Modeling alkali alanates for hydrogen storage by
density-functional band-structure calculations
Ole Martin Løvvika)
University of Oslo, Centre for Materials Science and Nanotechnology, 0318 Oslo, Norway
Ole Swang
SINTEF Materials and Chemistry, N-0314 Oslo, Norway
Susanne M. Opalka
United Technologies Research Center, East Hartford, Connecticut 06018
(Received 14 April 2005; accepted 10 June 2005)
The alanates (complex aluminohydrides) have relatively high gravimetric hydrogen
density and are among the most promising solid-state hydrogen-storage materials. In
this work, the crystal structure and electronic structure of pure and mixed-alkali
alanates were calculated by ground-state density-functional band-structure calculations.
The results are in excellent correspondence with available experimental data. The
properties of the pure alanates were compared, and the relatively high stability of the
Li3AlH6 phase was pointed out as an important difference that may explain the
difficulty of hydrogenating lithium alanate. The alkali alanates are nonmetallic with
calculated band gaps around 5 eV and 2.5–3 eV for the tetra- and hexahydrides. The
bonding was identified as ionic between the alkali cations and the aluminohydride
complexes, while it is polar covalent within the complex. A broad range of
hypothetical mixed-alkali alanate compounds was simulated, and four were found to be
stable compared to the pure alanates and each other: LiNa2AlH6, K2LiAlH6,
K2NaAlH6, and K2.5Na0.5AlH6. No mixed-alkali tetrahydrides were found to be stable,
and this was explained by the local coordination within the different compounds. The
only alkali alanate that seemed to be close to fulfilling the international hydrogen
density targets was NaAlH4.
I. INTRODUCTION
The search for solid-state hydrogen-storage materials
is a crucial part of the path toward implementation of a
hydrogen economy.1–7 Alkali alanates [complex hydrides with the formula MnAlH(n+3), where M is an alkali
element: Li, Na, K, . . .] are among the most promising
materials for this application, with high hydrogen density
available at moderate conditions.8–13
The fully hydrogenated alkali alanate phase, the monoalkali aluminium tetrahydride, MAlH4 desorbs hydrogen
stepwise through a series of reactions
3MAlH4 → M3AlH6 + 2 Al + 3 H2 ,
M3AlH6 → 3MH + Al + 3/2 H2
3MH → 3M + 3/2 H2
,
,
(1)
(2)
(3)
where M is Li, Na, or K. In the first reaction, the MAlH4
a)
Address all correspondence to this author.
e-mail: o.m.lovvik@fys.uio.no
DOI: 10.1557/JMR.2005.0397
J. Mater. Res., Vol. 20, No. 12, Dec 2005
phase disproportionates to form the trialkali aluminium
hexahydride, M3AlH6 phase, which during the second
reaction disproportionates into the monoalkali hydride,
MH. The last MH decomposition reaction takes place at
temperatures too high to allow it to be counted as accessible for in situ mobile applications. The total and accessible hydrogen content of the alkali alanates are listed in
Table I.
A. Lithium alanate
Since LiAlH4 is the lightest alanate, it is the most
attractive candidate from a gravimetric point of view.
The reversible hydrogenation of lithium alanate has
been pursued by several groups,14–35 and it is now clear
that, for lithium alanate, the decomposition of LiAlH4
[Eq. (1)] is spontaneous at room temperature, and the
reaction is apparently exothermic.14,16,35 The decomposition reactions (1) and (2) are promoted by ball milling14,17,36 and catalysis.19,27 It has been claimed that the
second step of the lithium alanate decomposition reaction
[Eq. (2)] is reversible,19 but this has not been reproduced.
It has rather been shown that, when doped with Ti, the
© 2005 Materials Research Society
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O.M. Løvvik et al.: Modeling alkali alanates for hydrogen storage by density-functional band-structure calculations
TABLE I. Calculated properties of the monoalkali alanates. The calculated space group and hydrogen volumetric density are compared to
experimental results. The total and accessible hydrogen weight percent are the amounts of hydrogen that theoretically may be extracted from the
compound when going to the elements and to the alkali metal hydrides, respectively. The volume density is based on the accessible hydrogen
content.
Compound
Space group
H vol density
(kg/m3)
H wt%
Formation
enthalpy
Reaction
enthalpy
Al–H distance
(pm)
Alkali–H
distance (pm)
H–Al–H angle
(deg)
Al–H coordination
Alkali–H coordination
LiAlH4
NaAlH4
KAlH4
Li3AlH6
This work
Experimental
This work
Experimental
Total
Accessible
P21/c
P21/c
73.4
73.8
10.6
8.0
I41/a
I41/a
72.0
72.6
7.5
5.6
Pnma
Pnma
52.6
53.2
5.8
4.3
(kJ/mol H2)
−55.5
−54.9
(kJ/mol H2)
Minimum
Maximum
Minimum
Maximum
Minimum
Maximum
669.7
162
165
185
198
107.8
111.5
4
5
670.2
164
164
241
241
107.5
113.5
4
8
equilibrium pressure for the first reaction [Eq. (1)] is
higher than 99 bar at 58 °C, and for the second reaction
[Eq. (2)], higher than 85 bar at 80 °C.35 Calculated crystal structures correspond well with experimental results.23,24,28,30,33 The calculated electronic density of
states (DOS) show that LiAlH4 and Li3AlH6 are insulators with band gaps of around 5 and 3.5 eV.23,24,26,32
B. Sodium alanate
For the sodium alanate phases, the forward and reverse
reactions (1) and (2) are kinetically hindered under equilibrium temperature and pressure reaction conditions. It
was discovered by Bogdanovic et al. that the reverse
reactions (1) and (2) above are made possible at moderate
equilibrium temperature and pressure conditions for sodium alanate by adding small amounts of a transition
metal as a catalyst or dopant.8 Significant efforts have
been invested to understand the role and nature of these
additives,8–13,37–76 and it is now clear that, for sodium
alanate Ti is the most efficient additive8,47 and exhibits
the best performance when added as nanoparticles.13,53,56
The effect of Ti may be enhanced by simultaneously
adding Zr37,41, Fe,72 or graphite.71 The kinetics may be
further improved by mechanochemical treatment (e.g.,
ball-milling).40 Ti is zero-valent after ball-milling.60,62,68
A major part of the Ti may after a few hydrogenation
cycles be found associated with Al,43,62,77 either as a
solid solution in Al62,63 or in the form of amorphous
TiAl3,54,55,68 dependent on the temperature used during
the cycling process.74 Some studies show that the structural parameters of NaAlH4 change after adding Ti,45,73
others do not.61,63,75 Substitution of Ti in the NaAlH4
3200
Na3AlH6
K3AlH6
R3̄
R3̄
57.2
56.8
11.2
5.6
P21/n
P21/n
43.8
43.7
5.9
3.0
P21/n
...
