IOP PUBLISHING
NANOTECHNOLOGY
Nanotechnology 19 (2008) 275704 (6pp)
doi:10.1088/0957-4484/19/27/275704
Theoretical investigations on low energy
surfaces and nanowires of MgH2
P Vajeeston1, P Ravindran and H Fjellvåg
Center for Materials Science and Nanotechnology, Department of Chemistry,
University of Oslo, Box 1033 Blindern, N-0315, Oslo, Norway
E-mail: ponniahv@kjemi.uio.no
Received 11 January 2008, in final form 16 April 2008
Published 28 May 2008
Online at stacks.iop.org/Nano/19/275704
Abstract
The phase stability, chemical bonding, and electronic structure of MgH2 nanowires and possible
low energy surfaces of α -MgH2 thin films have been investigated using the ab initio projected
augmented plane-wave method. Structural optimizations based on total energy calculations
predicted that, for the α -MgH2 phase, the (101) surface is more stable among the possible low
energy surfaces. The electronic structure study reveals that the nanowires also have nonmetallic
character similar to that of the bulk and thin film phases. Bonding analysis shows that the
character of chemical bonding in nanowires has been considerably changed compared with that
in bulk phases. Similarly, the bond distances in the surfaces of nanowires are found to be higher
than in the bulk material, suggesting that it is possible to remove hydrogen from the nanowires
considerably more easily than from bulk crystals.
(Some figures in this article are in colour only in the electronic version)
However, it is found [7] that these methods can only improve
the absorption and not the desorption kinetics, possibly
because even the smallest particle sizes (20 nm) obtainable
by these methods still primarily display bulk desorption
characteristics.
The shape, size, surface composition, and crystal
structure of materials are major factors that control the
hydrogenation properties for energy storage applications.
By hydrogen absorption and subsequent disproportionation
of bulk Mg24 Y5 , Zlotea et al [8] found the formation
of one-dimensional single crystalline MgH2 phases with
nanometer and micrometer ranges. These wires/whiskers
have been structurally and morphologically characterized by
x-ray diffraction and scanning and transmission electron
microcopies. Only limited information is available about the
nature (growth direction, stability, etc) of these wires. Saita
et al [9] also found the formation of such one-dimensional
needle-shaped single crystalline MgH2 using a chemical vapor
synthesis technique. It is interesting to study the structural
and physical properties of such nanophases of MgH2 in order
to improve its hydrogen sorption kinetics. In this paper we
present a surface energy study based on the calculated total
energy and electronic structure as well as a chemical bonding
analysis of α -MgH2 and its nanowires using the results from
band structure calculations.
1. Introduction
Metal hydrides such as LiH, MgH2 , and CaH2 have been
studied widely for hydrogen storage applications, and among
them, MgH2 has been considered seriously because of its
relative abundance, light weight, comparatively weaker metal–
hydrogen bonding, and higher hydrogen content. To act
as an efficient energy carrier, high quantities of hydrogen
should be absorbed and desorbed in materials easily. Even
though magnesium based hydrides have higher hydrogen
capacity, the slow hydrogen sorption kinetics has so far
hampered their commercial usage. One of the main reasons
for the slow kinetics of H desorption/adsorption in MgH2
is that its enthalpy of formation is high [1] (−76.2 ±
9.2 kJ mol−1 ) compared with that of metal hydrides, which
indicates that the hydrogen atoms bind very strongly with
the Mg atoms. Consequently, dehydrogenation of magnesium
hydrides requires high temperature (∼552 K at 1 atm). In
order to use MgH2 as an energy carrier in mobile applications
one has to find the possible ways to decrease the hydrogen
desorption temperature. Numerous studies have been focused
on improving the problematic sorption kinetics, including
mechanical ball milling [2–4] and chemical alloying [5, 6].
1 URL: http://folk.uio.no/ponniahv.
0957-4484/08/275704+06$30.00
1
© 2008 IOP Publishing Ltd Printed in the UK
Nanotechnology 19 (2008) 275704
P Vajeeston et al
2. Computational method
In order to model the extended nature of the nanowires and
surfaces, density functional theory (DFT) calculations under
periodic conditions by the supercell approach were carried out
using the Vienna ab initio simulation package (VASP) [10].
