The effect of light impurities on the binding energy of hydrogen in magnesium metal
and magnesium hydride
Finnbogi Óskarsson
Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavík, Iceland
Hannes Jónsson
Faculty of Science, University of Iceland, VR-II, IS-107 Reykjavík, Iceland
With the goal of finding a way to reduce the temperature at which hydrogen gas gets released upon
heating, we have used density functional theory calculations to study how the binding energy and
charge distribution of hydrogen atoms in magnesium and magnesium hydride are modified by the
addition of impurities of some of the lighter elements, namely aluminium, silicium, sodium, carbon
and boron. The binding energy is reduced by the addition of aluminium and silicium, elements
that are more electronegative than magnesium, but increased by the addition of sodium, a less
electronegative element. The most electronegative additives, carbon and boron, do not remain in
substitutional sites in the magnesium lattice but spontaneously move into interstitial sites where
they bind hydrogen atoms by strong covalent bonds. The charge of the interstitial hydrogen atoms
as judged by the charge density partitioning scheme of Bader is -1.1 to -1.3 e in the magnesium
metal, but -0.8 e in the hydride and is not affected strongly by the substitution of magnesium by
the other elements. A promising result was obtained by introducing aluminium into the magnesium
lattice, as the binding energy of hydrogen in the hydride was found to decrease linearly with the
amount of aluminium and reach 0.25 eV on average at about 15% Al. This is the target binding
energy for hydrogen atom release at 300 K. The weight percent of hydrogen in such an alloy would
still be high, nearly the same as in pure MgH2 . Such a material could possibly be made as an
amorphous Mgx Aly alloy, stabilised by a small amount of a third component.
PACS numbers:
I.
INTRODUCTION
One of the greatest hindrances on the road to a hydrogen economy is the problem of storing and transporting
hydrogen in a safe and economical manner. Some of the
requirements for a suitable hydrogen storage device are
the ability to contain at least 6.5 weight percent hydrogen when full, release hydrogen in the temperature range
between 0◦ C and 100◦ C, and reversibly absorb/desorb
hydrogen fast enough. One of the possibilities under consideration is storage of hydrogen in metal hydrides.
Magnesium can absorb hydrogen and form a hydride,
Mg + H2 ⇋ MgH2
where the weight percent of hydrogen is 7.6%. However,
hydrogen binds too strongly in pure magnesium hydride.
It needs to be heated to 300◦ C to release hydrogen gas at
1 atm1,2 . Also, the diffusion of hydrogen through the hydride is extremely slow and this results in only a thin film
of hydride forming at the surface of the crystal3 . We have
in a previous article4 presented results of a theoretical
study of hydrogen in magnesium metal and magnesium
hydride using density functional theory calculations. The
binding energy of hydrogen in magnesium hydride was
found to be 0.38 eV/H atom, in close agreement with experimental measurements. This illustrates the ability of
such theoretical calculations to predict how the binding
energy could be modified by changing the composition of
the solid.
For the system to reach a hydrogen equilibrium pres-
sure of 1 bar at 300 K, ∆H should amount to -0.20 eV/H
atom2,5 . In order to see how the binding energy of hydrogen in magnesium hydride could be lowered, while not
sacrificing the favourable hydrogen to metal weight ratio,
we have calculated the effects of the substition of a magnesium atom by some relatively light elements, namely
aluminium, boron, carbon, sodium and silicium.
II.
THEORETICAL METHODS
In our calculations, we made use of density functional
theory (DFT)6,7 with the PW91 functional8 and the
VASP code9–12 . Ultrasoft pseudopotentials13 were used
to represent the core electrons, and only the valence electrons were treated explicitly. A plane wave basis set was
used with an energy cutoff of 340 eV. The simulation
cells for studies of the magnesium metal were orthogonal
(measuring (12.8 × 11.1 × 10.4 Å) and contained 64 Mg
atoms in a HCP lattice. The 2 × 2 × 2 k-point grid used
to sample the Brillouin zone was reduced to 4 k-points
due to symmetry. In studies of the magnesium hydride,
the simulation cells used contained 16 Mg atoms and 32
H atoms in a rutile structure (corresponding to 2 × 2 × 2
unit cells) and the 2 × 2 × 4 k-point grid was reduced to
8 k-points due to symmetry. During structural optimisation, all the atoms in the simulation cell were allowed to
move but the size of the cell, which had previously been
optimised to obtain the lattice constants, was kept fixed.
