APPLIED PHYSICS LETTERS
VOLUME 84, NUMBER 1
5 JANUARY 2004
Structural stability of BeH2 at high pressures
P. Vajeeston, P. Ravindran,a) A. Kjekshus, and H. Fjellvåg
Department of Chemistry, University of Oslo, Box 1033 Blindern, N-0315 Oslo, Norway
共Received 4 September 2003; accepted 11 November 2003兲
The electronic structure and structural stability of BeH2 are studied using first-principles
density-functional calculation. The calculated structural parameters for ␣ -BeH2 at the equilibrium
volume are in very good agreement with experiments. At higher pressures ␣ -BeH2 successively
undergoes four structural transitions: 共i兲 ␣- to ␤ -BeH2 at 7.07 GPa; 共ii兲 ␤- to ␥ -BeH2 at 51.41 GPa;
共iii兲 ␥- to ␦ -BeH2 at 86.56 GPa; and 共iv兲 ␦- to ⑀ -BeH2 at 97.55 GPa 关an effective two-phase 共␥ and
␦兲 region is found at 73.71– 86.56 GPa兴. Density of states studies reveal that BeH2 remains
insulating up to 100 GPa whereupon anomalous changes are seen in the band-gap region with
increasing pressure. © 2004 American Institute of Physics. 关DOI: 10.1063/1.1637967兴
Metal hydrides are of great scientific and technological
interest in view of their potential applications, e.g., for hydrogen storage, in fuel cells and internal combustion engines,
as electrodes for re-chargeable batteries, and in energyconversion devices. Hydrides for hydrogen storage need to
be able to form hydrides with a high hydrogen-to-metal mass
ratio, but should not be too stable, so that the hydrogen can
easily be released without excessive heating. Beryllium and
magnesium and beryllium-magnesium-based hydrides contain a relatively high fraction of hydrogen by weight, but
need to be heated to at least 250 to 300 °C in order to release
the hydrogen. An improved understanding of the stability of
metal hydrides is a key to rationally investigate and design
potential hydrogen-storage materials.
The alkali–metal and alkaline–earth–metal hydrides
represent series with largely ionic bonding. The highpressure behavior of the alkali–metal monohydrides is expected to parallel that of the alkali–metal halides.1 However,
there is no systematic high-pressure study on the alkaline–
earth–metal hydrides. The incorporation of hydrogen into
metals as a means to enhance superconductivity is an interesting aspect. For example, PdH exhibits superconductivity
with a transition temperature of ⬃10 K whereas superconductivity is absent in Pd.2 Owing to low mass and high electron density, ‘‘metallic hydrogen’’ has been predicted to
show superconductivity with a transition temperature between 140 and 260 K.3 For example, if BeH2 becomes metallic when subjected to high pressures one can entertain the
possibility that its properties could resemble those of metallic hydrogen. This was another motive for the present highpressure study of BeH2 .
BeH2 is commonly considered a covalent hydride with a
postulated polymeric crystal structure made up of H-bridged
chains. However, mainly owing to experimental difficulties
in the synthesis of the material, the structure has long remained unknown.4 Recently, crystalline BeH2 has been synthesized and the structure has been established as bodycentered orthorhombic by synchrotron-radiation-based
powder x-ray diffraction.5 No electronic structure calculation
is available for this particular phase.
To examine the structural stability of BeH2 , we have
a兲
Electronic mail: ponniah.ravindran@kjemi.uio.no
used density-functional theory 共DFT兲6 within the generalized
gradient approximation 共GGA兲,7 as implemented with a
plane-wave basis in the Vienna ab initio simulations package
共VASP兲.8 Results are obtained using projector-augmented
plane-wave 共PAW兲9 potentials provided with the VASP. The
ions are relaxed toward equilibrium until the Hellmann–
Feynman forces are less than 10⫺3 eV/Å. Brillouin zone
integration are performed with a Gaussian broadening of 0.1
eV during all relaxations. For the BeH2 -type structure, we
have performed the calculations with 512 k points in the
whole Brillouin zone and a 600 eV plane-wave cutoff. In
order to avoid ambiguities regarding the free-energy results
we have always used the same energy cutoff and a similar
k-grid density for convergence for all structural variants
studied. The present type of theoretical approach has recently
been successfully applied10,11 to reproduce ambient- and
high-pressure phases computationally.
For our theoretical simulation we have considered 24
different types of structural variants. The involved structure
FIG. 1. Cell volume per formula unit vs free energy for BeH2 in different
possible structural modifications. In order to keep the illustration reasonable
simple only results for the 15 most relevant structure types are shown. The
remaining variants are found at higher energies and are not included in the
illustration. Transition points are marked with arrows, the letters 共a兲–共d兲
correspond to those in Fig. 2.
0003-6951/2004/84(1)/34/3/$22.00
34
© 2004 American Institute of Physics
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Appl. Phys. Lett., Vol. 84, No. 1, 5 January 2004
Vajeeston et al.
