APPLIED PHYSICS LETTERS 89, 071906 共2006兲
High hydrogen content complex hydrides: A density-functional study
P. Vajeeston,a兲 P. Ravindran, A. Kjekshus, and H. Fjellvåg
Center for Materials Sciences and Nanotechnology, Department of Chemistry, University of Oslo, Box 1033,
Blindern N-0315, Oslo, Norway
共Received 14 March 2006; accepted 11 May 2006; published online 15 August 2006兲
Density-functional-theory calculations within the generalized-gradient approximation are used to
establish the ground-state structure, optimized geometry, and electronic structure for Mg共AlH4兲2 and
Mg共BH4兲2. Among 28 structural arrangements used as inputs for structural optimization
calculations, the experimentally known framework is reproduced for Mg共AlH4兲2 共space group
P3̄m1兲 with positional and unit-cell parameters in good agreement with the experimental findings.
The crystal structure of Mg共BH4兲2 is predicted, the ground-state framework being orthorhombic
共space group Pmc21; Pearson symbol oP22 with a fascinating two-dimensional arrangement of
Mg2+ ions and 关BH4兴2− tetrahedra. The formation energy for the predicted Mg共BH4兲2 phase is
investigated along different reaction pathways. The electronic structures reveal that Mg共AlH4兲2 and
Mg共AlH4兲2 are insulators with calculated band gaps of around 4.5 and 6.2 eV, respectively. © 2006
American Institute of Physics. 关DOI: 10.1063/1.2217159兴
The implementation of the “hydrogen economy⬙ demands access to materials with a high weight percentage of
hydrogen which can operate 共hydrogen loading/unloading兲 at
acceptable temperatures and costs. To date known hydrides
共metal or complex hydrides兲 are unable to fulfill these requirements. Several complex hydrides have high hydrogen
content, but unfortunately poor kinetics and lack reversibility
with respect to hydrogen absorption/desorption. Recent experimental findings have shown that the decomposition temperature for certain complex hydrides can be modified by
introduction of additives.1,2 This has opened up research activity on identification of appropriate admixtures for known
or hitherto unexplored complex hydrides. Accurate structural
studies of hydrides have been limited owing to often complicated structural arrangements and the difficulties involved in
establishing hydrogen positions by x-ray diffraction
methods.3 As proposed in our earlier communications it
should be possible to form several series of hydrides with
alkali and alkaline-earth metals in combination with group
III elements of the Periodic table, but only few members of
these series have so far been experimentally explored. Mgbased hydrides have received special attention because of
their lower weight and manufacturing costs. In particular,
Mg共AlH4兲2 has been the focus of interest since, out of the
theoretical 9.3 wt % hydrogen, 7 wt % may be extracted at
temperatures as low as 135– 163 ° C.4–6 However, the lack of
reversibility represents a yet unsolved problem. In analogy
with Mg共AlH4兲2 it is possible to imagine a series of compounds with the general formula M共BH4兲2 共M = Be, Mg, Ca,
Sr, Ba兲. This letter focuses on the structural stability of
Mg共BH4兲2, which we will compare with that of the well
established Mg共AlH4兲2 phase. Mg共BH4兲2 can theoretically
store up to 16.8 wt % H and its existence and synthesis route
are already indicated in the literature.7 In addition to structure exploration, electronic structure properties of Mg共BH4兲2
are investigated within the scope of density-functional
theory. Studies of the rest of the M共AlH4兲2 series are in
progress and results will be reported in forthcoming articles.
a兲
Electronic mail: ponniahv@kjemi.uio.no
Total energies have been calculated by the projectedaugmented plane-wave8 共PAW兲 implementation of the Vienna ab initio simulation package 共VASP兲.9 The generalizedgradient approximation10 共GGA兲 was used to obtain accurate
exchange and correlation energies for particular configurations of atoms. Ground-state geometries were determined by
minimizing stresses and Hellman-Feynman forces with the
conjugate-gradient algorithm, until forces on all atomic sites
were less than 10−3 eV Å−1. Brillouin zone integration was
performed with a Gaussian broadening of 0.1 eV for all relaxations. In order to span a wide range of energetically accessible crystal structures, unit-cell volume and shape as well
as atomic positions were relaxed simultaneously in a series
of calculations made with progressively increasing precision.
