PHYSICAL REVIEW B 73, 224102 共2006兲
Structural stability and pressure-induced phase transitions in MgH2
P. Vajeeston,1,* P. Ravindran,1 B. C. Hauback,2 H. Fjellvåg,1,2 A. Kjekshus,1 S. Furuseth,1 and M. Hanfland3
1Department
of Chemistry, Center for Materials Sciences and Nanotechnology, University of Oslo,
Box 1033 Blindern, N-0315 Oslo, Norway
2
Institute for Energy Technology, N-2027 Kjeller, Norway
3European Synchrotron Radiation Facility, ESRF, BP 220, F-38043 Grenoble, France
共Received 26 October 2005; revised manuscript received 19 April 2006; published 2 June 2006兲
The structural stability of MgH2 has been studied up to 16 GPa using a high-pressure synchrotron x-ray
diffraction technique. Several pressure-induced phase transitions have been identified in this pressure range.
Owing to the close structural similarity between the ␣ and ␥ modifications the high-pressure ␥ form can be
stabilized as a metastable phase after pressure release. The experimentally observed structural transition sequence and the volume changes at the transition points as well as bulk modulii are found to be in good
agreement with theoretically calculated data. The bonding nature of MgH2 is analyzed with the help of
charge-density, charge-transfer, electron-localization-function, and Mulliken-population analyses which clearly
show that all polymorphs of MgH2 are to be classified as ionic materials with Mg and H in nearly 2⫹ and 1−
states, respectively.
DOI: 10.1103/PhysRevB.73.224102
PACS number共s兲: 71.20.⫺b, 71.15.Nc, 81.05.Je
I. INTRODUCTION
Hydrogen is considered to be one of the leading candidates for clean energy in the future. For safe and efficient
hydrogen storage, developments of new alloys are currently
being researched. Their hydrogen-storage capacity, reversibility, and desorption temperature and pressure are the most
important parameters for a storage material of practical interest. The hydrides ought to have a high hydrogen-to-metal
ratio and should not be too stable in order to achieve hydrogen release without excessive heating. Magnesium has as a
light metal already for decades attracted large attention owing to its large mass-adsorption capacity for hydrogen,
7.6wt. %. On this basis, magnesium and its alloys are promising materials for hydrogen storage. However, the high thermodynamic stability of the magnesium hydrides prevents dehydrogenation under mild conditions. Furthermore, the slow
cleavage of dihydrogen to atomic hydrogen and the low diffusion rate in MgH2 have prevented pure Mg from being a
real candidate material. In order to improve the hydrogenstorage properties of Mg-rich alloys, understanding of the
structural stability and bonding nature of MgH2 is considered
as essential.
Several steps have been discussed in the literature as rate
controlling for the hydrogen absorption and desorption processes. Improved kinetics has been found when Mg is mixed
with several metallic additives 共e.g., LaNi5, Pd, V, FeTi兲 and
ball milled.1–3 Therefore, recent attention has been paid to
the investigation of on specific material properties of Mg
alloys. In high-pressure syntheses of technologically important metal hydrides like Mg2NiH4, metastable ␥-MgH2 often
occurs as a by-product.4 Hence, a complete study of MgH2
including its stability at high pressures is desirable. Preparation of the MgH2, which is an electrical insulator, occurs
essentially at high temperatures 共⬎440 ° C兲 and high hydrogen pressures 共⬎30 atm兲.5 From the structural point of view
MgH2 is less stable 共easily changing from one polymorph to
another under the influence of pressure and temperature兲 than
other dihydrides such as those of the rare earths and other
saline hydrides like CaH2, SrH2 and BaH2.6 Recently we
1098-0121/2006/73共22兲/224102共8兲
have demonstrated by theoretical methods that the structural
stability of MgH2 highly depends on pressure, ␣-MgH2
transforming into four other modifications on application of
pressure.7 The theoretical findings have motivated the herereported high-pressure x-ray diffraction study. The positions
of the hydrogen atoms in metal hydrides should really be
determined by neutron diffraction since the scattering power
of hydrogen is too weak for an accurate determination by
x-ray diffraction. However, high-pressure neutron-diffraction
experiments face other difficulties which we could not cope
within this work. The aim of the present study has been to
remedy this situation by examining the high-pressure forms
of MgH2 by synchrotron-radiation-based x-ray diffraction
and with the knowledge of structure type, unit-cell dimensions, and the establish H positions by theoretical means.