In these calculations the exchange correlation energy was
calculated using the generalized gradient approximation
(GGA) implementation of DFT proposed by Perdew et al
[11], with the electronic states expanded using plane waves
as the basis set. The calculations were performed utilizing
the projected augmented wave method [12] implemented in
the VASP code. For the present calculations we have used
a plane-wave cutoff energy of 500 eV. The k-points were
generated using the Monkhorst–Pack method with a grid size
of 4 × 4 × 6 and 4 × 4 × 1 for structural optimization of the
bulk and surfaces, respectively. For calculation of electronic
properties the grid sizes were increased to 8 × 8 × 12 and
8 × 8 × 1, for the bulk and surfaces, respectively. Forces on the
ions were calculated using the Hellmann–Feynman theorem
as the partial derivatives of the free electronic energy with
respect to the atomic positions, and adjusted using the Harris–
Foulkes correction to the forces. This approach for calculating
the forces allows a geometry optimization using the conjugate
gradient scheme. Iterative relaxation of atomic positions was
stopped when the change in total energy between successive
steps was less than 1 meV/cell. With this criterion, the forces
generally acting on the atoms were found to be less than
−1
0.1 eV Å .
Different sizes of the nanowires have been constructed
from the optimized bulk phase with respect to different
supercell sizes. The k-points were generated using the
Monkhorst–Pack method with a grid size of 1 × 1 × 2 and
1 × 1 × 4, for structural optimization and electronic properties,
respectively. The maximum size of the wire was constructed
from a 6 × 6 × 2 supercell, and the width of that wire is
about 3.3 nm (see figure 1). During the wire construction
the MgH2 stoichiometry was always maintained. In order to
get the wire/spherical shape of the object systematically the
corner MgH2 species were removed. The vacuum is included
only in the x and y directions. The vacuum thickness was
considered wide enough to prevent wire-to-wire interactions,
and we found that a width of 12 Å was sufficient to ensure that
the energy was converged to less than 1 meV/atom.
Figure 1. Optimized MgH2 nanowire derived from α -MgH2 .
(BFDH) method implemented in the MS modeling package
(version 4.0). The main reason to use the BFDH method is
to obtain a rough estimate of the faces that are likely to be
important for the crystal habit. This information has been
used to pre-screen the face list used as an input to more
sophisticated VASP calculations. According to the BFDH
calculation (110), (101), (200), (111), and (210) are possible
low energy surfaces. For the surface models considered we
have included an integer number of MgH2 formula units, and
they are thus stoichiometric. We have also avoided generating
surface models that are significantly polar and consequently
would be artificially stable due to long-range electrostatic
forces. The constructed slab corresponding to a given Miller
face has an integer number of planes such that it is parallel
to the surface and has a center of symmetry at the slab
center. As a result, it can be mapped onto all parallel planes
below it by applying symmetry operators such as translations,
screw axes or glide planes, and thus the resulting slab has no
dipole moment. Previously reported [15] positional and cell
parameters were used for α -MgH2 ; they are almost similar to
the experimental data [13, 14]. For the surface calculations the
unrelaxed slabs have been cut from the optimized bulk crystal,
where bulk structures have been fully relaxed with respect to
stress and strain. All atoms in such created slabs have been
allowed to relax using the minimization of forces acting on
them.
The surface energy of a crystal can be calculated using the
following equation:
3. Result and discussion
3.1. Active low energy surfaces
α -MgH2 crystallizes in a TiO2 rutile-type structure at
ambient pressure and low temperatures [13, 14]. At higher
temperatures and pressures, it transforms to several other
polymorphs [15, 16]. In this study we have concentrated
mainly on the ambient condition α -MgH2 phase.
We
emphasize that one of the motivations for this work is to
determine the surface properties of thin films of α -MgH2 in
different morphologies. The possible low energy surfaces were
identified with the help of the Bravais–Friedel–Donnay–Harker
E surf (n) =
E tot (n) − E bulk (n)
2A
(1)
where E tot and A are the total energy and total surface area,
respectively. E bulk refers to the energy of the bulk α -MgH2
system containing the same number of molecular units as the
slab. Since the constructed supercell of slab has two surfaces,
the energy difference is normalized by twice the area of each
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Nanotechnology 19 (2008) 275704
P Vajeeston et al
2.0
2
Surface energy (J/m )
1.5
(101)
(110)
1.0
0.5
0
5
10
Figure 3. Calculated total energy (in eV/formula unit (f.u.)) as a
function of wire diameter for a nanowire derived from α -MgH2 .