31.8
...
4.0
2.0
−70.0
−102.8
−69.9
−78.5
668.0
163
164
270
354
107.7
112.1
4
12
1274.0
174
175
190
209
87.1
93.0
6
6
1193.3
176
177
222
277
89.0
91.0
6
6–8
1168.4
178
179
258
363
89.8
90.2
6
6–11
sublattice is metastable, and the most stable substitution
is for Al, near the surface.70
Some of the early discrepancies between various studies have been resolved as being due to differences in
sample preparation, different stages in the hydrogenationdehydrogenation cycles, etc. There still are some contradictions in the literature, particularly as to whether or not
the structural parameters change after Ti addition. This is
an important issue, since it has been shown that the structural parameters would change significantly upon substitutional doping and would be analytically detectable
even down to levels as low as 3% Ti doping.70 In any
case, there is still a need for better understanding of the
doping/catalysis process, since this would guide a systematic theoretical search for materials and additives
with effective properties for reversible hydrogen storage.
A number of theoretical studies have been devoted to
the sodium alanates.24,26,28,31,32,61,69,70,78–84 The calculated crystal structures24,26,28,32,61,69,78,83 and formation
enthalpies61,78,81 at 0 K are in good correspondence with
experimental results. The uncorrected electronic density
of states shows that NaAlH4 and Na3AlH6 are both
nonmetallic with band gaps of around 5 and 3 eV at
the generalized gradient approximation (GGA)
level,24,28,32,61,82,83 increasing to 6.9 and 4.6 eV when
adding quasiparticle GW corrections85,86 to the band
structure.82 The bonding is ionic between Na+ and the
AlH4− tetrahedra in NaAlH4. The bonding within the
tetrahedron has been suggested to be both ionic79 and
covalent,24 but it may probably best be described as covalent with a strong ionicity (polar covalent).61,82 Phonon calculations on NaAlH4 have shown that the AlH4−
anion remains stable up to the melting point,75 and
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O.M. Løvvik et al.: Modeling alkali alanates for hydrogen storage by density-functional band-structure calculations
thermodynamic functions are in good agreement with
experimental ones.83
The trisodium aluminium hexahydride phase has been
shown by experiment and calculations to exist as two
displacively related, allotropic phases, referred to as ␣
and ␤. The low-temperature ␣ disordered phase has a
monoclinic P21/n symmetry. The high-temperature ␤
phase has an orthorhombic Immm symmetry, analogous
to the well-known cryolite, Na3AlF6, perovskite structure.78,87
C. Potassium alanate
Potassium alanate is significantly heavier than lithium
or sodium alanate, but compared to interstitial transition
metal hydrides, it may still be of interest as a mediumtemperature hydride. It is much less studied than the
lighter alkali alanates,31,32,88–90 but it is known that hydrogenation of potassium alanate is reversible even without a catalyst, and the reactions take place between 250
and 340 °C. 88 The calculated crystal structure of
KAlH426,90 is in good correspondence with the experimental one.89 The crystal structure of K3AlH6 is not
known, but it has been predicted to be in the P21/n space
group.31,32 The electronic DOS shows that KAlH4 and
K3AlH6 are both insulators, with band gaps of 5.590 and
3 eV.32
D. Mixed-alkali alanates
The mixed alanate LiNa2AlH6 was synthesized for the
first time in 1982,91 and it was demonstrated to be a
reversible hydrogen storage material already in the seminal paper of Bogdanovic et al.8 It was later claimed that
mixtures with the nominal compositions Li1.3Na1.7AlH6
and Li1.5Na1.5AlH6 also could absorb hydrogen reversibly,92 but this has not been followed up by diffraction
measurements—the compositions could thus possibly be
mixtures of LiNa2AlH6 and Li3AlH6, where only the
former compound takes part in the hydrogenation. A
structure with the stoichiometry Li1.5Na1.5AlH6 proved
stable compared to the unmixed hexahydrides in a computational study, 81 but it is unstable compared to
LiNa2AlH6 and Li3AlH6. So far no mixed alanates in the
tetrahydride system [in the form MxM⬘(1−x)AlH4] have
been reported. The only published theoretical study on
this, in which the authors investigated the possibility of a
stable material with the composition NaxLi(1−x)AlH4 having the NaAlH4 structure, failed to identify any stable
compounds.81
The crystal structure of LiNa2AlH6 was suggested to
be cubic face-centered-cubic (fcc),91,93 and it was completely resolved in the Fm3̄m space group by a combined
synchrotron x-ray and neutron powder diffraction
study.35 Calculations show, however, that a monoclinic
structure is more stable at 0 K.31,81 This is an effect of
temperature, and phonon calculations indicate that the
cubic structure may be more favorable at higher temperatures.94 The calculations are supported by a recent diffraction study that shows distortions from cubic symmetry in LiNa2AlH6 at low temperature.95
The addition of Ti has the same positive effects on
the hydrogenation kinetics of LiNa2AlH6 as on that of
NaAlH4.8 It has later been shown that the addition of
La2O3 gives similar results.96,97
When potassium was included in the search for mixed
alanates, three other compounds were found to be stable
compared to the pure alanates: K2LiAlH6, K2NaAlH6,
and KNa2AlH6.31,32 The latter was not stable compared
to K2NaAlH6 and Na3AlH6, however, and a recent experimental study managed to synthesize K2LiAlH6 and
K2NaAlH6, but not KNa2AlH6.98 K2NaAlH6 was synthesized for the first time in 1987.99
E. This paper
Our objective for this paper was to summarize our
modeling investigations of the bulk alanates in the
ground state,29–32,70 with an emphasis on results that
were previously unpublished. Here, we first report on the
simulation of already known alkali alanate crystal structures to validate this relatively new methodology for
identifying correct structures, and also, to set the stage
for the simulation of unknown mixed alkali compounds.