Furthermore, the chemical nature of the polymorphs is considered in some detail using first-principles densityfunctional theory 共DFT兲 calculations.
II. EXPERIMENTAL AND COMPUTATION DETAILS
A. Synthesis
Magnesium powder was activated by heating at 450 ° C
under dynamical vacuum. After cooling to room temperature,
hydrogen was introduced at a pressure of 5 bars and the
temperature was then increased to 365 ° C under this hydrogen pressure. At 365 ° C the pressure was increased to 20
bars, and the sample was kept under these conditions for
about 12 h. The 20-bar hydrogen pressure was maintained
during the cooling of the sample to room temperature and
then released.
B. High-pressure experiments and data analyses
Angle-dispersive powder x-ray diffraction 共XRD兲 diagrams were collected at the ID9 beamline of the European
Synchrotron Radiation Facility, Grenoble 共␭ = 0.4176 Å,
x-ray beam size 30⫻ 30 ␮m2, sample distance 365 mm兲, using image plate detection. Integrated intensities were ob-
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PHYSICAL REVIEW B 73, 224102 共2006兲
VAJEESTON et al.
TABLE I. Experimentally observed and theoretically calculated 共in parentheses兲 structural parameters, bulk modulus 共B0兲, and pressure
derivative of bulk modulus 共B⬘0兲 for MgH2 in ambient and high-pressure phases.
␣, TiO2-rutile 共P42 / mnm兲
␤, Modified CaF2 共Pa3̄兲
PdF2–type
␥, ␣-PbO2 共Pbcn兲
␦⬘; AuSn2 共Pbca兲
Positional parameters
B0 共GPa兲
B⬘0
3.0206
3.0205a
2.9993兲
4.6655
Mg 共2a兲: 0, 0, 0
H 共4f兲: 0.304a, 0.304a, 0a 共0.3043, 0.3043, 0兲
45± 2
共55兲b; 共50兲c
共51兲
47.41± 4
3.35± .3
共3.45兲
3.49± 0.4
4.7902兲
4.9285
4.9168d
4.8985兲
4.3699
4.5625兲
H 共8c兲: 共0.3429,0.3429,0.3429兲
Mg 共4c兲: 0,0.3313d,1/4d 共0,0.3314,1/4兲
H 共8d兲: 0.2727d, 0.1089d, 0.0794d
共0.2717,0.1085,0.0801兲
Mg 共8c兲: 共0.8823,0.0271,0.2790兲;
H1 共8c兲: 共0.7970,0.3765,0.1651兲;
H2 共8c兲: 共0.9738,0.7433,0.5207兲
共56兲
44.03± 2
共48兲
共3.52兲
3.17± 0.4
共3.07兲
49.83± 5
共58兲
3.49± 0.6
共3.45兲
a
Unit cell 共Å兲
b
c
4.5176
4.5168a
共4.4853
4.6655
4.5176
4.5168a
4.4853
4.6655
共4.7902
4.5246
4.5051d
共4.4860
8.8069
共8.9476
4.7902
5.4442
5.4197a
5.4024
4.6838
4.6065
Modification, structure type
Mg 共4a兲: 0,0,0;
a
c
bTheoretical
dExperimental
tained from the images by the program FIT2D 共Ref. 8兲. The
instrumental resolution, taken as the full width at half maximum 共FWHM兲 of the diffraction peaks, was about 0.04°. The
orientational randomization of the powder samples was facilitated by rocking the pressure cell by 3° during the exposures. The gasket material was stainless steel, the pressure
medium was helium, and the ruby luminescence method
共Refs. 9 and 10兲 was used for pressure measurements. The
nonlinear hydrostatic pressure scale of Mao et al. 10 was
considered as the most appropriate in this case. However,
over the pressure range covered, the distinctions between
different pressure scales are really negligible. Unit-cell dimensions were derived by Le Bail fitting to the observed
XRD patterns by means of the general structure analysis
system11 共GSAS兲. Positional parameters obtained from the
theoretical calculations are used for the simulations of XRD
patterns together with experimental unit-cell dimensions derived by the Le Bail fittings.
and all calculations used a plane-wave cutoff of 400 eV.
