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Materials Science and Engineering B 140 (2007) 114–122
Energetics of the lithium-magnesium imide–magnesium amide andlithium hydride reaction for hydrogen storage: An ab initio study
Oleg I. Velikokhatnyi a, Prashant N. Kumta a,b,∗
a Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USAb Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Received 11 October 2006; received in revised form 20 April 2007; accepted 20 April 2007
Abstract
An ab initio study within the density functional theory of the recently described reversible hydrogen storage reactionMg(NH2)2 + 2LiH⇔Li2Mg(NH)2 + 2H2 has been conducted. The electronic structure, structural parameters, vibrational spectra, and enthalpies
of formation of all the reactants and products as well as the heat of the overall reaction at zero and finite temperature have been calculated in the
generalized gradient approximation (GGA) to the exchange correlation potential. The heat of the overall reaction is calculated to be 53.4 kJ/mol
H2 in contrast to the experimentally obtained overall heat of reaction of ∼44.1 kJ/mol H2. The difference of ∼20% between the experimental and
calculated values is discussed.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Hydrogen storage materials; Enthalpy of formation; Heat of the reaction; Ab initio calculations
1. Introduction
There has been a significant surge of activity targeted atidentifying and developing highly efficient solid-state hydrogen
storage materials for the forthcoming hydrogen economy of the
new millennium. This effort is particularly critical for harness-
ingandrealizing themuch publicized fuel cell technologies. The
burgeoning research activity in this emerging field has led to the
identification of several new complex chemical hydrides, and
carbonaceous materials, such as Mg-based metal hydrides, and
sodium aluminum chemical hydrides [1,2]. Recently, Chen et al.
[3] have demonstrated a promising reaction of lithium nitrides,
imides and amides for reversibly storing hydrogen. They have
shown that hexagonal Li3N absorbs hydrogen at elevated tem-
peratures of 185–255 ◦C transforming to cubic (fcc) Li2NH and
LiH which, in turn further absorbs hydrogen to form a body cen-
teredtetragonalLiNH2 and cubicLiHaccording to thefollowing
reaction:
Li3N+ 2H2→ Li2NH+ LiH+ H2→ LiNH2+ 2LiH (1)
∗ Correspondingauthorat: Department of MaterialsScience andEngineering,
CarnegieMellon University, Pittsburgh, PA 15213, USA.Tel.: +1 4122688739;
fax: +1 412 268 7596.
E-mail address: [email protected] (P.N. Kumta).
In this equation, the standard enthalpy change for the first step
( H ∼ 148 kJ/mol H2) [2] is too large and a temperature over
430◦
C is required for the complete recovery of Li3N fromthe hydrogenated state. This high-temperature characteristic of
the system makes it less attractive as a solid hydrogen-storage
material for portable consumer and mobile automotive trans-
port applications. Recent reports from theDepartment of Energy
indicate that for the material to be attractive for hydrogen stor-
age applications, it should be able to reversibly store hydrogen
with a minimum capacity of 6.5wt.% at a moderate desorption
temperature range of 60–120 ◦C, corresponding to an enthalpy
change between 30 and 48 kJ/mol H2 [4]. However, in reality
this minimal limit is insufficient and a greater capacity will be
needed for the materials to be utilized for vehicular applica-
tions as reported by Pinkerton and Wicke [5]. This suggests that
although there has been a surge of research activity and consid-
erable progress has been made, several factors still remain to be
addressed. Research in the materials based on lithium nitrides,
imides and amides is thus very much warranted before they can
be harnessed for practical automotive applications.
The study by Chen et al. [3] has inspired several
researchers to conduct research in hydrogen storage proper-
ties of Li2NH/LiNH2 systems to further improve the hydrogen
cycling of lithium amides and hydrides. In particular, the Li-
based ternary system Li–Mg–N–H in this regard appears to be
0921-5107/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.mseb.2007.04.010
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O.I. Velikokhatnyi, P.N. Kumta / Materials Science and Engineering B 140 (2007) 114–122 115
very promising [6–8]. Partial replacement of Li by Mg in the
LiNH2–LiH system could improve the sorption characteristics
since MgH2 is less stable than LiH (enthalpy of formation for
MgH2 is −74 kJ/mol versus −90 kJ/mol for LiH) [6]. Further-
more, compared with binary lithium amide, this ternary system
demonstrates much lower hydrogen absorption and desorption
temperatures, and a higher desorption pressure plateau. Thus,
by reacting Mg(NH2)2 with LiH or chemically reacting LiNH2
with MgH2, single phase of Li2Mg(NH)2 is obtained with the
release of hydrogen.
