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The role of nickel catalyst in hydrogen desorption from MgH2: A DFT study
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 4 0 ( 2 0 1 5 ) 9 3 2 6 e9 3 3 4
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The role of nickel catalyst in hydrogen desorption from MgH2: A DFT study Simone Giusepponi*, Massimo Celino ENEA, C. R. Casaccia, Via Anguillarese 301, 00123 Roma, Italy
article info
abstract
Article history:
Magnesium hydride is a very promising material for solid-state hydrogen storage. How-
Received 12 March 2015
ever, some drawbacks have to be overcome to use it in real applications. The use of cat-
Received in revised form
alysts is a viable solution to lower the desorption temperature and increase the overall
7 May 2015
kinetics. An accurate model has been developed to study the mechanism of action of the
Accepted 15 May 2015
catalyst and how it interacts with the interface MgH2eMg, through which H atoms diffuse.
Available online 10 June 2015
The accurate evaluation of the work of adhesion and defect energy formation, versus the distance from the interface are linked to the atomic-scale structural distortion induced by
Keywords:
the catalyst. Moreover, molecular dynamics simulations at several temperature provide a
Ab-initio calculations
clear description of the desorption mechanism and an estimate of the desorption
Hydrogen storage
temperature.
Hydrogen desorption
Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Interfaces
Introduction In the last years an increasing interest has been devoted to magnesium hydride material because it is one of the most promising candidate for solid-state hydrogen storage [1]. Magnesium hydride, MgH2, has both high gravimetric and volumetric hydrogen contents, rm (MgH2) ¼ 7.6 wt% H2 and rV (MgH2) ¼ 109 g H2/L, and a rutile structure, which suggests partly covalent bonding [2]. However, further research is needed because magnesium hydride has a high exothermic formation enthalpy (DH ~ 75 kJ/mol and DS ~ 135 kJ/mol [3]) that is not suitable for mobile applications. Several approaches have been proposed to improve both thermodynamics and kinetics of hydrogen desorption and absorption in magnesium hydride: nanoconfinement [4,5], nanostructuring by ball milling [6,7] utilization of catalytic additives [7e9] or alloying with different metals [10,11]. Additives appear to
influence the kinetics and often also the thermodynamics: among the others Al, Cu and Pd form alloys and Ni and Fe complex hydrides (Mg2 NiH4 or Mg2 FeH6 [12e15]). Magnesium in combination with a heat storage material (phase-change material) provides a safe and efficient method for stationary large-scale hydrogen storage (up to 700 kg), long lifetime (>5000 absorption/desorption cycles), without degradation of the hydrogen uptake capacity (>6.6 wt%) [16e18]. On the other hand, several numerical studies have addressed MgH2 materials to understand how to destabilize the atomic structure and thus to modify its thermodynamical stability [19e21]. Ab-initio calculations have compared the effect of several intermetallics on small isolated MgH2 clusters enlightening the dynamics of both Fe and Ni during H desorption [22]. The proposed process for H desorption suggests that phase transformation is always localized around the Fe particles that fasten up the nucleation of the new phase. A similar process is found experimentally by a
* Corresponding author. E-mail addresses: [email protected] (S. Giusepponi), [email protected] (M. Celino). http://dx.doi.org/10.1016/j.ijhydene.2015.05.092 0360-3199/Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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 4 0 ( 2 0 1 5 ) 9 3 2 6 e9 3 3 4
metallographic examination of partially desorbed MgH2 [7]. Moreover, ab-initio calculations show that the MgeH bond can be significantly weakened by a Fe atom inserted between two MgH2 clusters [23] and that H desorption involves concerted motions of charged defects [24]. Recently, the Mg diffusion has been also addressed via classical molecular dynamics to understand the role of surface oxidation [25]. The MgH2eMg interface has been modelled and characterized via ab-initio molecular dynamics (MD) simulations to enlighten the role of Fe catalysts in H desorption [26e28]. In this paper a detailed study of the H desorption near an interface has been addressed taking into account explicitly the presence of a catalyst. We provide a detailed description of ab-initio MD simulations to study a reliable MgH2eMg interface at different external temperatures: from room temperature to 900 K. In this range of temperatures our model describes accurately the hydrogen desorption along the interface. The computed desorption temperature is in very good agreement with the experimental indications. The insertion of a metal catalysts induces a destabilization of the crystalline structure and this is quantified and characterized in terms of formation energies, work of adhesion, atomic distances and atomic coordinations. In Section 2 we illustrate the computational details. In Section 3.1 we describe the physical systems constituted by the MgH2eMg interfaces and analyse the systems at the end of the ionic relaxations, then in Section 3.2, we characterize the temperature dependence of the hydrogen mobility and carry out the structural analysis of the interfaces.
Computational details All the calculations were performed by using the CPMD (CareParrinello Molecular Dynamics) code [29,30]. CPMD is an ab-initio electronic structure and MD program using a planewave/pseudopotential implementation of Density Functional Theory (DFT) [31,32]. GoedeckereTetereHutter pseudopotentials for magnesium, hydrogen and nickel together with Pade approximant LDA exchange-correlation potentials were used [33e35]. Despite the high accuracy of pseudopotentials which include semicore states (see for example Ref. [36]) the structural characterization of an interface requires large atomic systems to mimic bulk behaviour on both sides. Thus in view of large scale simulations, the pseudopotentials with fewer valence electrons have been chosen, in order to save computational time and simulate the largest system. The electronic wave functions were expanded in a plane-wave basis set with a kinetic energy cut-off equal to 80 Ry. The latter value was optimized by preliminary calculations on both simple molecules (Mg2, MgH and H2) and crystalline structures of metallic magnesium and magnesium hydride. All the calculations were performed in the supercell approximation, in view of the large-scale molecular dynamics simulation of the interface, with periodic boundary conditions (PBC) meant to mimic an infinitely extended system. The main constraint in building the interface is in the selection of two commensurate surfaces (one for Mg and one for MgH2) fulfilling a simulation cell with PBC. Such a constraint narrows the possibilities of finding two suitable free surfaces
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for a proper interface. Among the low Miller index surfaces of both materials, it is found that the MgH2(110) surface is nearly commensurate to either Mg(010) or Mg(100) surfaces, according to periodic boundary conditions, by minimizing the lattice pffiffiffi mismatch. In both cases we have 2 aMg x 2aMgH2 and 3 cMg x5 cMgH2 (aMg, cMg and aMgH2 , cMgH2 are the lattice parameters of the magnesium and magnesium hydride crystalline structures, respectively). Keeping fixed aMgH2 , a small distortion in the Mg and MgH2 lattice parameters is needed to obtain fully commensurable surfaces: the aMg and cMg are thus scaled of about 1% and 2%, respectively. As shown in Fig. 1, the MgH2eMg interface is built by putting nearby two free surfaces obtained cutting along the (110) and (010) Miller planes the MgH2 and Mg crystals, respectively. We considered six slabs of atoms in the magnesium hydride side and six slabs of atoms in the magnesium hcp side. Both sides of the whole system are long enough to take into account the structural modifications induced by the interface. Results reported in Ref. [37], on a similar system, confirm that the effects of relaxation propagate to the bulk atoms up to the third or fourth neighbour and that six neighbours are enough to attain bulk behaviour on both sides. On both sides of the system, a void region of length 2 Lx is considered to suppress the interaction, due to PBC, between the external surfaces of MgH2 ˚ , while in and Mg. The total length of the system is Ly ¼ 50.30 A ˚ and the x and z direction the system has Lx ¼ 6.21 A ˚ , respectively. Zero-temperature total energy calLz ¼ 15.09 A culations were used to evaluate interface stability. Throughout the paper all numerical errors were taken as low as possible performing accurate fitting of energy data and a careful application of ab-initio methods for the computation of energies. This procedure ensures that errors are at the level of accuracy allowed by DFT-based calculations [38]. Subsequently, MD simulations at constant volume and constant temperature (NVT ensemble) were performed by using Nose Hoover thermostats [39,40]. Further details on both the ab-initio implementation and the description of the interface are reported elsewhere [26,27].
