PHYSICAL REVIEW B 71, 092103 共2005兲
First-principles investigations of aluminum hydrides: M3AlH6 „M = Na, K…
P. Vajeeston,* P. Ravindran, A. Kjekshus, and H. Fjellvåg
Department of Chemistry, University of Oslo, Box 10339, Blindern N-0315, Oslo, Norway
共Received 15 October 2004; published 23 March 2005兲
The structural stability of Na3AlH6 and K3AlH6 has been systematically investigated using accurate densityfunctional total-energy calculations. The experimentally known crystal structure of ␣-Na3AlH6 is reproduced
and ␣-K3AlH6 is predicted to be isostructural 共␣-Na3AlF6 type; space group P21 / n兲. This structure contains a
pseudo-face-centered-cubic Al sublattice and each Al atom is surrounded by distorted octahedra of hydrogen
atoms with the long octahedral axis tilted from the 关001兴 direction toward 具111典. We predict that the ␣
modifications will not be stable at higher pressures. On application of pressure to Na3AlH6, the ␣ phase
transforms into a Cs3NdCl6-type structure at 19.8 GPa. Similarly ␣-K3AlH6 transforms into two high-pressure
forms: 共1兲 ␣ transforms to ␤ with Rb3TlF6-type structure at 53.4 GPa and 共2兲 ␤ transforms to ␥ with
U3ScS6-type structure at 60.2 GPa.
DOI: 10.1103/PhysRevB.71.092103
PACS number共s兲: 81.05.Je, 71.15.Nc, 71.20.⫺b
Alkali- and alkaline-earth-metal-based complex aluminum hydrides, MAlH4 关M = Li, Na, K兴 and Mg共AlH4兲2, are
expected to have a potential as viable modes for storing hydrogen. These hydrides have been demonstrated to have
higher hydrogen storage capacity at moderate temperatures
and pressures and lower cost than conventional hydride systems based on intermetallic compounds. The decomposition
of MAlH4 follows two-step endothermic processes. The first
step involves the decompositions products M 3AlH6, Al, and
H2 and the second step MH, Al, and H2. In order to obtain a
better understanding of the hydrogen absorption/desorption
of these systems, an essential piece of information is the
crystal structure. However, as these compounds contain light
elements, determination of the structures by x-ray or neutron
diffraction is not trivial, and for this reason structural information is very sparse. Owing to the favorable hydrogen
weight content and the discovery of reversibility of hydrogen
absorption/desorption with addition of some additives, the
MAlH4 phases have obtained special attention. The crystal
structures of LiAlH4 and NaAlH4 have been well established
by experimental and theoretical studies. The structure of
KAlH4 was first predicted1 by theoretical means and later
also confirmed experimentally.2 Similarly, in the M 3AlH6 series the crystal structures of Li3AlH6 and Na3AlH6 are well
established, whereas the structure of K3AlH6 has remained
unknown.
Recent experimental evidence shows that reversible hydrogen absorption/desorption proceeds smoothly in KAlH4
without introduction of catalytic additives.3 KAlH4 is thus
different from LiAlH4 and NaAlH4, which must be doped
with a transition-metal catalyst to obtain absorption/
desorption reversibility and kinetics. Hence, KAlH4 and
K3AlH6 now receive considerable attention among the
MAlH4 and M 3AlH6 phases. So far only a very limited number of theoretical studies on complex hydrides has been reported. To the best of our knowledge only one theoretical
attempt4 has been made so far to identify the crystal structure
of K3AlH6 using a so-called simulated annealing procedure.
However, this endeavor failed because the results did not
converge. In a previous study on Li3AlH6 we found that the
1098-0121/2005/71共9兲/092103共4兲/$23.00
equilibrium structure is not stable at elevated pressures and
three high-pressure forms were predicted.5 In this communication we report the crystal and electronic structures of
M 3AlH6 共M = Na, K兲 obtained by accurate density-functional
calculations.