35
FIG. 3. Calculated total density of state for ␣-, ␤-, ␥-, ␦-, and ⑀ -BeH2 .
Partial DOSs of H1 and Be1 in ␣ -BeH2 are shown in the inset.
FIG. 2. Calculated 共a兲 pressure vs volume relationship and 共b兲 stability
diagrams for hypothetical BeH2 phases 共difference in Gibbs free energy
⌬G) relative to ␣ -BeH2 . Transition points are marked by arrows, the letters
共a兲–共d兲 correspond to those in Fig. 1.
types are BeH2 , MnF2 , XeF2 , KF2 , NaF2 , SnF2 , LiF2 ,
BeF2 , PdF2 , MgF2 , HfH2 , ␥ -SnF2 , TiO2 (anatase),
TiO2 (brookite), TiO2 (rutile), modified CaF2 , ␣ -PbO2 ,
␦ -MgH2 , AlAu2 , InNi2 , TeAg2 , CaF2 , AuSn2 , and
CaCl2 . 12 Among the 24 structure types considered here, the
experimentally observed BeH2 modification has the lowest
total energy 共see Fig. 1兲 and the calculated structural parameters are also in very good agreement with the observations.
The calculated cell parameters differ by less than 1% from
the experimental values, which again confirm that the present
type of calculation is reliable and accurate. This bodycentered orthorhombic unit cell contains twelve BeH2 formula units and the primitive cell six formula units. Both Be
and H occupy two different types of sites 共see Table I兲. The
structure consists of BeH4 tetrahedra linked by hydrogens at
the corners, and there exists no known analog among other
compounds with tetrahedral building blocks. The packing in
the structure is not especially dense; consequently it is anticipated that it should be possible to produce a form with
higher density. When ␣ -BeH2 is exposed to external pres-
sures it transforms to the denser TiO2 (anatase)-type,
␤ -BeH2 modification. The calculated total energy versus
volume relation in Fig. 1 shows that several pressure-induced
structural transitions occur in BeH2 upon increasing pressure. Since it may be hard to identify the transition points
from Fig. 1, Fig. 2共a兲 gives the calculated pressure–volume
relation, and Fig. 2共b兲 gives the Gibbs free energy difference
relative to ␣ -BeH2 for the pressure-induced structural arrangements under consideration.
The application of pressure 共Fig. 2兲 transforms ␣- to
␤ -BeH2 at 7.07 GPa with a calculated volume discontinuity
at the transition point of ca. 19.2%; ca. 26.4% equilibrium
volume difference at ambient pressure 共the corresponding
energy difference being ⬃0.4 eV). Such a huge pressureinduced volume collapse is rather uncommon among hydrides as well as inorganic compounds in general. However,
large volume collapses 共9 to 20%兲 under pressure are observed for lanthanides and actinides associated with valence
transition or localized-to-delocalized transition of f electrons. In LiAlH4 there has also been established an unexpectedly large 共17%兲 volume collapse at a structural transition
point.13 ␤ -BeH2 remains stable over a wide pressure range
共7.07–51.41 GPa兲. At 51.41 GPa ␤ -BeH2 transforms to the
␥ modification with a CaCl2 -type structure which in turn is
converted into an effective two-phase region with the coexistence of ␥ -BeH2 and TiO2 (rutile)-type ␦ -BeH2 , at 73.71
GPa which is then converted into a single-phase region of
␦ -BeH2 共86.56 to 97.55 GPa兲. Above 97.55 GPa ␦ -BeH2 is
transformed to the PdF2 -type ⑀ modification. In the pressure
range 10 to 75 GPa ␤-, ␥-, and ␦ -BeH2 fall within a narrow
energy range of some 10 meV 共Fig. 1兲 and above 97.55 GPa
␤-, ␥-, ␦-, and ⑀ -BeH2 all fall in a similar narrow energy
range. This closeness in energy suggests that the relative appearance of these modifications will be quite sensitive to,
and easily affected by, other external factors like temperature
and remnant lattice stresses. Several pressure-induced structural modifications are predicted11 for the iso-electronic compound MgH2 共recently also verified by high-pressure
experiments14兲. However, the structural transition sequences
in BeH2 and MgH2 are entirely different,11 and quite different from the findings for the alkali-monohydride series15
where systematics in the pressure-induced phase transitions
has been observed.
The calculated values for the bulk modulus (B 0 ; see
Table I兲 vary between 23.79 and 94.74 GPa for the various
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36
Vajeeston et al.
Appl. Phys. Lett., Vol. 84, No. 1, 5 January 2004
TABLE I. Optimized structural parameters, bulk modulus (B 0 ), pressure derivative of bulk modulus (B ⬘0 ), and calculated energy band gap (E g ) for BeH2 in
different possible structural arrangements 共space group and structure types for the different phases are specified in parentheses兲. Unless otherwise specified
structure data refer to equilibrium.
