international journal of hydrogen energy 34 (2009) 1389–1398
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Stability and bonding mechanism of ternary (Mg, Fe, Ni)H2
hydrides from first principles calculations
Y. Songa,*, W.C. Zhanga, R. Yangb
a
School of Materials Science and Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road, Weihai 264209, China
Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, China
b
article info
abstract
Article history:
The stability and bonding mechanism of ternary magnesium based hydrides (Mg, X, Y)H2, X
Received 3 January 2008
or Y ¼ Fe or Ni, were studied by means of electronic structure and total energy calculations
Received in revised form
using the FP-LAPW method within the GGA. The influence of the selected alloying elements
23 July 2008
on the stability of the hydride was determined from the difference between the total
Accepted 14 November 2008
energy of the alloyed systems and those of the pure metal and the hydride. Full relaxation
Available online 23 December 2008
was carried out against the overall geometry of the supercell and the internal coordinates
of the H atoms. The bonding interactions between the alloying atoms and their
Keywords:
surrounding H atoms were estimated using the variation of the total energy against the
Hydride
coordinates of H atoms. The alloying elements, Fe and Ni, destabilised MgH2. This
MgH2
combined with the weak bonds between the alloying elements and H atoms improved the
DFT
dehydrogenation properties of MgH2.
Electronic structure
ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights
reserved.
1.
Introduction
Some metal–hydrogen systems are often considered for onboard hydrogen storage applications [1]. Magnesium hydride
(MgH2) is one such system due to its high storage capacity and
low cost. However, the high thermodynamic stability and
slow kinetics of both absorption and desorption of the pure
magnesium hydride are still the major obstacles to any practical application. Many current studies have tried to reduce
the destabilization of MgH2 by alloying with transition
elements in an attempt to reduce the high Mg–H bonding
energy.
Although most of the transition elements have very limited
solubilities in MgH2, it has been shown that metal elements Al,
Ti, Fe, Ni, Cu and Nb can be alloyed with Mg to improve its
dehydriding properties using non-equilibrium processing
methods, such as mechanical alloying [2,3]. Some
experimental findings show that the plateau pressure of MgH2
varies with multi-component additions, for example, in the
Mg–Al–Y, Mg–Li–Ni–Zn [4], Mg–Fe–Ti(Mn) [5] and Mg–Zn–Y [6]
systems. It is not clear how these elements influence the
plateau level, especially the interaction within one material.
Theoretical investigations have been carried out under the
first principles framework [7–11]. Hydrogen absorption/
desorption properties of a hydride are very much dependent
on the constituents, and the metal–hydrogen bonding plays
a major role in the stability of the hydride. Previous theoretical
investigations focused on the identification of the bonding
nature of the pure magnesium hydride [7,8] and of some
binary magnesium hydrides [9,10], where the influence of
a single alloying element (Al, Ti, Fe, Ni, Cu and Nb) on the
stability of the magnesium hydride has been studied. It has
been shown that the addition of the Fe or Ni strongly reduces
the stability of MgH2 [9]. Ab initio cluster calculations have
* Corresponding author. Tel./fax: þ86 631 5687772.
E-mail address: [email protected] (Y. Song).
0360-3199/$ – see front matter ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijhydene.2008.11.046
1390
international journal of hydrogen energy 34 (2009) 1389–1398
synergistic effect of co-additives to achieve optimum
hydrogen storage properties. In this paper, Ni and Fe were
selected to extend the first principles study to ternary
magnesium hydrides (Mg, Fe, Ni)H2 in an attempt to clarify
this synergistic effect in multi-component systems. Both the
nature of bonding between the alloying elements and
hydrogen atoms, and the electronic structures of (Mg, Fe,
Ni)H2 are particularly examined. The computational method
is briefly described, followed by the simulation results and
a discussion of our findings.
Fig. 1 – Supercell used in the calculation. The large,
medium, and small balls are the alloying, magnesium, and
hydrogen atoms, respectively. The different alloying atoms
were labeled as X and Y, while the non-equivalent
magnesium and hydrogen atoms are denoted by 1–6.
shown that using the 3d transition metals as catalysts can
reduce the activation barrier of the Mg–H dissociation in MgH2
[11]. This is because when the Mg–H bond of MgH2 is activated
by a transition metal, M, the electrons of the bonding orbitals
of MgH2 are donated to the unoccupied orbitals of the M
(donation), while the electrons of the occupied orbitals of the
M are donated back to the antibonding orbitals of MgH2 (back
donation), resulting in easier Mg–H dissociation. Ni and Fe
have a comparatively high effect on the electron transition as
they cause a large amount of the back-donated electrons to
occupy the antibonding orbitals of MgH2 [11]. Experimentally,
the H2 desorption temperature decreases to about 100 C and
60 C in MgH2 when mechanically alloyed with Ni and Fe
nanoparticles, respectively [12]. Practical hydride systems are
likely to involve multi-component alloying using the
2.