15
Number of layers
Table 1. Calculated surface energy (σ ; in J m−2 ) and band gap ( E g ;
in eV) values for MgH2 in different possible low energy surfaces.
Figure 2. Calculated surface energy as a function of layer thickness
for α -MgH2 in the thin film geometry with (101) and (110) surfaces.
surface in equation (1). Figure 2 shows the calculated surface
energy as a function of number of layers in the 101 and
110 directions. It clearly indicates that the surface energy
becomes stabilized from the eighth layer onwards. In all the
thin film geometries studied we have found that an 8–10 layer
supercell (depending upon the surface) is sufficient to get a
well-converged surface energy.
The calculated surface energies for possible low energy
surfaces are given in table 1, which indicates that the
surface energy is almost the same for both (101) and (210)
surfaces. The visualization of the atomic stacking for both
(101) and (210) surfaces shows that they are almost the
same. On the other hand the surface energies for (101),
(110), (111), and (200) surfaces are considerably different
from each other, resulting from the large difference in their
atomic arrangements. Among the surfaces considered the
(101) surface has the lowest surface energy and hence it
becomes the most stable surface in α -MgH2 . This observation
is consistent with that of Saita et al [9], who found that
one-dimensional needle-shaped single-crystalline MgH2 grows
along 101 directions. It may be noted that the growth
direction is also influenced by the catalytic behavior of the
tip and/or the orientation as well as the lattice mismatch of
the substrate where the crystal grows. The analysis of the
(101) slab shows that the Mg atoms are arranged in a sheet-like
manner and the H atoms are placed between these Mg layers.
The calculated Mg–H interatomic distance varies from 1.91 to
2.02 Å at the surface layer, and this distance is considerably
longer than that in the bulk phase (1.93 Å and 1.95 Å for γ MgH2 according to theory and experiment, respectively) where
the Mg–H distance is 1.91 Å at the top of the slab.
Direction
σ
Eg
(101)
(110)
(111)
(200)
(210)
0.58
1.72
0.82
1.95
0.69
2.6
1.9
2.0
2.7
2.6
the nanowire size decreases the total energy becomes more
positive (i.e. the formation energy decreases with decrease of
nanowire diameter). In particular, there is a steep increase in
the total energy when the diameter of the wire is below 1.5 nm.
This is in agreement with experimental studies in the sense
that the whiskers identified experimentally have diameters
much higher than 1.5 nm. The decrease in the structural
stability of nanowires with diameter may be attributed to the
following. Below a critical wire diameter of about 1 nm,
most of the Mg and H atoms are exposed to the surface. It
is at this region that the properties of the material begin to
differ drastically from that of the bulk material. Moreover,
in ultra-small MgH2 wires, the hydrogen atoms are generally
found to occupy the less stable top and bridge sites at the
surfaces compared with the more stable three-dimensionally
coordinated sites commonly found in thicker wires (diameter
above 1.5 nm). The calculated Mg–H distances versus number
of bonds (see figure 4) for the biggest nanowire indicate that
the values were very scattered compared with that in the bulk
phase. In particular, several of the Mg–H bonds are longer than
in the bulk. This type of structural arrangement is expected in
nanophases and amorphous phases with no three-dimensional
crystallinity. From figure 4 it is clear that most of the Mg–
H bonds are of length 1.93 Å, and this corresponding to the
Mg–H distance in bulk α -MgH2 . Closer inspection of the Mg–
H distance reveals that in the center of the wire the Mg–H
distance is still the same as that of the bulk (in figure 4 the
arrow mark at 1.93 Å indicates the Mg–H distance in the bulk
α -MgH2 phase). Interestingly, some of the Mg–H bond lengths
are of the very short value of 1.91 Å, which corresponds to that
3.2. Nanowires
The calculated total energy as a function of the wire dimension
is shown in figure 3. From this figure it is clear that if
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Nanotechnology 19 (2008) 275704
P Vajeeston et al
EF
30
nano wire
1.5
20
1.0
1.93
0.5
15
DOS (states/f.u.)
Number of bonds
Å
25
10
5
1.5
2
2.5
3
3.5
(101) slab
1.5
1.0
0.5
Bond distance (Å)
Figure 4. Calculated interatomic distance between Mg and H in an
optimized nanowire derived from α -MgH2 . The arrow mark
indicates the Mg–H bond length for the bulk α -MgH2 phase.