A decomposition of the electron density along minimal
2
density dividing surfaces14 was used to map the electron
density of the system to the individual atoms, thus obtaining the charges of the atoms. The size of the grid
used was 200 × 200 × 200 points. A fast and robust algorithm based on finding the steepest ascent path that
assigns each grid point to the nearest density maximum
was used15 .
III.
RESULTS AND DISCUSSION
A.
Impurities in magnesium metal
Within the hexagonal close packed magnesium crystal
there are two sets of holes which the hydrogen atom
can occupy, tetrahedral (Td ) holes where the hydrogen
atom is fourfold-coordinated and octahedral (Oh ) holes
where the hydrogen atom is sixfold-coordinated. Energy
minimisation has been conducted in order to determine
the optimum geometry for both types4 . The hydrogen
prefers to occupy the Td holes with a binding energy
of -0.04 eV (negative binding energy means that the
energy of hydrogen in the hole is higher than that of
hydrogen in a gas phase molecule). The octahedral holes,
Oh , are less favorable, giving a binding energy of -0.21 eV.
Aluminium impurity
Aluminium is slightly heavier and more electronegative
than magnesium. An Al-atom has a smaller atomic
radius than magnesium by 0.25 Å. The substitution of a
magnesium atom with aluminium (one out of sixty-four)
results in a slight contraction (about 0.06 Å) of the
magnesium lattice close to the aluminium atom, see
table I, and a charge transfer of 0.3 e from the closest
magnesium to the aluminium, see table II. When a
hydrogen atom is introduced in a hole adjacent to the
aluminium atom, a relatively high charge density is
located between the hydrogen atom and the aluminium
atom, suggesting covalent bonding, as shown in figure
1. When hydrogen is inserted into the lower energy Td
hole closest to the substitutional aluminium atom, it
moves 0.12 Å closer to the aluminium atom than the
magnesium atoms coordinating the hole. The fourfold
symmetry of the Td hole is therefore broken. The energy
of the hydrogen atom in this hole is 0.13 eV higher than
in pure magnesium. The same applies to the Oh hole,
except that the hydrogen atom moves even further away
from the magnesium atoms, having a Al-H bond length
of 1.93 Å as opposed to 2.26 Å for Mg-H in an Oh hole.
The binding of hydrogen in the hole is also decreased
as compared with the binding in pure magnesium, but
only by 0.06 eV. To summarise, it appears that a low
concentration of aluminium decreases the binding of
hydrogen by about 0.1 eV without drastically changing
the structure. Therefore, it might be a suitable substitutional impurity in magnesium to reduce the binding
energy. The effect of aluminium substitution on the
hydride is discussed in section III B.
Silicium impurity
Silicium is even heavier and more electronegative than
aluminium and has a smaller atomic radius, 1.10 Å.
Therefore, it causes a similar effect as the aluminium,
only to a larger extent. The silicium atom contracts
the magnesium lattice around it by 0.10 Å and has
a negative charge of 2.5 e, see table II. The large
contraction of the lattice leads to a decrease in the
volume of the Td hole and as a result the hydrogen atom
does not fit in there anymore. When a hydrogen atom is
introduced in a Td hole adjacent to the silicium atom, it
spontaneously moves away from the silicium atom into
the next Td hole. The energy of the hydrogen atom in
this second-neighbour hole is still less than in a Td hole
of the pure magnesium. The elimination of the site in
the nearest-neighbour hole makes silicium substitution
less interesting in a magnesium based hydrogen storage
medium, since the addition of silicium reduces the
number of holes available for hydrogen, thus reducing
the efficacy of the storage. Although the Oh hole is
also contracted by the substitution by the silicium
atom it can still house a hydrogen atom, and shows
the same trend as aluminium, the Si-H bond is even
shorter than the Al-H bond, only 1.73 Å, and the insertion of hydrogen is endothermic by 0.39 eV, see table I.
