i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 0 1 4 9 e1 0 1 5 8
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Prediction of crystal structure, lattice dynamical, and
mechanical properties of CaB2H2
P. Vajeeston a,*, P. Ravindran a, B.C. Hauback b, H. Fjellvåg a
a
Department of Chemistry, Center for Materials Sciences and Nanotechnology, University of Oslo, P.O. Box 1033 Blindern,
N-0315 Oslo, Norway
b
Department of Physics, Institute for Energy Technology, P.O. Box 40, Kjeller NO-2027, Norway
article info
abstract
Article history:
The phase stability of CaB2H2 phase at ambient and high pressures was investigated using
Received 1 March 2011
the state-of-the-art ab initio program based on density functional theory. At ambient
Received in revised form
conditions CaB2H2 crystallizes in orthorhombic phase (a-modification; space group Cmc21)
4 May 2011
and at high pressure it transforms into trigonal structure (b-modification; space group
Accepted 7 May 2011
P3 m1). From the lattice dynamics simulation and mechanical properties study we have
Available online 11 June 2011
found that the predicted phases are dynamically as well as mechanically stable. The
chemical bonding in CaB2H2 is discussed on the basis of electronic structures, charge
Keywords:
density, and bond overlap population analysis. In order to verify the possible existence of
Structural prediction
this compound experimentally we have simulated the Raman, IR spectra and NMR related
Crystal structure of CaB2H2
parameters like isotropic chemical shielding, quadrupolar coupling constant, and quad-
Mechanical properties
rupolar asymmetry parameters. The electronic structures reveal that a- and b-CaB2H2
Raman and IR studies
modifications are indirect band gap semiconductor with estimated band gap vary between
0.32 and 1.98 eV.
Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
reserved.
1.
Introduction
Complex hydrides have attracted considerable attention as
hydrogen storage materials, because of their high gravimetric
and Schwickardi have
hydrogen densities. Since Bogdanovic
reported catalyzed sodium alanate NaAlH4 shows reversible
hydrogen desorption and absorption reactions at moderate
condition, many experimental and theoretical studies have
been made on complex hydrides mainly from the viewpoint of
kinetics [1e10]. Unfortunately, no break through has yet been
achieved to use them in mobile applications.
The search for the optimum complex metal hydrides for
use in a hydrogen storage system has continued through the
work of many experimental and computational research
groups. The focus remains largely on alanates, borohydrides,
and amide-like systems of early first and second group metals,
as these offer high hydrogen mass densities [11e19]. As yet, no
material has been identified that simultaneously posses high
hydrogen densities, favorable kinetics and thermodynamics
for use in a hydrogen storage system. Complex hydrides based
on boron (borohydrides) exhibit the highest weight capacity
for hydrogen and are, therefore, obvious candidates to meet
the capacity requirements. Calcium borohydride, Ca(BH4)2 is
one of the promising material for hydrogen storage applications due to high weight capacity of hydrogen and cheap as
well as abundant nature of constituents. This material
contains 11.6 wt% hydrogen in total and exists in a number of
polymorphs at room temperature. Further, it is not clear
* Corresponding author.
E-mail address: ponniah.vajeeston@kjemi.uio.no (P. Vajeeston).
0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijhydene.2011.05.038
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 0 1 4 9 e1 0 1 5 8
which dehydrogenation path this calcium borohydride
system takes. Hence, it is important the characterize possible
intermediate phases during the dehydrogenation reaction of
Ca(BH4)2. A number of studies have revealed that it is the b and
g forms of Ca(BH4)2 that decompose [20,21] and that the
dehydrogenation is a two-step process [20e25]. It is also
evident that CaH2 is formed in the dehydrogenation reaction
[20e25]. Solid-gas preparation techniques from possible
dehydrogenation products have been demonstrated [26,27].
Experimental evidence exists for a number of intermediate
and product compounds, including CaB2Hx [22], CaB6 [21],
CaB12H12 [22], and orthorhombic [28] and amorphous [24]
phases. It should be noted that it might be possible to form
CaB2H2 phase also. But existence of such compound is
unknown in the literature. Most of the compounds
crystallize at some point during their production process.
The knowledge about the crystal structures is a prerequisite
for the rational understanding of the solid-state properties
of new materials. Hence, it would be desirable to accurately
estimate the thermodynamical properties and in particular,
the stability of new materials before substantial resources is
expended on their synthesis and characterization. Firstprinciples calculations of the total crystal binding energies
using the density functional theory (DFT) have proven
to be a sufficiently accurate tool for obtaining hydride
thermodynamics, but they need the crystal structure as
input, which is often unavailable.
In connection with the above aspects, we have explored
the possible existence of CaB2H2 phases and their stability
using density functional theory in this article.
2.
Computational details
Total energies have been calculated using the projectedaugmented plane-wave (PAW) [29,30] implementation in the
Vienna ab initio simulation package (VASP) [31,32]. All these
calculations were made with the generalized gradient
approximation (GGA) of the Perdew, Burke, and Ernzerhof
(PBE) [33] exchange-correlation functional. It should be noted
that both PW91 [34] and PBE functionals gave almost the
same result. The differences in the energetics and structures
of using the two functional were found to be negligible, and
the results reported here were computed with the PBE
functional. Ground-state geometries were determined by
minimizing stresses and HellmaneFeynman forces using the
conjugate-gradient algorithm with force convergence less
than 103 eV Å-1. Brillouin zone integration was performed
with a Gaussian broadening of 0.1 eV during all relaxations.