The Mulliken-population analysis was made with the
help of the CRYSTAL03 code in which we used 5-11G and
8-61G basis sets for H and Mg, respectively.15 To estimate
the bond strength we have used crystal-orbital
Hamiltonian-population16 共COHP兲 analyses, as is implemented in the TBLMTO-47 package.17
Experimental value from Refs. 18 and 19.
value from Refs. 21 and 20.
Theoretical value from Refs. 21 and 20.
value from Ref. 22.
C. Computational details
The ab initio generalized-gradient approximation12
共GGA兲 was used to obtain accurate exchange and correlation
energies for a given structural arrangement. The structures
are fully relaxed for all volumes considered using force as
well as stress minimization. Experimentally established
crystal-structure data were used as input when available. The
projected-augmented-wave13 共PAW兲 implementation of the
Vienna ab initio simulation package14 共VASP兲 was used for
the total-energy calculations to establish phase stability and
transition pressures. In order to avoid ambiguities regarding
the free-energy results the same energy cutoff and a similar
k-grid density for convergence were always used. In all calculations 500 k points in the whole Brillouin zone were used
for ␣-MgH2 and a similar density of k points was used for all
structural arrangements. A criterion of 0.01 meV atom−1 was
placed on the self-consistent convergence of the total energy,
III. RESULTS AND DISCUSSION
Experimentally observed and theoretically optimized
structural parameters for ␣-, ␤-, ␥-, and ␦⬘-MgH2 are listed
in Table I. Observed and calculated diffraction patterns for
the different modifications of MgH2 are displayed in Figs. 1
and 2. Figure 1 shows that the sample also contain a small
amounts of unreacted magnesium 共hexagonal; P63 / mmc;
a = 3.2089 Å, c = 5.2101 Å兲. The experimental unit-cell dimensions for ␣-MgH2 are very good agreement with data
reported in the literature 共see Refs. 18 and 19 and Table I兲.
The relative amount of unreacted Mg apparently diminishes
during the exposure to high pressures, thus making the
sample apparently phase pure above some 10 GPa. The theoretical calculations identified the tetragonal TiO2-rutile-type
phase as the ground state. At higher temperatures and pressures
␣-MgH2 transforms into the orthorhombic ␥-MgH2 form
with ␣-PbO2-type structure 共see the structural illustrations in
Fig. 3兲. Recently Bortz et al.22 established the full structure
of ␥-MgH2 from powder neutron-diffraction data collected at
2 GPa. However, it should be emphasized that a complete
conversion of ␣-MgH2 into ␥-MgH2 was never achieved in
the present study and the actual ␣-to-␥-MgH2 transition pressure could accordingly not be established.
Our recent theoretical structural stability study7 of MgH2
predicted several pressure-induced structural transitions for
MgH2. In the calculated energy-difference plot with respect
to ␣-MgH2 共Fig. 4兲 transitions are marked by the arrows. The
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STRUCTURAL STABILITY AND PRESSURE-INDUCED¼
FIG. 1. Observed 共solid line兲 and simulated 共points marked by
⫹兲 XRD pattern for ␣-MgH2. Positional parameters obtained by
theoretical calculation are used for the simulated XRD patterns together with experimental unit-cell dimensions derived separated by
Le Bail fitting of the observed data.
calculated transition pressure for the ␣-to-␥-MgH2 conversion is 0.387 GPa 关Fig. 5共a兲兴. The total energies for the two
modifications are nearly the same at the equilibrium volume
共Fig. 4兲, which is natural since ␣- and ␥-MgH2 take nearly
the same structural arrangement. This may be the reason why
the two phases in practice coexist in a certain pressure range.
A subsequent phase transition from ␥- to ␤-MgH2 is calculated to occur at 3.84 GPa. In the pressure range from 6.7 to
10.2 GPa the structural arrangements of the ␤, ␦, and ␦⬘
modifications lie within a narrow energy range of some
10 meV 共Fig. 4; a further transformation to ⑀-MgH2 is pre-
FIG. 2. Observed 共solid line兲 and simulated 共points marked by
⫹兲 XRD patterns of ␣-MgH2 at 2.5 GPa, ␥-MgH2 at ambient pressure 共after pressure release兲, ␤-MgH2 at 8.56 GPa, and ␦⬘-MgH2 at
15.36 GPa. Simulated patterns are obtained with positional parameters from theoretical calculations and experimental unit-cell dimensions from separate Le Bail fittings of the observed data.
dicted at 10.26 GPa, but this is not verified experimentally兲.