Fig. 1 e Schematic of the MgH2-Mg interface in the simulation box. The structure is infinitely extended in both x and z directions. Free surfaces and interface are perpendicular to y axis. H atoms are in green, Mg atoms are in light blue in the hydride side and dark blue for magnesium crystalline side. Positions POSx (with x ¼ 1,2 and 3) indicate the Mg atoms that are substituted by Ni atoms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Results and discussion Following the scheme developed in Ref. [27], we replaced in turn one atom of Mg in positions POS1, POS2 and POS3 (see Fig. 1) with an atom of nickel. Three different interfaces were obtained, in which the Ni atom is at an increasing distance from the interface. POS1, POS2 and POS3 are on the first, on the second and on the third Mg layer of MgH2 side, respectively. One key quantity to predict the mechanical properties of the interface and to verify the reliability of our model, is the work of adhesion. The latter quantity is defined as the bonding energy per unit area needed to completely separate an interface in two free surfaces, neglecting plastic and diffusional degrees of freedom. Moreover, another quantity that gives insights on the stability of the interface is the formation energies of the substitutional defect. The work of adhesion W is defined by the difference in total energy between the interface and its isolated slabs: . Mg MgH þNi A ENi W ¼ Eslab þ Eslab 2 inter Mg
(1) MgH þNi
where Eslab is the total energy of the Mg slab, Eslab 2
Moreover, to establish the preferred substitutional site of the catalyst atoms, formation energies for the various positions were calculated from total energies according to the following equation: i h 0 0 DH ¼ ENi inter þ E ðMgÞ ½Einter þ E ðNiÞ
(2)
where ENi inter is defined as before, Einter is the total energy for the pure MgH2eMg interface and E0 is the total energy of one isolated atom in the simulation box.
Geometry optimization For the three interfaces in which a Ni atom is substituted on POS1, POS2 and POS3, respectively, we performed total energy calculations followed by geometry optimization. Ionic relaxation was reached when the residual force on each atom is ˚ . In Fig. 2 the configurations of the three less than 102 eV/A interfaces at the end of the geometry optimization are shown. Moreover, to better highlight the nickel effect, we also report the completely relaxed interface without catalyst. The calculated values of the work of adhesion W and the formation
is the total
POSx POSx POSx ; DHPOSx energy DH, before ðWow ow Þ and after ðWog ; DHog Þ
energy of the MgH2 slab with a nickel atom, ENi inter is the total energy for the MgH2eMg interface doped with a nickel atom in one of the substitutional positions and A is the surface area (A ¼ Lx Lz).
geometry optimization, are summarized in Table 1. In addition, to better evaluate the role of the catalyst, in this Table we also report the values of W for the MgH2eMg interface without catalyst (Wow ¼ 605 mJ/m2 and Wog ¼ 395 mJ/m2) [26] and the
Fig. 2 e Snapshots of the MgH2eMg interface without Ni catalyst and with Ni in POS1, POS2 and POS3 at the end of the ionic relaxation: panels a), b), c) and d), respectively. H atoms are in green, Mg atoms are in light (MgH2 side) and dark (Mg side) blue and Ni atom is in yellow. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Table 1 e Work of adhesion and formation energy before POSx POSx POSx ðWow ; DHPOSx ow Þ and after ðWog ; DHog Þ ionic relaxations of the interfaces. The first row refers to interface without catalyst [26], from the second to the fourth rows, values for the interfaces with nickel catalyst (this work), and the last three lines refer to interfaces with iron catalyst [27]. Values of W are compared to the corresponding values for MgH2eMg interface without catalyst. Differences are reported in parenthesis. Catalyst
POSx
Work of adhesion (mJ/m2) WPOSx ow
No catalyst [26]
605
WPOSx og 395
Formation energy (eV) DHPOSx DHPOSx ow og e
e
Ni
POS1 POS2 POS3
928 (þ323) 588 (þ193) 694 (þ89) 394 (1) 654 (þ49) 346 (49)
3.35 2.46 2.18
5.07 3.84 3.52
Fe [27]
POS1 POS2 POS3
776 (þ171) 668 (þ273) 614 (þ9) 400 (þ5) 606 (þ1) 334 (61)
4.42 4.46 4.40
6.66 6.26 6.01
values of W and DH corresponding to the MgH2eMg interface with Fe catalyst [27]. First of all we observe a decreasing of the values of W with the increase of the distance of the position of substituted atom and WPOS1 are the from the interface. The values of WPOS1 ow og biggest, and compared to Wow and Wog there is an increment of þ323 and þ193 mJ/m2, respectively. Moreover, for nickel in POS2 and POS3, variations of work of adhesion are in the order of tens of mJ/m2. After the ionic relaxations we calculated the ¼ 588 mJ/m2, WPOS2 ¼ 394 mJ/m2 following values for W: WPOS1 og og 2 POS3 and Wog ¼ 346 mJ/m . If the substituted atom is on the interface, we have WPOS1 og [Wog; the presence of the catalyst in the interface increases the interaction between the two slabs. Indeed, the nickel atom attracts the nearest neighbour atoms more than the Mg atom placed in the same position. The comparison of the panels a) and b) of Fig. 2 is helpful. For the is very close to Wog system with Ni in POS2 the value of WPOS2 og (a difference of only 1 mJ/m2). Indeed, there is not a clear approach between the two slabs (see Fig. 2c). Finally, for the last interface with the Ni atom in the deeper position (POS3) of the hydride side, WPOS1 og
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computing the energy of both Ni (Fe) and Mg in their isolated form. To have a better characterization of the system, we checked the coordination of the nickel atom in the three positions before and after geometry optimizations. By using the MgH2 crystalline structure [26], in a bulk magnesium hydride each magnesium atom has 2H atoms in the 1st H-shell (1NNH),1 4H atoms in the 2nd H-shell (2NN-H), 4H atoms in the 3rd H-shell (3NN-H), 4H atoms in the 4th H-shell (4NN-H) and 8H ˚ , 1.94 A ˚, atoms in the 5th H-shell (5NN-H), at distance 1.89 A ˚ , 3.56 A ˚ , and 3.94 A ˚ , respectively (see the second column 3.34 A of Table 2). With regard to the magnesium coordination, each magnesium atom has 2 Mg atoms in the 1st Mg-shell (1NN-Mg) ˚ , 8 Mg atoms in the 2nd Mg-shell (2NN-Mg) at 3.45 A ˚, at 3.02 A ˚ and 4 Mg atoms in the 3rd Mg-shell (3NN-Mg) at 4.39 A (see the second column of Table 3). Now, considering the interface systems (see the third column of Table 2 and Table 3), it is noted that the atoms in position POS2 and POS3 have the same coordination of the bulk MgH2. On the contrary, the atom in POS1 being on the interface, has a different H and Mg coordinations. The differences are: 1 1NN-H atom, 2 4NN-H atoms and 4 5NN-H atoms; 9 2NN-Mg atoms (3 of which belong to magnesium side) and 6 3NN-Mg atoms (4 of which belong to magnesium side). In the fourth column of Table 2 and Table 3 are reported the H and Mg coordinations for the completely relaxed interface without catalyst. The atomic arrangements at the end of the ionic relaxations (see the fifth column of Table 2 and Table 3), reveal that the presence of Ni atom alters the positions of the atoms in its proximity (see Fig. 2). This effect is in addition to the deformation due to coupling of the hydride surface with the magnesium surface. In details, we observe for all the systems a reduction of the distance between nickel and hydrogen atoms. As a consequence, the main result is that the 2nd Hshell becomes empty. The H atoms in the 1st and the 2nd H˚ . This shell approach the Ni atoms at average distance 1.63 A distance value is in agreement with previous ab-initio computations of the NieH distance at the same MgH2 surface [41]. The difference is more evident with respect to the completely relaxed interface without catalyst. With regard to the external H-shells (3rd, 4th, and 5th) coordination, they depend on the substitutional atom position. In the case of POS2 and POS3 interfaces, the H coordination after geometry optimization does not change significantly compared to the initial and final configurations. There is only a slight increase of the distance and a reduction of the 5NN-H atoms (from 8 to 7) for the interface with Ni in POS2. On the contrary, the analysis of the POS1 interface reveals a more complex situation. Now we ˚ in place of 4H at 3.34 A ˚ ; the have 3 3NN-H atoms at 3.33 A number and the distance of H atoms in the 4th H-shell are ˚ to 5 atoms at 3.71 A ˚ ; and increased from 2 atoms at 3.56 A finally, the 5NN-H changes from 4 to 5 with an increase of the ˚. distance from 3.94 to 3.97 A The same analysis can be drawn for the Mg coordination. Small differences can be detected between initial and final configurations of the interface when the Ni atom is in POS2 and POS3. More significant changes are observed when Ni is in 1
1NN first-nearest neighbour, 2NN second-nearest neighbour, 3NN third-nearest neighbour, and so on.