Computational details
2.1.
Method
All calculations were carried out within the DFT framework of
where the many-body problem of interacting electrons and
nuclei was mapped to a series of one-electron equations
(Kohn–Sham equations). Self-consistent calculations were
carried out for all structures using a scalar-relativistic version
of the full-potential augmented plane wave þ local orbitals
(APW þ lo) method [13,14]. The generalized gradient approximation (GGA) of Perdew et al. [15] (PBE) was selected to
account for the exchange-correlation energy in the total
energy calculation. The wave functions, charge density, and
potential were expanded into spherical harmonics within
nonoverlapping atomic spheres of a radius RMT, and in plane
waves in the remaining space. An RMT of 1.8 a.u. was selected
for Mg and alloying elements, and 1.0 a.u. for H. The wave
functions in the interstitial region were expanded in plane
waves with a cutoff Kmax of 6.0 a.u.1. The total energy was
computed according to Weinert et al. [16] and self-consistency
was achieved in all calculations with a tolerance of 0.1 mRy in
the total energy. A mesh of 1 1 5 k points was used for the
Brillouin zone sampling.
2.2.
Table 1 – Structure of the supercell used in the present
calculations. The space group is P42/mnm (No. 136) with
lattice parameters of a0 [ 3a, and c0 [ c. The X and Y
denote the alloying elements. The non-equivalent atoms
are denoted by the numbers 1–6. x–z are atomic
coordinates in terms of lattice vectors a–c, respectively.
The coordinates of H1–H3 atoms are specialized by u(H1)–
u(H3), which are variables with regard to the relaxation of
the supercell. The initial values of u(H1)–u(H3) are 0.1016,
0.4350, and 0.2317, respectively.
Atom
X
Y
Mg1
Mg2
H1
H2
H3
H4
H5
H6
x
y
z
Number of atoms
0
2/3
1/3
1/3
u(H1)
u(H2)
u(H3)
0.1016
0.1016
0.4350
0
1/3
0
1/3
u(H1)
u(H2)
u(H3)
0.4350
0.7683
0.7683
0
0
0
0
0
0
0
0
0
0
2
4
8
4
4
4
4
8
8
8
Supercell geometry
The ground state of MgH2 is characterized by a tetragonal
symmetry (P42/mnm, group No. 136), where the Mg atom
occupies the 2a (0, 0, 0) site and the H atom the 4f (0.303, 0.303,
0) site [17]. In this study we employed a supercell 3 times the
size of the unit cell in both the a and the b axes to maintain
the symmetry (Fig. 1). Details of the supercell are listed in
Table 1. There are four and six non-equivalent sites for
magnesium and hydrogen atoms, respectively. Among them,
two magnesium sites (0, 0, 0) and (2/3, 1/3, 0), were replaced
by alloying atoms, Fe or Ni, as labeled in Fig. 1. The hydrogen
atoms are labeled as H1–H6. Among them the H1–H3 atoms
are the nearest neighbour atoms of the alloying elements
with internal coordinates denoted as u(H1)–u(H3). These vary
symmetrically, relative to the x and y axes during the relaxation of the supercell. The initial values of these are 0.1016,
0.4350, and 0.2317. The relaxation of the H4–H6 atoms was
performed so that the change of the fraction coordinates is
same in both the x and the y directions. The accuracy of the
total energy against the k points was checked. The total
energy of the supercell was 7254.7982, 7254.7120,
7254.7077, and 7254.7077 Ry for 1 1 2, 1 1 5,
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international journal of hydrogen energy 34 (2009) 1389–1398
Table 2 – Final structure of the supercell after relaxation. The lattice parameters and volume of the supercell, the
coordinates of H1–H6, and relative stability, DEr, of alloyed ternary magnesium hydrides.
a (nm)
c (nm)
V0 (nm3)
Mg18H36
(Mg12Fe2Ni4)H36
(Mg12Ni2Fe4)H36
1.3605
0.3033
0.5614
1.2707
0.2852
0.4605
1.2680
0.2857
0.4594
x
0.1016
0.4350
0.2317
0.1016
0.1016
0.4350
u(H1)
u(H2)
u(H3)
u(H4)
u(H5)
u(H6)
DEr (kJ/mol H2)
y
0.1016
0.4350
0.2317
0.4350
0.7683
0.7683
x
0.1010
0.4464
0.2141
0.1016
0.1014
0.4260
y
0.1010
0.4464
0.2141
0.4350
0.7670
0.7524
0
39.7
2 2 10, and 3 3 13 k points, respectively. The 1 1 5 k
mesh was chosen for computational efficiency and accuracy.