The k-points were generated using the MonkhorstePack
method. From various sets of calculations it was found that
600 k-points in the whole Brillouin zone for the ZnRb2O2
-type structure with a 600 eV plane-wave cut-off is sufficient
to ensure optimum accuracy in the computed results. The
k-points were generated using the MonkhorstePack method
with a grid size of 10 10 10 for structural optimization. A
similar density of k-points and energy cut-off were used to
estimate total energy as a function of volume for all the
structures considered for the present study. Iterative
relaxation of atomic positions was stopped when the change
in total energy between successive steps was less than
1 meV/cell. With this criterion, the forces generally acting on
the atoms were found to be less than 10-3 eV Å-1.
Density functional perturbation theory (DFPT) [35] as
implemented in CASTEP [36] was used for phonon calculations.
For the phonon calculation we have used norm-conserving
pseudopotentials with 700 eV energy cut-off for all atoms
together with an 8 8 6 mesh of k-points, with the
energy conversion threshold of 0.01 meV/atom, maximum
displacement of 0.001 Å and maximum force of 0.03 eV/Å,
yielding a high accuracy for the energy and atomic
displacements. For B and Ca atoms the valence states were
modeled using the 2 s2, 2p1 and 3 s2, 3p6 electrons, respectively.
3.
Structural investigation
Twenty two potentially applicable structure types (AB2X2; A, B,
and X represent the first, second, and third elements in the
following structures) have been used as starting inputs in the
structural optimization calculations for the CaB2H2 phase
(space group and space group numbers are given in parenthesis): ZnRb2O2 (P121/c1, 14); PbO2K2 (P-1, 2); PtK2S2 (Immm,
71); BaCu2O2 (I41/AMDZ, 141); CeAl2Ga2 (IMMM, 139); BaCu2S2
(Pnma, 62); Na2NiO2 (Cmc21, 36); SC2N2 (PBCa, 61); PdP2K2
(CmCm, 63); HgC2N2 (T4-2D, 122); ZrN2Li2 (P3-m1, 164); ThN2Li2
(P3, 147); CoZr2Si2 (B112/M, 12); ZnC2N2 (P4-3m, 215); PbAg2O2
(12/c1, 15); SnRb2O2 (P212121, 19); ZnS2Na2 (IBAM, 72); CeB2Ir2
(FDD2, 70); CuFe2Ge2 (Pnma, 51); TlSb2Zn2 (I4, 79); NiAg2O2
(R3-mh, 166): and FeS2Cu2 (F4-3m, 216). The present type
of theoretical investigations are highly successful to predict
the ground-state structure of hydrides [37] and other
materials [38,39]. The reliability of the calculations depends
upon the number of input structures considered in the
calculations. Though it is tedious process to select input
structures from the 518 entries for the AB2X2 composition in
the ICSD data base [40], which also involves tremendous
computations, several compounds/phases have the same
structure type and in some cases have only small variations
in the positional parameters (of certain atoms). These
possibilities are omitted, because during the full geometry
optimization, such structures mostly will be converted to one
particular type of structural arrangements. In this particular
composition only 22 structure types have unique structural
arrangements.
Among the considered structure models for CaB2H2 chemical composition, a NiNa2O2 derived model atomic arrangements occur at the lowest total energy (see Fig. 1; named
a-CaB2H2). This particular structure is highly porous where
the B atoms are formed in one dimensional chains along the
x axis, where the H atoms are bonded in a fascinating way
that the B and H atoms are formed in a zigzag chains along
the x direction as shown in Fig. 2a. The Ca atoms are stacked
in between the BeH chains. The calculated BeH distance is
1.246 Å, BeB distance is 1.710 Å, and the average CaeH
distance is 2.31Å. The next energetically favorable phase is
ZrN2Li2 derived structure model which occur at the reduced
volume i.e. at high pressures. It is interesting to note that,
during the theoretical simulations, many of the initially
assumed different trial structures relaxed toward the
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 0 1 4 9 e1 0 1 5 8
Fig. 1 e Calculated unit cell volume vs. total energy for
CaB2H2 in selected lowest energy structures.