A final high accuracy calculation of the total energy was
performed after completion of the relaxations with respect to
k-point convergence and plane-wave cutoff. From various
sets of calculations it was found that 512 k points in the
whole Brillouin zone with a 500 eV plane-wave cutoff are
sufficient for the Mg共AlH4兲2 structure to ensure optimum
accuracy in the computed results. A similar density of k
points and energy cutoff were used for the other structures/
phases considered. The present type of theoretical approach
has recently been applied11 to explore ambient- and high
pressure phases, which in many cases have later been experimentally verified.12 For the exploration of possible reaction
pathways we have also computed the total energy for Mg
共P63 / mmc兲, MgH2 共P42 / mnm兲, MgB2 共P6 / mmm兲, B2H6
共P21 / n兲, and B 共P42 / nnm兲 in their ground-state structures
with full geometry optimization. The reaction enthalpy were
calculated from the total energy of the reactants and products
involved in the reaction concerned. The validity of such an
approach is tested and found satisfactory for known hydride
phases. Even though temperature effects were not included
in this approach one can reliably reproduce/predict formation
enthalpies, viz. temperature effects roughly cancel owing to
similarities in the phonon spectra among reactants and product.
Twenty-eight potentially applicable structure types have
been used as inputs in the structural optimization calcula-
0003-6951/2006/89共7兲/071906/3/$23.00
89, 071906-1
© 2006 American Institute of Physics
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071906-2
Appl. Phys. Lett. 89, 071906 共2006兲
Vajeeston et al.
TABLE I. Optimized structural parameters, bulk modulus 共B0兲, pressure derivative of bulk modulus 共B⬘0兲, and calculated energy band gap for Mg共AlH4兲2 and
Mg共BH4兲2 phases.
Phase
共Space group兲
Cell constants 共Å兲
Mg共BH4兲2
共Pmc21兲
a = 4.3086
b = 6.0878
c = 8.3888
Mg共AlH4兲2
a = 5.2533共5.2084兲a
共P3̄m1兲
c = 6.0241共5.8392兲a
Sites: Positional parameters
B0 共GPa兲
B⬘0
Eg 共eV兲
Mg共2a兲 : 0, 0.3014, 0.0005; B1共2b兲 : 1 / 2 0.898 06 0.478 98
B2共2a兲 : 0, 0.5179, 0.2449; H1共2b兲 : 1 / 2, 0.7007, 0.4426
H2共4c兲 : 0.2810, 0.9419, 0.5665; H3共2a兲 : 0 0.417 34, 0.371 85
H4共2a兲 : 0, 0.2823, 0.7559; H5共4c兲 : 0.2388, 0.5317, 0.6763
H6共2b兲 : 1 / 2, 0.0075, 0.3607
Mg共1a兲 : 0, 0, 0; Al共2d兲 : 1 / 3, 2 / 3, 0.7067 共0.699兲a
7.82
5.2
6.2
10.87
5.7
4.4
H1共2d兲 : 1 / 3, 2 / 3, 0.4392 共0.424兲a
H2共6i兲 : 0.1628, −0.1628, 0.8123 共0.1671, −0.1671, 0.8105兲a
Experimental values at 8 K 共Ref. 14兲.
a
tions for the Mg共BH4兲2 and Mg共AlH4兲2 phases 共alphabetical
order with Pearson structure-classification notation in parenthesis兲: BaAu2F8 共tI44兲, Ba共MnO4兲2 共oF88兲, BaTm2F8
共mC22兲, Be共BH4兲2 共tI176兲, Ca共BF4兲2 共oP88兲, Cd共AlCl4兲2
共mP22兲, Co共AlCl4兲2 共mI44兲, Co共ClO4兲2 共hR33兲, Cu共AlCl4兲2
共mP22兲, Hf共MoO4兲2 共hP66兲, K2WO8 共hR66兲, Mg共AlH4兲2
共hP11兲, Mo2UO8 共oP44兲, ␣ − MoV2O8 共mC22兲, MoV2O8
共oC22兲, Ni共AuF4兲2 共mP22兲, Sr共AlCl4兲2 共tI88兲, Th共MoO4兲2
共hP99兲, Th共MoO4兲2 共oP88兲, Ti共AlCl4兲2 共mP22兲, Tl共AlBr4兲2
共oP22兲, U2MoO8 共oP44兲, UMo2O8 共oP44兲, UTa2O8
共hP11兲, Yb共AlCl4兲2 共tI88兲, Zr共SO4兲2 共oP44兲, Zr共WO4兲2
共cP44兲, and Zr共WO4兲2 共oP132兲.13 It should be noted that
during the stress and stain relaxations some of the initial
structures are converted into another structure type or a
structure which was not included amoung the selected guess
structures.