Total energies have been calculated by the projected augmented plane-wave 共PAW兲6 implementation of the Vienna ab
initio simulation package 共VASP兲.7 The generalized-gradient
approximation 共GGA兲8 were used to obtain accurate exchange and correlation energies for a particular configuration
of the ions which is relaxed toward equilibrium until the
Hellmann-Feynman forces are less than 10−3 eV/ Å. Brillouin zone integrations are performed with a Gaussian broadening of 0.1 eV during all relaxations. For the
␣-Na3AlF6-type structure we used 512 k points in the whole
Brillouin zone. A similar density of k points were used for
the other structures. All calculations are performed with
500 eV plane-wave cutoff. In order to avoid ambiguities regarding the free-energy results we have used the same energy
cutoff and a similar k-grid density for convergence for all
structural variants tested. The present type of theoretical approach has recently been applied successfully1,9,10 to computationally reproduce ambient- and high-pressure phases.
For the theoretical simulation 22 closely related potential
structure types have been considered. The involved structure
types are ␣-Na3AlF6, ␤-Na3AlF6, U3ScS6, Cu3TeO6,
Er3GaS6, Mg3TeO6, Cu3WO6, Hg3TeO6, Rb3TlF6, Pb3SO6,
B3BiO6, Hg3NbF6, Na3CrCl6, Nb3BaO6, Fe3BO6, Li3AlF6,
Nb3VS6, I3AsF6, K3TlF6, Hg3SO6, K3ReD6, and K3MoF6.11
From the above structural starting points, full geometry optimization has been carried out without any constrains on the
atomic positions and unit-cell parameters.
Among the considered atomic arrangements the ␣Na3AlF6-type structure 共Table I; Fig. 1兲 is seen to have the
lowest total energy 共Fig. 2兲. The calculated unit-cell dimensions and positional parameters at 0 K and ambient pressure
are in excellent agreement with the room-temperature experimental findings 共Table I兲 for Na3AlH6. The deviations in the
unit-cell parameters along the a and b axes are almost zero
and the 1.2% underestimation found in the c direction is
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©2005 The American Physical Society
PHYSICAL REVIEW B 71, 092103 共2005兲
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TABLE I. Optimized equilibrium structural parameters, bulk modulus 共B0兲, and derivative of bulk modulus 共B0⬘兲 for Na3AlH6 and
K3AlH6.
Compound
共structure type; space group兲
Unit cell 共Å or °兲
Positional parameters
B0 共GPa兲
B⬘0
␣-Na3AlH6
a = 5.3574 共5.39兲a
31.9
4.1
共␣-Na3AlF6 ; P21 / n兲
b = 5.4898 共5.514兲a
c = 7.6011 共7.725兲a
␤ = 89.79 共89.86兲a
Na1共2b兲: 0, 0, 1 / 2; Na2共4e兲: −0.0065, 0.4604, 0.2518
共−0.006, 0.461, 0.252兲a
Al共2a兲: 0, 0, 0
H1共4e兲: 0.0959, 0.0415, 0.2185 共0.091, 0.041, 0.215兲a
H2共4e兲: 0.2315, 0.3261, 0.5448 共0.234, 0.328, 0.544兲a
H3共4e兲: 0.1656, 0.2673, 0.9421 共0.165, 0.266, 0.944兲a
␥-Na3AlH6
a = 4.8651
共Cs3NdCl6 ; Pbcm兲
At 19.8 GPa
b = 8.3188
c = 15.8384
␣-K3AlH6
共␣-Na3AlF6 ; P21 / n兲
a = 6.1771
b = 5.8881
c = 8.6431
␤ = 89.30
K1共2b兲: 0, 0, 1 / 2; K2共4e兲: −0.0058, 0.4828, 0.2544
Al共2a兲: 0, 0, 0
H1共4e兲: 0.0617, 0.0089, 0.2042
H2共4e兲: 0.2799, 0.3136, 0.5349
