correspond the dsw distance (see text). Black open circles are the equilibrium distances of the two H atoms after relaxation of the forces, green open circles are the initial distances. On top or below the initial distance, the initial position label T1x with x = 4, 5, 6, 7, 8. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

of the octahedral position is given. All these initial positions were tested for all the investigated V and Fe clusters. Mixed configurations were also tested, that is configurations where a H atom sits on the first T site and the second atom sits on an octahedral site. This proved to be relevant for X = Ni in the V matrix. Except for the Ni doped V matrix, only the T1x with x = 4,5,6,7,8 configurations resulted stable after the self-consistent calculation and the relaxation of the forces. Fig. 5 displays the variation of the total energy as a function of the H–H distance, the zero of energy is taken at the most stable configuration. For the V matrix, the minimum energy corresponds to hydrogen atoms at fourth distance (T15) to each other. The H–H distance is clearly shorter in the V matrix, where it amounts to 2.01 Å, than in the Fe one, where the minimum energy corresponds to hydrogen atoms at sixth distance (T17) to each other, 2.51 Å. We note that in the case of the Fe matrix, a local minimum is also observed at the same H–H distance as in V matrix. Whatever the matrix, the distance that fulfills the minimum energy is superior or equal to the 2.0 Å Switendick’s criterion [37] that will be referred to as dsw in what follows. Below this dsw distance, the interaction between the two H atoms appears as repulsive in both V and Fe matrices. This can be assigned to the repulsive coulomb interaction between the H atoms. In fact, the H atoms donate

N.B. Nguyen et al. / Journal of Alloys and Compounds 545 (2012) 19–27

5. H–H interaction in doped Fe and V matrices Fig. 6 presents the evolution of the H–H distance as a function of the doping impurity within the doped V matrix. As in the pure V matrix, all the H–H separations correspond to hydrogen atoms at fourth distance of each other. Fig. 6 demonstrates that for doping elements like X = Mn, Fe or Co it is possible to go below the dsw limit. The H–H shortening can be assigned, for these particular doping impurities, to the observed shrinking of the H–X distance. In fact, the H–X separation, not plotted here, has been followed as well. It decreases monotonically from almost 2.0 Å for X = Sc to 1.58 Å for X = Ni. This H–X distance evolves exactly in the same way for one or two H atoms in the vicinity of the X impurity. This finding suggests that doping with transition metal elements like Mn, Fe, Co can locally enhance the H density. The reported trend for the H–H separation is broken in the case of X = Ni, for which the two interstitial sites are of different kinds. In fact, a coexistence of a tetrahedral and an octahedral interstitial site is associated with a subsequent lengthening of the H–H distance. Interestingly, it is worth noting that H is known to form an hydride within Ni that crystallize in a rock-salt structure [10], where the H atoms sit exclusively in octahedral sites. Insofar the dissolution energy is concerned, it is lowered if X = Sc, Ti whereas it raises (and reaches a plateau) from X = Cr to Ni. This result confirms that the V–Ti alloys are very auspicious compounds for H insertion, the H–H separation being slightly larger than dsw; this is no longer true if X = Sc since the H–H distance amounts to a value of approximately 2.6 Å. It can also be stressed that doping impurities like Cr, Mn, Fe or Co which reduce the H–H distance below dsw, seem less favorable to store a second H atom. As stated in the work of Ouyang and Lee [12] it is very likely that the H–H interaction is no longer negligible as the H–H separation becomes smaller than the dsw limit. To get more insight into this issue, we decomposed the insertion energies E? into a purely electronic contribution and a contribution of the structural expansion upon H insertion. This latter contribution is computed as an energy difference of the metal clusters before and after H loading, using the H atoms as ghost atoms in the H-free and H-loaded systems. The electronic term, referred to as EðnÞ e , is the sum of the E? and the energy associated ðnÞ with the ionic displacement labeled Ei . This term encompasses the hydrogen–metal and the X–V(Fe) interactions when only one H atom is absorbed. It contains the contribution of the H–H interaction as soon as a second H atom is inserted. Table 4 gathers all

d H-H (Å)

2.5

2.0

200 150

(2)