α-MgH2
1.5
1.0
0.5
in the bulk γ -MgH2 phase. On the other hand, in the surface of
the wire the calculated Mg–H distances are much higher than in
the bulk phases. This indicates that the bonding interactions in
surface layers are considerably weaker than at the center of the
wire. As a result, one can expect that the removal of hydrogen
from the surface of the wire is much easier than from the bulk
or from the inner part of the wire.
-8
-6
-4
-2
0
2
Energy (eV)
4
6
8
Figure 5. Calculated total density of states (DOS) for the bulk phase,
thin film with (101) surface and nanowire of α -MgH2 . The Fermi
level is set at zero energy and is marked by the vertical dotted lines.
3.3. Electronic structure
that in bulk materials. Similarly all the nanowires (all sizes
considered in the present investigation) also have nonmetallic
character. But the magnitude of the band gap value in the
nanowires is reduced to almost half compared to that of bulk
phase. The smaller band gaps in thin films and nanowires once
again indicate that the formation of nanophases weakens the
bonding interactions compared with the bulk crystal. If we
scale the band gap for the underestimation then the expected
experimental value is about 3.34 eV for a nanowire of diameter
>1.5 nm. Hence one can expect that the nanowires will
have considerably different optical properties than those of
the bulk phase. The stability of different modifications of
nanoparticles/wire compared to the other MgH2 modifications
and their optical properties are under study, and the results will
be published in a forthcoming article.
From the characteristic features of the density of states (DOS)
one may be able to rationalize the bonding interaction between
the constituents in the nanowires. Though MgH2 is considered
as one of the important materials for hydrogen storage
applications, to our knowledge, no electronic structure studies
have been undertaken so far for thin films and nanowires
of MgH2 . The present study shows that in general all
modifications (thin films and wires) of the α -MgH2 phase have
a finite band gap ( E g ) between the valence and conduction
band (see table 1 and figure 5) which classifies them as
insulators. The calculated energy gap is 3.8 eV for α MgH2 , whereas an experimental UV absorption study [17]
gave an absorption edge of 5.16 eV. In fact, the underestimation
of the band gap (1.36 eV) is typical for the accuracy
obtained from first-principles density functional calculations
for semiconductors and insulators. As the band gap is an
excited state property, such distinctions probably originate
from the use of GGA-based exchange correlation functionals.
However, the inclusion of self-energy corrections into the
calculation will improve the predicting capability of the band
gap in insulators, which is beyond the scope of the present
study. The magnitude of the band gap varies depending upon
the different orientations along which the slab is constructed.
However, all the slabs have a nonmetallic character, and the
band gap values vary between 1.9 to 2.7 eV (see table 1;
minimum in (110) and maximum in (200)). It is interesting to
note that the band gap in the thin films is always smaller than
3.4. Chemical bonding
A number of investigations have been focused on characterizing the chemical bonding behavior of bulk phases of magnesium hydride [18, 19]. Both the experimental and theoretical charge-density maps clearly demonstrated the striking ionic
character of α -MgH2 , with small localized charges around the
hydrogen sites. The substantial difference in the electronegativity between Mg and H suggests the presence of strong ionic
character, i.e. the Mg valence electrons transferred to the H
sites resulting in an insulator with the stoichiometric MgH2
composition. According to our earlier study [16], the bonding
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Nanotechnology 19 (2008) 275704
P Vajeeston et al
Mg
Mg
H
H
Mg
H
H
H
H
H
Mg
H
H
Mg
H
Mg
Mg
Mg
H
H
H
H
H
H
H
H
(a)
(b)
Mg
Mg
Mg
H
H
H
H
Mg
Mg
Mg
H
H
H
H
H
Mg
H
H
H
H
Mg
H
H
H
(c)
H
(d)
Figure 6. Charge density distribution at (a) the center and (b) the edge of the α -MgH2 -derived nanowire. The corresponding ELF distributions
are given in (c) and (d), respectively.
characteristics are virtually the same for all the MgH2 polymorphs. In order to gain further understanding about the bonding situation in nanowires, we turn our attention to the charge
density and electron localization function (ELF) analyses. According to the charge density distribution at the Mg and H sites
in the center (figure 6(a)) and edges (figure 6(b)) of the wire, it
is evident that the highest charge density resides in the immediate vicinity of the nuclei. The almost spherical charge distribution at the Mg sites clearly reflects the ionic character. The
charge density distribution is almost similar to that for the bulk
phase (see figure 6(b)) reported in [16]. But a closer examination at the Mg and H sites shows a significant difference in the
charge density distribution. In particular, the charges are little
directional dependent at the Mg sites towards the H sites in the
next layers. In contrast, at the H site the charge distribution
is not spherically symmetric, and hence it can be concluded
that considerable covalent interaction is present between Mg
and H.