Phase
␣ -BeH2
(Ibam)
␤ -BeH2 (I4 1 /amd;
TiO2 -anatase兲
␥ -BeH2
( Pnnm; CaCl2 )
␦ -BeH2 ( P4 2 /mnm;
TiO2 -rutile兲
⑀ -BeH2
( P2 1 3; PdF2 )
a
Cell constants 共Å兲
a⫽8.9823 共9.082兲
b⫽4.1563 共4.160兲a
c⫽7.6455 共7.707兲a
a⫽3.2178
c⫽6.7895
a⫽3.8427
b⫽3.8334
c⫽2.3003
a⫽3.8400
c⫽2.2986
a⫽3.9715
a
Coordinates
Be1 (4a) : 0, 0, 1/4; Be2 (8 j) : 0.1678, 0.1207, 0 共0.1699, 0.1253, 0兲
H1 (16k) : 0.0720, 0.1842, 0.1361 共0.0895, 0.1949, 0.1515兲a
H2 (8 j) : 0.3097, 0.2790, 0 共0.3055, 0.2823, 0兲a
Be (4a) : 0, 0, 0
H (8e) : 0, 0, 0.2281
Be (2a) : 0, 0, 0
H (4g) : 0.3054, 0.1964, 0 共0.2989, 0.2030, 0兲b
Be (2a) : 0, 0, 0
H (4 f ) : x, x, 0; x⫽0.3045 共0.2975兲b
Be (4a) : 0, 0, 0; H1 (4a) : x, x, x; x⫽0.3522 共0.3588兲b
H2 (4a) : x, x, x; x⫽0.6477 共0.6412兲b
a
B 0 共GPa兲
B 0⬘
E g 共eV兲
23.79
4.24
5.51
73.78
3.22
2.39
85.00
3.91
4.07
85.17
3.44
4.57
94.74
3.35
5.55
Experimentally observed values from Ref. 5 at ambient.
Atomic coordinates at the transition point.
b
structural arrangements. Among the five involved structure
variants ␣ -BeH2 shows the smallest B 0 value and the
⑀ -BeH2 the highest 共Table I兲, which appears to be a consequence of the variation in the equilibrium volumes 共monotonically decreasing from 23.79 Å 3 /f.u. for ␣ -BeH2 to
15.66 Å 3 /f.u. for ⑀ -BeH2 ).
The calculated total density of states 共DOS兲 for the different modifications of BeH2 共at the transition pressures for
␤-, ␥-, ␦-, and ⑀ -BeH2 and at the equilibrium volume for the
␣ phase兲 in Fig. 3 shows that all involved phases have a
nonmetallic character with finite band gaps (E g ). From ␣- to
␤ -BeH2 the calculated band gap is reduced from 5.51 to 2.39
eV, whereas from ␤- to ⑀ -BeH2 the estimated band gap is
drastically increased from 2.39 to 5.55 eV 共see Table I兲. In
isoelectronic MgH2 11 the estimated band gap is monotonically reduced on increasing pressure. The variation in the
band gap established for the BeH2 phases certainly is not
common, but has for example been established for WO3 , 16
where the findings have been attributed to the tilting of octahedra in the pressure modifications. The calculated
valence-band width is increased from 6.5 eV in ␣ -BeH2 to
21.2 eV in the ⑀ phase, which may be attributed to the reduction in the bonding interatomic distances upon increasing
pressure. Usually the hydrides of alkali and alkaline–earth
metals have ionic bonding which reflects the low ionization
energy of these metals. For example, LiH is a wide-gap insulator with the H-1s band ca. 5 eV below the Li-2s conduction band.17 In a hypothetical simplified ionic picture for
BeH2 the Be valence electrons would have been transferred
to the H atoms, but the calculated DOS shows that Be-2s
and H-1s states are energetically degenerate in the energy
range ⫺6.25 to 0 eV 共see the inset of Fig. 3兲 and the valence
electron charge density 共not shown兲 confirms a finite electron
distribution between the Be and H atoms, viz. reflecting the
covalent interaction which is also responsible for the stabilization of the low symmetric structure of ␣ -BeH2 . Hence it is
not surprising that BeH2 significantly deviates from the other
alkaline–earth dihydrides. Contrary to the MgH2 phases
which gradually undergo conversion from ionic to more metallic character upon application of pressure, BeH2 changes
from covalent to ionic bonding character upon application of
pressure. This should explain why BeH2 behaves differently
from the rest of the alkaline–earth dihydride series.
In summary, BeH2 becomes unstable upon application of
pressure, and at higher pressures ␣ -BeH2 transforms to ␤-,
␥-, ␦-, and ⑀ -BeH2 . Up to 100 GPa BeH2 remains an insulator, hence the possibility of obtaining high-pressure phases
with superconducting properties is ruled out. There occurs a
huge volume collapse at the ␣-to-␤ phase transition and only
smaller volume changes at the ␤-to-␥, ␥-to-␦, and ␦-to-⑀
transitions. The band gap attains a minimum value at the
␤ -BeH2 phase.
The authors gratefully acknowledge the Research Council of Norway for financial support and for the computer time
at the Norwegian supercomputer facilities and R. Vidya for a
critical reading of the manuscript.
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