Compared with a previous high-accuracy calculation for
MgH2 with 1000 k points [9], the difference in the total energy
per unit cell is about 0.01 Ry. This may lead to an error of
about 7.0 kJ/mol H2 in the calculation of the heat of formation
of MgH2, which is within the range of experimental
uncertainty.
3.
Results and discussion
3.1.
Stability
x
0.1057
0.4489
0.2211
0.1015
0.1013
0.4275
y
0.1057
0.4489
0.2211
0.4347
0.7664
0.7551
44.5
should not be regarded as an Fe2Ni4 or Ni2Fe4 compound). The
gravimetric density of hydrogen in the two alloys is 5.38 wt%
and 5.43 wt%, respectively. The alloying elements Fe and Ni
were selected for their great effects in reducing the stability of
MgH2 noted in previous experimental and theoretical studies
[3,9,11,12].
Another parameter to describe the stability of a system is
the reaction enthalpy. This parameter is dependent on the
heat of formation and the products of the reaction. In the
considered systems, a possible decomposition reaction for
Fe2Ni4 (1a) and Fe4Ni2 (2a) is
Mg12Fe2Ni4H36 / 2Mg2FeH6 þ 4Mg2NiH4 þ 4H2 for Fe2Ni4
In general, the stability of a hydride depends on its heat of
formation, a measure of the H2 chemical potential in equilibrium with the metal and the hydride. With the above
supercell, we calculated the total energies of ternary magnesium hydrides (Mg12Fe2Ni4)H36 and (Mg12Ni2Fe4)H36, which we
denoted as Fe2Ni4 and Ni2Fe4 in the following sections (and
0.80
Fe2Ni4
Relative stability ΔEr (eV/H2)
0.75
(1a)
or
Mg12Fe4Ni2H36 / 4Mg2FeH6 þ 2Mg2NiH4 þ 2H2 for Fe4Ni2
(2a)
Because Mg2NiH4 is less stable than Mg2FeH6 (the formation
enthalpies are 62.7 kJ/mol H2 for Mg2NiH4 and 79.2 kJ/
mol H2 for Mg2FeH6 [18,19]), Mg2NiH4 will further decompose
to Mg2Ni and H2. Therefore, the possible decomposition
reaction of the considered systems is
Fe4Ni2
Mg12Fe2Ni4H36 / 2Mg2FeH6 þ 4Mg2Ni þ 12H2 for Fe2Ni4
0.70
0.65
(1b)
or
0.60
Mg12Fe4Ni2H36 / 4Mg2FeH6 þ 2Mg2Ni þ 6H2 for Fe4Ni2
(2b)
0.55
0.50
0.45
0.40
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
(V-V0)/V0
Fig. 2 – Heat of formation curves against the relative
change of the supercell volume; V0 is the volume
corresponding to the equilibrium experimental lattice
parameter of MgH2.
Using the total energies of Mg2NiH4 and Mg2FeH6 calculated
in our previous work [9], the reaction enthalpies are 43.71 kJ/
mol H2 for reaction (1a) and 72.94 kJ/mol H2 for (2a). Both the
reactions are exothermic. A recent DFT calculation shows that
the reaction enthalpy of Mg2NiH4 decomposing into Mg2Ni
and H2 is 63.68 kJ/mol H2 without the zero point energy [20].
Such, the overall reaction enthalpies of reactions (1b) and (2b)
are 19.97 kJ/mol H2 and 9.26 kJ/mol H2, respectively. This
means that the Fe2Ni4 system is the most suitable for practical
applications. As some of H atoms are held by the relatively
stable Mg2FeH6, as reactions (1) release about 3.59 wt%
hydrogen and reactions (2) about 1.81 wt%.
1392
a
b
H1 vibration
H2 vibration
c
H3 vibration
F(H3)
Etot
100
F(H1)
F(H2)
-7254.50
-7254.55
50
-7254.60
0
-7254.65
-50
Total energy (Ry)
Force on hydrogen atoms (mRy/a.u.)
international journal of hydrogen energy 34 (2009) 1389–1398
-7254.70
-100
0.08
0.10
0.12
0.42
0.44
0.46
0.22
0.24
0.26
150
d
H4 vibration
F(H4)
F(H5)
e
H5 vibration
f
H6 vibration
F(H6)
Etot
100
-7254.45
-7254.50
50
-7254.55
0
-7254.60
Total energy (Ry)
Force on hydrogen atoms (mRy/a.u.)
Internal coordinate u(Hx)
-50
-7254.65
-100
0.95
1.00
1.05 0.96 0.98 1.00 1.02 1.04 0.96 0.98 1.00 1.02 1.04
u(Hx)/u0(Hx)
Fig. 3 – Forces on hydrogen atoms and total energy of Mg18H36 system. The square, the circle, and the triangle symbols
denote the forces on H1–H3 ((a)–(c)), and on H4–H6 ((d)–(f)), respectively, while the diamond denotes the total energy of the
systems.