ZrN2Li2-type structure (SrAl2H2-type; named b-CaB2H2). This
finding strongly emphasizing that, this particular atomic
arrangement is one of the more favorable structures for the
CaB2H2 phase at high pressures. In this structure Ca located
at 1a, B located at 2d, and H located at another 2d Wykoff
positions (see Table 1). The unit cell contains only one
formula unit, i.e., CaB2H2. Each B atom is surrounded by one
H atom with 1.238 Å and three B atoms with 2.028Å at the
equilibrium volume. The B atoms are making a network
(6 rings) along the ac plane and this structure can be
considered as a layered structure as shown in Fig. 2b. Similar
to the a-modification one hydrogen atom is bonded to each B
atom, alternating above and below the net. The HeH
separation in this phase is 2.338 Å. Due to the HeH repulsive
interaction of the negatively charged H ions, the networks
are well separated. The Ca atoms are located like sandwich
in the space between these nets. Each Ca atom is surrounded
10151
by six H atoms with the distance of 2.094 Å. It is important to
note that the predicted phase for the CaB2H2 composition is
quite different from the experimentally proposed structure
for the CaB2Hx (x composition is not clear). It might be
possible to change the structure when we change the H
content or contamination of the sample. This study is
currently under investigation both experimentally and
theoretically and the results will be published in a forth
coming article. The calculated transition pressure for the ato b-CaB2H2 conversion is 10.8 GPa and the involved energy
difference between these two modifications is 0.27 eV/f.u. at
their equilibrium volumes. At the a-to-b phase transition
point for CaB2H2 the estimated difference in cell volume is
ca. 12.58 Å3/f.u. The pressure induced a-to-b transition
involves reconstructive (viz. bonds are broken and reestablished) rearrangements of the cation and anion sublattices. It interesting to noted that the X-ray and powder
neutron diffraction data on existing isoelectronic phases
such as SrAl2H2 [41], SrGa2H2 [42], and BaGa2H2 [42] are
showing isostructural structural character and crystallize in
the P-3m1 symmetry. On the other hand, the present CaB2H2
compound stabilizes in the Cmc21 symmetry. In general, the
borides are behaved differently than the aluminides and
galides. The possible reason is that the outermost electrons
jin Al and Ga are more diffuse in nature than that in B. As
a result, due to the strong directional BeH interaction (see
more details in the BOP section) in CaB2H2, it crystallizes in
a lower symmetry structure than the SrAl2H2, SrGa2H2, and
BaGa2H2 phases. Usually the application of pressure reduces
the covalency in solides and make the valence electrons
more diffuse than that at ambient condition. Due to the loss
of covalency, this lower symmetric a-modification CaB2H2
transform into high symmetric b-modification.
In order to understand the dynamical stability of the predicted phases, we have also calculated phonon DOS at the
equilibrium volume for these phases, which are shown
in Fig. 3. From this figure it is clear that these a- and
b-modifications have no imaginary frequency which indicate
that the predicted phases for this composition is either
ground-state/metastable phases, or at least they are
dynamically stable phases [43]. As per the theory, the
predicted phases are found to be dynamically stable and
Fig. 2 e Theoretically predicted crystal structures for CaB2H2: (a) orthorhombic a-modification at ambient conditions and (b)
trigonal b-modification at high pressure. The legends for the different kinds of atoms are given in the illustration.
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Table 1 e The calculated equilibrium structural parameters (a and c are in Å) and band-gap (in eV) values for the CaB2H2
phases.
Compound Space group
Cell parameters (Å)
Atom
Site
Position
Band gap
a-CaB2H2
Cmc21 (36)
Na2NiO2-type
a ¼ 3.1983
b ¼ 8.7658
c ¼ 7.7526
a ¼ 3.4739
c ¼ 3.9784
4a
4a
4a
4a
4a
1a
2d
2d
1/2, 0.6517, 0.0561
1/2, 0.9071, 0.2692
1/2, 0.3724, 0.2014
1/2, 0.9744, 0.4115
1/2, 0.6731, 0.5470
0,0,0
1/3, 2/3, 0.4622
1/3, 2/3, 0.1511
0.32 indirect
b-CaB2H2
P-3m1 (164)
SrAl2H2-type
Ca
B1
B2
H1
H2
Ca
B
H
hence we need experimental verification to confirm our result.
From Fig. 3, because of the novel structural arrangements, the
a- and b-modifications have quite different phonon DOS.
Owing to the one dimensional structural arrangement, the
calculated phonon DOS for the a-modification is very
narrow. In both phases the partial phonon DOS are
displayed in Fig. 4. Since the mass of H atom is much
smaller than that of B and Ca atoms, the phonon
frequencies originating from H atoms are having higher
value. Fig. 4 shows that, for the b-phase, the high frequency
modes above 30 THz are dominated by H atom and in
a-phase the corresponding frequencies are well scattered
over the frequency range from 20 to 63 THz. In both phases
the low frequency modes below 10 THz are mainly
dominated by Ca atom. The B modes in b-phase are present
between 10 and 20 THz frequency range and for the a-phase
the corresponding modes are present between 10 and 30 THz.
The electronic DOS of a- and b-CaB2H2 phases given in
Fig. 5 show that these two phases have nonmetallic character
with finite energy gaps (0.32 and 1.98 eV, respectively). These
band-gap values are much smaller than that observed in
most of the known alanates and borohydrides. The present
study shows that both these phases are indirect band gap
semiconductors. In general, compared to experimental
1.98 indirect
band-gap values, density-functional calculations always
underestimate band-gap values significantly. In order to
estimate better theoretical band-gap values, we have used
parameterized HCTH [44] functionals for the density of
states calculations in the present study. In general, HCTH
functionals give more reliable band-gap values than the
usual LDA or GGA functionals [44]. HCTH is a semi-empirical
GGA functional which includes local exchange-correlation
information (for more details see Ref. [44]). For example, the
calculated GGA band-gap value for a-MgH2 is 4.2 eV [45]
which is lower than the obtained HCTH band-gap value of
4.96 eV. The corresponding experimentally reported value
for a-MgH2 is 5.16 eV [46]. Hence, one can expect that the
CaB2H2 polymorphs might have band-gap value slightly
higher than the corresponding predicted band-gap values
reported here. It should be noted that the isoelectronic
compounds such as SrAl2H2, SrGa2H2, and BaGa2H2 are
having metallic character (for more details see refs.[42,
47e49]). The possible reason is due to difference in the
bonding between the present system and the isoelectronic
compounds mentioned above. In particular the formation of
stronger directional BeH bond (due to the less diffusivity of
outermost electrons in B) in the CaB2H2, the electronic
structure is different from that of SrAl2H2, SrGa2H2, and
Fig. 3 e The calculated total phonon density of states for the a- and b-CaB2H2 phases at their equilibrium volume.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 0 1 4 9 e1 0 1 5 8
10153
Fig. 4 e Calculated partial phonon density of states for the a- and b-CaB2H2 phases at their equilibrium volume.