Sodium impurity
Sodium, being less electronegative than magnesium and
having a larger atomic radius (see table I) shows the
reverse effect. The lattice around the sodium atom is
expanded by 0.03 Å and the energy of an interstitial
hydrogen atom is lower than in the case of pure magnesium. The binding energy of hydrogen in the Oh hole
being -0.16 eV and +0.03 eV in the Td hole, which is
the first exothermic hydrogen addition seen in these
calculations. The Na-H bonds are both approximately
0.15 Å longer than the corresponding Mg-H bonds in
pure magnesium crystal. The lower electronegativity of
sodium causes it to transfer some of its charge (0.7 e)
to the surrounding magnesium atoms, thus negatively
charging them, see table II. The stronger binding of the
sodium doped magnesium makes it a worse candidate
for hydrogen storage than the pure magnesium crystal,
since the temperature needed to release the hydrogen
would be even higher.
Boron impurity
When substituting a magnesium atom with a boron atom
we found that boron, having an atomic radius of less than
60% of that of magnesium would hop into the nearest octahedral hole and leave a vacancy in the Mg-lattice. As
the interaction between magnesium and boron is stronger
than the Mg-Mg interaction, a magnesium atom would
then hop into the vacancy, leaving another vacancy further away from the boron atom. The binding energy
of boron in the Oh hole of a perfect magnesium crystal
was calculated and found to be 0.65 eV. Positioning the
3
boron atom in the Oh hole causes the magnesium lattice to expand by 0.05 Å around the interstitial boron
atom. A calculation of the energy of hydrogen in the
Oh hole closest to the one occupied by boron, a B-H
distance of 3.05 Å, yielded a binding energy of -0.09 eV.
When the hydrogen was positioned in the Td hole next to
the boron and the energy of the system minimised, the
hydrogen spontaneously hopped into the same hole as
boron was occupying forming a covalent B-H bond with
a bond length of 1.26 Å, which is only slightly longer (by
0.03 Å) than the gas phase B-H bond length as measured
by spectroscopy16. The binding energy of hydrogen was
found to be 0.11 eV, see table III.
When the charge density of the magnesium crystal
with boron impurities was analysed, we found that in
the final state, where the boron atom is positioned in an
Oh hole it has a charge of -3.2 e and the surrounding
magnesium atoms have a positive charge of +0.6 e.
The addition of hydrogen into the nearest Oh hole
causes the charges of the magnesium atoms in between
the two holes to acquire a positive charge of +0.7
e, whereas the ones next to the hydrogen atom have
a charge of +0.5 e. The charges on the magnesium
atoms next to the boron atom stay the same when the
hydrogen atom is introduced to the nearest-neighbour
Oh hole but when the hydrogen atom is positioned in
the nearest-neighbour Td hole, after hopping into the
same Oh hole as boron, much of the charge density of
the boron atom is transferred to the hydrogen atom,
leaving boron with a charge of -1.2 e and hydrogen with
a charge of -1.8 e, see table IV. It is interesting to see
that in the former case, both the hydrogen atom and the
boron atom bind strongly to the magnesium lattice, but
there seems to be no bonding between the Mg-H and
Mg-B clusters, see figure 2.