These calculations are the required first step to prepare
for the prediction of unmeasured, or difficult to measure,
alkali alanate finite temperature thermodynamic properties by first-principles methods.
We have extended our previous search for mixedalkali alanates,31,32 and in the following, we present a
broad range of hypothetical hexahydride mixtures [of the
form MxM⬘(3−x)AlH6]. Additionally we have performed a
comprehensive search for mixed-alkali tetrahydrides [of
the form MxM⬘(1−x)AlH4] based on Li, Na, and K. The
paper starts with a presentation of the theoretical tools
used in the calculations, followed by results for the pure
and unmixed alkali alanates. A summary and assessment
of the future of alanates as hydrogen-storage materials
conclude the paper.
II. METHODOLOGY
Most of the calculations in this work have been performed using the Vienna ab initio simulation package
(VASP),100,101 employing the projector augmented wave
(PAW) method102 at the GGA level.103 The spacing of
the integration grid in k-space was at the most 0.05 Å−1,
in many of the cases below 0.02 Å−1. Self-consistency of
the electronic density was defined to be reached when the
total energy of two consecutive runs differed by less than
0.01 meV. The single-particle orbitals were smeared by a
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O.M. Løvvik et al.: Modeling alkali alanates for hydrogen storage by density-functional band-structure calculations
Gaussian convolution with a width of 0.2 eV in most of
the cases. The cutoff energy for the plane wave expansion was set to 780 eV. The overall convergence of the
total energy with respect to the mentioned sources of
error was in all cases on the order of 1 meV.
Ionic relaxations were performed by the residual minimization method direct inversion in iterative subspace
implementation of the quasi-Newton algorithm. In some
difficult cases a conjugate-gradient algorithm was used
in combination with the quasi-Newton method. The
criterion for relaxation was that the forces be less than
0.05 eV/Å. The search for unknown crystal structures
was performed by using a number of representative crystal structures from equivalent compounds as input structures for the ionic relaxation. The input structures were
chosen to represent as large a variation in coordination
numbers and crystal systems as possible. The full minimization method used allowed simultaneous relaxation
of ionic coordinates, unit cell size, and shape. Thus, both
known and unknown crystal structures were surveyed,
including a large part of the realistic crystal structure
space in the search. The input structures for the full
structural minimization calculations were based on
NaClO 4 (F4̄ 3m), NaAlH 4 (P4/mmm), KAuCl 4 (Pc),
RbAlF 4 (Pmmn), LiBH 4 (P6 3 mc), KAlD 4 (Pnma),
NaAlD 4 (I4 1 /a), LiAlD 4 (P2 1 /c), KAlF 4 (P2 1 /m),
NaAlCl4(P212121), KAlCl4(P21), and NaGdCl4(P1̄) for
the tetrahydrides. The hexahydrides were relaxed from the
following input models: K3MoF6(Fm3m), Ti3NiS6(R3̄),
Na 3 AlF 6 (Pmmn), Li 3 AlF 6 (Pna2 1 ), Na 3 AlD 6 (P2 1 /n),
K 3 Fe(CN) 6 (P2 1 /c), and triclinically distorted
Ti3NiS6(P1). References to the model structures have
been published elsewhere.30
The crystal orbital overlap populations and Hirshfeld
charges HihHH were calculated using ADF-BAND.104,105
This program uses linear combinations of atomic orbitals
as basis functions. We used combinations of Slater-type
and numerical atomic orbitals as basis sets, one of each
for valence electrons and in addition two Slater-type orbitals as polarization functions. The electronic structure
was calculated self-consistently within the local density
approximation, and the zeroth order regular approximation was used to include relativistic effects. The number
of k-points and integration accuracy were chosen to give
total energy convergence within 10 meV per unit cell.
III. RESULTS
A. Monoalkali alanates
The crystal structures of almost all the lightest MAlH4
and M3AlH6 phases, based on Li, Na, and K, are by now
well known, except that of K3AlH6. The crystal structures have been experimentally described in detail elsewhere.20,21,89,106,107
We have listed our calculated structures compared to
3202
the experimental ones in Table I. In all cases, the agreement with experiment is very good: The correct space
group is reproduced, and the calculated volume is within
some 1% of the experimental volume. The calculated
atomic positions (not shown here) are also very close to
the experimental ones. We should not expect any better
agreement than this, since our calculations are performed
at 0 K, while the experiments are at finite temperatures,
in many cases at room temperature. We also did not
include zero-point motion in any of our calculations,
which has been shown to change the lattice constants of
NaAlH4 by up to 2%.83
It is interesting to see that the Al–H distance and
coordination are almost constant both in the tetrahydrides (four-coordinated with Al–H distances of
around 163 pm) and the hexahydrides (six-coordinated
with Al–H distances of around 177 pm). This shows that
the AlH4 tetrahedra and AlH6 octahedra are quite stable
units independent of the local environment, consistent
with the stability of the AlH4 tetrahedra observed at elevated temperatures in NaAlH4 by Raman scattering.75
This is also supported by the calculated H–Al–H angles
within the aluminohydride complexes, which consistently deviate from perfect polyhedra. The only apparent
trend is that the deviation from perfect octahedra in the
hexahydrides decreases when the size of the alkali cation
increases; thus the angles within the AlH6 octahedron in
K3AlH6 differ only by up to 0.2° from 90°, while they
differ by up to 3° in Li3AlH6. Apart from this, all the
differences in local environment between the different
alkali alanates are manifested by the alkali atom and the
aluminohydride complex functioning as independent
units. The alkali atom-H coordination naturally increases
when the radius of the alkali atom increases, and so does
the alkali-H distance. If the bonding is assumed to be
ionic, the Shannon ionic radii may be good measures on
the atomic sizes within the structure.108,109 When the
tetrahedral and octahedral Shannon ionic radii of Al are
subtracted from the Al–H distances, we obtain an effective ionic radius of hydrogen of 109 to 111 pm when
tetrahedrally coordinated to Al (in the tetrahydrides) and
between 107 and 111 pm when octahedrally coordinated
(in the hexahydrides). That is, the hydrogen size is virtually unchanged when going from tetrahedral to octahedral coordination in this picture. If these radii are used
for the hydrogen atom, we similarly obtain effective radii
for the alkali atoms from the alkali–H distances. In
LiAlH4 the radii obtained in this way vary from 76 to
87 pm, that is between the Shannon ionic radii of tetrahedrally coordinated Li (73 pm) and octahedrally coordinated Li (90 pm), consistent with the 5-fold coordinated Li in this structure. For NaAlH4, however, the effective ionic radius of Na is between 130 and 132 pm,
significantly higher than the tetrahedral (113 pm) and
octahedral (116 pm) Shannon ionic radii. The difference
J. Mater. Res., Vol. 20, No. 12, Dec 2005
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is even larger in KAlH4, with estimated effective ionic
radii between 161 and 243 pm, compared to the octahedral Shannon ionic radius of 152 pm. Since the latter
structure has 11-coordinated K, we could expect slightly
larger radii than the octahedral Shannon ionic radius. It is
nevertheless clear that the Li ion takes relatively less
space in the structure than what should be expected from
the ionic radius and the structures of the other alanates.