In order to investigate the influence of the alloying
elements on the stability of the pure MgH2, we introduce
a parameter, DEr, defined as
DEr ¼
1 Etot ðXn Ym Þ Etot Mg18 H36 ½nEtot ðXÞ þ mEtot ðYÞ
18
ðn þ mÞEtot ðMgÞ
(3)
to describe the relative stability of the alloyed systems relative
to the pure MgH2, where Etot(M) denotes the total energy of
system M. The total energies of the hydride and metals were
calculated using the FP-LAPW method described in Section 2,
and the total energy of the alloying elements was calculated
using the same method previously [9].
In order to take into account the influence of the alloying
elements on the stability of the hydrides, the relaxation was
performed in two steps: first the geometry was relaxed, and
secondly the internal coordinates. We first changed the
supercell volume of the alloyed systems by keeping the ratio
of the lattice parameters a and c constant, but changing their
values to obtain the energy surface against the lattice
parameters a and c. The theoretical equilibrium values of
a and c were obtained from the minima of the energy surface.
Table 2 lists the final values of the geometric parameters of the
considered systems after the relaxation.
Fig. 2 shows the variation of DEr defined in eq. (3) of Fe2Ni4
and Ni2Fe4 against changes in the relative volume. Here V0 is
the equilibrium volume of MgH2 and V is the volume of the
alloyed hydride. It shows that these alloying elements tend to
reduce the volume of the supercell. It has been found experimentally that the addition of some transition elements into
MgH2 reduces the unit cell volume of the matrix [2,3]. This
interaction is also noted in our previous calculations of
selected binary magnesium alloy systems [9]. The alloying
elements considered here greatly reduce the lattice volume, as
noted in Table 2, consequently enhance the volumetric
density about 18%. The variation of the unit cell volume has
been empirically correlated with the change of the plateau
pressure of hydrides. For instance, a volume contraction is
reported to increase the plateau pressure in the La(Ni1xMx)5
hydrides [21]. According to the Van’t Hoff equation, an
increase in the plateau pressure corresponds to a reduction of
the hydrogen absorption temperature. This implies that the
present systems should improve hydrogen desorption/
adsorption properties of MgH2.
Further relaxation of the internal coordinates was carried
out in order to analyse the bonding characteristics of the H
atoms and the alloying elements. Structural analysis shown
that H1 and H2 (Fig. 1, Table 1) are the nearest neighbours of
1393
international journal of hydrogen energy 34 (2009) 1389–1398
a
H1 vibration
F(H1)
F(H2)
200
b
coordinates of the H4–H6 atoms remained almost unchanged
in the alloyed systems when compared to the pure MgH2,
which is consistent with the finding that the interaction
between the alloying elements and their surrounding atoms is
localised [9]. In the following section, we therefore focus on
the interaction between the alloying elements and their
nearest neighbours, H1–H3 atoms. It is also noted that in all
the systems the H2 atom tends to move closer to the X atom,
while the H3 atom tends to move further away from its
nearest neighbour, the Y atom. The H1 atoms behave differently. In the Fe2Ni4 system, the internal coordinate u(H1) of
each H1 atoms is slightly reduced, while in the Ni2Fe4 systems
the H1 atoms tended to move away from the Ni atom. These
features are associated with the bonding nature between the
alloying elements Fe or Ni and the HX (x ¼ 1, 2, or 3) atoms,
which will be discussed below.
3.2.
Bonding mechanisms
As shown above, the change of the position of each H atom
can be regarded as the vibration of each atom around its
equilibrium position (Figs. 3 and 4). This gives us a guide to
investigate the bonding mechanism between the H atom and
the matrix atoms including the alloying elements.
The bonding energy per atom of a system containing N
atoms may be defined as,
H2 vibration
c
H3 vibration
F(H3)
0.8
ΔEr
150
0.7
100
0.6
50
0
0.5
-50
0.4
-100
0.08
0.10
0.12
0.42
0.44
0.46
0.20
0.22
0.24
Relative stability ΔEr (eV/H2)
Force on hydrogen atoms (mRy/a.u.)
the alloying element X, and H3 is the nearest neighbour of Y.
The relaxation was performed by changing one of the internal
coordinates while keeping the others constant. For each H
atom we then estimated the forces on the other H atoms, the
total energy and the relative stability against the internal
coordinates u(Hx) of the Hx atom. The relaxation was first
performed for MgH2 with the supercell shown in Fig. 1. It was
found that the force on the H atoms was almost independent
of the relaxation of the other H atoms. Fig. 3 shows the variations of the total energy and forces on the H atoms plotted
against their internal coordinates ((a)–(c), relaxation of H1–H3
atoms) and against their relative internal coordinates ((d)–(f),
relaxation of H4–H6 atoms). The square, circular, and triangular symbols in Fig. 3 denote the forces on the H atoms, while
the diamond denotes the total energy of the Mg18H36 system.