0.12 e per H atom in the Fe matrix and 0.17 e per H atom in the V matrix (the charge per H atom amounts to 0.88 e in the Fe matrix and to 0.83 e in the V matrix). As a consequence, the coulomb repulsion can explain the intensity of the H–H repulsion in both matrices. Our results are thus in keep with the findings of Ouyang and Lee [12] that conclude to the impossibility to put two H atoms closer to 1.8 Å. In the case of the V matrix and for a distance superior to dsw, the H–H separation diminishes after relaxation of forces. A feature that points toward an attractive character of the H–H interaction. It is at odd with what is observed for the Fe matrix after relaxation as there is no change of the H–H separation. It might reflect the stronger rigidity of the H–Fe bond as compared to the H–V bond. In fact the H atoms maintain a constant distance of 1.68 Å to the central Fe atom whatever the T1x position 1.75 Å with the central V atom. Since the H–Fe distance is shorter than the H–V distance, stronger hybridization is expected to occur between the 1s state of H and the 3d states of Fe than with the corresponding 3d states for V. This last point illustrates the prominent role of the H–V (Fe) bonding in the H–H interaction, that will be alluded in more details in the following section.

E dis (meV)

24

100 50 0 -50 -100

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Fig. 6. Variation of distance and energy as a function of the X doping element. Upper panel: distance dH–H between two H atoms compared to the dsw distance of 2.00 Å (dashed horizontal line). Lower panel: change of the dissolution energy per atom of the most stable H–H position when the impurity atom X substitutes to V.

the data for the doping impurity within the V matrix and for pure Fe matrix. One can notice that the electronic term is always very ðnÞ negative and much larger than the positive energy Ei of the atomðnÞ ic displacements. The sign of Ee reflects the exothermic character of the formation of the mixed H–X bonding and H–V bonding. In ðnÞ the V matrices, the contribution Ei is small for X = Sc, Ti and V as compared to what is obtained when the doping impurity is Cr, Mn, Fe, Co or Ni. This is consistent with the weaker bulk modulus of Sc, Ti and V. The energy required to distort the cell is appreciably smaller if X = Sc, Ti and V than with the other 3d impurities. Last column of Table 4 reports the difference of the electronic part for 1 and 2 inserted H atoms. There is no clear relation between this difference and the evolution of the dH–H distance as shown, for instance, in the pure Fe matrix. Let us focus first on the V based systems. Negative values of this energy difference are obtained for an H–H separation inferior to dsw, suggesting an attractive character with X = Mn, Fe doping impurities. For these ð1Þ impurities we notice that Eð2Þ e is more negative than Ee . This result could explain why the addition of a low percentage of iron in V–Ti alloys increases the H storage capacity[13]. In fact, when a large content of H atoms is already inserted, H atoms are forced to sit at the vicinity of iron; this impurity then increases locally the hydrogen density. Ravindran et al. [38] provided a very convincing argument to explain the violation of the 2 Å H–H separation in RTInH1.33 metal hydrides (R = La, Ce, Pr or Nd; T = Ni, Pd, Pt). This argument is based on an electron localization function analysis. It is demonstrated that the electron distribution at the H site is polarized toward La and In which reduces the repulsive interaction between negatively charged H atoms. In our systems there is indeed a charge transfer from the hydrogen atoms to the metal matrix that amounts to 0.2 e. A repulsive coulomb interaction between the positively charged H atoms is thus expected. To better understand why there is attraction instead of repulsion, we have plotted in Fig. 7 the orbital projected densities of states of the immediate H atom neighborhood, with Ti and Fe as doping impurities. The shortening of the H–H distance when X = Fe gives way to two bonding states that are separated by 2.0 eV against 1.4 eV when X = Ti. More importantly, the hybridization between the TM 3d states and the upper 1s state of the hydrogen atoms is more pronounced with iron than with titanium. Hybridization is also re-

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N.B. Nguyen et al. / Journal of Alloys and Compounds 545 (2012) 19–27

Table 4 ðnÞ ðnÞ Energy decomposition of the insertion energy EðnÞ ! as a sum of an electronic and an ionic term Ee and Ei , respectively. Upper part of the table is devoted to X doping impurity in a V matrix, lower part is for the pure Fe-matrix. The doping X element is given in the first column. The second column gives the H–H separation in Å. The following block of columns displays the insertion of one hydrogen atom with the corresponding electronic and ionic terms, the second block of columns yields the same information for the insertion of two H atoms. The last column is the difference between the electronic terms. All the energies are given in eV. dHH

Eð1Þ !