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Table 2 e Hydrogen coordination till the fifth shell, of an atom in POS1, POS2 and POS3 (see Fig. 1). For each POSx seven columns report the coordination for the bulk hydride, for the starting configuration (SC), after geometry optimization with an Mg in POSx (Mg), after geometry optimization with a Ni in POSx (Ni), and for the MD simulations at T ¼ 400 K, T ¼ 500 K, and T ¼ 600 K, respectively. Shells are determined on the basis of distances in the MgH2 bulk. Average distance inside each ˚ ). shell is reported in parenthesis (A H-shell POS1 1st 2nd 3rd 4th 5th Ntot POS2 1st 2nd 3rd 4th 5th Ntot POS3 1st 2nd 3rd 4th 5th Ntot
MgH2 bulk
SC
Mg
Ni
T ¼ 400 K
T ¼ 500 K
T ¼ 600 K
2 (1.89) 4 (1.94) 4 (3.34) 4 (3.56) 8 (3.94) 22
1 (1.89) 4 (1.94) 4 (3.34) 2 (3.56) 4 (3.94) 15
0 () 5 (1.99) 4 (3.36) 2 (3.72) 0 () 15
5 (1.63) 0 () 3 (3.33) 5 (3.71) 5 (3.97) 18
4.36 (1.57) 0 () 3.35 (3.28) 4.85 (3.60) 5.07 (3.93) 17.63
4.22 (1.56) 0 () 3.51 (3.27) 5.11 (3.60) 5.77 (3.93) 18.61
4.01 (1.55) 0 () 3.73 (3.26) 4.65 (3.60) 5.14 (3.94) 17.53
2 (1.89) 4 (1.94) 4 (3.34) 4 (3.56) 8 (3.94) 22
2 (1.89) 4 (1.94) 4 (3.34) 4 (3.56) 8 (3.94) 22
0 () 6 (1.93) 4 (3.36) 4 (3.59) 6(3.99) 20
6 (1.63) 0 () 4 (3.36) 4 (3.58) 7 (3.98) 21
5.00 (1.53) 0 () 5.32 (3.25) 6.04 (3.60) 6.54 (3.93) 22.90
5.00 (1.54) 0 () 5.21 (3.25) 5.46 (3.60) 7.18 (3.93) 22.85
4.99 (1.54) 0 () 5.56 (3.24) 5.91 (3.60) 6.74 (3.93) 23.20
2 (1.89) 4 (1.94) 4 (3.34) 4 (3.56) 8 (3.94) 22
2 (1.89) 4 (1.94) 4 (3.34) 4 (3.56) 8 (3.94) 22
0 () 6 (1.94) 4 (3.34) 4 (3.60) 8 (4.02) 22
6 (1.63) 0 () 4 (3.34) 4 (3.59) 8 (3.96) 22
5.00 (1.54) 0 () 4.67 (3.26) 4.62 (3.59) 8.20 (3.95) 22.49
5.00 (1.55) 0 () 4.82 (3.23) 5.30 (3.60) 7.68 (3.94) 22.80
5.00 (1.54) 0 () 4.49 (3.25) 5.38 (3.60) 7.67 (3.94) 22.54
Table 3 e Magnesium coordination till third shell, of an atom in POS1, POS2 and POS3 (see Fig. 1). For each POSx seven columns report the coordination for the bulk hydride, for the starting configuration (SC), after geometry optimization with an Mg in POSx (Mg), after geometry optimization with a Ni in POSx (Ni), and for the MD simulations at T ¼ 400 K, T ¼ 500 K, and T ¼ 600 K, respectively. Shells are determined on the basis of distances in the MgH2 bulk. Average distance inside each ˚ ). shell is reported in parenthesis (A Mg-shell POS1 1st 2nd 3rd Ntot POS2 1st 2nd 3rd Ntot POS3 1st 2nd 3rd Ntot
MgH2 bulk
SC
Mg
Ni
T ¼ 400 K
T ¼ 500 K
T ¼ 600 K
2 (3.02) 8 (3.45) 4 (4.39) 14
2 (3.02) 9 (3.43) 6 (4.56) 17
3 (3.12) 8 (3.47) 6 (4.53) 17
5 (2.79) 5 (3.47) 4 (4.34) 14
6.35 (2.78) 3.11 (3.57) 5.16 (4.44) 14.62
6.36 (2.80) 3.13 (3.56) 5.70 (4.44) 15.19
6.36 (2.75) 3.00 (3.59) 6.67 (4.47) 16.03
2 (3.02) 8 (3.45) 4 (4.39) 14
2 (3.02) 8 (3.45) 4 (4.39) 14
2 (3.02) 8 (3.48) 4 (4.53) 14
3 (3.01) 7 (3.41) 4 (4.47) 14
5.16 (2.85) 3.30 (3.56) 5.44 (4.39) 13.90
5.12 (2.84) 3.45 (3.58) 5.45 (4.39) 14.02
5.32 (2.84) 3.68 (3.55) 5.28 (4.40) 14.28
2 (3.02) 8 (3.45) 4 (4.39) 14
2 (3.02) 8 (3.45) 4 (4.39) 14
2 (3.01) 8 (3.50) 4 (4.45) 14
2 (2.93) 8 (3.41) 4 (4.40) 14
4.46 (2.90) 4.58 (3.55) 5.01 (4.37) 14.05
4.71 (2.85) 4.00 (3.56) 5.32 (4.38) 14.03
4.58 (2.87) 4.08 (3.55) 5.45 (4.37) 14.11
POS1. In the latter case, we note a sharp increase of the number of 1NN-Mg atoms with a reduction of the mean dis˚ to 5 Mg atoms at 2.79 A ˚ . This tance: from 2 Mg atoms at 3.02 A deformation produces an empty space at the distance of the 2nd Mg-shell; in the initial configuration there are 9 Mg atoms ˚ , on the contrary after the ionic at mean distance of 3.43 A ˚ . The mean distance is relaxation, the Mg atoms are 5 at 3.47 A increased because the inner Mg atoms are displaced in the 1st Mg-shell. Also the 3rd Mg-shell is less populated (from 6 to 4) ˚ ). Ionic even if at slightly smaller distance (from 4.56 to 4.34 A relaxation for system with nickel in middle position (POS2) does not produce evident changes in Mg coordination. There
is only one Mg atom that moves from the 2nd to the 1st Mgshell. The distance between this atom and nickel atom, ˚ . The others 2 1NN-Mg atoms are at changes from 3.45 to 3.21 A ˚ 2.91 and 2.92 A, respectively. Finally, for the third case, the coordination at the beginning and at the end of the geometry optimization remains the same, the only difference is the approaching of the 1NN-Mg atoms to the Ni atom. The mean ˚. distance is reduced from 3.02 to 2.93 A In conclusion, the main effect of the presence of nickel is an increase of the number of atoms in the 1st Mg-shell and in the 1st H-shell associated with a reduction of the distances. The outcome of this behaviour is more evident when the
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substituted atom is on the interface (POS1). In this situation, the magnesium side slab of the interface is more directly involved by the catalyst. Thus, a deeper interaction between the two slabs is yielded with consequent growth of the work of adhesion. This effect is magnified comparing the Mg and H coordination with respect to the geometry optimization of the interface without catalyst (fourth column of Table 2 and Table 3). Finally, it is worth to note that the same general trends in both the interface energies and atomic displacements were found in the case of Fe catalyst as reported in Ref. [27]. However, we point out that the difference in work of adhesion between relaxed interfaces with catalyst in POS1 2 2 POS1 (WPOS1 og (Ni) ¼ 588 mJ/m and Wog (Fe) ¼ 668 mJ/m ) can be explained in terms of the Mg coordination. In fact at the end of the geometry optimization in the former case (nickel) we have 5 1NN-Mg atoms, instead in the latter case (iron) we have 6 1NN-Mg atoms, with a consequent stronger interaction between the two slabs of the interface.