Carbon impurity
In much the same way, a substitution of a carbon atom,
which has an even smaller atomic radius than boron, ends
in a hop of both the carbon atom and the resulting vacancy to form a vacancy in a second-nearest neighbour
lattice site to the carbon atom. As in the case of boron,
the binding energy of carbon as an interstitial in a perfect
magnesium crystal was calculated and found to be 1.41
eV. However, unlike boron, the interstitial carbon causes
the magnesium lattice to contract by approximately 0.10
Å. This is probably due to higher electronegativity of
carbon and smaller atomic radius. A calculation of the
energy of hydrogen in the Oh hole closest to the one occupied by carbon yielded a binding energy of -0.07 eV,
which is lower energy than in the case of boron. The
C-H distance is 2.95 Å, and as for boron, positioning the
hydrogen in a Td hole next to the carbon caused a hop of
the hydrogen and a formation of a covalent C-H bond of
1.14 Å, which is close to the gas phase C-H bond length
(1.12 Å) as estimated by spectroscopy16. The calculated
binding energy of hydrogen was -0.21 eV, see table III.
Charge density analysis of the magnesium crystal
with carbon impurities shows that the interstitial carbon
atom has a charge of -3.1 e in the magnesium crystal,
causing the nearest magnesium atoms to keep a positive
charge of +0.8 e. Addition of hydrogen into an adjacent
tetrahedral hole results in a charge of -1.2 e for the hydrogen, -3.0 e for the carbon, +0.8 e for the magnesium
atoms in between the hydrogen and the carbon and a
charge of +0.4 e for the magnesium atoms next to the
hydrogen. Again, the addition of hydrogen has no effect
on the second nearest neighbour magnesium atoms (see
table IV). In the case where the hydrogen atom hops
into the Oh hole occupied by carbon, some of its charge
is transferred to the carbon atom, leaving carbon with
a charge of -2.3 e and hydrogen with a charge of -0.4
e. This is the opposite of what happened in the case of
boron and is in accordance with what one would expect
from the Pauling electronegativities of the elements;
hydrogen, boron and carbon having electronegativities
2.10, 2.04 and 2.55, respectively.
B.
Impurities in magnesium hydride
The more important issue is the effect of impurities
on the hydride. It is the energy of H-atoms in the hydride compared with gas phase hydrogen molecules which
determines the desorption temperature. Below approximately 2 GPa and 1100 K, magnesium hydride has a
rutile structure (α-MgH2 ), where the hydrogen ions are
arranged approximately octahedrally around the magnesium ions, which in turn are arranged trigonally around
the hydrogen ions The binding energy of hydrogen in
the magnesium hydride has been calculated to be 0.38
eV/atom within the DFT/PW91 approximation as described in a previous article4 .
From the preliminary studies in section III A, it is
clear that aluminium was the most promising candidate
of the elements tried. Therefore, we substituted magnesium atoms from a MgH2 cell with aluminium and
calculated its effects on the average binding energy of
hydrogen in the compound (as one cannot decompose
the total energy into a sum of atomic contributions, the
effect on the average binding energy of the hydrogen
atoms in the simulation cell is the only thing that can
be calculated rigourously). This was done using a cell
which originally contained 16 Mg-atoms and 32 H-atoms.
Aluminium impurity
When a magnesium atom of the hydride was substituted
by an aluminium atom, the lattice contracted around the
aluminium atom in much the same way as it did for the
substitution in magnesium metal, i.e. the distance between the aluminium atom and the surrounding equitorial hydrogen ions was found to be 1.79 Å instead of 1.95
Å in the pure magnesium hydride and the distance between the aluminium atom and its apical hydrogen ions
was reduced from 1.92 Å to 1.82 Å. The average binding
4
energy of hydrogen in the hydride was, however, lowered
by 0.052 eV/atom. Substitution of another magnesium
by an aluminium atom, corresponding to Al concentration of 12.5%, yielded a similar contraction of the lattice
around it, and lowered the average binding energy of hydrogen in the hydride even more, to 0.269 eV/atom. The
substitution of a third magnesium atom by an aluminium
atom also lowered the average binding energy of hydrogen, now to 0.210 eV/atom, see table V. However the
substitution of a fourth magnesium atom lead to an instability of the crystal structure.