BaGa2H2 phases. It is quite true, for example, when we
compare the electronic structures of IVa group elements
(C, Si, Ga, Sn and Pb) in the Periodic table, they changes from
insulator-to-semiconductor-to-metallic nature one go down
in the Periodic table. The reason is that, the outermost
electrons in C are less diffuse in nature than that in the Pb
case and as a consequence of that it has strong covalent
bond with the neighbors.
4.
Single crystal elastic constants and
mechanical stability
In order to understand the mechanical stability of the predicted phases, we have computed the elastic constants from
Fig. 5 e The calculated total electronic density of states for
the a- and b-CaB2H2 phases at their equilibrium volume.
The Fermi level is set at zero energy and marked by the
vertical dotted line.
linear response DFPT calculations. The elastic constants of
a material describe its response to an applied stress or,
conversely, the stress required to maintain a given deformation. Both stress and strain have three tensile and three shear
components, giving six components in total. The linear elastic
constants form a 6 6 symmetric matrix, having 27 different
components and 21 of which are independent. However, any
symmetry presented in the structure may reduce the number
of these components. For an orthorhombic crystal, the independent elastic stiffness tensor reduces to nine components
C11, C22, C33, C44, C55, C66, C12, C13 and C23 in the Voigt notation
[50]. The well-known Born stability criteria [51] for an
orthorhombic system are
B1 ¼ C11 þ C22 þ C33 þ 2ðC12 þ C13 þ C23 Þ> 0
(1)
B2 ¼ C11 þ C22 2C12 > 0
(2)
B3 ¼ C11 þ C33 2C13 > 0
(3)
B4 ¼ C22 þ C33 2C23 > 0
(4)
The calculated independent single crystalline elastic stiffness constants for a-CaB2H2 are given in Table 2. The
computed B1, B2, B3, and B4 values for the a-CaB2H2 are 642,
212, 220, and 54 GPa, respectively. All the four conditions for
mechanical stability given in Eqs. (1)e(4) are simultaneously
satisfied and this clearly indicates that the predicted a-phase
is mechanically stable phase.
For the predicted trigonal phase has seven independent
single crystalline elastic constants such as C11 ¼ C22, C12,
C13 ¼ C23, C14 ¼ C24, C56, C33, C44 ¼ C55, and C66. All these values
are calculated and listed in Table 2. If a crystal is mechanically
stable, then the elastic-wave energy is positive. This is
equivalent to having the elastic constant matrix be positive
and definite. According to the mechanical Born stability
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Table 2 e The calculated single crystal elastic constants Cij
(in GPa), bulk modulus B0 (in GPa), and compressibility
(GPaL1) for CaB2H2 polymorphs.
Elastic constants (Cij)
Bulk modulus (in GPa)
Young’s modulus (in GPa)
Compressibility (in 1/GPa)
b-CaB2H2
a-CaB2H2
Properties
C11 ¼ 234
C12 ¼ 47
C13 ¼ 42
C22 ¼ 72
C23 ¼ 44
C33 ¼ 70
C44 ¼ 27
C55 ¼ 47
C66 ¼ 38
56.6
200 (along x)
41.9 (along y)
41.8 (along z)
0.018
C11
C12
C13
C14
C33
C44
C66
¼
¼
¼
¼
¼
¼
¼
183
88
52
27
172
111
48
101
122 (along x and y)
152 (along z)
0.00988
criteria for trigonal structure there are various constraints in
its elastic constants which are given by Eqs. (5)e(7) [51].
constants and the calculated values are tabulated in Table 2.
There is strong anisotropy in the calculated Young modulus
(four times larger along x direction compared with y and z
directions) in the a-phase and this is associated with the
presence of one dimensional borohydride chains in this
phase. In general, even though complex hydrides are having
very strong metal-hydrogen bond, they are having very low
bulk modulus compared with that in intermetallics and
oxides. This is partially due to the weaker bonding interaction
between the cations and the complexes. Hence, generally
these hydrides can be considered as soft materials and easily
compressible. On the other hand the present hydride has
much higher bulk modulus and lower compressibility than
the other borohydrides we have investigated so far. The
possible reason for such higher hardness can be explained by
the stronger BeB interaction. In general, most of the complex
hydrides, there is strong chemical bond present in between
the metal and H within the local molecular-like units. In
contrast, there is no such strong bonding interaction present
between the molecular-like units in a-CaB2H2. On the other
hand, in b-CaB2H2 the BeB interaction is present along the ac
plane and it has a two dimensional network (see Fig. 1b).