This may partially be explained by the relatively weak
ionicity and large Li–H overlap in Li alanate, as we shall
see later. Despite this, the volume of LiAlH4 is only
about 2% less than that of NaAlH4. On the other hand,
the volume of Li3AlH6 is 30% less than that of Na3AlH6.
This reflects a packing of the ions in Li3AlH6 much more
efficient than that in LiAlH4, and we shall see that this
results in significant differences in the relative stability
between the two phases of Li alanate compared to the
heavier alanates.
Morioka et al. observed K3AlH6 during the desorption
of KAlH4,88 but this phase has not yet been crystallographically resolved. Earlier, we reported cell parameters
and ionic positions of K3AlH6,32 but the structure has not
been discussed in detail elsewhere. The predicted crystal
structure of K3AlH6 shown in Fig. 1 is very similar to
that of Na3AlH6, with the unit cell size being the largest
difference. It is also slightly closer to the cubic Fm3̄m
structure than Na3AlH6 in that the unit cell exhibits
smaller deviations from cubic symmetry; the largest deviations of the lattice constants are 2.3% and 1.3%, and
the largest deviations from 90° are 0.8° and 0.4° in Na
and K alanate, respectively. Also, the AlH6 octahedra are
less tilted (by around 6°) from the ideal perovskite structure. The potassium atoms in Wyckoff position d (two in
the unit cell) are six-coordinated in quite regular octahedra (K–H distances between 258 and 260 pm and H–K–H
angles between 87.4° and 92.6°). Those in Wyckoff position e (four in the unit cell) occupy interstitial voids
between the AlH6 and KH6 octahedra and do not form
regular polyhedra. They have coordination numbers of 8
or 11, depending on whether when hydrogen neighbours
up to 310 or 360 pm distance are included, respectively.
The calculated formation enthalpies and reaction enthalpies of the monoalkali alanates are also shown in
Table I. The formation enthalpy Hform of the compound
MnAlH(n+3) is defined as
Hform[MnAlH(n+3)] ⳱ E[MnAlH(n+3)] – n
E(M) – E(Al) – (n + 3)/2 E(H2) ,
(4)
where E is the calculated total electronic energy of the
alanate and the elements in their standard state, as calculated by VASP at 0 K. The reaction enthalpies are
defined in accordance to the disproportionation reactions
(1) and (2) for the tetrahydrides and the hexahydrides,
respectively:
Hreact(MAlH4) ⳱ E(MAlH4) – 1/3 E(M3AlH6)
(5)
– 2/3 E(Al) – E(H2) ,
Hreact(M3AlH6) ⳱ 2/3 E(M3AlH6) – 2 E(MH)
– 2/3 E(Al) – E(H2) .
FIG. 1. Crystal structure of K3AlH6. The octahedra are AlH6 complexes, and the balls are K atoms.
(6)
A more negative formation enthalpy is indicative of a
more stable phase, relative to other candidate structures.
Likewise, a more negative reaction enthalpy represents
an increased favorability for disproportionation and release of H2. Table I shows that all the alanates are stable
compared to the elements (negative formation enthalpy.)
There is no clear trend in the formation enthalpy when
going down the alkali series, but there is one important
difference: Li3AlH6 has a much more negative formation
enthalpy than the heavier hexahydrides. This may be an
important reason why the reverse reaction (1) is difficult
to achieve in the Li alanates: the hexahydride is too
stable, making this reaction thermodynamically unfavorable. One reason why the Li hexahydride is so stable is
simply the small size of the Li ion. This makes the hexagonal R3̄ structure accessible, which, as mentioned before, has significantly denser packing of the structure
than the other hexahydrides, more than should be expected simply from the size of the ion. There is no such
structure available for the Li tetrahydride, so the relative
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stability of the two Li alanates is more in favor of the
hexahydride than that of the heavier alanates. This picture of the difficult hydrogenation of LiAlH4 could of
course be accompanied by kinetic barriers impeding the
reaction. In addition, we should expect significant effects
on the hydrogenation from finite temperature and zeropoint motion, but that is beyond the scope of this work.