A Bader charge density analysis was performed on both
the pure magnesium hydride and the hydride after a substitution of a magnesium atom by an aluminium atom.
We found that the substitution has very little effect on
the charge distribution of the system, see table VI. The
only noticeable difference is a partial electron transfer
(0.1 e) from the aluminium atom to the nearest magnesium ions. There is only a very small charge transfer to
the hydrogen ions, about 0.02 e for the equitorial hydrogen ions, but less than 0.01 e for the apical ones, see figure
3. This small effect of the substitution is not surprising
as MgH2 is an insulator and its electrons are highly localised.
IV.
CONCLUSIONS
We have found that the effect of impurities on the
binding energy of hydrogen in magnesium metal depends
on the difference in electronegativity between magnesium
and the impurities. Less electronegative impurities lower
the charge density around them and thereby attract the
hydrogen atoms and bind them more strongly than the
rest of the metal. Slightly more electronegative impurities decrease the binding of hydrogen in the metal and
may, therefore, be suitable for doping of magnesium in
order to improve its hydrogen storage properties. However, if the impurities have a significantly higher electronegativity than magnesium, hydrogen tends to form
covalent bonds with the impurity atoms, and thus bind
much stronger.
Charge density analysis showed that when a magnesium atom is substituted by a more electronegative atom,
such as aluminium or silicium, the negative charge of the
interstitial hydrogen atom is diminished. In pure magnesium, the charge on an interstitial hydrogen atom is -1.29
e in the Oh hole and -1.1 e in the Td hole4 . These electronegative substitutional atoms also absorb some of the
charge on the nearest magnesium atoms, leaving them
more ionised than in the pure magnesium crystal. This
effect is reversed for sodium, which is less electronegative than magnesium and therefore transfers some of its
1
L. Schlapbach, in Hydrogen in Intermetallic Compounds I:
Electronic, Thermodynamic and Crystallographic Proper-
charge onto the next magnesium atoms. More surprisingly, sodium causes the interstitial hydrogen atoms to
lose some of their charge to the magnesium atoms as
well.
Of the impurities tried, the effect of aluminium was
most promising; it raised the energy of an interstitial Hatom in the metal by 0.13 eV in the tetrahedral holes and
0.06 in the octahedral holes, without having much effect
on the lattice structure even in concentrations as high
as 19%. Furthermore, since aluminium is only slightly
heavier than magnesium, the effect on the weight percent
of hydrogen is small.
When the binding energy of the hydride was calculated, it was found that adding aluminium again reduced
the average binding energy of hydrogen in the crystal. In
fact, increasing the concentration of aluminium seemed
to weaken the binding of hydrogen in the hydride almost
linearly, as shown in figure 4. At a concentration of 15%,
the binding energy has dropped to 0.25 eV, the value
appropriate for thermal release at room temperature1,2 .
However, according to the phase diagram17 for the
Al/Mg system, the solubility of aluminium in the magnesium hcp (δ) phase is only 3%. At higher concentrations
of aluminium, a different (γ) phase starts forming alongside the hcp phase. At present, we have not studied the
latter phase. Another possibility is that an amorphous
phase of magnesium, aluminium and a third element,
preferably one with a larger atomic radius than magnesium, could be formed and used for hydrogen storage.
An amorphous solid made of magnesium and aluminium
may offer the flexibility in composition that is needed to
be able to tune the hydrogen binding energy. The difference in atomic size of aluminium and magnesium is
about 20% based on atomic radii so it should be possible to form an amorphous phase. A third element could
be needed to stabilise the amorphous phase, especially as
the system needs to be able to go through multiple cycles
of hydrogen absorption/desorption.
V.