The same procedures were performed for the alloyed
(Mg12XnYm)H36 systems, and the results are plotted using the
same notation in Fig. 4. There is a relatively large difference in
total energy in these systems as the number of the Fe and the
Ni atoms is different, so the relative stability DEr was used
instead of the total energy. It is clear from Figs. 3 and 4 that the
force on the relaxed H atom varies linearly with the internal
coordinate, and the variation of both the relative stability DEr
and the total energy of the considered systems is approximately parabolic. The final geometrical results after the
relaxation are listed in Table 2. It is noted that the internal
0.26
d
100
H4 vibration
F(H6)
ΔEr
e
H5 vibration
F(H4)
F(H5)
f
H6 vibration
0.9
0.8
50
0.7
0
0.6
-50
0.5
-100
0.4
-150
Relative stability ΔEr (eV/H2)
Force on hydrogen atoms (mRy/a.u.)
Internal coordinate u(Hx)
0.3
0.96 0.98 1.00 1.02 1.04 0.96 0.98 1.00 1.02 1.04 0.96 0.98 1.00 1.02 1.04
u(Hx)/u0(Hx)
Fig. 4 – Forces and relative stability of relaxed (Mg, Fe, Ni)H2 systems. The square, the circle, and the triangle symbols denote
the forces on H1–H3 ((a)–(c)), and on H4–H6 ((d)–(f)), respectively, while the diamond denotes the relative stability of the
systems. The solid symbols are for the Fe2Ni4 system and the open symbols are for the Ni2Fe4 systems.
1394
-4.87
international journal of hydrogen energy 34 (2009) 1389–1398
(3), but are the isolated atoms in eq. (4). With the present
relaxation model, the variation of the bonding energy against
the internal coordinate in Figs. 3 and 4 is caused by the change
in the interaction between the relaxed H atom and the host
atoms. It is reasonable to use the bonding energy defined in
eq. (4) to discuss the bonding mechanism between the relaxed
atom and its nearest neighbour atoms. Fig. 5 plots the data of
the bonding energy against the bond length. Owing to the fact
that the vibration of an Hx atom is harmonic the changes of
the internal coordinate of the H atoms are around their
equilibrium positions as the vibration of an Hx atom is
harmonic. This can be observed in Figs. 3 and 4, which show
that the forces on the relaxed Hx atoms are linearly related to
the change of the internal coordinates of the H atoms. This
meant we could fit the data in Fig. 5 to a parabola in the form,
a
-4.88
-4.89
-4.90
-4.91
-4.92
-4.93
Mg-H1
Mg-H2
Mg-H3
-4.94
-4.95
-4.96
Bond energy (eV)
-5.32
-5.34
b
-5.36
-5.38
-5.40
-5.42
Fe-H1 in Fe2Ni4
-5.44
-5.48
-5.38
1
Eb ¼ Eb0 þ kðr r0 Þ2
2
Fe-H2 in Fe2Ni4
Fe-H3 in Fe4Ni2
-5.46
c
-5.40
-5.42
-5.44
Ni-H1 in Fe4Ni2
Ni-H2 in Fe4Ni2
Ni-H3 in Fe2Ni4
-5.46
-5.48
0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
Bond length (nm)
Fig. 5 – Bond energy curves against the bond length for Mg–
H (a), Fe–H (b) and Ni–H (c) bonds. Square, circle and
triangles denote the M–H1, M–H2, and M–H3 bonds,
respectively.
3
2
1 4 sys X
Eb ¼
Nj Eatom ðjÞ5
E N tot
j
(4)
sys
Etot denotes the total energy of the considered system, and Nj
and Eatom( j ) are the number and the total energy of the jth
type atoms in the system. The difference between eqs. (3) and
(4) is that the references are the metals and the hydride in eq.
(5)
Eb0 is the bond energy, r0 is the bond length, and k is the
strength of the harmonic vibration, and can be regarded as
a parameter that describes the bond interaction. The results
are listed in Table 3, where we used the ratio kx/kMg as
a parameter to describe the influence of the alloying elements
on the bond interaction between the Hx atoms and their
matrix atoms. kx denotes the strength of the harmonic
vibration of the H atoms around the alloying atom X. In most
cases the bond interaction between Hx and their matrix atoms
was reduced by the addition of the alloying elements. The
exception is the Fe–H3 in Ni2Fe4 (kFe/kMg ¼ 1.23). This weakening of the bond between the H atoms and their matrix
atoms implies that these H atoms are relatively easy to
release, which benefits the dehydriding properties. It should
be pointed out that the absolute value of the bond energy Eb0 of
the alloyed systems in Table 3 is greater than that of the pure
magnesium hydride. This is because the bond energy is estimated from the average energy difference between the total
energy of the considered system and the energies of the isolated atoms (eq. (4)), and the selected alloying elements have
much higher bonding energies in their pure metal state than
that of Mg. We, therefore, used the parameter k in eq. (5) to
describe the bonding interaction rather than the Eb0 itself.