This closeness in energy suggests that the relative appearance of these modifications will be quite sensitive to, and
easily affected by, external factors like temperature and remanent lattice stresses, as well as by kinetics. In this connection it should be recalled that the theoretical simulation relates to a defect-free pure phase at 0 K, whereas the highpressure diffraction experiments were performed at room
temperature on a sample burdened with likely defects and
impurities.
The theoretically obtained and the experimentally measured pressure versus volume relations are displayed in Fig.
5. At ambient pressure 共1 bar兲 and room temperature MgH2
stabilizes in the TiO2-rutile-type structure with space group
P42 / mnm.23,24 The primitive unit cell 关Fig. 3共a兲兴 contains
two Mg and four H atoms. Each Mg atom is octahedrally
coordinated to six H atoms, whereas each H atom is coordinated to three Mg atoms in the same plane. During compression ␥-MgH2 starts to form at 5.5 GPa and coexists along
with ␣-MgH2 up to some 9.5 GPa. In a narrow pressure window between 9.35 and 10.36 GPa, the ␤-MgH2 polymorph
exists in a three-phase mixture with the ␣ and ␥ modifications. The ␥-phase Mg is octahedrally coordinated by six H
atoms, and these octahedra are strongly distorted 共Mg-H
bond lengths in the range 1.920–2.011 Å, H-Mg-H bond
angles between 88 ° and 102 °兲 compared to the less distorted ␣-MgH2 共Mg-H distances from 1.944 to 1.961° Å,
ideal 90° H-Mg-H bond angles兲. With respect to the cubic ␤
polymorph, the diffraction data alone were unable to distinguish between a more ideal CaF2-type structure and variants
thereof. The structure takes in any cases an fcc sublattice of
Mg atoms. However, the theoretical investigation 共Fig. 4兲
shows that the calculated total energy for the ideal CaF2-type
variant occurs at 1.5 eV higher energy than that for a modified CaF2-type structure. Hence, we here simply postulate
that the ␤ polymorph takes a modified CaF2-type structure.
This sequence of experimentally established high-pressure
polymorphs generally agrees with the theoretical predictions,
although the observed transition pressures deviate somewhat
from the calculated values. The latter findings may reflect
that neither entropy nor temperature effects are taken into
account in the theoretical simulation and, furthermore, that
the experimental sample is not 100% pure. In addition,
nucleation of new phases at a first-order transition may have
slow kinetics. In comparison, for alkali-metal monohydrides
the experimentally observed and the theoretically calculated
transition pressures vary 3–7 GPa.25 In this perspective, the
presently predicted and observed transition pressures may
even be regarded as in good mutual agreement.
At pressure above 10 GPa the experimentally established
␣-, ␥-, and ␤-phase mixture transforms into an AuSn2-type
phase 共this polymorph being hereafter denoted ␦⬘兲. This
phase is structurally quite different from the theoretically
predicted orthorhombic ␦ phase 共space group Pbc21兲. However, a closer look at Fig. 4 shows that the energy difference
between these two modifications is indeed very small, less
than 1 meV. Hence, the discrepancy between theory and experiment may be explained as metastability of the ␦⬘ phase—
e.g., invoked by the particular pressure sequence used experimentally. Similar to the other polymorphs, the structure
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VAJEESTON et al.
FIG. 3. Crystal structures of
the 共a兲 ␣, 共b兲 ␤, 共c兲 ␥, and 共d兲 ␦⬘
modifications of MgH2.
of the ␦⬘ modification contains Mg atoms in octahedraly coordination by six H atoms and like in the ␥ polymorph these
octahedra are strongly distorted 共Mg-H bond lengths between 1.796 and 1.899 Å and H-Mg-H bond angles between
83° and 108°兲. The ␦⬘ phase remained stable up to the highest pressures 共16 GPa兲 reached in these experiments. It may
be emphasized that the theoretical calculations suggest that
an AlAu2-type polymorph 共⑀兲 should be stabilized above
10.26 GPa.
Considerable hysteresis is observed in the phase changes
upon pressure release. The ␦⬘ phase transforms into the ␤
polymorph at 9.85 GPa under decreasing pressure. This
phase remains stable and constitutes the dominating phase at
6.23 GPa. The observed volume jump at the ␦⬘-to-␤ transition is 1.29 Å3 f.u.−1 and an ␣, ␥ two-phase region is found
between 6.23 and 1.79 GPa. The ␣, ␥ mixture finally converts into a single-phase product of ␥-MgH2 at 1.79 GPa.