Molecular dynamics After geometry optimizations, we performed MD simulations at constant volume and constant temperature starting from the three relaxed interfaces. Simulation temperatures are from room temperature till 900 K, however the most interesting effects are in the range 500e600 K. In this range, the catalytic effect of Ni is able to reduce the hydrogen desorption temperature. Following the procedure developed in our previous works [26,27], we characterized the hydrogen atoms behaviour at each temperature in all the three cases. Five groups of H atoms (Hra, Hrb, Hrc, Hrd, Hrbulk) were defined
on the basis of their proximity to the interface. Hrx, with x ¼ a, b, c and d are groups of five H atoms (near the interface) belonging to the same line in the MgH2 side. Hrbulk is the group of the remaining H atoms in the MgH2 side that feel a bulk environment (see Fig. 3 in Ref. [26]). To quantify the hydrogen mobility we calculated the average displacements 〈d(t)〉 of these groups of H atoms. The trend of the average displacements 〈dðtÞ〉Hra , 〈dðtÞ〉Hrb , 〈dðtÞ〉Hrc , 〈dðtÞ〉Hrd and 〈dðtÞ〉Hrbulk at the proceed of the molecular dynamics simulations are shown in Fig. 3. To facilitate the comparison with the systems with Fe catalyst, the same colour palette as in Refs. [26,27] is adopted. That is, 〈dðtÞ〉Hra , 〈dðtÞ〉Hrb , 〈dðtÞ〉Hrc , 〈dðtÞ〉Hrd and 〈dðtÞ〉Hrbulk are drawn in blue line, red line, green line, orange line and black line, respectively. Graphics on the left and on the right in Fig. 3, refer to MD simulations at T ¼ 500 K (panels a, b, and c) and T ¼ 600 K (panels d, e, and f), respectively. Fig. 3 reveals that hydrogen displacements can be clearly detected already at T ¼ 500 K: if Ni in POS1 both first and second line of hydrogen diffuse, if Ni in POS2 only first line of hydrogen moves toward the interface. On the contrary at T ¼ 600 K the hydrogen diffusion process is completely settled and involves not only the first two lines of hydrogen atoms but also the third one, as shown in panel d) of Fig. 3. The hydrogen diffusion process is favoured by the distortion due to the presence of the catalyst atom. The increase of coordination of the catalyst respect to the Mg atoms is confirmed and enhanced during the MD simulations. Indeed, the 2nd H-shells are empty, whereas in the 1st H-shell there are on the average 4 hydrogen atoms when Ni is in POS1 and 5 hydrogen atoms when Ni is in POS2 and POS3. The mean
T = 500 K
(Å)
5 4 3 2 1 0 5 4 3
T = 600 K
a) POS1
d) POS1
b) POS2
e) POS2
c) POS3
f) POS3
2 1 0 5 4 3 2 1 0
0
1
2
3
4
5
6 0 t (ps)
1
2
3
4
5
6
Fig. 3 e Average displacements of the hydrogen atoms. Three different interfaces are considered depending on the Ni atom position: POS1, POS2 and POS3. T ¼ 500 K on the left and T ¼ 600 K on the right. The average displacements 〈dðtÞ〉Hra , 〈dðtÞ〉Hrb , 〈dðtÞ〉Hrc , 〈dðtÞ〉Hrd and 〈dðtÞ〉Hrbulk are drawn in blue line, red line, green line, orange line and black line, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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˚ . The distances of these H atoms are in the range of 1.53e1.57 A average NieH distance is in agreement with previous ab-initio [15] and experimental [42] estimates where, in the high tem˚ and perature Mg2 NiH4 structure this distance is around 1.57 A ˚ , respectively. 1.55 A The number of 1NN H is reduced by one unit compared to the geometry optimization configurations: from 5 to 4 for Ni in POS1 and from 6 to 5 for Ni in POS2 and POS3. We also recall for convenience that in the bulk magnesium hydride ˚ , and 4H at 1.94 A ˚ in the 1st and the 2nd there are 2H at 1.89 A H-shells, respectively. For what concerns the 3rd H-shell coordinations, different results are shown from the three systems. The coordination ranges between 3 and 4 for Ni in POS1, it ranges between 5 and 6 for Ni in POS2 and, it ranges between 4 and 5 for Ni in POS3. The corresponding values at the end of the ionic relaxations are 3, 4 and 4 respectively. Thus, the effect of the temperature is to increase the number of the H atoms in the 3rd H-shells compared to the ionic relaxed configurations. The mean distances between Ni and ˚ , values that are slightly H atoms are in the range 3.23e3.28 A lower compared to MgH2 bulk value and to geometry optimizations values. On the contrary, the mean distance of H ˚ , is a little greater than atoms in the 4th H-shells, that is 3.60 A ˚ , whereas the mean distance of the hydride bulk value 3.56 A H atoms in the 5th H-shells are very close to the bulk value ˚ . The 4th H-shells are populated on average by 5H 3.94 A ˚ ), one atom in atoms (values are in the range 4.65e6.04 A addition compared to MgH2 bulk and to ionic relaxed configurations (the exception is the system with Ni on POS1). Instead, the population of the 5th H-shell has a dependence on the POSx, indeed, the atomic coordination is on the average 5 for Ni in POS1, 7 for Ni in POS2, and 8 for Ni in POS3, respectively. These values confirm those at the end of the ionic relaxations, but are lesser than the magnesium hydride bulk value. H coordinations and mean distances are summarized in Table 2. To sum up, comparing to the relaxed configurations, we can observe that the temperature produces a reduction of one atom in the 1st H-shells, and in addition, it produces an increment of the H coordination in the 3rd and in the 4th H-shells. Moreover, as already found in Ref. [27] in the case of iron catalyst, the nickel atom attracts the H atoms and empties the 2nd H-shells. However, now there are one H atom less in the 1st H-shells, whereas the 3rd H-shells are generally more populated. We also measured the coordination of magnesium atoms during the molecular dynamics at constant temperature and volume. We observed the increase of the number of Mg atoms in the 1st Mg-shell with respect to the starting configurations (SC). The Mg atomic coordination increases from 2 to 6.4 for Ni in POS1, to 5.2 for Ni in POS2 and to 4.6 for Ni in POS3, respectively. Moreover, these values are greater than the corresponding values at the end of the ionic relaxations (fifth column in Table 3). The mean distances between Ni ˚ for Ni in POS1, atom and 1NN-Mg atoms are: 2.75e2.80 A ˚ for Ni in POS2 and 2.85e2.90 A ˚ for Ni in POS3. In the z 2.85 A ˚ . Thus, during the MD MgH2 bulk there are 2 1NN-Mg at 3.02 A simulations, the 1st Mg-shells become more populated with shorter mean distances. The increase of the 1NN-Mg atoms produces the reduction of the coordination of the 2nd Mgshells. Indeed, the number of atoms in these shells, varying
between 3 and 5, is smaller than the values corresponding to the starting configurations (SC) and to the value of hydride bulk. During the MD simulations the mean distances are ˚ , values that are bigger compared to between 3.55 and 3.59 A ˚ . Then, in the 2nd Mg-shells there are MgH2 bulk value 3.45 A less atoms and at bigger distances. The emptying of the 2nd Mg-shells is also accompanied by the raise of the 3rd Mgshells coordination. The number of 3NN-Mg atoms is >5, whereas, at the end of the ionic relaxations there are 4 Mg atoms in this shell. The mean distances approach to bulk value for systems with Ni in POS2 and POS3, instead, when Ni atom is in POS1 the mean distances are slightly greater. Mg coordinations and mean distances are summarized on Table 3. Therefore, we observed that the temperature produces the increase of the 1NN and 3NN-Mg atoms associated with the depletion of the 2nd Mg-shells. The comparison of these outcomes with those yielded in Ref. [27] with iron catalyst, does not highlight an extremely market difference. The substitutional atom (Ni or Fe) attracts the surrounding Mg atoms causing the increase of the number of atoms in the 1st Mg-shell and the emptying of the 2nd Mg-shells. Even if, this behaviour is more evident with iron atom, in fact generally, the Fe atom has more 1NN-Mg and less 2NN-Mg atoms compared to Ni atom. The exception is for substitutional atoms in POS3.
Conclusions In the present paper we report a detailed study of the role played by the Ni atoms acting as catalyst for H desorption from MgH2. In particular, the interplay between the catalyst and an interface MgH2eMg has been characterized in terms of defect formation energies, work of adhesion, coordination numbers and distance from the interface. Ni atoms are able to destabilize the MgH2 atomic structure in a similar way already found for Fe catalyst in our previous work [27]. The catalyst attracts both H and Mg atoms increasing the local coordination and creating voids on longer distances. These distortions are the cause of an increase of both work of adhesion and defect formation energies. Comparing the energy values computed for Fe catalyst with those for Ni, we conclude that Fe is more destabilizing than Ni. This is in good agreement with experimental results, indeed in Ref. [8] the comparison of the desorption kinetics with several catalysts reveals that Fe catalyst is more effective than Ni. Moreover, MD simulations confirm that the presence of Ni catalyst lowers the desorption temperature. Thus, our model is able to reproduce the lowering of the hydrogen desorption temperature due the presence of metal catalysts and it provides information about the structural rearrangements induced by the different doping elements.
Acknowledgements The computing resources and the related technical support used for this work have been provided by CRESCO-ENEAGRID High Performance Computing infrastructure and its staff
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 4 0 ( 2 0 1 5 ) 9 3 2 6 e9 3 3 4
[43]. CRESCO-ENEAGRID High Performance Computing infrastructure is funded by ENEA, the “Italian National Agency for New Technologies, Energy and Sustainable Economic Development” and by national and European research programs. This work was supported by the project “HYDROSTORE” funded by the Italian Industria 2015 Program and by Action MP1103 “Nanostructured materials for solid state hydrogen storage”. Figures and graphics were made using software in Ref. [44,45].