H3共4e兲: 0.1786, 0.2281, 0.9652
23.2
4.1
␤-K3AlH6
共Rb3TlF6 ; I4 / mmm兲
At 53.4 GPa
a = 4.4441
c = 7.8098
K1共2b兲: 0, 0, 1 / 2, K2共4d兲: 0, 1 / 2, 1 / 4
Al共2a兲: 0, 0, 0
H1共4e兲: 0, 0, 0.2128, H2共8i兲: 0.3429, 0, 0
␥-K3AlH6
共U3ScS6 ; Pnnm兲
At 60.2 GPa
a = 10.8885
b = 10.2576
c = 2.5538
K1共4g兲: 0.2347, 0.0344, 0; K2共4g兲: 0.55047, 3 / 4, 0
K3共4g兲: 0.6910, 0.2178, 0
Al共2b兲: 1 / 2, 1 / 2, 0; A2共2c兲: 0, 1 / 2, 0
H1共4g兲: 0.9388, 0.0715, 0; H2共4g兲: 0.5928, 0.3931, 0
H3共4g兲: 0.3085, 0.3814, 0; H4共4g兲: 0.0632, 0.3708, 0
H5共4g兲: 0.4194, 0.0352, 0.0; H6共4g兲: 0.8387, 0.3512, 0
aExperimental
Na1共8e兲: −0.3037, −0.0901, 0.6535; Na2共8e兲: −0.1853,
0.2507, 0.8341
Na3共8e兲: −0.2649, −0.0838, 0.0515
Al1共4d兲: 0.2616, 0.0785, 3 / 4; Al2共4c兲: 0.2154, −1 / 4,
1/2
H1共4d兲: 0.1338, 0.2658, 3 / 4; H2共4d兲: 0.3977, −0.1061,
3/4
H3共8e兲: 0.4712, 0.1299, 0.6732; H4共8e兲: −0.0368,
−0.1823, 0.5620
H5共8e兲: 0.4519, −0.1685, 0.5621; H6共8e兲: 0.0475,
0.0254, 0.6744
H7共8e兲: 0.2215, −0.0817, 0.4455
value from Ref. 12.
typical for the state-of-the-art approximation of densityfunctional theory. This means that one can reliably
reproduce/predict the crystal structure of quite complex systems with this type of approach. Normally such theoretical
simulations demand huge computer resources, but the development in the computer technology has made it possible to
handle such systems 共viz. structures with a considerable
number of atoms per unit cell兲 within a reasonable time limit.
Using a similar approach we have predicted structural parameters for the structurally uncharacterized K3AlH6 compound. Calculated total energy versus cell volume curves for
potential structures for K3AlH6 are shown in Fig. 2. In order
to have a good viewability among the 22 alternatives, we
have displayed only the 13 types with the lowest total energy
in Fig. 2. Among the considered structural arrangements for
␣-K3AlH6, the ␣-Na3AlF6 type is seen to possess the lowest
total energy at 0 K and ambient pressure with unit-cell
dimensions a = 6.1771, b = 5.8881, c = 8.6431 Å, and ␤
= 89.30°. The calculated formation energy for KAlH4 and
␣-K3AlH6 共⌬H = −128.01 and −224.69 kJ/ mol, respectively兲
shows that both phases are stable.
Total-energy calculations show that Na3AlH6 in the ␣Na3AlF6- and ␤-Na3AlF6-type structures are close in energy
at the equilibrium volume, and the involved energy difference between the two variants is only ⬃0.13 eV/ f.u. This
indicates that the competition between these structural arrangements will be sensitive to the synthesis and examination temperature. The positional parameters for K3AlH6 in
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FIG. 1. 共Color online兲 The ␣-Na3AlF6-type crystal structure of
␣-Na3AlH6 and ␣-K3AlH6. Legends to the different kinds of atoms
are given for ␣-K3AlH6 on the illustration.
the ␣- and ␤-Na3AlF6-type structures are closely related except that the higher orthorhombic symmetry has enforced
alignment of the 关AlH6兴3− octahedra to take low index directions in the ␤-Na3AlF6-type arrangement.
The atomic arrangement of ␣-K3AlH6 is shown in Fig. 1.