Hence, ␥-MgH2 remains as the final product after the completed decompression cycle. ␥-MgH2 is obviously metastable
with respect to the stable ␣ modification at ambient pressure.
According to the theoretical calculations the involved energy
difference between the ␣ and ␥ modifications is just
0.81 meV f.u.−1 This closeness in energy can easily explain
the occurrence of the ␥ modification as a kinetically stabilized phase at ambient pressure. The observed volume difference between the ␣ and ␥ modifications at 298 K and 1 bar
is small, ␥-MgH2 notably exhibiting the smaller volume
关30.82 vs 30.65 共experiment兲, 30.64 vs 30.14 Å3 f.u.−1
共theory兲兴. The observed volume jump between the ␥ and ␤
polymorphs upon compression 共note two-phase mixture兲 is
1.16 Å3 f.u.−1, which is in good agreement with the theoretically obtained value of 1.45 Å3 f.u.−1The initial impurity of
Mg in the ␣-MgH2 sample appears to have disappeared on
cycling of the sample through the ␦⬘ phase 关compression to
15.36 GPa 共␦⬘ phase兲, decompression to 7.48 GPa 共␤ phase兲,
decompression to ambient pressure 共almost pure ␥ phase兲兴. It
should be noted that a phase change has been observed in
carbonaceous MgB2 above 9 GPa at 300 K after stress relaxation by laser heating.26 Continued research with such thermal annealing may bring out more insight into the kinetics of
the ␣-to-␥ phase transition.
All the experimentally verified MgH2 polymorphs have
distinct structural aspects in common. Closely related are
␣- and ␥-MgH2, both comprising MgH6 octahedra and threecoordinated hydrogen. Linear chains of edge-shared octahe-
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FIG. 4. 共Color online兲 Calculated cell volume vs total energy
difference 共with respect to ␣-MgH2兲 relations for MgH2 in actual
and possible structural arrangements 共see legends on the illustration兲. Arrow indicates transition points, but the actual transition
pressures are calculated from the Gibbs free-energy curves.
dra run along the fourfold axis of the TiO2-rutile-type structure of ␣-MgH2, whereas the octahedra are zigzag arranged
in ␥-MgH2 with the ␣-PbO2-type structure. On turning to the
␤- and ␦⬘-MgH2 modifications the chains no longer prevails.
In ␤-MgH2 the three-coordinated hydrogen atoms connect
MgH6 octahedra by corner sharing, whereas in the ␦⬘ polymorph edge sharing and increased effective coordination
numbers 共increased Mg-H distances; see Table II兲 for both H
and Mg are observed. The MgH6 octahedra become more
severely distorted on increasing pressure. Furthermore, the
H-H distance shrinks considerably, from around 2.5 Å in
␣-MgH2 to 2.3 Å in ␦⬘-MgH2. The pressure induced ␣-to␥-to-␤-to-␦⬘ transition sequence involves reconstructive rearrangements 共viz., some bonds are broken and others reestablished兲.
The bulk modulus 共B0兲 and its pressure derivative 共B0⬘兲
were extracted by fitting the experimentally observed pressure versus volume data to the third-order Birch-Murnaghan
equation of state27 共EOS兲 using the computer program EOSFIT V5.2.28 As inputs for ␣-MgH2 we used the equilibrium
volume 共V0 = 30.82 Å3 f.u.−1兲 together with B0 = 50 GPa and
B0⬘ = 4, the refined values of B0 and B0⬘ for the different polymorphs being included in Table I. In general, the theoretical
B0 values are slightly overestimated compared with those
based on the experimental data. This is due to the underestimation of the equilibrium volume in the total energy calculations. The bulk moduli for the MgH2 phases exceed that of
Mg metal 共35.4 GPa兲, implying that the introduction of hydrogen increases the stiffness. All MgH2polymorphs have
rather similar B0 values: according to the present data
FIG. 5. 共a兲 Calculated and 共b兲 observed pressure vs volume
relation for MgH2. Pressure stability regions for the different modifications 共see Table I and text兲 are indicated.
␥-MgH2 has the lowest 共44.03 GPa兲 and ␦⬘-MgH2 the highest 共49.84 GPa兲 B0 value. Compared to, e.g., transition-metal
dioxides, MgH2 is a soft material, on the other hand, 3–4
times harder than alkali-metal aluminum hydrides.29,30
Bonding
A number of investigations of magnesium hydrides using
perturbative or other approximate methods are reported.