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Available online at www.sciencedirect.com
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The role of nickel catalyst in hydrogen desorption from MgH2: A DFT study Simone Giusepponi*, Massimo Celino ENEA, C. R. Casaccia, Via Anguillarese 301, 00123 Roma, Italy
article info
abstract
Article history:
Magnesium hydride is a very promising material for solid-state hydrogen storage. How-
Received 12 March 2015
ever, some drawbacks have to be overcome to use it in real applications. The use of cat-
Received in revised form
alysts is a viable solution to lower the desorption temperature and increase the overall
7 May 2015
kinetics. An accurate model has been developed to study the mechanism of action of the
Accepted 15 May 2015
catalyst and how it interacts with the interface MgH2eMg, through which H atoms diffuse.
Available online 10 June 2015
The accurate evaluation of the work of adhesion and defect energy formation, versus the distance from the interface are linked to the atomic-scale structural distortion induced by
Keywords:
the catalyst. Moreover, molecular dynamics simulations at several temperature provide a
Ab-initio calculations
clear description of the desorption mechanism and an estimate of the desorption
Hydrogen storage
temperature.
Hydrogen desorption
Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Interfaces
Introduction In the last years an increasing interest has been devoted to magnesium hydride material because it is one of the most promising candidate for solid-state hydrogen storage [1]. Magnesium hydride, MgH2, has both high gravimetric and volumetric hydrogen contents, rm (MgH2) ¼ 7.6 wt% H2 and rV (MgH2) ¼ 109 g H2/L, and a rutile structure, which suggests partly covalent bonding [2]. However, further research is needed because magnesium hydride has a high exothermic formation enthalpy (DH ~ 75 kJ/mol and DS ~ 135 kJ/mol [3]) that is not suitable for mobile applications. Several approaches have been proposed to improve both thermodynamics and kinetics of hydrogen desorption and absorption in magnesium hydride: nanoconfinement [4,5], nanostructuring by ball milling [6,7] utilization of catalytic additives [7e9] or alloying with different metals [10,11]. Additives appear to
influence the kinetics and often also the thermodynamics: among the others Al, Cu and Pd form alloys and Ni and Fe complex hydrides (Mg2 NiH4 or Mg2 FeH6 [12e15]). Magnesium in combination with a heat storage material (phase-change material) provides a safe and efficient method for stationary large-scale hydrogen storage (up to 700 kg), long lifetime (>5000 absorption/desorption cycles), without degradation of the hydrogen uptake capacity (>6.6 wt%) [16e18]. On the other hand, several numerical studies have addressed MgH2 materials to understand how to destabilize the atomic structure and thus to modify its thermodynamical stability [19e21]. Ab-initio calculations have compared the effect of several intermetallics on small isolated MgH2 clusters enlightening the dynamics of both Fe and Ni during H desorption [22]. The proposed process for H desorption suggests that phase transformation is always localized around the Fe particles that fasten up the nucleation of the new phase. A similar process is found experimentally by a
* Corresponding author. E-mail addresses: [email protected] (S. Giusepponi), [email protected] (M. Celino). http://dx.doi.org/10.1016/j.ijhydene.2015.05.092 0360-3199/Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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metallographic examination of partially desorbed MgH2 [7]. Moreover, ab-initio calculations show that the MgeH bond can be significantly weakened by a Fe atom inserted between two MgH2 clusters [23] and that H desorption involves concerted motions of charged defects [24]. Recently, the Mg diffusion has been also addressed via classical molecular dynamics to understand the role of surface oxidation [25]. The MgH2eMg interface has been modelled and characterized via ab-initio molecular dynamics (MD) simulations to enlighten the role of Fe catalysts in H desorption [26e28]. In this paper a detailed study of the H desorption near an interface has been addressed taking into account explicitly the presence of a catalyst. We provide a detailed description of ab-initio MD simulations to study a reliable MgH2eMg interface at different external temperatures: from room temperature to 900 K. In this range of temperatures our model describes accurately the hydrogen desorption along the interface. The computed desorption temperature is in very good agreement with the experimental indications. The insertion of a metal catalysts induces a destabilization of the crystalline structure and this is quantified and characterized in terms of formation energies, work of adhesion, atomic distances and atomic coordinations. In Section 2 we illustrate the computational details. In Section 3.1 we describe the physical systems constituted by the MgH2eMg interfaces and analyse the systems at the end of the ionic relaxations, then in Section 3.2, we characterize the temperature dependence of the hydrogen mobility and carry out the structural analysis of the interfaces.
Computational details All the calculations were performed by using the CPMD (CareParrinello Molecular Dynamics) code [29,30]. CPMD is an ab-initio electronic structure and MD program using a planewave/pseudopotential implementation of Density Functional Theory (DFT) [31,32]. GoedeckereTetereHutter pseudopotentials for magnesium, hydrogen and nickel together with Pade approximant LDA exchange-correlation potentials were used [33e35]. Despite the high accuracy of pseudopotentials which include semicore states (see for example Ref. [36]) the structural characterization of an interface requires large atomic systems to mimic bulk behaviour on both sides. Thus in view of large scale simulations, the pseudopotentials with fewer valence electrons have been chosen, in order to save computational time and simulate the largest system. The electronic wave functions were expanded in a plane-wave basis set with a kinetic energy cut-off equal to 80 Ry. The latter value was optimized by preliminary calculations on both simple molecules (Mg2, MgH and H2) and crystalline structures of metallic magnesium and magnesium hydride. All the calculations were performed in the supercell approximation, in view of the large-scale molecular dynamics simulation of the interface, with periodic boundary conditions (PBC) meant to mimic an infinitely extended system. The main constraint in building the interface is in the selection of two commensurate surfaces (one for Mg and one for MgH2) fulfilling a simulation cell with PBC. Such a constraint narrows the possibilities of finding two suitable free surfaces
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for a proper interface. Among the low Miller index surfaces of both materials, it is found that the MgH2(110) surface is nearly commensurate to either Mg(010) or Mg(100) surfaces, according to periodic boundary conditions, by minimizing the lattice pffiffiffi mismatch. In both cases we have 2 aMg x 2aMgH2 and 3 cMg x5 cMgH2 (aMg, cMg and aMgH2 , cMgH2 are the lattice parameters of the magnesium and magnesium hydride crystalline structures, respectively). Keeping fixed aMgH2 , a small distortion in the Mg and MgH2 lattice parameters is needed to obtain fully commensurable surfaces: the aMg and cMg are thus scaled of about 1% and 2%, respectively. As shown in Fig. 1, the MgH2eMg interface is built by putting nearby two free surfaces obtained cutting along the (110) and (010) Miller planes the MgH2 and Mg crystals, respectively. We considered six slabs of atoms in the magnesium hydride side and six slabs of atoms in the magnesium hcp side. Both sides of the whole system are long enough to take into account the structural modifications induced by the interface. Results reported in Ref. [37], on a similar system, confirm that the effects of relaxation propagate to the bulk atoms up to the third or fourth neighbour and that six neighbours are enough to attain bulk behaviour on both sides. On both sides of the system, a void region of length 2 Lx is considered to suppress the interaction, due to PBC, between the external surfaces of MgH2 ˚ , while in and Mg. The total length of the system is Ly ¼ 50.30 A ˚ and the x and z direction the system has Lx ¼ 6.21 A ˚ , respectively. Zero-temperature total energy calLz ¼ 15.09 A culations were used to evaluate interface stability. Throughout the paper all numerical errors were taken as low as possible performing accurate fitting of energy data and a careful application of ab-initio methods for the computation of energies. This procedure ensures that errors are at the level of accuracy allowed by DFT-based calculations [38]. Subsequently, MD simulations at constant volume and constant temperature (NVT ensemble) were performed by using Nose Hoover thermostats [39,40]. Further details on both the ab-initio implementation and the description of the interface are reported elsewhere [26,27].