ACKNOWLEDGEMENTS
We would like to thank William Stier and Sveinn
Ólafsson for helpful discussions on modifications of the
magnesium-hydrogen system. We would also like to
thank Andri Arnaldsson and Graeme Henkelman for
helpful discussions, in particular with regard to the
charge analysis. This work was supported by the research
council of Iceland (RANNIS) and by the U.S. Department of Energy, Division of Materials Research. FÓ was
supported in part by the Icelandic Research Fund for
Graduate Students
ties, Preparation, Vol. 67 of Topics Appl. Phys., edited by
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6
Table I: The effects of substitution of a magnesium atom by
aluminium, silicium and sodium on the crystal lattice and the
binding energy of hydrogen. Aluminium and silicium cause
the crystal lattice to contract around the substitutional atom
and thus decrease the binding of the hydrogen in both holes.
In the case of silicium, the contraction is so great that the hydrogen atom does not fit into the Td hole anymore and moves
into the next Td hole, coordinated by magnesium atoms (the
results for hydrogen in the Td hole with silicium are in parentheses). Negative binding energy means higher energy as compared with hydrogen in a H2 molecule.
Property
Pauling electronegativity of X
Atomic radius of X18 (Å)
Mg-X bond length (Å)
H-X bond length in Oh hole (Å)
H-X bond length in Td hole (Å)
Binding energy of H in Oh hole (eV)
Binding energy of H in Td hole (eV)
Mg
1.31
1.50
3.21
2.26
2.00
-0.21
-0.04
Al
1.61
1.25
3.15
1.93
1.88
-0.27
-0.17
Si
1.90
1.10
3.11
1.73
(3.42)
-0.39
(-0.14)
Na
0.93
1.80
3.24
2.41
2.17
-0.16
+0.03
Table II: Atomic charge estimates using Bader decomposition
of the charge density. When a magnesium atom is substituted
by a more electronegative atom, such as aluminium or silicium, the negative charge of the interstitial hydrogen atom is
somewhat diminished. The substitutional atoms also attract
some of the electrons from the nearest magnesium atoms (see
explanation of parentheses in table caption I). A substitutional Na-atom looses some of its electrons to nearby Mgatoms, making them more negative than in the pure metal.
Charge (e)
X in Mg lattice
Mg next to X
Mg second to X
H in Oh hole
X next to H in Oh
Mg next to H in Oh
H in Td hole
X next to H in Td
Mg next to H in Td
Mg
0.0
0.0
0.0
-1.3
+0.3
+0.3
-1.1
+0.3
+0.3
Al
-2.5
+0.3
+0.2
-1.2
-1.7
+0.4
-1.1
-1.7
+0.3
Si
-2.5
+0.3
+0.2
-1.0
-1.7
+0.4
(-1.1)
(-2.5)
(+0.6)
Na
+0.7
-0.1
-0.1
-1.2
+0.7
+0.3
-1.0
+0.7
+0.3
Table III: Properties of B- and C-atoms and their interaction
with H-atoms inside the magnesium crystal. The impurity
atoms occupy Oh interstitial sites. When a hydrogen atom is
inserted into a Td hole next to the impurity atoms, it hops
into the same Oh hole, thus forming a covalent bond.
Property
Pauling electronegativity of X
Atomic radius of X18 (Å)
Mg-X bond length (Å)
H-X bond length in next Oh holes (Å)
H-X bond length in same Oh hole (Å)
Binding energy of H in next Oh hole (eV)
Binding energy of H in same Oh hole (eV)
B
2.04
0.85
2.29
3.05
1.26
-0.09
0.11
C
2.55
0.70
2.19
2.95
1.14
-0.07
-0.20
7
Table IV: Atomic charge estimates using Bader decomposition
of the charge density. Both B- and C-atoms are quite ionised
in the Oh holes of the magnesium metal, having charges of
-3.2 e and -3.1 e, leaving the nearest magnesium atoms with
charges of +0.6 e and +0.8 e, respectively. The hydrogen ions
in the adjacent Oh holes are a bit more negatively charged
than in pure magnesium. When the hydrogen ions are in the
same holes as the boron/carbon atom it is interesting that in
the case of boron, there is more charge on the hydrogen than
the boron atom, but this is reversed for carbon.