The overall reaction can therefore be written as follows:
(2)
where the first reaction (I) is only favored to the right, while
the second reaction (II) represents a reversible transformation
of lithium magnesium imide with hydrogen to form magnesiumamide and lithium hydride. According to LuoandRonnebro [8],
the initial reactants LiNH2 and MgH2 convert irreversibly to a
new single phase Li2Mg(NH)2 during dehydrogenation, while
the backward hydrogenation reaction leads to the formation of
pureMg(NH2)2 andLiH without exhibiting any signsof forming
the starting materials, namely the lithium amide and magne-
sium hydride. Further cycling of these reactants thus results in
the reaction progressing reversibly involving the products of
the second (reversible) reaction. The heat of the endothermic
hydrogen desorption reaction measured by differential scanning
calorimetry has been reported to be 44.1kJ/mol H2, which is
favorable for PEM Fuel Cell application. However, the rela-tively higher activation energy ( E a =102 kJ/mol) sets a kinetic
barrier.Thematerialneverthelesscanreversibly absorb 5.2 wt.%
H2 at a pressure of 30bar at 200 ◦C (the theoretical capacity is
about 5.5 wt.% H2) which is reasonably sufficient for permitting
onboard vehicle applications [7].
There has been an increasing body of literature describing
the use of ab initio techniques for predicting the thermodynamic
properties of hydrogen storage systems. The technique has
become increasingly popular with the widespread availability
of various simulation packages combined with the relative ease
of access to supercomputing facilities. Many studies have thus
been reported in the literature. However, not many papers have
been published dedicated to the ab initio theoretical investiga-tion of thehydrogen storage characteristicsof compoundsbased
on lithium nitrides, imides, amides and corresponding systems
containing additional alloying elements substituting for alkali
metals, nitrogen or hydrogen. HerbstandHector [9], Miwa et al.
[10], and Song et al. [11] have performed calculations showing
theformationenthalpies forall thecomponents involved in reac-
tions (1) using differentab initionumerical methods basedon the
Density Functional Theory. Herbst and Hector [9] have inves-
tigated the energetics of the second step of reaction (1) taking
into account the temperature dependent vibration contributions
andzero-point energy corrections (ZPE) to the enthalpies of for-
mation for Li2NH, LiNH2 and LiH as well as to the enthalpy
change in the second step of reaction (1). Miwa et al. [10], on
the other hand, have calculated the enthalpies of formation for
Li3N, LiNH2 and LiH and the heat of formation for the overall
reaction (1) including ZPE corrections while however neglect-
ing phonon contributions at finite temperatures. Song and Guo
in their very recent publication [11] have reported the use of an
ab initio full potential approach for investigating all the compo-
nents in reaction (1) andthe heat of formation of the two steps of
the reaction. In their calculations they excluded the ZPE correc-
tions while also neglecting the vibration contributions. Despite
some discrepancy, the calculated enthalpies of formation from
all these three publications are in reasonable agreement with the
experimental values.Furthermore, thesereports demonstrate the
feasibility of using first-principle ab initio methods for calculat-
ing enthalpies of formation and heat of the overall reactions
involving lithium nitrides, imides, and amides.
Barring these limited first-principles studies published, there
are no theoretical investigations of hydrogen storage reac-
tions involving lithium nitrides and/or lithium amides doped
with different elements, such as Mg, Ca, and others. In thismanuscript we numerically explore the validity of the second
(reversible) step of reaction (2) pertaining to the hydrogenation
of Li2Mg(NH)2, which may complement and provide further
informationon the fundamental propertiesof prospective hydro-
gen storage materials at the micro-scale level.
2. Calculation procedures
Since the reversibility of reaction (2) is only observed
for the hydrogenation reaction of Li2Mg(NH)2 giving
Mg(NH2)2 + LiH, we focused our attention only on this promis-
ing system from its potential for hydrogen storage applications.For calculating the total energies, electronic structure and den-
sity of electronic states the Vienna Ab initio Simulation Package
(VASP) was used within the projector-augmented wave (PAW)
method [12,13] and the generalized gradient approximation
(GGA) for the exchange-correlation energy functional in a form
suggested by Perdew and Wang [14]. This program calculates
the electronic structure and, via the Hellmann–Feynman theo-
rem, the inter-atomic forces aredeterminedfromfirst-principles.
Standard PAW potentials were employed for the elemental con-
stituents and the H, Li, N, and Mg potentials thus accordingly
contained one, three, five, and eight valence electrons, respec-
tively.