B1 ¼ C11 jC12 j > 0
(5)
B2 ¼ ðC11 þ C12 ÞC33 2C213 > 0
(6)
5.
B3 ¼ ðC11 C12 ÞC44 2C214 > 0
(7)
In general, the prepared samples from various methods often
contain more than one phase (mixed phases), and in such
situations we can use the theoretically simulated spectra such
as Raman, IR and NMR to distinguish different phases within
the sample. So, the theoretical studies on spectroscopic
properties of materials will be complementary to experimental studies to characterize contaminated or multiphase
samples. In connection with that we have simulated the
Raman and IR spectra and NMR related parameters like
isotropic chemical shielding (siso), quadrupolar coupling
constant (CQ), and quadrupolar asymmetry parameter (hQ) for
this newly predicted a- and b-phases of CaB2H2. Theoretically
simulated Raman and IR spectra for a- and b-CaB2H2 are
shown in Fig. 6. Due to the symmetry changes both a- and bphases have considerably different Raman and IR spectra.
The lower symmetry a-phase has several Raman and IR
The first criterion ensures stability with respect to the elastic
deformation in the xy plane. The second condition is related to
the dilatations and ensures a positive compressibility. The
third condition is associated with shear deformations in planes
different from xy plane. The computed B1, B2 and B3 values for
b-CaB2H2 in its equilibrium volume are 94.92, 41,116.17, and
9074.39 GPa, respectively. All the three conditions given in Eqs.
(5)e(7) are simultaneously satisfied and this clearly indicates
that, similar to the a-phase, the predicted b-phase is also
mechanically stable. Like the elastic constant tensor, the bulk
and shear moduli contain information regarding the hardness
of a material with respect to various types of deformation.
Properties such as bulk moduli, shear moduli, Young’s moduli
and Poisson’s ratio can be computed from the values of elastic
Spectroscopic studies
Fig. 6 e Theoretically simulated Raman (left) and IR (right) spectra for the CaB2H2 phases. The corresponding symmetry of
the Raman and IR active modes are marked in the figure.
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Table 3 e The calculated Raman and IR frequency (in cmL1) for the modes at the G point of the Brillouin zone for CaB2H2
phase. Computed NMR parameters such as isotropic chemical shielding (siso; in ppm), quadrupolar coupling constant (CQ;
in MHz), and quadrupolar asymmetry (hQ) parameters for the CaB2H2 phases.
Compound
a-CaB2H2
b-CaB2H2
Raman active modes
A1: 125, 270, 295, 453, 752,
785, 1002, 2059, 2151.
A2: 165, 222, 853, 1052, 1200.
B1: 167, 284, 313, 487, 776,
787, 978, 2077, 2157.
B2: 266, 856, 1049, 1208.
Eg: 538; 1354
A1g: 759; 2350
IR active modes
NMR
atom
siso (ppm)
CQ (MHz)
hQ
A1: 125, 270, 295, 453, 752,
785, 1002, 2059, 2151.
B1: 167, 284, 313, 487, 776,
787, 978, 2077, 2157.
B2: 266, 856, 1049, 1208.
Ca
B1
B2
H1
H2
1112
45
31
28
27
1.8
2.2
2.1
0.1
0.09
0.88
0.92
0.74
0.04
0.04
A2u: 307; 2775
Eu: 337; 1242
Ca
B
H
1004
91
34
0.062
0.31
0.103
0.0
0.0
0.0
peaks and the frequencies for all these peaks are listed in
Table 3. However, the high symmetry b-phase has well
separated 4 Raman (two Eg and two A1g modes) and 4 IR (two
Eu and two A2u) active modes. The calculated values of siso,
CQ, and hQ for both the polymorphs are displayed in Table 3.
The calculated siso value for Ca atom scattered between 1004
and 1112 ppm, that for the B atom between 31 and 91 ppm,
and for H atom from 27 to 34 ppm. It should be noted that
the calculated siso values cannot be compared directly to the
experimental values. Because, the calculated values are
corresponding to absolute chemical shielding, whereas,
most experimental siso values are usually reported with
shifts relative to a known standard. However, the direct
comparison between experiment and theory can be made
on comparative shifts between the different peaks. For
example, in a- polymorph the B1 and B2 atoms are shifted
14 ppm relative to each other and in contrast, the chemical
shift peaks corresponding to H1, and H2 peaks are spread in
a narrow region. Similarly, the CQ and hQ values are also
scattered in wide range and these values are directly
comparable with experimental values. We believe that the
present study motivate experimentalists to perform NMR
measurements for the polymorphs of CaB2H2.
6.
Chemical bonding
The a- and b-CaB2H2 exhibit similar features and in view of that
we have only documented the charge density and ELF plots for
b-CaB2H2. Fig. 7 and b show the charge density distribution at
the Ca, B, and H sites, from which it is evident that the
highest charge density resides in the immediate vicinity of
the nuclei. Further, the spherical charge distribution shows
that the bonding interactions between CaeH and CaeB have
predominantly ionic character. On the other hand, in the
interactions between BeH and BeB are predominantly
directional characters. The substantial difference in the
electronegativity between Ca and B/H suggests the presence
Fig. 7 e The calculated valence electron charge density distribution (a and b) and ELF (c and d) for the b-CaB2H2 phase.