Charge (e)
B
C
X in Oh hole
-3.2 -3.1
Mg next to X
+0.6 +0.8
H in next Oh hole
-1.2 -1.2
X in Oh hole
-3.2 -3.0
Mg between H and X +0.7 +0.8
Mg next to H
+0.5 +0.4
Mg next to X
+0.6 +0.8
H in same Oh hole
-1.8 -0.4
X in Oh hole
-1.2 -2.3
Mg next to H
+0.2 +0.3
Mg next to X
+0.6 +0.7
Table V: The effect of Al substitution into MgH2 . As in the
case for the metal, aluminium causes a contraction in the lattice and the binding energy of hydrogen decreases. When the
concentration of aluminium is increased, the binding energy
continues to decrease. An Al concentration of about 15% in
the magnesium lattice would decrease the binding enough for
hydrogen to be released at 1 atm at a temperature around
100◦ C.
Property
Mg
Atomic radius of X18 [Å]
1.50
H(e)-X bond length (Å)
1.95
H(a)-X bond length (Å)
1.92
Average binding energy of H in hydride (1:16) (eV) 0.378
Average binding energy of H in hydride (2:16) (eV) 0.378
Average binding energy of H in hydride (3:16) (eV) 0.378
Al
1.25
1.79
1.82
0.326
0.269
0.210
Table VI: Atomic charge estimates using Bader decomposition
of the charge density. Substitution of a magnesium atom by
an aluminium atom has little effect on the charge distribution
of the hydride, it only causes the electron density around the
very closest magnesium atoms to increase by 0.1 e.
Charge of (e)
X in hydride
Mg next to X in hydride
H in hydride
H(a) next to X in hydride
H(e) next to X in hydride
Mg
+1.6
+1.6
-0.8
-0.8
-0.8
Al
+2.0
+1.5
-0.8
-0.8
-0.8
8
(a)
(b)
Figure 1: (a) Charge density iso-surfaces around the substitutional aluminium atom (in the centre) in a magnesium crystal
as reported from the Bader analysis. It can be seen that the
charge density of the aluminium atom (-2.5 e) is higher than
on the magnesium atoms (+0.3 e). The triangular distortion seen in the charge density of aluminium is because of the
magnesium atoms in the next layer of the crystal. (b) The hydrogen atom in a Td hole, along with the three Mg-atoms and
the Al-atom that define the hole. Note that the large charge
density between hydrogen and aluminium suggests covalent
bonding between the two atoms, while no charge density appears between hydrogen and magnesium.
9
(a)
(b)
Figure 2: Charge density iso-surfaces around the boron atom
in an Oh hole of a magnesium crystal as reported from the
Bader analysis (a) before and (b) after the addition of hydrogen in the closest Oh hole. Note that the Mg-B and Mg-H
clusters seem to be quite isolated from each other.
10
Figure 3: Charge density iso-surfaces for the surroundings
of an aluminium atom substituted for a magnesium atom in
magnesium hydride. As can be seen, there is more charge density between the aluminium ion and the equitorial hydrogen
than between the aluminium and the apical hydrogen ions.
The charges of the aluminium, equitorial hydrogen and apical hydrogen ions are +2.0 e, -0.8 e and -0.8 e, respectively.
Average binding energy of hydrogen (eV/atom)
0.38
0.36
0.34
0.32
0.3
0.28
0.26
0.24
0.22
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Molefraction of Al
Figure 4: The calculated average binding energy of hydrogen
in magnesium hydride with aluminium impurities as a function of the concentration of aluminium. This relationship is
nearly linear. At an aluminium concentration of 15%, the
binding energy is as low as 0.25 eV/H-atom, whereas in pure
magnesium hydride it is 0.38 eV/H-atom.
0.16
0.18
0.2