The total and local DOS of the tetrahydrides are shown
in Fig. 2. (The corresponding plots for the hexahydrides
are shown in Ref. 32). Many properties are similar between the three compounds, with some exceptions. The
calculated band gap increases from Li alanate (4.7 eV)
via Na (4.8 eV) to K (5.2 eV) alanate. Quasiparticle GW
calculations have shown that the band gap of NaAlH4 is
underestimated by 2–3 eV,82 so we may expect that all
three compounds have quite large band gaps, at least on
the order of 7 eV. The calculated band gaps of the hexahydrides are 3.1, 2.4, and 2.9 eV for the Li, Na, and K
alanates. Most of the orbitals have distinctly different
regions of available states in the valence and conduction
bands, which means that the bonding is either ionic or
polar covalent. The largest differences in the DOS are
found between the two lightest alanates and K alanate.
The band widths of K alanate are much smaller than
those of the others, similar to what is seen in the hexahydrides.32 This means that we should expect smaller
overlaps between the ions in K alanate than in the lighter
alanates, and thus relatively lower density than expected
from the size and mass of the atoms alone. There are no
signs from the DOS that could explain the different hydrogenation behaviors of the alanates.
Another quantitative measure of the bonding is the
charge distribution and amount of overlap between the
atoms. The calculated Hirshfeld charges and overlap
populations are shown in Table II. Some clear trends may
be read out of these data: while the charge on the alkali
atom increases while moving from Li to K alanate, the
charge on Al decreases. The charge on H also decreases
slightly, so the charge on AlH4 balances that of the alkali
atom. This is similar to what was found for the hexahydrides,32 and the same arguments apply here. Since the Li
atom is small and has a very small degree of polarizability and low Pauling electronegativity, it is less cationic
than the heavier atoms. The overlap population between
Li and H in LiAlH4 is on the other hand higher than that
in the heavier tetrahydrides, which shows a slightly
stronger covalence in this compound. There is a significant overlap between Al and H in all the alanates, and
this shows that the bonding between Al and H is covalent
with strong ionicity, as it was put forward by Peles et al.
for NaAlH4.82
It is interesting to see which orbitals contribute to the
overlap, and the calculated crystal orbital overlap population (COOP) is presented in Fig. 4. The overlap is small
or negative (antibonding) for the alkali–H interaction,
while the Al–H overlap is large and bonding for all three
alanates. The latter gives further strength to the Al–H
interactions described as polar covalent. The s, p, and d
orbitals of Al all contribute to the overlap: the s orbitals
in the lower region of the valence band and the p and d
orbitals in the upper.
The electron localization functions (ELF)110 of the
FIG. 2. Total and local DOS of the tetrahydrides LiAlH4, NaAlH4, and KAlH4. The DOS projected on alkali atoms, Al, and H are shown from
left to right, with the total DOS together with H. s-, p-, and d-projected orbitals are shown as shaded gray, solid, and dotted curves, while the total
DOS is plotted as a solid curve. The Fermi level is marked with a dashed line.
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O.M. Løvvik et al.: Modeling alkali alanates for hydrogen storage by density-functional band-structure calculations
FIG. 3. COOP between H and the metal atoms in the pure monoalkali aluminium tetrahydrides, calculated by ADF-BAND. The shaded gray,
solid, and dotted curves represent metal s, p, and d orbitals. Positive and negative overlap represents bonding and anti-bonding, respectively. The
Fermi level is marked with a dashed line.
three monoalkali aluminium tetrahydrides are shown in
Fig. 3. There is no localization between the atoms in any
of the cases, so there are no pure shared-electron bonds in
any of the alanates. There are, however, strong core attractors at the hydrogen positions for all the compounds,
which is consistent with the polar covalent bond between
Al and H. Accordingly, no localization is found near the
Al cores. The alkali atoms all have spherical attractors
around the cores, indicative of the ionic bonding between
the alkali atoms and AlH4. It is necessary to include the
1 s state in the lithium potential to see the attractor
around Li; the attractors around Na and K are both of
p-type.
TABLE II. Hirshfeld charges and overlap populations for the pure
alanates as calculated by ADF-BAND. Two values are given when two
non-equivalent positions of the atom give different results.
Overlap
population
Hirshfeld charges (e)
LiAlH4
NaAlH4
KAlH4
Li3AlH6
Na3AlH6
K3AlH6
M
Al
H
M–H
Al–H
0.18
0.27
0.35
0.16
0.24/0.26
0.30/0.34
0.33
0.25
0.21
0.24/0.27
0.16
0.11
−0.12/0.14
−0.13
−0.13/−0.14
−0.12
−0.15
−0.18
0.20
0.13
0.13
0.21
0.23
0.22
0.73
0.68
0.79
0.49
0.40
0.51
J. Mater. Res., Vol. 20, No. 12, Dec 2005
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O.M. Løvvik et al.: Modeling alkali alanates for hydrogen storage by density-functional band-structure calculations
reversible hydrogenation is relatively easily achieved in
Na and K alanate but not in Li alanate, we need to point
out significant and versatile differences between Li alanate and the others to make such predictions. Unfortunately, this does not seem to be possible, since the only
significant difference that has been described here is the
relatively high stability of the Li hexahydride, explained
by the small size of the Li cation. Since this effect is
specific to Li, it has a limited relevance to the prediction
of other alanate phases. Complete thermodynamic calculations of the relevant phases thus probably need to be
carried out to predict the temperature-dependent thermodynamic properties that designate potentially good hydrogen-storage materials. These calculations are more
computationally demanding than mere ground-state calculations but yield more reliable predictions of hydrogenation properties. Efforts to move in this direction are in
progress.
B. Mixed-alkali alanates
In the following, we present results for all possible
combinations of the form MxM⬘(1−x)AlH4 (tetrahydrides)
and MxM⬘(3−x)AlH6 (hexahydrides), where M and M⬘ are
Li, Na, or K, and x can take the values 0, 0.25, 0.5, and
0.75 in the former case and 0, 0.5, 1, 1.5, 2, and 2.5 in the
latter. This completes our search for mixed-alkali alanates. Their stability is defined relative to the monoalkali
alanates, and may be measured by the mixing enthalpy
Hmix
Hmix[MxM⬘(n−x)AlH3+n] ⳱ E[MxM⬘(n−x)AlH3+n] – x
E(MAlH3+n) – (n − x) E(M⬘AlH3+n) ,
FIG. 4. Electron localization function of the tetrahydrides LiAlH4,
NaAlH4, and KAlH4. High values mean high degree of localization.