Fig. 1 e Schematic of the MgH2-Mg interface in the simulation box. The structure is infinitely extended in both x and z directions. Free surfaces and interface are perpendicular to y axis. H atoms are in green, Mg atoms are in light blue in the hydride side and dark blue for magnesium crystalline side. Positions POSx (with x ¼ 1,2 and 3) indicate the Mg atoms that are substituted by Ni atoms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Results and discussion Following the scheme developed in Ref. [27], we replaced in turn one atom of Mg in positions POS1, POS2 and POS3 (see Fig. 1) with an atom of nickel. Three different interfaces were obtained, in which the Ni atom is at an increasing distance from the interface. POS1, POS2 and POS3 are on the first, on the second and on the third Mg layer of MgH2 side, respectively. One key quantity to predict the mechanical properties of the interface and to verify the reliability of our model, is the work of adhesion. The latter quantity is defined as the bonding energy per unit area needed to completely separate an interface in two free surfaces, neglecting plastic and diffusional degrees of freedom. Moreover, another quantity that gives insights on the stability of the interface is the formation energies of the substitutional defect. The work of adhesion W is defined by the difference in total energy between the interface and its isolated slabs: . Mg MgH þNi A ENi W ¼ Eslab þ Eslab 2 inter Mg
(1) MgH þNi
where Eslab is the total energy of the Mg slab, Eslab 2
Moreover, to establish the preferred substitutional site of the catalyst atoms, formation energies for the various positions were calculated from total energies according to the following equation: i h 0 0 DH ¼ ENi inter þ E ðMgÞ ½Einter þ E ðNiÞ
(2)
where ENi inter is defined as before, Einter is the total energy for the pure MgH2eMg interface and E0 is the total energy of one isolated atom in the simulation box.
Geometry optimization For the three interfaces in which a Ni atom is substituted on POS1, POS2 and POS3, respectively, we performed total energy calculations followed by geometry optimization. Ionic relaxation was reached when the residual force on each atom is ˚ . In Fig. 2 the configurations of the three less than 102 eV/A interfaces at the end of the geometry optimization are shown. Moreover, to better highlight the nickel effect, we also report the completely relaxed interface without catalyst. The calculated values of the work of adhesion W and the formation
is the total
POSx POSx POSx ; DHPOSx energy DH, before ðWow ow Þ and after ðWog ; DHog Þ
energy of the MgH2 slab with a nickel atom, ENi inter is the total energy for the MgH2eMg interface doped with a nickel atom in one of the substitutional positions and A is the surface area (A ¼ Lx Lz).
geometry optimization, are summarized in Table 1. In addition, to better evaluate the role of the catalyst, in this Table we also report the values of W for the MgH2eMg interface without catalyst (Wow ¼ 605 mJ/m2 and Wog ¼ 395 mJ/m2) [26] and the
Fig. 2 e Snapshots of the MgH2eMg interface without Ni catalyst and with Ni in POS1, POS2 and POS3 at the end of the ionic relaxation: panels a), b), c) and d), respectively. H atoms are in green, Mg atoms are in light (MgH2 side) and dark (Mg side) blue and Ni atom is in yellow. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Table 1 e Work of adhesion and formation energy before POSx POSx POSx ðWow ; DHPOSx ow Þ and after ðWog ; DHog Þ ionic relaxations of the interfaces. The first row refers to interface without catalyst [26], from the second to the fourth rows, values for the interfaces with nickel catalyst (this work), and the last three lines refer to interfaces with iron catalyst [27]. Values of W are compared to the corresponding values for MgH2eMg interface without catalyst. Differences are reported in parenthesis. Catalyst
POSx
Work of adhesion (mJ/m2) WPOSx ow
No catalyst [26]
605
WPOSx og 395
Formation energy (eV) DHPOSx DHPOSx ow og e
e
Ni
POS1 POS2 POS3
928 (þ323) 588 (þ193) 694 (þ89) 394 (1) 654 (þ49) 346 (49)
3.35 2.46 2.18
5.07 3.84 3.52
Fe [27]
POS1 POS2 POS3
776 (þ171) 668 (þ273) 614 (þ9) 400 (þ5) 606 (þ1) 334 (61)
4.42 4.46 4.40
6.66 6.26 6.01
values of W and DH corresponding to the MgH2eMg interface with Fe catalyst [27]. First of all we observe a decreasing of the values of W with the increase of the distance of the position of substituted atom and WPOS1 are the from the interface. The values of WPOS1 ow og biggest, and compared to Wow and Wog there is an increment of þ323 and þ193 mJ/m2, respectively. Moreover, for nickel in POS2 and POS3, variations of work of adhesion are in the order of tens of mJ/m2. After the ionic relaxations we calculated the ¼ 588 mJ/m2, WPOS2 ¼ 394 mJ/m2 following values for W: WPOS1 og og 2 POS3 and Wog ¼ 346 mJ/m . If the substituted atom is on the interface, we have WPOS1 og [Wog; the presence of the catalyst in the interface increases the interaction between the two slabs. Indeed, the nickel atom attracts the nearest neighbour atoms more than the Mg atom placed in the same position. The comparison of the panels a) and b) of Fig. 2 is helpful. For the is very close to Wog system with Ni in POS2 the value of WPOS2 og (a difference of only 1 mJ/m2). Indeed, there is not a clear approach between the two slabs (see Fig. 2c). Finally, for the last interface with the Ni atom in the deeper position (POS3) of the hydride side, WPOS1 og
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computing the energy of both Ni (Fe) and Mg in their isolated form. To have a better characterization of the system, we checked the coordination of the nickel atom in the three positions before and after geometry optimizations. By using the MgH2 crystalline structure [26], in a bulk magnesium hydride each magnesium atom has 2H atoms in the 1st H-shell (1NNH),1 4H atoms in the 2nd H-shell (2NN-H), 4H atoms in the 3rd H-shell (3NN-H), 4H atoms in the 4th H-shell (4NN-H) and 8H ˚ , 1.94 A ˚, atoms in the 5th H-shell (5NN-H), at distance 1.89 A ˚ , 3.56 A ˚ , and 3.94 A ˚ , respectively (see the second column 3.34 A of Table 2). With regard to the magnesium coordination, each magnesium atom has 2 Mg atoms in the 1st Mg-shell (1NN-Mg) ˚ , 8 Mg atoms in the 2nd Mg-shell (2NN-Mg) at 3.45 A ˚, at 3.02 A ˚ and 4 Mg atoms in the 3rd Mg-shell (3NN-Mg) at 4.39 A (see the second column of Table 3). Now, considering the interface systems (see the third column of Table 2 and Table 3), it is noted that the atoms in position POS2 and POS3 have the same coordination of the bulk MgH2. On the contrary, the atom in POS1 being on the interface, has a different H and Mg coordinations. The differences are: 1 1NN-H atom, 2 4NN-H atoms and 4 5NN-H atoms; 9 2NN-Mg atoms (3 of which belong to magnesium side) and 6 3NN-Mg atoms (4 of which belong to magnesium side). In the fourth column of Table 2 and Table 3 are reported the H and Mg coordinations for the completely relaxed interface without catalyst. The atomic arrangements at the end of the ionic relaxations (see the fifth column of Table 2 and Table 3), reveal that the presence of Ni atom alters the positions of the atoms in its proximity (see Fig. 2). This effect is in addition to the deformation due to coupling of the hydride surface with the magnesium surface. In details, we observe for all the systems a reduction of the distance between nickel and hydrogen atoms. As a consequence, the main result is that the 2nd Hshell becomes empty. The H atoms in the 1st and the 2nd H˚ . This shell approach the Ni atoms at average distance 1.63 A distance value is in agreement with previous ab-initio computations of the NieH distance at the same MgH2 surface [41]. The difference is more evident with respect to the completely relaxed interface without catalyst. With regard to the external H-shells (3rd, 4th, and 5th) coordination, they depend on the substitutional atom position. In the case of POS2 and POS3 interfaces, the H coordination after geometry optimization does not change significantly compared to the initial and final configurations. There is only a slight increase of the distance and a reduction of the 5NN-H atoms (from 8 to 7) for the interface with Ni in POS2. On the contrary, the analysis of the POS1 interface reveals a more complex situation. Now we ˚ in place of 4H at 3.34 A ˚ ; the have 3 3NN-H atoms at 3.33 A number and the distance of H atoms in the 4th H-shell are ˚ to 5 atoms at 3.71 A ˚ ; and increased from 2 atoms at 3.56 A finally, the 5NN-H changes from 4 to 5 with an increase of the ˚. distance from 3.94 to 3.97 A The same analysis can be drawn for the Mg coordination. Small differences can be detected between initial and final configurations of the interface when the Ni atom is in POS2 and POS3. More significant changes are observed when Ni is in 1
1NN first-nearest neighbour, 2NN second-nearest neighbour, 3NN third-nearest neighbour, and so on.