The calculated ELF plot (figure 6(b); for more information
about the ELF see [20–22]) shows a predominant maximum
of about 1 at the H site, and these electrons have a paired
character. The ELF value at the Mg site is very low. The
inference from this observation is that charges are transferred
from the Mg site to the H sites, and there are certainly very few
paired valence electrons left at the Mg site. A certain polarized
character is found in the ELF distribution at the H sites in all the
complex hydrides we have investigated earlier [23]. The ELF
distribution is, on the contrary, quite isotropic in bulk MgH2
as well as at the center of the nanowire (figure 6(c)). On the
other hand, the ELF for the H site at the edges of the wire is
highly polarized, similar to that in complex hydrides where we
have observed finite covalent character. The main noticeable
change in bonding interactions for nanowires compared with
that in bulk phases is that both the center and the edges of
the wire have high ELF in the vicinity of Mg sites. These
high ELF regions are directed towards the domain between
two adjacent H atoms. This high ELF is associated with the
polarization of unpaired Mg s states. As this ELF feature is
not present in bulk phases, this indicates that, in the outer part
of the wires, the atoms have not fully transferred their charges
to their nearest neighbors in a three-dimensional way, and the
excess charges move towards the inner parts of the wires. This
may be the possible reason for the presence of such high ELF
in the vicinity of the Mg site.
In an attempt to quantify the bonding interactions
and estimate the amount of electrons on and between the
participating atoms, we have made a Bader topological
analysis. Although there is no unique definition to identify
how many electrons are associated with an atom in a molecule
or an atomic grouping in a solid, it has nevertheless proved
useful in many cases to perform Bader analyses [24–26]. In
the Bader charge (BC) analysis each atom of a compound is
surrounded by a surface (called Bader regions) that run through
minima of the charge density, and the total charge of an atom
is determined by integration within the Bader region. The
calculated BC for Mg and H in bulk α -MgH2 is +1.65 and
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Nanotechnology 19 (2008) 275704
P Vajeeston et al
−0.82 electrons, respectively. The estimated BC for Mg and
H in the bulk α -MgH2 indicates that the interaction between
Mg and H is almost purely ionic. In nanowires the BC value
for Mg is scattered from +1.48 to +1.55 electrons. Similarly,
for H sites the value varies between −0.73 to −0.81 electrons
(minimum for the hydrogen at the edges and maximum for
that at the center of the wire), which is much smaller than the
pure ionic picture. This is partly associated with enhancement
in the covalency in nanowires compared with bulk materials,
and this finding is consistent with the charge density and ELF
analyses. The BC analysis always qualitatively shows that the
magnitude of the charge transfer from the Mg to the H site is
significantly different from that in the bulk phase. However, it
clearly indicates that Mg donates electrons to the H site similar
to that in bulk phase.
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4. Conclusion
In conclusion, the phase stability as well as electronic structure
of MgH2 nanowires and possible low energy surfaces of
α -MgH2 have been investigated. The present calculations
predicted that in the α -MgH2 phase the (101) surface is
energetically more stable than other possible low energy
surfaces. In the lowest energy (101) surface, Mg atoms are
arranged in a sheet-like manner and the H atoms are present
between these Mg layers. If one reduces the diameter of the
wire below 1 nm, the stability of the wire is drastically reduced,
and we have identified that in such nanowires all atoms are
almost exposed to the surface. The formation energy decreases
with a decrease in nanowire diameter. Similar to the bulk
phase, both nanowires and surfaces have nonmetallic character.
However, the estimated band gap values are reduced to almost
half the value in the bulk material. In nanowires the chemical
bonding interaction is considerably changed compared with
the bulk phase, and in particular they have a higher degree
of covalency. The reconstruction of the bonding arrangement
suggests that the possibility to remove H from the nanowire is
much easier than in the bulk crystal.
Acknowledgments
The authors gratefully acknowledge the Research Council
of Norway for financial support and for computer time
at the Norwegian supercomputer facilities. PV and PR
acknowledge Claudia Zlotea and Yvonne Andersson for useful
communications.
6