10156
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 0 1 4 9 e1 0 1 5 8
of strong ionic character (i.e., the Ca valence electrons
transferred to the H/B sites) and the small difference in the
electronegativity between B and H suggests the presence of
strong covalent character.
The calculated ELF plot (Fig. 7c and d; for more details about
ELF see Refs. [52e54]) shows a maximum of ca. 1 at the H and
Ca sites as well as in between two B atoms and these electrons
have a paired character. The inference from this observation
is that charges are transferred from the Ca sites to the H and
B sites and there are certainly very few paired valence
electrons left at the Ca sites. A certain polarized character is
found in the ELF distribution at the H sites in most of the
complex hydrides. Similarly, in the CaB2H2 phases also the
ELF distribution is not spherically symmetric at the H site.
But the polarization is considerably lower in CaB2H2 phases
than that in boron and aluminum based complex hydrides.
In order to quantify the bonding and estimate the amount
of electrons on and between the participating atoms we have
made Mulliken-population analysis. Although there is no
unique definition to identify how many electrons are associated with an atom in a molecule or an atomic grouping in
a solid, it has nevertheless proved useful in many cases to
perform population analyses. Due to its simplicity, the Mulliken-population [55] scheme has become the most popular
approach. However, the method is more qualitative than
quantitative, providing results that are sensitive to the
atomic basis. The calculated Mulliken charges are reported
in Table 4 for CaB2H2 polymorphs. For the studied CaB2H2
polymorphs the MEC value for the Ca is vary from þ1.49 to
þ1.67e (minimum in b-phase and maximum in a-phase).
This finding is consistent with the charge density analyzes
and the magnitude of the MEC shows that Ca does not
completely donate its two valence electrons to the B and H
atoms, which is much smaller than in a pure ionic picture.
To understand the bonding interaction between the
constituents the bond overlap population (BOP) values are
calculated on the basis of Mulliken-population analysis. The
BOP values can provide useful information about the bonding
property between atoms. A high BOP value indicates a strong
covalent bond, while a low BOP value indicates an ionic
interaction. The calculated BOP values for the CaB2H2 polymorphs are displayed in Table 4. The BOP values for the CaeB
bonds in the calculated two structures vary between 0.02
and 0.12. Similarly, the calculated BOP values for the BeH
bonds vary between 0.49 and 0.83. Therefore, the CaeB
bonds in these hydrides have dominant ionic character,
Table 4 e Mulliken-population charge density analysis
for CaB2H2 polymorphs and the bond overlap population
is denoted as BOP. The Mulliken-effective charges (MEC)
are given in terms of e.
Compound
a-CaB2H2
b-CaB2H2
Element
MEC
BOP
Ca
B
H
Ca
B
H
þ1.67
0.57
0.27
þ1.49
0.49
0.25
2.2 (BeB)
0.83 (BeH)
0.12 (CaeB)
0.83 (BeB)
0.49 (BeH)
0.02 (CaeB)
whereas the BeH, and BeB interactions have noticeable
covalent character. When we compare the BOP values for the
different bonding interaction between atoms in a- and
b-phases; overall the bonding interactions are much stronger
in a-CaB2H2 and relatively weaker in b-CaB2H2. This finding is
in contrast to the bulk modulus calculation where the
calculated bulk modulus is much higher in b-phase and
minimum in a-phase. The possible reason is that, in the a-phase,
even though the BeB and BeH interactions are relatively
stronger, the basic structure is one dimensional. On the other
hand, in b-phase, the B atoms are arranged in a stronger 6 ring
configuration. Moreover, the equilibrium volume for the
b-phase is much smaller than that of a-CaB2H2 and this could
explain the higher value of bulk modulus in b-phase.
7.
Conclusion
The structural phase stability, electronic structure, thermodynamical, mechanical and spectroscopic properties of
CaB2H2 in two different polymorphs have been studied by
state-of-the-art density-functional calculations. The groundstate crystal structure and equilibrium structural parameters
of two polymorphs of CaB2H2 have been predicted from
structural optimization with 22 distinct structures as input
using force as well as stress minimizations. At ambient
condition CaB2H2 crystallizes in orthorhombic phase and at
10.8 GPa pressure it transform in to trigonal structure (space
group P-3m1). The phonon density of states at the equilibrium
volume for these two different polymorphs of CaB2H2 are
calculated by using perturbation theory and found that
the predicted phases are dynamically stable. Similarly, the
calculated single crystal elastic constants revealed that the
predicted phases have fulfilled the mechanical stability
criteria. For the experimental verification in future, we have
simulated the Raman and IR spectra, and calculated the NMR
related parameters such as isotropic chemical shielding,
quadrupolar coupling constant, and quadrupolar asymmetry.
The calculated electronic structures reveal that both phases
are indirect band gap semiconductor with estimated band gap
of 0.32 and 1.98 eV for a-CaB2H2 and b-CaB2H2, respectively.
Acknowledgments
The authors gratefully acknowledge the Research Council of
Norway 460829 and European Union seventh frame work
program under the “NanoHy” (Grant agreement no.: 210092)
project for financial support. PV acknowledges the Research
Council of Norway for providing the computer time at the
Norwegian supercomputer facilities and M.D Riktor for useful
communications.
references
[1] Zidan RA, Takara S, Hee AG, Jensen CM. Hydrogen cycling
behavior of zirconium and titaniumezirconium-doped
sodium aluminum hydride. J Alloys Compd 1999;285:119e22.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 0 1 4 9 e1 0 1 5 8
[2] Zaluski L, Zaluska A, Ström-Olsen JO. Hydrogenation
properties of complex alkali metal hydrides fabricated
by mechano-chemical synthesis. J Alloys Compd 1999;290:
71e8.