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Table 2 e Hydrogen coordination till the fifth shell, of an atom in POS1, POS2 and POS3 (see Fig. 1). For each POSx seven columns report the coordination for the bulk hydride, for the starting configuration (SC), after geometry optimization with an Mg in POSx (Mg), after geometry optimization with a Ni in POSx (Ni), and for the MD simulations at T ¼ 400 K, T ¼ 500 K, and T ¼ 600 K, respectively. Shells are determined on the basis of distances in the MgH2 bulk. Average distance inside each ˚ ). shell is reported in parenthesis (A H-shell POS1 1st 2nd 3rd 4th 5th Ntot POS2 1st 2nd 3rd 4th 5th Ntot POS3 1st 2nd 3rd 4th 5th Ntot
MgH2 bulk
SC
Mg
Ni
T ¼ 400 K
T ¼ 500 K
T ¼ 600 K
2 (1.89) 4 (1.94) 4 (3.34) 4 (3.56) 8 (3.94) 22
1 (1.89) 4 (1.94) 4 (3.34) 2 (3.56) 4 (3.94) 15
0 () 5 (1.99) 4 (3.36) 2 (3.72) 0 () 15
5 (1.63) 0 () 3 (3.33) 5 (3.71) 5 (3.97) 18
4.36 (1.57) 0 () 3.35 (3.28) 4.85 (3.60) 5.07 (3.93) 17.63
4.22 (1.56) 0 () 3.51 (3.27) 5.11 (3.60) 5.77 (3.93) 18.61
4.01 (1.55) 0 () 3.73 (3.26) 4.65 (3.60) 5.14 (3.94) 17.53
2 (1.89) 4 (1.94) 4 (3.34) 4 (3.56) 8 (3.94) 22
2 (1.89) 4 (1.94) 4 (3.34) 4 (3.56) 8 (3.94) 22
0 () 6 (1.93) 4 (3.36) 4 (3.59) 6(3.99) 20
6 (1.63) 0 () 4 (3.36) 4 (3.58) 7 (3.98) 21
5.00 (1.53) 0 () 5.32 (3.25) 6.04 (3.60) 6.54 (3.93) 22.90
5.00 (1.54) 0 () 5.21 (3.25) 5.46 (3.60) 7.18 (3.93) 22.85
4.99 (1.54) 0 () 5.56 (3.24) 5.91 (3.60) 6.74 (3.93) 23.20
2 (1.89) 4 (1.94) 4 (3.34) 4 (3.56) 8 (3.94) 22
2 (1.89) 4 (1.94) 4 (3.34) 4 (3.56) 8 (3.94) 22
0 () 6 (1.94) 4 (3.34) 4 (3.60) 8 (4.02) 22
6 (1.63) 0 () 4 (3.34) 4 (3.59) 8 (3.96) 22
5.00 (1.54) 0 () 4.67 (3.26) 4.62 (3.59) 8.20 (3.95) 22.49
5.00 (1.55) 0 () 4.82 (3.23) 5.30 (3.60) 7.68 (3.94) 22.80
5.00 (1.54) 0 () 4.49 (3.25) 5.38 (3.60) 7.67 (3.94) 22.54
Table 3 e Magnesium coordination till third shell, of an atom in POS1, POS2 and POS3 (see Fig. 1). For each POSx seven columns report the coordination for the bulk hydride, for the starting configuration (SC), after geometry optimization with an Mg in POSx (Mg), after geometry optimization with a Ni in POSx (Ni), and for the MD simulations at T ¼ 400 K, T ¼ 500 K, and T ¼ 600 K, respectively. Shells are determined on the basis of distances in the MgH2 bulk. Average distance inside each ˚ ). shell is reported in parenthesis (A Mg-shell POS1 1st 2nd 3rd Ntot POS2 1st 2nd 3rd Ntot POS3 1st 2nd 3rd Ntot
MgH2 bulk
SC
Mg
Ni
T ¼ 400 K
T ¼ 500 K
T ¼ 600 K
2 (3.02) 8 (3.45) 4 (4.39) 14
2 (3.02) 9 (3.43) 6 (4.56) 17
3 (3.12) 8 (3.47) 6 (4.53) 17
5 (2.79) 5 (3.47) 4 (4.34) 14
6.35 (2.78) 3.11 (3.57) 5.16 (4.44) 14.62
6.36 (2.80) 3.13 (3.56) 5.70 (4.44) 15.19
6.36 (2.75) 3.00 (3.59) 6.67 (4.47) 16.03
2 (3.02) 8 (3.45) 4 (4.39) 14
2 (3.02) 8 (3.45) 4 (4.39) 14
2 (3.02) 8 (3.48) 4 (4.53) 14
3 (3.01) 7 (3.41) 4 (4.47) 14
5.16 (2.85) 3.30 (3.56) 5.44 (4.39) 13.90
5.12 (2.84) 3.45 (3.58) 5.45 (4.39) 14.02
5.32 (2.84) 3.68 (3.55) 5.28 (4.40) 14.28
2 (3.02) 8 (3.45) 4 (4.39) 14
2 (3.02) 8 (3.45) 4 (4.39) 14
2 (3.01) 8 (3.50) 4 (4.45) 14
2 (2.93) 8 (3.41) 4 (4.40) 14
4.46 (2.90) 4.58 (3.55) 5.01 (4.37) 14.05
4.71 (2.85) 4.00 (3.56) 5.32 (4.38) 14.03
4.58 (2.87) 4.08 (3.55) 5.45 (4.37) 14.11
POS1. In the latter case, we note a sharp increase of the number of 1NN-Mg atoms with a reduction of the mean dis˚ to 5 Mg atoms at 2.79 A ˚ . This tance: from 2 Mg atoms at 3.02 A deformation produces an empty space at the distance of the 2nd Mg-shell; in the initial configuration there are 9 Mg atoms ˚ , on the contrary after the ionic at mean distance of 3.43 A ˚ . The mean distance is relaxation, the Mg atoms are 5 at 3.47 A increased because the inner Mg atoms are displaced in the 1st Mg-shell. Also the 3rd Mg-shell is less populated (from 6 to 4) ˚ ). Ionic even if at slightly smaller distance (from 4.56 to 4.34 A relaxation for system with nickel in middle position (POS2) does not produce evident changes in Mg coordination. There
is only one Mg atom that moves from the 2nd to the 1st Mgshell. The distance between this atom and nickel atom, ˚ . The others 2 1NN-Mg atoms are at changes from 3.45 to 3.21 A ˚ 2.91 and 2.92 A, respectively. Finally, for the third case, the coordination at the beginning and at the end of the geometry optimization remains the same, the only difference is the approaching of the 1NN-Mg atoms to the Ni atom. The mean ˚. distance is reduced from 3.02 to 2.93 A In conclusion, the main effect of the presence of nickel is an increase of the number of atoms in the 1st Mg-shell and in the 1st H-shell associated with a reduction of the distances. The outcome of this behaviour is more evident when the
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substituted atom is on the interface (POS1). In this situation, the magnesium side slab of the interface is more directly involved by the catalyst. Thus, a deeper interaction between the two slabs is yielded with consequent growth of the work of adhesion. This effect is magnified comparing the Mg and H coordination with respect to the geometry optimization of the interface without catalyst (fourth column of Table 2 and Table 3). Finally, it is worth to note that the same general trends in both the interface energies and atomic displacements were found in the case of Fe catalyst as reported in Ref. [27]. However, we point out that the difference in work of adhesion between relaxed interfaces with catalyst in POS1 2 2 POS1 (WPOS1 og (Ni) ¼ 588 mJ/m and Wog (Fe) ¼ 668 mJ/m ) can be explained in terms of the Mg coordination. In fact at the end of the geometry optimization in the former case (nickel) we have 5 1NN-Mg atoms, instead in the latter case (iron) we have 6 1NN-Mg atoms, with a consequent stronger interaction between the two slabs of the interface.