This structure consists of isolated 关AlH6兴3− octahedra with
the Al atoms arranged in a pseudo-face-centered-cubic sublattice. Within the distorted octahedra the hydrogen atoms
along the long octahedral axis are tilted from the 关001兴 direction toward 具111典. The other apices of the octahedra are
oriented toward the corners of the unit cell and these four
nearly equatorial hydrogen atoms are aligned to form a hy-
drogen superlattice in the 关001兴 direction. Within the
关AlH6兴3− units of ␣-K3AlH6 the Al- H bond lengths range
from 1.76 to 1.81 Å, closely corresponding to the interatomic Al- H distances in ␣-Na3AlH6 共1.75– 1.77 Å兲. The
calculated H - Al- H bond angles within the 关AlH6兴3− octahedra vary from 83.09 to 107.37°.
On application of pressure, ␣-Na3AlH6 transforms to the
Cs3NdCl6-type ␥ phase at 19.8 GPa. A ␤ modification has
been identified by Bastide et al.13 at elevated temperature.
However, the calculated total energy for this phase has almost 0.24 eV higher energy than the ground state ␣Na3AlH6 at ambient pressure. The equilibrium volume for
the ␣ and ␥ modifications are almost the same 共113.1 and
112.6 Å3 / f.u., respectively兲, but the involved energy difference is large 共⬃0.23 eV/ f.u. at ambient pressure兲. Even
though the ␤ and ␥ phases have almost the same energy at
equilibrium volume, the two modifications have a much
larger energetic deviation at higher pressures. The calculated
volume difference between the involved structures at the
pressure-induced transition point is ⬃4.5%. The highpressure ␥ phase is stable at pressures above 19.8 GPa, the
transition pressure being evaluated from the crossover point
in the Gibbs free energy curves between ␣- and ␥-Na3AlH6
at a in 关Fig. 3共a兲兴.
␣-K3AlH6 is stable up to 53.4 GPa where it transforms
into a Rb3TlF6-type ␤ modification 共see Figs. 2 and 3兲. In
this pressure range the ␣-Na3AlF6, ␤-Na3AlF6, and Rb4TlF6
structure types are close in energy 共within less than 10 meV兲.
At higher pressures 共around 60.2 GPa兲 the ␤ modification
transforms into a ␥ modification with U3ScS6-type structure.
However, also the involved energy differences between these
phases and the other closely related structural arrangements
are very small. Our calculations have not included temperature effects, and at higher pressures one can expect multiphase or superstructure formation or any one of the above
FIG. 2. Calculated total energy versus cell
volume curve for K3AlH6 in different possible
structural arrangements 共structure types stated on
the illustration兲. Arrows indicate the crossover
points in the total energy curves. Magnified versions around the structural transition points are
shown on the right-hand side of the illustration.
The transition pressures are calculated from the
Gibbs free energy curves.
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PHYSICAL REVIEW B 71, 092103 共2005兲
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FIG. 3. Stability of the high-pressure ␤ / ␥
phases of 共a兲 Na3AlH6 and 共b兲 K3AlH6 with respect to their equilibrium phases, transition pressures being marked by arrows at the corresponding transition points.
mentioned higher-temperature variants in single-phase form
depending on the experimental conditions. The calculated
density of states for the equilibrium structures 共␣ modifications兲 of Na3AlH6 and K3AlH6 shows that the conduction
and valence bands are separated by almost 3.0 eV, and these
materials must accordingly be classified as nonmetals. It is
interesting to note that another member of the series,
Li3AlH6, has almost the same sized band gap 共3.5 eV兲 although this compound stabilizes with a rather different
structure.5
In conclusion, the calculated structural parameters for ␣Na3AlH6 are in excellent agreement with the experimental
findings. The crystal structure of ␣-K3AlH6 is predicted. ␣-
Na3AlH6 and ␣-K3AlH6 stabilize in the ␣-Na3AlF6-type
structure. We found that the ground-state structure of these
M 3AlH6 phases becomes unstable at higher pressures. The
high-pressure modifications and equilibrium structures have
almost similar equilibrium volumes and the energy difference between the involved phases is very small for K3AlH6.
The electronic structures show that all the equilibrium and
high-pressure modifications of these compounds have nonmetallic character.
*Electronic address: ponniahv@kjemi.uio.no
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The authors gratefully acknowledge the Research Council
of Norway for financial support and for computer time at the
Norwegian supercomputer facilities.
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