The contour plots are taken through planes with all three atom types in
or close to the plane, that is 013(LiAlH4), 100(NaAlH4), and
010(KAlH4). The approximate positions of in-plane or near-plane atoms are indicated in the plots. Unit cell directions are included in the
bottom left corners. For the sake of comparison, the plots are out of scale.
It would be very convenient to formulate certain properties from calculations to indicate whether or not a
hydride is suitable as a hydrogen storage material, to
expedite future searches of potential materials. Since
3206
(7)
where n ⳱ 1 for the tetrahydrides and 3 for the hexahydrides.
The results are presented in Table III and Fig. 5 for the
tetrahydrides and in Table IV and Fig. 6 for the hexahydrides. No stable mixed tetrahydrides are found for any
of the series with 25%, 50%, or 75% substitution. It is
thus more difficult to dissolve a minor alkali species in
the tetrahydrides. This is unfortunate, since mixed tetrahydrides would be needed to achieve a hydrogen storage
system with higher hydrogen density than NaAlH4.
Mixed-alkali alanate systems where stable hexahydrides
exist are hence useful in the last reaction step [Eq. (2)]
only. This has so far been reported only for LiNa2AlH6,
and around 80% of the theoretical hydrogen content was
obtained reversibly; that, is slightly less than 3 wt%.97,98
The reason it is difficult to form mixed-alkali tetrahydrides may to a certain extent be understood from the
local coordination of the alkali atoms. While some of
the alkali sites always remain in low coordination (octahedral) in the hexahydrides even when going to K alanate, the coordination of all alkali atoms change in the
J. Mater. Res., Vol. 20, No. 12, Dec 2005
O.M. Løvvik et al.: Modeling alkali alanates for hydrogen storage by density-functional band-structure calculations
TABLE III. The most stable structures, densities, formation enthalpies, and mixing enthalpies of the mixed-alkali tetrahydrides, on the form
MxM⬘(1−x)AlH4. The enthalpies are defined in the text. The end symmetry has been determined using an accuracy of 5 pm and 0.05°. The densities
are based on the accessible hydrogen content (reactions 1 and 2.)
H vol density (kg
H/m3)
MxM⬘(1−x)
Most stable
model
This
work
Experimental
This work
Experimental
H wt%
Formation
enthalpy
(kJ/mol
atom)
Li
Li0.75Na0.25
Li0.5Na0.5
Li0.25Na0.75
Na
K0.25Na0.75
K0.5Na0.5
K0.75Na0.25
K
K0.75Li0.25
K0.5Li0.5
K0.25Li0.75
LiAlD4
KAuCl4
KAuCl4
NaAlD4
NaAlD4
NaAlD4
NaAlD4
KAlD4
KAlD4
KAlD4
NaAlCl4
NaAlCl4
P21/c
Pm
Pc
P4̄
I41/a
P4̄
I4̄
Pm
Pnma
Pm
P21
P1
P21/c
...
...
...
I41/a
...
...
...
Pnma
...
...
...
73.36
83.34
75.88
77.26
72.04
66.68
61.68
55.27
52.56
56.01
58.37
65.07
73.81
...
...
...
72.64
...
...
...
53.15
...
...
...
7.97
7.21
6.58
6.05
5.60
5.21
4.87
4.58
4.31
4.87
5.60
6.57
−55.5
−53.9
−51.6
−50.8
−54.9
−54.6
−58.2
−64.1
−70.0
−61.8
−58.7
−53.6
Space group
FIG. 5. Mixing enthalpy [defined in Eq. (7)] of the mixed-alkali tetrahydrides LixNa(1−x)AlH4 (solid curve), K(1−x)NaxAlH4 (dashed
curve), and K(1−x)LixAlH4 (dotted curve) as a function of x.
tetrahydrides (see Table I). The energy penalty for substituting a large atom with high coordination by a smaller
atom is thus much larger than if the large atom has relatively low coordination in the first place; in the latter case
there may actually be an energy gain, as we shall see for
the hexahydrides.
The mixed-alkali hexahydrides with two different alkali cations have already been studied elsewhere, and
four stable compounds were identified.31,32 The only
stoichiometries investigated in the previous studies were
those in which x assumes integral values. When we extend the scope to intermediate stoichiometries, this
represents ordered versions of solid solutions. These
structures are created by using unit cells with Z at least
Mixing
enthalpy
(kJ/mol atom)
...
0.5
1.2
1.4
...
1.3
1.4
0.7
...
1.5
1.3
1.8
equal to 2 (the conventional cell.) We also created supercells with Z ⳱ 4 to check different configurations of
the two alkali atoms within the cell. In most of the cases,
the difference in total energy between the different alternatives was negligible, and we have only used the configuration with largest separation distances between the
minor alkali atoms.
The three hexahydrides with a lighter alkali atom substituting one out of three alkali atoms of either Na3AlH6
or K 3 AlH 6 (that is, LiNa 2 AlH 6 , K 2 LiAlH 6 , or
K2NaAlH6) are all stable compared to the pure alanates.
In addition KNa2AlH6 is stable compared to the pure
alanates but not when compared to K2NaAlH6 and
Na3AlH6 (it is then unstable by 1.54 kJ/mol atom). This
is consistent with the experimental results of Graetz
et al., where only the three compounds with one lighter
substitution atom were found.98 Our results are also consistent with their proposed crystal structures for the
mixed compounds (all cubic in the Fm3̄m space group),
except that of LiNa2AlH6, where we predict a monoclinic
distortion. This is valid only at 0 K, however. There are
signs from the lattice dynamics direct method that the
cubic Fm3̄m structure may be more stable at higher temperatures.94 Moreover, a lower-symmetry phase of the
same compound has been observed at low temperatures
by powder neutron diffraction experiments.95 The reason
these structures are stable may be understood from the
local coordination of the different alkali atoms. In all the
stable structures, the smallest alkali atom occupies an
octahedrally coordinated site, while the larger atoms occupy sites with higher coordination (10–12). Since there
are twice as many of the latter sites, it is not surprising that
the preferred mixing factor is one third light alkali atoms.