Ei

Eeð1Þ

ð2Þ E!

Ei

Eð2Þ e

DEe ¼ Eeð2Þ  Eeð1Þ

Sc Ti V Cr Mn Fe Co Ni Fe Fe

2.58 2.04 2.01 2.00 1.93 1.89 1.89 2.13 2.51 2.06

2.251 2.219 2.228 2.229 1.962 1.981 1.992 1.995 1.952 1.952

0.065 0.026 0.103 0.184 0.155 0.189 0.229 0.281 0.141 0.141

2.316 2.245 2.331 2.413 2.117 2.170 2.221 2.276 2.093 2.093

2.237 2.207 2.157 2.002 1.967 1.986 1.994 1.986 1.990 1.982

0.123 0.125 0.133 0.223 0.287 0.299 0.299 0.246 0.138 0.141

2.360 2.332 2.260 2.225 2.254 2.285 2.244 2.232 2.128 2.123

0.044 0.087 0.071 0.188 0.137 0.115 0.023 0.044 0.035 0.030

ð1Þ

-5

-10 3.0 2.5

0

5

2

1.5

Ti-3d

V-3d

1.0

DOS (states/eV)

2.0

H-1s

0.5 0.0

DOS (states/eV)

3.0

Fe-3d

dHH=1.89 Å

2.5

d

HH

0

5

0

5

Fe-3d

=2.06 Å

1 0

H-1s -1 -2

1.5

V-3d

2

1.0

H-1s

0.5

-5

0

5

E-E F (eV) Fig. 7. Partial density of states for the Ti and Fe doped V matrix, upper and lower panel, respectively. The 3d states of the impurity atom are the black lines, the 3d states of the vanadium atoms are green (light gray) circles, the dashed blue (dark gray) lines are the 1s states of the H inserted atoms. The arrows on both panels point out the 3d TM-1s hybridization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

d H-H (Å) 2.0

500 400 300 200 100 0

d

HH

Fe-3d

=2.51 Å

1 0 -1

H-1s

-2 -10

-5

E-E F (eV) Fig. 9. Partial density of states in pure Fe matrix for two H–H separations, the larger separation corresponding to the most stable configuration. The 3d states of the Fe central atom are the black lines, the dashed blue (dark gray) lines are the 1s states of the H inserted atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2.5

(2)

-5

2.0

0.0 -10

E dis (meV)

ð2Þ

-10

d HH =2.04 Å

DOS (states/eV)

DOS (states/eV)

X

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Fig. 8. Variation of distance and energy as a function of the X doping element. Upper panel: distances dH–H between two H atoms compared to the dsw distance of 2.00 Å. Lower panel: change of energy of the most stable H–H position when the impurity X atom substitutes to Fe.

flected in states located at 5 eV; this contribution is more important with iron as doping impurity. This is obviously related, on the one hand, to the shorter H–X distance in the case of X = Fe, and, on the other hand, to the higher density of electrons of iron as compared to titanium. The contribution of the 3d states of the V does not depend on the doping element. In the study of the H–H interaction, the contribution of the metal–hydrogen interaction appears as a key ingredient that controls the magnitude of the H–H interaction. This correlation between the hydrogen–metal and the H–H interaction was already pointed out by Ouyang and Lee [12]. Fig. 8 displays the evolution of the H–H distance as X goes from Sc to Ni in the Fe matrix. Contrary to what we obtained in the V matrix, now the H–H distance shortens for X = Sc to V with a minimum for V that amounts to 2.20 Å. A maximum in the H–H distance occurs for X = Cr and from X = Cr to Ni it stabilizes around 2.50 Å. In the meantime the H–X separation decreases monotonically from a value of 2.20 Å for X = Sc to a value of 1.58 Å for X = Ni. The H–X distance evolves in much the same way if one or two H atoms are located at the immediate vicinity of the X impu-