Molecular dynamics After geometry optimizations, we performed MD simulations at constant volume and constant temperature starting from the three relaxed interfaces. Simulation temperatures are from room temperature till 900 K, however the most interesting effects are in the range 500e600 K. In this range, the catalytic effect of Ni is able to reduce the hydrogen desorption temperature. Following the procedure developed in our previous works [26,27], we characterized the hydrogen atoms behaviour at each temperature in all the three cases. Five groups of H atoms (Hra, Hrb, Hrc, Hrd, Hrbulk) were defined
on the basis of their proximity to the interface. Hrx, with x ¼ a, b, c and d are groups of five H atoms (near the interface) belonging to the same line in the MgH2 side. Hrbulk is the group of the remaining H atoms in the MgH2 side that feel a bulk environment (see Fig. 3 in Ref. [26]). To quantify the hydrogen mobility we calculated the average displacements 〈d(t)〉 of these groups of H atoms. The trend of the average displacements 〈dðtÞ〉Hra , 〈dðtÞ〉Hrb , 〈dðtÞ〉Hrc , 〈dðtÞ〉Hrd and 〈dðtÞ〉Hrbulk at the proceed of the molecular dynamics simulations are shown in Fig. 3. To facilitate the comparison with the systems with Fe catalyst, the same colour palette as in Refs. [26,27] is adopted. That is, 〈dðtÞ〉Hra , 〈dðtÞ〉Hrb , 〈dðtÞ〉Hrc , 〈dðtÞ〉Hrd and 〈dðtÞ〉Hrbulk are drawn in blue line, red line, green line, orange line and black line, respectively. Graphics on the left and on the right in Fig. 3, refer to MD simulations at T ¼ 500 K (panels a, b, and c) and T ¼ 600 K (panels d, e, and f), respectively. Fig. 3 reveals that hydrogen displacements can be clearly detected already at T ¼ 500 K: if Ni in POS1 both first and second line of hydrogen diffuse, if Ni in POS2 only first line of hydrogen moves toward the interface. On the contrary at T ¼ 600 K the hydrogen diffusion process is completely settled and involves not only the first two lines of hydrogen atoms but also the third one, as shown in panel d) of Fig. 3. The hydrogen diffusion process is favoured by the distortion due to the presence of the catalyst atom. The increase of coordination of the catalyst respect to the Mg atoms is confirmed and enhanced during the MD simulations. Indeed, the 2nd H-shells are empty, whereas in the 1st H-shell there are on the average 4 hydrogen atoms when Ni is in POS1 and 5 hydrogen atoms when Ni is in POS2 and POS3. The mean
T = 500 K
5 4 3 2 1 0 5 4 3
T = 600 K
a) POS1
d) POS1
b) POS2
e) POS2
c) POS3
f) POS3
2 1 0 5 4 3 2 1 0
0
1
2
3
4
5
6 0 t (ps)
1
2
3
4
5
6
Fig. 3 e Average displacements of the hydrogen atoms. Three different interfaces are considered depending on the Ni atom position: POS1, POS2 and POS3. T ¼ 500 K on the left and T ¼ 600 K on the right. The average displacements 〈dðtÞ〉Hra , 〈dðtÞ〉Hrb , 〈dðtÞ〉Hrc , 〈dðtÞ〉Hrd and 〈dðtÞ〉Hrbulk are drawn in blue line, red line, green line, orange line and black line, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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˚ . The distances of these H atoms are in the range of 1.53e1.57 A average NieH distance is in agreement with previous ab-initio [15] and experimental [42] estimates where, in the high tem˚ and perature Mg2 NiH4 structure this distance is around 1.57 A ˚ , respectively. 1.55 A The number of 1NN H is reduced by one unit compared to the geometry optimization configurations: from 5 to 4 for Ni in POS1 and from 6 to 5 for Ni in POS2 and POS3. We also recall for convenience that in the bulk magnesium hydride ˚ , and 4H at 1.94 A ˚ in the 1st and the 2nd there are 2H at 1.89 A H-shells, respectively. For what concerns the 3rd H-shell coordinations, different results are shown from the three systems. The coordination ranges between 3 and 4 for Ni in POS1, it ranges between 5 and 6 for Ni in POS2 and, it ranges between 4 and 5 for Ni in POS3. The corresponding values at the end of the ionic relaxations are 3, 4 and 4 respectively. Thus, the effect of the temperature is to increase the number of the H atoms in the 3rd H-shells compared to the ionic relaxed configurations. The mean distances between Ni and ˚ , values that are slightly H atoms are in the range 3.23e3.28 A lower compared to MgH2 bulk value and to geometry optimizations values. On the contrary, the mean distance of H ˚ , is a little greater than atoms in the 4th H-shells, that is 3.60 A ˚ , whereas the mean distance of the hydride bulk value 3.56 A H atoms in the 5th H-shells are very close to the bulk value ˚ . The 4th H-shells are populated on average by 5H 3.94 A ˚ ), one atom in atoms (values are in the range 4.65e6.04 A addition compared to MgH2 bulk and to ionic relaxed configurations (the exception is the system with Ni on POS1). Instead, the population of the 5th H-shell has a dependence on the POSx, indeed, the atomic coordination is on the average 5 for Ni in POS1, 7 for Ni in POS2, and 8 for Ni in POS3, respectively. These values confirm those at the end of the ionic relaxations, but are lesser than the magnesium hydride bulk value. H coordinations and mean distances are summarized in Table 2. To sum up, comparing to the relaxed configurations, we can observe that the temperature produces a reduction of one atom in the 1st H-shells, and in addition, it produces an increment of the H coordination in the 3rd and in the 4th H-shells. Moreover, as already found in Ref. [27] in the case of iron catalyst, the nickel atom attracts the H atoms and empties the 2nd H-shells. However, now there are one H atom less in the 1st H-shells, whereas the 3rd H-shells are generally more populated. We also measured the coordination of magnesium atoms during the molecular dynamics at constant temperature and volume. We observed the increase of the number of Mg atoms in the 1st Mg-shell with respect to the starting configurations (SC). The Mg atomic coordination increases from 2 to 6.4 for Ni in POS1, to 5.2 for Ni in POS2 and to 4.6 for Ni in POS3, respectively. Moreover, these values are greater than the corresponding values at the end of the ionic relaxations (fifth column in Table 3). The mean distances between Ni ˚ for Ni in POS1, atom and 1NN-Mg atoms are: 2.75e2.80 A ˚ for Ni in POS2 and 2.85e2.90 A ˚ for Ni in POS3. In the z 2.85 A ˚ . Thus, during the MD MgH2 bulk there are 2 1NN-Mg at 3.02 A simulations, the 1st Mg-shells become more populated with shorter mean distances. The increase of the 1NN-Mg atoms produces the reduction of the coordination of the 2nd Mgshells. Indeed, the number of atoms in these shells, varying
between 3 and 5, is smaller than the values corresponding to the starting configurations (SC) and to the value of hydride bulk. During the MD simulations the mean distances are ˚ , values that are bigger compared to between 3.55 and 3.59 A ˚ . Then, in the 2nd Mg-shells there are MgH2 bulk value 3.45 A less atoms and at bigger distances. The emptying of the 2nd Mg-shells is also accompanied by the raise of the 3rd Mgshells coordination. The number of 3NN-Mg atoms is >5, whereas, at the end of the ionic relaxations there are 4 Mg atoms in this shell. The mean distances approach to bulk value for systems with Ni in POS2 and POS3, instead, when Ni atom is in POS1 the mean distances are slightly greater. Mg coordinations and mean distances are summarized on Table 3. Therefore, we observed that the temperature produces the increase of the 1NN and 3NN-Mg atoms associated with the depletion of the 2nd Mg-shells. The comparison of these outcomes with those yielded in Ref. [27] with iron catalyst, does not highlight an extremely market difference. The substitutional atom (Ni or Fe) attracts the surrounding Mg atoms causing the increase of the number of atoms in the 1st Mg-shell and the emptying of the 2nd Mg-shells. Even if, this behaviour is more evident with iron atom, in fact generally, the Fe atom has more 1NN-Mg and less 2NN-Mg atoms compared to Ni atom. The exception is for substitutional atoms in POS3.
Conclusions In the present paper we report a detailed study of the role played by the Ni atoms acting as catalyst for H desorption from MgH2. In particular, the interplay between the catalyst and an interface MgH2eMg has been characterized in terms of defect formation energies, work of adhesion, coordination numbers and distance from the interface. Ni atoms are able to destabilize the MgH2 atomic structure in a similar way already found for Fe catalyst in our previous work [27]. The catalyst attracts both H and Mg atoms increasing the local coordination and creating voids on longer distances. These distortions are the cause of an increase of both work of adhesion and defect formation energies. Comparing the energy values computed for Fe catalyst with those for Ni, we conclude that Fe is more destabilizing than Ni. This is in good agreement with experimental results, indeed in Ref. [8] the comparison of the desorption kinetics with several catalysts reveals that Fe catalyst is more effective than Ni. Moreover, MD simulations confirm that the presence of Ni catalyst lowers the desorption temperature. Thus, our model is able to reproduce the lowering of the hydrogen desorption temperature due the presence of metal catalysts and it provides information about the structural rearrangements induced by the different doping elements.
Acknowledgements The computing resources and the related technical support used for this work have been provided by CRESCO-ENEAGRID High Performance Computing infrastructure and its staff
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 4 0 ( 2 0 1 5 ) 9 3 2 6 e9 3 3 4
[43]. CRESCO-ENEAGRID High Performance Computing infrastructure is funded by ENEA, the “Italian National Agency for New Technologies, Energy and Sustainable Economic Development” and by national and European research programs. This work was supported by the project “HYDROSTORE” funded by the Italian Industria 2015 Program and by Action MP1103 “Nanostructured materials for solid state hydrogen storage”. Figures and graphics were made using software in Ref. [44,45].
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