Results for the intermediary mixed alanates with actual stoichiometry MnM⬘(6−n)Al2H12 (n uneven) are also
J. Mater. Res., Vol. 20, No. 12, Dec 2005
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TABLE IV. The most stable structures and mixing enthalpies of the mixed-alkali hexahydrides, on the form MxM⬘(3−x)AlH6. The hydrogen
densities are the accessible amount when releasing hydrogen down to the alkali monohydrides. The mixing enthalpy is defined in the text. The
end symmetry has been determined using an accuracy of 5 pm and 0.05°.
MxM⬘(3−x)
Most stable
model
This work
Experiment
This work
Experiment
H wt%
Formation
enthalpy
(kJ/mol
H2)
Li3
Li2.5Na0.5
Li2Na
Li1.5Na1.5
LiNa2
Li0.5Na2.5
Na3
K0.5Na2.5
KNa2
K1.5Na1.5
K2Na
K2.5Na0.5
K3
K2.5Li0.5
K2Li
K1.5Li1.5
KLi2
K0.5Li2.5
Ti3NiS6
Ti3NiS6
Na3AlD6
K3MoF6
Na3AlD6
Ti3NiS6
Na3AlD6
Li3AlF6
Na3AlD6
K3MoF6
Na3AlD6
K3MoF6
Na3AlD6
K3Fe(CN)6
Na3AlD6
K3MoF6
Na3AlD6
Ti3NiS6
R3̄
P1
P21
P1
P21/n
P1
P21/n
P21
P21
P4̄m2
Fm3̄m
P4/mmm
P21/n
P1
Fm3̄m
P4̄m2
P21
P1
R3̄
...
...
...
Fm3̄m
...
P21/n
...
...
...
Fm3̄m
...
...
...
Fm3̄m
...
...
...
57.20
53.36
54.94
52.44
50.46
42.58
43.85
41.09
40.08
38.96
37.85
34.81
31.83
33.05
41.87
44.75
47.03
46.45
56.83
...
...
...
49.46
...
43.74
...
...
...
37.50
...
...
...
40.15
...
...
...
5.62
4.89
4.33
3.88
3.52
3.22
2.96
2.75
2.56
2.40
2.56
2.13
2.01
2.25
2.56
2.96
3.52
4.32
−102.8
−94.0
−88.2
−85.4
−84.5
−71.7
−69.9
−68.9
−75.8
−82.8
−92.1
−85.3
−78.5
−77.8
−100.5
−89.5
−87.7
−90.2
H vol density (kg
H/m3)
Space group
FIG. 6. Mixing enthalpy (defined in the text) of the mixed-alkali
hexahydrides LixNa(3−x)AlH6 (solid curve), K(3−x)NaxAlH6 (dashed
curve), and K(3−x)LixAlH6 (dotted curve) as a function of x.
included in Table IV. The only stable compound in this
form is K2.5Na0.5AlH6. This is also a cubic structure in
the Fm3̄m space group, and it is marginally stable compared to K2NaAlH6 and K3AlH6. This suggests that Na is
soluble in K3AlH6 from low levels and up to at least 33%
substitution of K by Na. Since the crystal structure is the
same for all three levels of substitution (0%, 17%, and
33%), the only way this may be detected by diffraction
experiments is probably by the changed lattice parameters. They are shown indirectly in Table III (the volume
3208
Mixing
enthalpy
(kJ/mol atom)
...
1.0
1.1
0.3
−1.1
1.1
...
0.7
−0.9
−2.6
−4.9
−2.5
...
1.4
−4.2
0.3
2.1
2.6
may be found from the hydrogen volume density) and
are a ⳱ 810, 832, and 858 pm for K 2 NaAlH 6 ,
K 2.5 Na 0.5 AlH 6 , and K 3 AlH 6 . The latter compound
deviates slightly from cubic symmetry, and the lattice
constants for K3AlH6 in the cubic-like supercell are
852, 858, and 863 pm. It seems that the lattice constant
increases linearly with increasing Na content and that
the changes are large enough to be seen in diffraction
experiments. The compound with 50% Na and K is also
stable compared to the pure alanates, but it is unstable
compared to K2NaAlH6 and Na3AlH6. The solubility
limit for Na in K3AlH6 is thus between 33% and
50%, probably near 33% if judged from the curve. We
have not found any stable intermediate compounds between K2LiAlH6 and K3AlH6 or between LiNa2AlH6
and Na3AlH6. This may be because we have not found
the correct crystal structure for these structures. In that
case, however, the crystal structure must be significantly different in the intermediate compound, and we no
longer speak of a solid solution, but rather a distinct
phase. This leads us to propose that the solubilities of
Li in K3AlH6 and Na3AlH6 do not represent a general
trend, and that only the ordered phases with 33% Li
exist. We have used the same configuration of alkali
atoms of the phase Na1.5Li1.5AlH6 as described in
Ref. 81, but while they obtained a stable structure (by
approximately 0.4 kJ/mol atom), ours is slightly unstable compared to the pure alanates (by approximately
0.3 kJ/mol atom). The difference is not very big, however, and is clearly within what could be expected when
comparing results from different methods (they used, for
J. Mater. Res., Vol. 20, No. 12, Dec 2005
O.M. Løvvik et al.: Modeling alkali alanates for hydrogen storage by density-functional band-structure calculations
instance, ultrasoft pseudopotentials in Ref. 81, while we
use the projector augmented wave method.) In any
case, Na1.5Li1.5AlH6 is unstable compared to LiNa2AlH6
and Na3AlH6, so we do not expect that it will be observed in experiments, unless it exists as a metastable
phase.