[3] Gross KJ, Guthrie S, Takara S, Thomas G. In-situ X-ray
diffraction study of the decomposition of NaAlH4. J Alloys
Compd 2000;297:270e81.
[4] Bogdanovic B, Brand RA, Marjanvi A, Schwickardi M, Tölle J.
Metal-doped sodium aluminium hydrides as potential
new hydrogen storage materials. J Alloys Compd 2000;302:
36e58.
[5] Jensen CM, Gross KJ. Development of catalytically enhanced
sodium aluminum hydride as a hydrogen-storage material.
Appl Phys A Mater Sci Pro 2001;72:213e9.
[6] Sun D, Kiyobayashi T, Takeshita H, Kuriyama N, Jensen CM.
X-ray diffraction studies of titanium and zirconium doped
NaAlH4: elucidation of doping induced structural changes
and their relationship to enhanced hydrogen storage
properties. J Alloys Compd 2002;337:L8e11.
[7] Meisner GP, Tibbetts GG, Pinkerton FE, Olk CH, Balog MP.
Enhancing low pressure hydrogen storage in sodium
alanates. J Alloys Compd 2002;337:254e63.
[8] Sandrock G, Gross K, Thomas G. Effect of Ti-catalyst content
on the reversible hydrogen storage properties of the sodium
alanates. J Alloys Compd 2002;339:299e308.
[9] Morioka H, Kakizaki K, Chung SC, Yamada A. Reversible
hydrogen decomposition of KAlH4. J Alloys Compd 2003;353:
310e4.
[10] Lee SH, Manga VR, Liu ZK. Effect of Mg, Ca, and Zn on
stability of LiBH4 through computational thermodynamics.
Int J Hydrogen Energ 2010;35:6812e21.
[11] Løvvik OM, Swang O, Opalka SM. Modeling alkali alanates for
hydrogen storage by density-functional band-structure
calculations. J Mater Res 2005;20:3199e213.
[12] Herbst Jr JF, Hector LG. Energetics of the Li amide/Li imide
hydrogen storage reaction. Phys Rev B 2005;72:125120.
[13] Vajeeston P, Ravindran P, Kjekshus A, Fjellvåg H. Structural
stability of alkali boron tetrahydrides ABH4 (A ¼ Li, Na, K, Rb,
Cs) from first principle calculation. J Alloys Compd 2005;387:
97e104.
[14] Fichtner M, Fuhr O, Kircher O. Magnesium alanateda
material for reversible hydrogen storage? J Alloys Compd
2003;356e357:418e22.
[15] Alapati SV, Johnson JK, Sholl DS. Large-scale screening of
metal hydride mixtures for high-capacity hydrogen storage
from first-principles calculations. J Phys Chem C 2008;112:
5258e62.
[16] Frankcombe TJ, Kroes GJ. Quasi harmonic approximation
applied to LiBH4 and its decomposition products. Phys Rev B
2006;73:174302.
[17] Frankcombe TJ, Kroes GJ. The HeD isotope effect in
the stability of lithium alanate. Chem Phys Lett 2006;423:
102e5.
[18] Weidenthaler C, Frankcombe TJ, Felderhoff M. First
crystal structure studies of CaAlH5. Inorg Chem 2006;45:
3849e51.
[19] Marashdeh A, Frankcombe TJ. Ca(AlH4)2, CaAlH5, and
CaH2þ6LiBH4: calculated dehydrogenation enthalpy,
including zero point energy, and the structure of the phonon
spectra. J Chem Phys 2008;128:234505.
[20] Riktor MD, Sørby MH, Chlopek K, Fichtner M, Buchter F,
Züttel A, et al. In situ synchrotron diffraction studies of
phase transitions and thermal decomposition of Mg(BH4)2
and Ca(BH4)2. J Mater Chem 2007;17:4939e42.
[21] Kim Y, Reed D, Lee Y-S, Lee JY, Shim J-H, Book D, et al.
Identification of the Dehydrogenated product of Ca(BH4)2.
J Phys Chem C 2009;113:5865e71.
[22] Riktor MD, Sørby MH, Chlopek K, Fichtner M, Hauback BC.
The identification of a hitherto unknown intermediate phase
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
10157
CaB2Hx from decomposition of Ca(BH4)2. J Mater Chem 2009;
19:2754e9.
Kim J-H, Jin S-A, Shim J-H, Cho YW. Thermal decomposition
behavior of calcium borohydride Ca(BH4)2. J Alloys Compd
2008;461:L20e2.
Wang L-L, Graham DD, Robertson IM, Johnson DD. On the
reversibility of hydrogen-storage reactions in Ca(BH4)2:
characterization via experiment and theory. J Phys Chem C
2009;113:20088e96.
Rongeat C, Lindemann I, Borgschulte A, Schultz L,
Gutfleisch O. Effect of the presence of chlorides on the
synthesis and decomposition of Ca(BH4)2. Int J Hydrogen
Energ 2011;36:247e53.