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N.B. Nguyen et al. / Journal of Alloys and Compounds 545 (2012) 19–27

rity. As to the dissolution energies, they are plotted for the ferromagnetic solution and are found always to be positive, which means that there is no metal impurity capable of trapping H atoms in a Fe matrix. Since the H–H distance is in the range 2.2–2.5 Å the H–H interaction is expected to be negative and thus attracting. In the lower part of Table 4, we have compared two possible configurations for two H atoms at the vicinity of Fe, namely the T17 and the T15 according to the labeling of Table 2. The first configuration corresponds to a H–H separation of 2.51 Å, the second configuration to a H–H separation of 2.06 Å. There is almost no change of ð1Þ the difference Eð2Þ e  Ee . The orbital projected densities of states have also been plotted in Fig. 9 for the two most stable H–H configurations. Whatever the H–H separation, a strong hydrogen 1s–iron 3d state hybridization is observed in the tail of the 3d states (5 eV) and for the two bonding states located at 8 eV and 9 eV. As previously (see Fig. 6) a shortening of the H–H distance gives way to a larger energy separation of the bonding states (1.5 eV against 1.0 eV for the shorter H–H distance). The negligible change of the electronic features when the H–H separation is decreased indicates that the H–H interaction is mediated in a large extent by the metal–hydrogen bonding [12]. This can be related to the equilibrium H–Fe distance of 1.68 Å already pointed out in the previous section.

6. Conclusions We have investigated the insertion of one and two hydrogen atoms in bcc Fe and V matrices of 65 atoms doped with a 3d transition-metal atomic impurity. A doping impurity X = Sc, Ti, V, Cr, Mn, Fe, Co or Ni replaces the central atom of the matrix. We have used the DFT code SIESTA to analyze the influence of the different doping impurities in an hydrogenation process where a first H atom is inserted and then a second H atom. Our model system can be seen as representative of a local environment encountered in binary alloys in the dilute limit. The general trends obtained in our simulations are summarized as follows: (i) For the H free systems, structural and electronic arguments have been derived in favor or against H trapping. The f+ Fukui function is used as an indicator of the reactivity of the environment towards H trapping. This function suggests a stronger reactivity in the V based matrices than in the Fe based matrices. (ii) Hydrogen insertion is always more favorable in a V-rich matrix than in a Fe-rich one. The V matrix fulfills the condition of shorter H–H distance and more negative value of the dissolution energy. In the Fe matrix there is no doping impurities, among the tested elements, able of lowering sufficiently the dissolution energy. In Fe, the minimum value of 0.15 eV for the dissolution energy obtained for Mn as an impurity is still endothermic and in good agreement with the data of Jiang and Carter on the pure Fe matrix [15]. (iii) The Ti doped V matrix fulfills the condition of a short H–H separation though larger than the dsw limit,  as well as a neg ð2Þ ative value of the dissolution energy Edis ¼ 60 meV . Finally, even though elements like iron or manganese are not auspicious to H insertion, when a weak percentage is added in a matrix that favors H trapping, these latter impurities enhance the hydrogen density. (iv) In the V matrix, two inserted H atoms are preferentially located on tetrahedral interstices at fourth distance to each other, except when Ni is the doping impurity. At the vicinity of the Ni impurity, a first H atom sits in an octahedral interstice and the second one in a tetrahedral interstice.

Subsequently the H–H separation is increased above the 2.0 Å limit. Insofar the Fe matrix is concerned, the two H atoms sit preferentially at sixth distance to each other, with a separation in the range of 2.2–2.5 Å. (v) The elastic energy increases abruptly from X = Cr to X = Ni whereas this energy is weak for the element at the left of vanadium in the periodic table. (vi) The magnitude of the H–H interaction is controlled to a large extent by the hydrogen–metal interaction. A noticeable hybridization is found between the H 1s-state and the TM 3d states, especially for elements with a 3d band more than half filled (Mn, Fe, Co), Ni being the exception for the reason given at point (iv).