Table 3 implies that the Fe–Ni systems, Fe2Ni4 and Ni2Fe4,
should possess superior dehydriding properties to MgH2 as all
the bonds between H1–H3 atoms and Fe or Ni atoms were
Table 3 – Bond characteristics between alloying elements and their first and second nearest neighbour hydrogen atoms.
The bonding energy, Eb0 , bond length, r0, the bond interaction parameter k were obtained by fitting the bonding energy
curves against the bond length defined in eq. (5), and the ratio of kx/kMg.
Eb0
r0 (nm)
k (eV/nm2)
kx/kMg
H1
H2
H3
4.955
4.957
4.957
0.19925
0.19684
0.19740
88.376
96.397
80.093
1.000
1.000
1.000
Fe
H1 in Fe2Ni4
H2 in Fe2Ni4
H3 in Ni2Fe4
5.390
5.410
5.491
0.18699
0.17383
0.17232
36.310
74.765
99.657
0.411
0.775
1.244
Ni
H1 in Ni2Fe4
H2 in Ni2Fe4
H3 in Fe2Ni4
5.439
5.474
5.449
0.17852
0.16993
0.16889
44.461
85.943
78.738
0.503
0.892
0.983
Element
Hydrogen
Mg
international journal of hydrogen energy 34 (2009) 1389–1398
100
1395
EF
Fe2Ni4
Total
50
0
Ni s
Ni p
Ni d
20
2
1
10
0
-5.0
-4.5
-4.0
-3.5
-3.0
0
Fe s
Fe p
Fe d
20
4
3
2
1
10
0
-4.5
-4.0
-3.5
Density of states
0
H1 s
H2 s
H3 s
1.0
0.5
0.0
Mg1 s
Mg1 p
Mg1 d
0.2
0.1
0.0
Mg2 s
Mg2 p
Mg2 d
0.2
0.1
0.0
H4 s
H5 s
H6 s
1.0
0.5
0.0
-10
-8
-6
-4
-2
0
2
4
Energy relative to the Fermi energy (eV)
Fig. 6 – Total and partial density of states of (Mg12Fe2Ni4)H36 alloy in units of state per eV. Insets show the partial DOSs of Fe
and Ni atoms.
weakened with the exception of the Fe–H3 bond in Ni2Fe4. The
data in Tables 2 and 3 clearly show that Fe2Ni4 may possess
much improved hydrogen sorption properties among the
systems we considered.
3.3.
Electronic structure
The total and partial densities of states (DOSs) of the considered systems are shown in Figs. 6 and 7. There is a bonding
peak just below the Fermi energy in the total DOS of the F2Ni4
system (Fig. 6). This is contributed by not only the alloying
atoms Ni d and Fe d, and their surrounding H1 s electrons, but
also the matrix Mg1 p and H6 s electrons. Due to the structure
of the supercell, this peak can be largely attributed to the Fe–
H1 and the Mg1–H6 interactions. Below the Fermi energy, the
first few peaks belong to the Fe d electrons, and the later ones
are the contributions by the Ni d electrons. The peaks that are
located in the energy range from 4.5 to 2.5 eV are due to the
1396
international journal of hydrogen energy 34 (2009) 1389–1398
100
EF
Fe4Ni2
Total
50
0
Ni s
Ni p
Ni d
20
2.0
1.5
1.0
0.5
10
0.0
-6
-5
-4
-3
0
Fe s
Fe p
Fe d
20
1.5
1.0
0.5
10
0.0
-5
-4
-3
Density of states
0
H1 s
H2 s
H3 s
1.0
0.5
0.0
Mg1 s
Mg1 p
Mg1 d
0.2
0.1
0.0
Mg2 s
Mg2 p
Mg2 d
0.2
0.1
0.0
H4 s
H5 s
H6 s
1.0
0.5
0.0
-10
-8
-6
-4
-2
0
2
4
Energy relative to the Fermi energy (eV)
Fig. 7 – Total and partial density of states of (Mg12Ni2Fe4)H36 alloy in units of state per eV. Insets show the partial DOSs of Fe
and Ni atoms.