Experimental studies6,14 have established that
Mg共AlH4兲2 is stabilized in a structure following the symmetry of space group P3̄ml. According to the optimization calculations for the considered 28 structural inputs, the experimental variant proved to have the lowest total energy with
good agreement between the calculated structural parameters
and the low temperature powder neutron diffraction data14
共see Table I兲. The crystal structure of Mg共AlH4兲2 共see Fig. 2
in Ref. 14兲 can be viewed as comprising isolated, slightly
distorted 关AlH4兴2− tetrahedral anions and Mg2+ cations. Each
Mg is coordinated to six hydrogen atoms sharing one corner
with each of six different AlH4 tetrahedra to form a distorted
MgH6 octahedron. The bridging hydrogen atoms are located
at the H2 site, whereas the hydrogen atoms in the H1 position are terminal in the crystallographic c direction. This
structure thus results in a sheetlike arrangement along the c
axis. The sheets are parallel to the ab plane and interconnected by van-der-Waals-like bonding rather than more regular stronger bonds.
For the Mg共BH4兲2 phase the Cd共AlCl4兲2-type input
structure proved to have the lowest total energy. However,
after the completed minimization procedure it turned out that
the original monoclinic Cd共AlCl4兲2-type arrangement had
obtained the higher symmetry of the orthorhombic space
group Pmc21. The thus obtained structure is to be named as
another type 关hereafter denoted as Mg共BH4兲2 type兴 in the
1:2:8-composed family.13 The stress and strain relaxed calculations which were constrained to the proper
Cd共AlCl4兲2-type symmetry turned out to have 0.08 eV
higher energy than the ultimate Mg共BH4兲2-type solution ac-
cording to space group Pmc21. Similar to the Mg共AlH4兲2
structure, the Mg共BH4兲2 atomic arrangement also exhibits
sheetlike features 共see Fig. 1兲, but in this case the sheets are
stacked along the b axis. The Mg共BH4兲2 structure consists of
slightly distorted BH4 tetrahedra with B–H distances varying
between 1.195 and 1.240 Å. The Mg atoms are surrounded
by six hydrogen atoms in a slightly distorted octahedral arrangement, with Mg–H distances varying between 1.992 and
2.208 Å.
Formation enthalpy is the best aid to establish whether
theoretically predicted phases are likely to be stable and such
data may serve as guide for possible synthesis routes. The
formation enthalpy for Mg共AlH4兲2 is already introduced in
the literature and the findings suggest that Mg共AlH4兲2 should
be unstable.16 In this study we have considered the following
eight possible reaction pathways for Mg共BH4兲2 and estimated the associated formation enthalpy 共given in parenthesis; rounded-off values in kJ mol−1兲: 共1兲 MgB2 + 4H2
→ Mg共BH4兲2共−196兲; 共2兲 B2H6 + MgH2 → Mg共BH4兲2共−134兲;
共3兲 2B + 4H2 + Mg→ Mg共BH4兲2共−282兲; 共4兲 21 MgH2 + 2B
共5兲
B2H6 + H2 + Mg
+ 27 H2 + 21 Mg→ Mg共BH4兲2共−250兲;
1
1
7
共6兲
MgH
+
MgB
→ Mg共BH4兲2共−198兲;
2
2 + B + 2 H2
2
2
→ Mg共BH4兲2共−207兲; 共7兲 MgH2 + 2B + 3H2 → Mg共BH4兲2
1
1
1
共−218兲;
and
共8兲
2 MgH2 + 2 MgB2 + 2 B2H6 + 2H2
→ Mg共BH4兲2共−165兲. According to the energy gain along the
different reaction pathways, it is evident that all routes are
energetically favorable, pathways 3 and 4 being the most
FIG. 1. 共Color online兲 共a兲 Three-dimensional view of the proposed crystal
structure for Mg共BH4兲2 and 共b兲 projection of the structure along 关010兴. Atoms are labeled on the illustrations. The tetrahedral BH4 coordinations are
emphasized in all illustrations.