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VAJEESTON et al.
TABLE II. Interatomic distance 共in Å兲 for the MgH2 in the ␣, ␤,
␥, and ␦⬘ polymorphs 共multiplicity in parentheses兲 derived using
theoretically calculated positional parameters together with experimentally derived unit-cell dimensions.
Distance
␣-MgH2
␥-MgH2
␤-MgH2
␦⬘-MgH2
Mg-H
1.944共2x兲
1.961共4x兲
1.920共2x兲
1.955共2x兲
2.011共2x兲
1.906 共6x兲
Mg-Mg
3.021共2x兲
3.534共8x兲
2.501共1x兲
3.073共2x兲
3.299共12x兲
2.507共1x兲
2.489 共6x兲
1.796共1x兲
1.870共1x兲
1.879共1x兲
1.880共1x兲
1.882共1x兲
1.899共1x兲
2.085共1x兲
2.849共1x兲
3.023共2x兲
2.263共1x兲
2.449共1x兲
H-H
Stander and Pacey31 performed a Born-Mayer type of calculation of the lattice energy assuming that MgH2 is purely
ionic. Despite obvious significant overestimation, this theoretical value has been interpreted as evidence for appreciable
covalent contributions to the bonding. The substantial difference in the electronegativities of Mg and H suggests strong
ionic character with the Mg valence electrons transferred to
the H sites under the formation of an insulator with stoichiometric MgH2 composition. According to the present study
the bonding characteristics are virtually the same in all
MgH2 polymorphs. The recent experimental study by
Noritake et al.32 mapped the charge-density distribution of
␣-MgH2, and owing to the mentioned similarity between the
polymorphs, we display the only charge density, charge
transfer, and ELF distribution for this polymorph in Figs. 6
and 7. The experimental 共room temperature32兲 and theoretically obtained 共0 K兲 charge densities are indeed very similar,
the distribution around Mg being almost spherical as expected for a nearly ideal ionic substance. The much lower
charge density around the H sites is experimentally found to
be slightly nonspherical with spreading in the direction toward neighboring Mg and H atoms. A closer look at the
experimental electron distribution near the H sites shows that
the deviation from spherical shape is higher than the corresponding feature in the theoretical distribution. This could be
due to the effect of the different temperatures used in the two
studies or an artifact produced by systematic discontinuities
in the experimental data. However, both the experimental
and theoretical charge-density maps clearly demonstrate the
stricking ionic character of ␣-MgH2 with small localized
charges around the hydrogen sites. Following the common
practice for ionic substances we assign ionic radii to the Mg
and H ions on the assumption that the nearest-neighbor ions
make touching contact. In this case an estimate of the radius
for H isobtained from the shortest H-H distance and that for
Mg from the shortest Mg-H distance 共Table II兲. This gives a
radius of 1.26 Å for H− and 0.69 Å for Mg2+, which is quite
different from the Pauling value of 2.08 Å for H−, whereas
the radius of Mg2+ 共0.69 Å兲 is consistent with the Pauling
value 共0.65 Å兲.
A qualitative perspective of the charge transfer in
␣-MgH2 is given in Fig. 7共a兲 which clearly shows a loss of
charge from the Mg sites and a redistribution of this charge
at the H sites, viz., another piece of evidence of strong ionic
interaction between Mg and H. A different perspective of the
bonding is provided by the ELF 共an indicator of the electronpair distribution, which takes values between 0 and 1; see
Refs. 33–35兲. Figure 1共b兲 displays ELF contours similar to
the charge densities in Fig. 6 and shows high ELF values, not
only at the Mg sites, but also at the H sites. These characteristics nicely reveal the very distinct ionic nature of MgH2.
The ELF values between Mg and H is very low although a
degree of polarization is visible, especially at the H− sites.
In order to further explore the bonding and estimate the
amount of electrons on and between the participating atoms,
we have performed Mulliken-population analysis. The calculated Mulliken effective charges 共MECs兲 are listed in Table
III for all MgH2 polymorphs. MEC is +1.87e for magnesium
and −0.93e for hydrogen in ␣-MgH2 whereas the overlap
population between Mg2+ and H− is almost zero. Similar
MEC values and overlap populations are found for the other
polymorphs, which leads to the conclusion that the bonding
is virtually identical in all MgH2 polymorphs. The bond
strength between Mg and H in the various MgH2 polymorphs, as expressed in terms of COHP, is displayed in Fig. 8.