bonding both between the matrix Mg and the H atoms, and
between the alloying atoms and the H atoms. The Fe–H1
and Fe–H2 interactions contribute to the bonding peaks just
below 4.0 eV and at about 3.6 eV, respectively. Note that
the H2 s peak at 3.6 eV is higher than the H1 s peak just
below 4.0 eV, and that the Fe d peak at 3.6 eV is about twice
as high as the peak just below 4.0 eV. This implies that the
Fe–H2 bond is stronger than that of the Fe–H1 bond. The bond
interaction parameter k in Table 3 confirms this conclusion
(kFe–H2/kFe–H1 ¼ 2.056 from Table 3). The Ni–H3 interaction has
a broader bonding range, from 4.5 to 3.5 eV, resulting in
a slightly stronger bonding than the Fe–H2 bond in this
system. This means that the desorption is likely to initiate
from the Fe–H1 bond.
international journal of hydrogen energy 34 (2009) 1389–1398
Unlike the Fe2Ni4 system, the first two peaks below the
Fermi energy in the total DOS of the Ni2Fe4 system show Fe
d characteristics, and then the Ni d characteristics (Fig. 7),
where there is no contribution from the matrix atoms. The
states in the energy range from 5.0 to 3.0 eV below the
Fermi energy contribute to the bonding between the alloying
atoms and the matrix H atoms. The Ni–H1 bonding is located
at 4.0 eV and the Ni–H2 bonding at 4.5 eV. As in the Fe2Ni4
system, the Ni d electrons contribute more to the Ni–H2 bond
than to the Ni–H1 bond. This is consistent with the data in
Table 3, where the bond interaction parameter k for the Ni–H2
bond is 85.94 and 44.46 eV/nm2 for the Ni–H1 bonds. The
partial DOSs of Fe–H3 interaction also show broader bonding
feature.
It is worth noting that the sharp peaks contributed by the
d electrons of the alloying elements Fe and Ni appear at the
Fermi energy in the total DOSs of the two present systems.
This implies that the spin polarization has an influence on the
stability of the two systems. Therefore, the spin orbital
calculations were performed to ascertain the extent of the
influence of spin polarization on the stability. The difference
in the total energy when the spin orbitals are added is 0.01 Ry
per unit cell for the Fe2Ni4 and 0.005 Ry for the Fe4Ni2 systems.
This means that the influence of the spin polarization on the
stability is relatively weaker than that of the alloying itself,
which is consistent with a recent calculation on the FeTi–H
system [22].
3.4.
between Ni–H3 in the Fe2Ni4 system than between Fe–H3 in
the Ni2Fe4 system. Because the alloying element mainly
influences interactions in its vicinity weaker interactions
lower the stability of the compound. This is consistent with
the overall heat of formation of the two systems.
4.
Conclusions
The stability and the bond mechanism of selected ternary
magnesium based hydrides were studied using the electronic
structure and total energy calculations of the FP-LAPW
method within the GGA. We used the difference between the
total energies of alloyed systems and the total energies of
the pure metal and the hydride to determine the influence of
the selected alloying elements on the stability of MgH2. Full
relaxations, geometry and the internal coordinates of the H
atoms were carried out. We also estimated the bond interaction between the alloying atoms and their surrounding H
atoms using the harmonic vibration model of the relaxed H
atoms around their matrix atoms, and discussed the mechanism of bonding based on the electronic structures. The
alloying elements Fe and Ni have strong effects on destabilizing MgH2 and weakening the bonds between both themselves and the H atoms, and between the matrix Mg atoms
and H atoms. This means that the addition of alloying
elements will improve the sorption properties of MgH2.
Influence of alloying elements
Our previous study shows that the alloying elements considered here reduce the stability of MgH2 in binary (Mg, X)H2
systems [9]. This behaviour is also confirmed in the ternary
(Mg, X, Y)H2 systems. The relative stability DEr is 39.7 kJ/mol H2
for the Fe2Ni4 system and 44.5 kJ/mol H2 for the Ni2Fe4 system.
Partial DOSs of the two systems (Figs. 6 and 7) show that
bonding interaction between Mg1, Mg2 and H4, H5 atoms is
stronger in the Ni2Fe4 system than in the Fe2Ni4 system. On
the other hand, the interaction of Fe–Hx (x ¼ 1 or 2) is stronger
in Fe2Ni4 than the interaction of Ni–Hx (x ¼ 1 or 2) in Ni2Fe4.
The difference in charge distributions between the whole
system and the individual atoms in the supercell on the (110)
plane shows the bonding features in the two systems (Fig. 8).
There are more electrons between the Fe and the H2 atoms in
the Fe2Ni4 system than between the Ni and the H2 atoms in
the Ni2Fe4 system. There are also more electrons located
Fe
1397
H1
H3
-0.01
0.1 Ni
Mg2
0.1
0.1
H2
H2
Mg2
H3
0.1
0.1
Fe -0.01
-0.01 Ni
-0.01 -0.01
0.1
0.1
0.1
-0.01 Fe
0.1
-0.01
Ni
-0.01
0.1
0.1
0.1 Fe
H1
-0.01
-0.01
Fe2Ni4
Fe4Ni2
Fig. 8 – Charge distribution difference on the (110) plane of
the Fe2Ni4 (top) and the Ni2Fe4 (bottom) systems in unit of
e3/a.u.2. Solid and dashed lines denote positive and
negative values, respectively.