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071906-3
Appl. Phys. Lett. 89, 071906 共2006兲
Vajeeston et al.
FIG. 2. Calculated total DOSs for Mg共AlH4兲2 and Mg共BH4兲2. The Fermi
level is set at zero energy.
favorable. This suggests that preparation from the pure elements should be a better synthesis route than the start from
binary hydrides. However, the situation may turn out to be
quite different when reaction kinetics is taken into account.
The magnitude of the formation enthalpy suggests that
Mg共BH4兲2 is much more stable than Mg共AlH4兲2.
By fitting the total energy as function of cell volume
using the so-called universal equation of state,15 the bulk
modulus 共B0兲 and its pressure derivative 共B0⬘兲 are obtained
共Table I兲, but no experimental data for comparison are yet
available. Compared to intermetallic-based hydride phases,
both of these phases have low B0 values implying that the
materials are soft and easily compressible solids. Hence, one
can suspect that destabilization of some of the hydrogen atoms from the matrix may be feasible. However, the B–H
and/or Al–H bonds are likely to be strong. In fact, the experience from other complex aluminum-containing hydrides
shows that one needs high temperature to break Al–H bonds.
The formation enthalpy for Mg共BH4兲2 indicates that its bond
strength exceeds that of the technologically important MgH2
phase 共⌬H = −74.7 kJ/ mol兲. These findings suggest that
Mg共BH4兲2 and Mg共AlH4兲2 are not likely to find use as hydrogen reservoirs in vehicles. However, the introduction of
suitable additives may be able to improve absorbtion/
desorption properties for hydrogen. In order to verify or reject this possibility further research is need.
The calculated total densities of states 共DOSs兲 for
Mg共BH4兲2 and Mg共AlH4兲2 in the ground-state configurations
are shown in Fig. 2. Mg共BH4兲2 and Mg共AlH4兲2 are both
nonmetallic compounds with calculated band gap of 6.2 and
4.4 eV, respectively. It should be noted that the GW level of
approximation in the calculations for Mg共AlH4兲2 共Ref. 17兲
enhanced the band gap by ⬃2 eV. Our experience from
similar calculations for MgH2 is that the band gap discrepancy between theory and experiment for this class of hydrides should be within 12%.11 Based on such an assumption, we estimate the band gap in Mg共BH4兲2 and Mg共AlH4兲2
to be ⬃7.0 and 5.0 eV, respectively. The valence band is
split into two bands for both phases, the split region being
very narrow in Mg共AlH4兲2. A similar feature is observed18
for LiAlH4 and NaAlH4. Common structural features for all
these phases is the tetrahedral BH4 / AlH4 unit and a very
similar bonding situation. The basically ionic interaction between Mg and BH4 / AlH4 also has its parallel for alkali metal
to AlH4 interaction in LiAlH4 and NaAlH4. More specifically we see the B – H / Al– H interaction within the
BH4 / AlH4 tetrahedra as ionocovalent and that between Mg
and H as more purely ionic.
In summary, from the structure-optimization calculation
with 28 different input structure models, the crystal structure
of Mg共AlH4兲2 is reproduced and the structure of Mg共BH4兲2
is predicted. Mg共BH4兲2 can theoretically store up to
16.8 wt %. Our estimated values for formation enthalpy suggest that it should be possible to synthesize this phase. Studies of various constructed reaction pathways suggest that
preparation of Mg共BH4兲2 from the pure elements is energetically more favorable than synthesis via binary intermediates.
Density-of-state studies reveal that both these phases are
wide-band-gap insulators.
The authors greatfully acknowledge the Research Council of Norway for financial support and for computer time at
the Norwegian supercomputer facilities.
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