The valence band is in all cases seen to comprise mainly
bonding orbitals 共negative COHP兲, whereas antibonding or-
FIG. 6. 共a兲 Experimentally observed 关at room
temperature 共Ref. 32兲兴 and 共b兲 calculated 共at 0 K兲
charge-density distribution in the 共001兲 plane of
␣-MgH2. The contour lines are drawn from 0.0 to
1.5 at 0.15e Å−3 intervals.
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FIG. 7. 共Color online兲 共a兲 Calculated charge-transfer 共see text兲 and 共b兲 electron-localization-function maps for ␣-MgH2 in the 共001兲
plane.
bitals are found above EF. The integrated COHP’s 共ICOHP’s兲
up to EF for the Mg-to-H bond gave values between −1.61
and −1.71 for the different polymorphs. This indicates that
the different polymorphs are in nearly in the same bonding
situation. Furthermore, it may be recorded that the value of
the ICOHP for the Mg-H interactions takes almost half of
that for the Al-H interaction in AAlH4 共A = alkali metal兲
series.36 A quantitative oriented partitioning scheme for assessment of energies associated with covalent and metallic
bonds in solids has been proposed by Bester and Fähnle
recently.37 However, the present focus has been on MgH2
where ionic interactions dominate and for such problems
COHP analysis still provides the best aid.
Let us finally recall that kinetic enhancement of hydrogen
desorption from ␣-MgH2 共viz., destabilization of the
␣-MgH2 structure兲 has been achieved by the introduction of
certain substitutional ingredients. On this background it
seems logical to attempt such a substitution also in highpressure form to see if this can stabilize or metastabilize
some of the other modifications at ambient conditions as well
as improving the desorption properties compared with
␣-MgH2. Note that a previous density-functional study20
suggests that substitution of MgH2 with monovalent or trivalent elements may introduce some metallic character in this
salt. If this turns out to be of some relevance, it would certainly be interesting to explore the other polymorphs of
MgH2 along the same line.
TABLE III. Mulliken-population analysis for the MgH2 polymorphs. The Mulliken effective charges 共MEC兲 are given in terms
of e.
Polymorph
␣
␤
␥
␦⬘
Atom
MEC
Overlap population
Mg
H
Mg
H
Mg
H
Mg
H
+1.87
−0.93
+1.99
−0.99
+1.98
−0.98
+2.01
−1.01
−0.040 共Mg-H兲
−0.124 共H-H兲
−0.021 共Mg-H兲
−0.122 共H-H兲
−0.024 共Mg-H兲
−0.115 共H-H兲
−0.032 共Mg-H兲
−0.183 共H-H兲
FIG. 8. Calculated crystal-orbital-Hamiltonian-population
共COHP兲 profiles for the Mg-to-H bonds in different MgH2 polymorphs. Integrated COHP value for ␣-, ␤-, ␥-, and ␦⬘-MgH2 is −1.61,
−1.65, −1.70, and −1.62 eV, respectively.
224102-7
PHYSICAL REVIEW B 73, 224102 共2006兲
VAJEESTON et al.
IV. CONCLUSION
The present combined experimental and theoretical study
has shown that ␣-MgH2 undergoes several pressure-induced
structural transitions up to 17 GPa. Theoretical simulations
have predicted that ␣-MgH2 transforms into ␥, ␤, ␦, and ⑀
modifications upon exposure to pressure, the ␥ and ␤ forms
being verified experimentally. Calculated and experimental
unit-cell parameters are in excellent agreement wherever a
comparison can be made. The high-pressure ␥ modification
is maintained as the metastable phase when the pressure is
released at room temperature after a completed pressure
loading-unloading cycle. A possible reason for this behavior
is identified from the theoretical simulation. Instead of a theoretical ␦ modification with AuSn2-type structure a ␦⬘ modification is established experimentally, whereas the existence
*URL: http://folk.uio.no/ponniahv. Electronic address:
ponniahv@kjemi.uio.no
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ACKNOWLEDGMENTS
The authors gratefully acknowledge the Research Council
of Norway for financial support and M. Sørby for preparing
the MgH2 sample for the experimental study.
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