Acknowledgements
This work was supported by the National Basic Research
Program of China Grant 2006CB605104, the Natural Science
Foundation of Shandong, China (Y2007F61), the Program of
Young Scientists of Shangdong, China (2006130), and the
Program of excellent team of Harbin Institute of Technology.
references
[1] Schlapbach L, Züttel A. Hydrogen-storage materials for
mobile applications. Nature 2001;414:353.
[2] Liang G. Synthesis and hydrogen storage properties of Mgbased alloys. J Alloys Compd 2004;370:123.
[3] Shang CX, Bououdina M, Song Y, Guo ZX. Mechanical
alloying and electronic simulations of (MgH2 þ M) systems
(M – Al, Ti, Fe, Ni, Cu and Nb) for hydrogen storage. Int J
Hydrogen Energy 2004;29:73.
[4] Nachman JF, Rohy DA. In: Veziroglu TN, editor. Miami Beach,
FL, 13–15 April 1981Proceedings of the Miami international
symposium on metal–hydrogen systems. New York:
Pergamon Press; 1982. p. 557.
[5] Mandal P, Srivastava ON. Hydrogenation behavior of the new
composite storage material Mg-x-percent FeTi. J Alloys
Compd 1994;205:111.
[6] Zaluska A, Zaluski L, Strom-Olsen JO. Nanocrystalline
magnesium for hydrogen storage. J Alloys Compd 1999;288:217.
[7] Smithson H, Marianetti CA, Morgan D, Van der Ven A,
Predith A, Ceder G. First-principles study of the stability and
electronic structure of metal hydrides. Phys Rev B 2002;66:
144107.
1398
international journal of hydrogen energy 34 (2009) 1389–1398
[8] Miwa K, Fukumoto A. First-principles study on 3d transitionmetal dihydrides. Phys Rev B 2002;65:155114.
[9] Song Y, Guo ZX, Yang R. Influence of selected alloying
elements on the stability of magnesium dihydride for
hydrogen storage applications: a first-principles
investigation. Phys Rev B 2004;69:094205.
[10] Chen D, Wang YM, Chen L, Liu S, Ma CX, Wang LB. Alloying
effects of transition metals on chemical bonding in
magnesium hydride MgH2. Acta Mater 2004;52:521.
[11] Tsuda M, Diňo WA, Kasai H, Nakanishi H, Aikawa H. Mg–H
dissociation of magnesium hydride MgH2 catalyzed by 3(d)
transition metals. Thin Solid Films 2006;509:157.
[12] Hanada N, Ichikawa T, Fujii M. Catalytic effect of
nanoparticle 3d-transition metals on hydrogen storage
properties in magnesium hydride MgH2 prepared by
mechanical milling. J Phys Chem B 2005;109:7188.
[13] Blaha P, Schwarz K, Luitz J. WIEN2K. Vienna University of
Technology; 2000.
[14] Singh D. Plane waves, pseudopotentials, and the LAPW
methods. New York: Kluwer Academic; 1994.
[15] Perdew JP, Burke S, Ernzerhof M. Generalized gradient
approximation made simple. Phys Rev Lett 1996;77:3865.
[16] Weinert M, Wimmer E, Freeman AJ. Total-energy all-electron
density functional method for bulk solids and surfaces. Phys
Rev B 1982;26:4571.
[17] Noritake T, Aoki M, Towata S, Seno Y, Hirose Y, Nishibori E,
et al. Chemical bonding of hydrogen in MgH2. Appl Phys Lett
2002;81:2008.
[18] Yamaguchi M, Akiba E. In: Cahn RW, Haasen P, Kramer EJ,
editors. Materials science and technology. Electronic and
magnetic properties of metals and ceramics, Part II, vol. 3B.
Weinheim: VCH; 1994. p. 333.
[19] http://hydpark.ca.sandia.gov.
[20] van Setten MJ, de Wijs GA. Ab initio study of the effects of
transition metal doping of Mg2NiH4. Phys Rev B 2007;76:075125.
[21] Percheron-Guegan A. In: Grandjean F, Long GJ, Buschow KHJ,
editors. Interstitial intermetallic alloys. Nato ASI series,
series E – Applied sciences, vol. 281; 1995 [chapter 5].
[22] Kinaci A, Aydinol MK. Ab initio investigation of FeTi–H
system. Int J Hydrogen Energy 2007;32:2466.