Rönnebro E, Majzoub EH. Calcium borohydride for hydrogen
storage: catalysis and reversibility. J Phys Chem B 2007;111:
12045.
Barkhordarian G, Klassen T, Dornheim M, Bormann R.
Unexpected kinetic effect of MgB2 in reactive hydride
composites containing complex borohydrides. J Alloys
Compd 2007;440:L18.
Aoki M, Miwa K, Noritake T, Ohba N, Matsumoto M, Li H-W,
et al. Structural and dehydriding properties of Ca(BH4)2. Appl
Phys A Mater Sci Pro 2008;92:601e5.
Blöchl PE. Projector augmented-wave method. Phys Rev B
1994;50:17953e79.
Kresse G, Joubert J. From ultrasoft pseudopotentials to the
projector augmented-wave method. Phys Rev B 1999;59:
1758e75.
Kresse G, Hafner J. Ab initio molecular dynamics for liquid
metals. Phys Rev B 1993;47:558e61.
Kresse G, Furthmuller J. Efficiency of ab-initio total
energy calculations for metals and semiconductors
using a plane-wave basis set. Comput Mater Sci 1996;6:
15e50.
Perdew JP, Burke S, Ernzerhof M. Generalized gradient
approximation made simple. Phys Rev Lett 1996;77:3865e8.
Perdew JP, Chevary JA, Vosko SH, Jackson KA,
Pederson MR, Singh DJ, et al. Atoms, molecules, solids, and
surfaces: applications of the generalized gradient
approximation for exchange and correlation. Phys Rev B
1992;46:6671e87.
Refsen K, Clark SJ, Tulip PR. Variational density-functional
perturbation theory for dielectrics and lattice dynamics. Phys
Rev B 2006;73:155114.
Clark SJ, Segall MD, Pickard CJ, Hasnip PJ, Probert MJ,
Refson K, et al. First principles methods using CASTEP. Z
Fuer Krist 2005;220:567e70.
Vajeeston P, Ravindran P, Fjellvåg H, Kjekshus A. Crystal
structure of KAlH4 from first principle calculations. J Alloys
Compd 2003;363:L8e12.
Skriver HL. Crystal structure from one-electron theory. Phys
Rev B 1985;31. 1909e23.
Söderlind P, Eriksson O, Johansson B, Wills JM, Boring AM. A
unified picture of the crystal structures of metals. Nature
1995;374:524e5.
Inorganic crystal structure database, vol. 2. Germany: Gmelin
Institut; 2006.
Gingl F, Vogt T, Akiba E. Trigonal SrAl2H2: the first Zintl phase
hydride. J Alloys Compd 2000;306:127e32.
Björling T, Norèus D, Häussermann U. Polyanionic hydrides
from Polar intermetallics AeE2(Ae ¼ Ca, Sr, Ba; E ¼ Al, Ga, in).
J Am Chem Soc 2006;128:817e24.
Souvatzis P, Eriksson O, Katsnelson MI, Rudin SP. Entropy
driven stabilization of energetically unstable crystal
structures explained from first principles theory. Phys Rev
Lett 2008;100:095901.
Boese AD, Handy NC. A new parametrization of
exchangeecorrelation generalized gradient approximation
functionals. J Chem Phys 2001;114:5497.
10158
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 0 1 4 9 e1 0 1 5 8
[45] Vajeeston P, Ravindran P, Kjekshus A, Fjellvåg H. Pressureinduced structural transitions in MgH2. Phys Rev Lett 2002;
89:175506.
[46] Pfrommer B, Elsässer C, Fähnle M. Possibility of LieMg and
AleMg hydrides being metallic. Phys Rev B 1994;50:5089e93.
[47] Orgaz E, Aburto A. Bonding properties of the new Zintl-phase
hydrides. Int J Quantum Chem 2005;101:783e92.
[48] Lee MH, Sankey OF, Björling T, Moser D, Norèus D, Parker SF,
et al. Vibrational properties of polyanionic hydrides SrAl2H2
and SrAlSiH: new insight into AleH bonding interactions.
Inorg Chem 2007;46:6987e91.
[49] Subedi A, Singh DJ. Bonding in Zintl phase hydrides: density
functional calculations for SrAlSiH, SrAl2H2, SrGa2H2, and
BaGa2H2. Phys Rev B 2008;78:045106.
[50] Ravindran P, Fast L, Korzhayyi PA, Johansson B, Wills JM,
Eriksson O. Density functional theory for calculation of
[51]
[52]
[53]
[54]
[55]
elastic properties of orthorhombic crystals: application to
TiSi2. J Appl Phys 1998;84:4891e904.
Fedorov FI. Theory of elastic waves in crystals. New York:
Plenum; 1968. pp. 33.
Savin A, Becke AD, Flad J, Nesper R, Preuss H, von
Schnering HG. A new look at electron localization. Angew
Chem Int Ed Engl 1991;30:409e12.
Becke AD, Edgecombe KE. A simple measure of electron
localization in atomic and molecular systems. J Chem Phys
1990;92:5397e403.
Silvi B, Savin A. Classification of chemical bonds based on
topological analysis of electron localization functions.
Nature (London) 1994;371:683e6.
Mulliken RS. Electronic population analysis on
LCAO-MO molecular wave functions. J Chem Phys 1955;23:
1833e40.