In this study, we have investigated a rather large number of hypothetical mixed-alkali structures, but the field
is not necessarily exhausted. Since we have included
only a limited number of input models in the relaxation
procedure, there is a chance that some compounds have
more stable structures not accessible from our set of
input structures. Low-symmetry structures may be made
accessible by deliberately breaking symmetry of highersymmetry structures,111 but this makes the calculations
much more expensive. It is also possible to investigate
a larger number of different configurations of the alkali
atoms; we have only done this in the most stable structures of the hexahydrides, based on the Na3AlD6 and
Li3AlD6 structures. Again, if a large number of different configurations were included for all the input structures of all the hypothetical compounds, the computational effort needed would be insurmountable with
our current resources. Since we have calculated only
ordered structures in this study, we also expect that
configurational entropy may stabilize some of the mixed
compounds. Most importantly, temperature effects included by for instance phonon calculations would
give valuable information on the relative stability of
the various phases as a function of temperature and pressure.
Nevertheless, there is small chance that any of these
methods provide stabilization effects sufficient for
some of the light mixed-alkali tetrahydrides to be found
stable compared to the pure ones. This means that
NaAlH4 is the lightest remaining alanate with proven
reversible hydrogenation at moderate conditions and
that mixing of the LiAlH4 and NaAlH4 phases does not
seem to be a feasible way toward a viable hydrogen
storage system.
IV. SUMMARY AND OUTLOOK
The crystal structure and detailed electronic structure
of pure and mixed alkali alanates in the ground state have
been calculated by density-functional calculations within
the generalized gradient approximation. The correspondence with experimentally known values is excellent
in almost all the cases. All known monoalkali crystal
structures are reproduced within very small deviations,
and the crystal structure of K3AlH6 has been predicted.
The only exception to this very good correspondence
is LiNa2AlH6, where the predicted crystal structure is
weakly monoclinic, whereas the experimental one is
cubic. This discrepancy may, however, be entirely due
to the fact that our models give equilibrium structures
at a temperature of 0 K while experimental work is
performed at higher temperatures A recent diffraction
study of this compound95 reveals a low-temperature
phase of this compound with lower symmetry that
may be consistent with our proposed crystal structure
at 0 K.
It is important to know why it is much more difficult
to hydrogenate Li alanate from the gas phase than the
heavier compounds, since Li alanate would have been a
highly desirable hydrogen-storage material from a gravimetric point of view. One reason seems to be the relatively high stability of the Li3AlH6 phase, which has a
totally different crystal structure than the heavier hexahydrides, apparently because of the small size of the Li
cation. Since no similar, more stable structure exists for
LiAlH4, the relative stability of the tetra- and hexahydrides is different in Li alanate from that in the Na and K
alanates, and thus hydrogenation of Li alanate is more
difficult. It is also likely that kinetic barriers hinder the
hydrogenation of Li alanates, particularly of the hexahydrides [reverse reaction (2)].
The electronic structures of the different alanates are
all quite similar. They reveal a polar covalent bond
within the aluminohydride complexes and ionic bonding
between the alkali cation and the complex. Lithium
shows a stronger degree of covalence in its interaction
with hydrogen than the heavier alkali metals. This may
be readily explained by its low polarizability and high
ionization potential compared to the latter. The alanates
are insulators, with calculated band gaps around 5 eV for
the tetrahydrides and 2.5–3 eV for the hexahydrides.
These band gaps are probably underestimated by 2–3 eV.
The presently reported work completes our search for
mixed-alkali alanates, and no stable mixed-alkali tetrahydride phases [on the form MxM⬘(1−x)AlH4 with M and
M⬘ ⳱ Li, Na, K, and x ⳱ 0.25,0.50, and 0.75] were
found. The only mixed-alkali hexahydride phases [in the
form MxM⬘(3−x)AlH6 with M and M⬘ ⳱ Li, Na, K, and
x ⳱ 0.5, 1, 1.5, 2, and 2.5] found to be stable were
LiNa2AlH6, K2LiAlH6, K2NaAlH6, and K2.5Na0.5AlH6.
In addition, K1.5Na1.5AlH6 and KNa2AlH6 were found to
be stable compared to the pure alanates, but unstable
compared to K2NaAlH6 and the pure alanates at the
ground state. The shape of the calculated mixing enthalpy as a function of the M⬘ content suggests that there
is general solubility of Na in K3AlH6 up to 1/3 Na, but
the LiNa2AlH6 and K2LiAlH6 phases are unique structures with possibly highly ordered distribution of the alkali atoms.
We see from Tables I, III, and IV that the only (existing) alkali alanates that satisfy the international density
targets for hydrogen-storage materials112 of 5 wt% and
70 kg/m3 are LiAlH4 and NaAlH4. If the volumetric density is not too important, Li3AlH6 could also be an
J. Mater. Res., Vol. 20, No. 12, Dec 2005
3209
O.M. Løvvik et al.: Modeling alkali alanates for hydrogen storage by density-functional band-structure calculations
interesting material, with the same gravimetric hydrogen
density as NaAlH4 released in a single step. Since reversible hydrogenation of Li alanates does not occur at
reasonable conditions,35 however, the only remaining usable alkali alanate satisfying this goal is NaAlH4. Further, if the United States Department of Energy Freedom
CAR target of 6 wt% hydrogen for the storage system113
is to be followed, only LiAlH4 has a sufficiently high
hydrogen density among the alkali alanates. Hence, the
Freedom CAR density target will probably not be
reached using alkali alanates. Even the international target of 5 wt% may be difficult to reach using NaAlH4,
since only partial hydrogenation is achievable with reasonable kinetics at moderate hydrogen pressure (which is
important to avoid the need for bulky containers for the
hydride).
This means that one has to search among other groups
of hydrides for lighter storage materials if the international goals are to be reached. Possible candidates may
include alkaline earth alanates, borohydrides, imides and
amides, or magnesium-based hydrides. The ideal system
has not yet been found, and the search continues. Hydrogen storage is a crucial, still unresolved part of a future
hydrogen energy system, and the feasibility of such a
system may depend strongly upon the success of this
search.
ACKNOWLEDGMENTS
Economic support from the NANOMAT program of
the Norwegian research council and supercomputing resources from the NOTUR project are acknowledged by
OML and OS. Economic support by the United States
Department of Energy under Contract No. DE-FC36014012 is acknowledged by SMO.
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