Acknowledgments We acknowledge the financial support from the Spanish Ministry of Science and Innovation in conjunction with the European Regional Development Fund (Project FIS2011-22957/FIS) and the Junta de Castilla y León (Project VA104A11-2). A.V. acknowledges the financial support and the kind hospitality from the Université de Brest (UBO), France. The authors acknowledge the numerical support of the Pole de Calcul Intensif pour la Mer (Brest) and the Pole de Calcul Intensif des Pays de la Loire (Nantes). References [1] Preeti Kamakoti, Bryan D. Morreale, Michael V. Ciocco, Bret H. Howard, Richard P. Killmeyer, Anthony V. Cugini, David S. Sholl, Science 30 (2005) 569. [2] K. Kobayashi, M. Yamauchi, H. Kitagawa, Y. Kubota, K. Kato, M. Takata, J. Am. Chem. Soc. 130 (2008) 1818. [3] Louis Schlapbach, Andreas Züttel, Nature 414 (2001) 353. [4] Y. Filinchuk, D. Chernyshov, A. Nevidomskyy, V. Dmitriev, Angew. Chem., Int. Ed. 47 (2008) 529. [5] Y. Filinchuk, R. Czerny, H. Hagemann, Chem. Mater. 21 (2009) 925. [6] M. Gupta, R.P. Gupta, J. Alloys Compd. 446-447 (2007) 319. [7] L-P. Ma, P. Wang, H-B. Dai, L-Y. Kong, H-M. Cheng, J. Alloys Compd. 466 (2008) L1. [8] H. Arashima, F. Takahashi, T. Ebisawa, H. Itoh, T. Kabutomori, J. Alloys Compd. 405 (2003) 356. [9] T. Huang, Z. Wu, G. Sun, N. Xu, J. Alloys Compd. 450 (2008) 505. [10] H. Smithson, C.A. Marianetti, D. Morgan, A. Van der Ven, A. Predith, G. Ceder, Phys. Rev. B 66 (2002) 144107. [11] K. Miwa, A. Fukumoto, Phys. Rev. B 65 (2002) 155114. [12] C. Ouyang, Y.S. Lee, Phys. Rev. B 83 (2011) 045111. [13] B. Massicot, M. Latroche, J.M. Joubert, J. Alloys Compd. 509 (2010) 372. [14] Maximilian Fichtner, Adv. Eng. Mater. 7 (2005) 443. [15] D.E. Jiang, Emily A. Carter, Phys. Rev. B 70 (2004) 064102. [16] H. Wu, S.R. Desai, L.-S. Wang, Phys. Rev. Lett. 77 (1996) 2436. [17] L.-S. Wang, H.-S. Cheng, J. Fan, J. Chem. Phys. 102 (1995) 9480. [18] J.M. Soler, E. Artacho, J.D. Gale, A. Garcia, J. Junquera, P. Ordejón, D. SánchezPortal, J. Phys. Condens. Matter 14 (2002) 2745. [19] P. Ordejón, E. Artacho, J.M. Soler, Phys. Rev. B 53 (1996) R10441. [20] D. Sánchez-Portal, P. Ordejón, E. Artacho, J.M. Soler, Int. J. Quantum Chem. 65 (1997) 453. [21] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [22] S.G. Louie, S. Froyen, M.L. Cohen, Phys. Rev. B 26 (1982) 1738. [23] N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. [24] L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48 (1982) 1425. [25] E.M. Fernandez, M.B. Torres, L.C. Balbas, Int. J. Quantum Chem. 99 (2004) 39. [26] R.C. Robles, J. Izquierdo, A. Vega, L.C. Balbás, Phys. Rev. B 63 (2000) 172406. [27] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [28] A. Lebon, A. Mokrani, A. Vega, Phys. Rev. B 78 (2008) 184401. [29] J. Izquierdo, A. Vega, L.C. Balbás, D. Sánchez-Portal, J. Junquera, E. Artacho, Jose M. Soler, P. Ordejón, Phys. Rev. B 61 (2000) 13639. } m, A. Bergman, O. Eriksson, Phys. Rev. B 77 (2008) 144408. [30] B. Skubic, E. Holstro [31] B. Drittler, N. Stefanou, S. Blügel, R. Zeller, P.H. Dederichs, Phys. Rev. B 40 (1989) 8203. [32] Graeme Henkelman, Andri Arnaldsson, Hannes Jónsson, Comput. Mater. Sci. 36 (2006) 354. [33] L.-C. Duda, P. Isberg, P.H. Andersson, P. Shytt, B. Hjörvarsson, J.H. Guo, C. Såthe, J. Nordgren, Phys. Rev. B 55 (1991) 12914. [34] P. Fuentealba, P. Pérez, R. Contreras, J. Chem. Phys. 113 (2000) 2544. [35] W. Yang, R.G. Parr, Proc. Natl. Acad. Sci. USA 82 (1985) 6723. [36] P. Geerlings, F. De Proft, W. Langenaeker, Chem. Rev. 103 (2003) 1793. [37] A.C. Switendick, Z. Phys. Chem. 89 (1979) 117.

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