For all thematerialsconsidered theplane wavecut-off energyof 520 eV has been chosen to maintain high accuracy of the total
energy calculations. The lattice parameters and internal posi-
tions of atoms were fully optimizedduring the double relaxation
procedure employed and the minima of the total energies with
respect to the lattice parameters andinternal ionic positionshave
been determined. This geometry optimization was obtained by
minimizing the Hellman–Feynman forces via a conjugate gra-
dient method, so that the net forces applied on every ion in
the lattice are close to zero. The total electronic energies were
converged within 10−5 eV/unit cell resulting in residual force
components on each atom to be lower than 0.01 eV/ A/atom,
thus allowing the accurate determination of force-constants.
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116 O.I. Velikokhatnyi, P.N. Kumta / Materials Science and Engineering B 140 (2007) 114–122
This would also finally lead to calculation of the phonon spectra
with minimal errors. The Monkhorst-Pack scheme was used to
sample the Brillouin zone (BZ) and generate the k -point grid
for the solids and the different molecules used in the study. A
choice of the appropriate number of k -points in the irreducible
part of the BZ was based on convergence of the total energy
to 0.1 meV/atom. For Li2Mg(NH)2, Mg(NH2)2, LiH, Li (bcc),
and Mg (hcp) the following numbers of k -points in the irre-
ducible parts of BZ were used: 14, 12, 280, 256, and 222 points,
respectively. For total energy calculations of isolated molecules
H2 and N2 a cubic box with edge of 10 A× 10 A× 10 A was
chosen to eliminate interaction between molecules caused by
periodicboundaryconditions. Testcalculations withtheboxsize
of 15 A× 15 A× 15 A have shown a difference in total energies
within 0.2 meV/atom.
For calculation of the thermodynamic properties, such as
enthalpy needed for obtaining the enthalpies of formation of
individual reactants and the heat of the overall reaction (2)
depending on temperature (in particular, at T =298 ◦K), there
is a need to calculate the vibrational term (phonon energy)and estimate the zero-point energy arising from the quantum
zero-vibrations at zero temperature. The phonon spectra and
vibrational frequencies of all the solid components of reaction
(2) as well as the gas molecules H2 and N2 were calculated
using the so called direct method and implemented in the pro-
gram PHON. This program written by Dario Alfe is available
readily over the internet as a freeware [15]. The lattice dynam-
ics was determined using the forces acting on the atoms in the
super-cell. The details of the direct method are presented else-
where [16,17]. Briefly, in the direct method, the inter-atomic
force-constant matrix is derived from a set of calculations on a
periodically repeated super-cell that is a multiple of several unitcells. As a starting point, all the atoms are placed in their equi-
librium positions. An atom is then slightly displaced, and the
forces on all the atoms in the cell are calculated. These forces
are proportional to the inter-atomic force-constants times the
displacement. By considering all the symmetrically nonequiv-
alent displacements, the complete force-constant matrix can be
obtained. The phonon frequencies as a function of a q vector
are then obtained by a straightforward diagonalization of the
dynamical matrix.
The VASP code as mentioned above has been utilized as
a computational engine for all calculations of forces applied
to every atom in distorted super-cells. The PAW GGA poten-
tials, cut-off energies, and the self-consistent field convergenceparameters have been chosen to be the same as for the total
energy calculations discussed above. The appropriate dimen-
sions of the super-cells and k -point grids utilized for all the
reactants and simple elements participating in reaction (2) will
be discussed later in the text. A fraction of a percent of the near-
est neighbor distancewas assumed to bea good value to keep the
atomic displacements within the harmonic region [15]. Hence,
for all materials calculated in the present work the displacement
of ±0.01 A hasbeenused.Calculatedforcesfor positiveand neg-
ative displacements have been averaged to obtain more accurate
results. It is worth while mentioning that in the present cal-
culations no longitudinal optical (LO)/transverse optical (TO)
zone center splitting has been computed. This is because for
the purposes of present study, namely for calculating zero-point
energies and vibration energies this contribution is not criti-
cal due to the integration of the phonon spectra over the entire
Brillouin zone.
According to a report of Gao et al. [18] and a paper recently
published by Rijssenbeek et al. [19] there are three differ-
ent structure types for lithium magnesium imide Li2Mg(NH)2
depending on the temperature, namely an orthorhombic low-
temperature () phase below 350 ◦C, a primitive cubic structure
() between 350 ◦C and 500 ◦C, and a high-temperature fcc-
based structure () above 500 ◦C. Since reaction (2) occurs
at a temperature of ∼200 ◦C we considered only the low-
temperature orthorhombic crystal structure with Iba2 (No. 45)
space group existing below 350 ◦C. Table 1 contains the experi-
mental and calculated data related to the unit cell and structural
parameters for the low-temperature -Li2Mg(NH)2 phase. A
primitive cell contains 28 atoms with fractional occupancies
of Mg and Li atoms at (4b) and (8c) sites of the cell. To sat-
isfy these fractional occupancy conditions we have chosen afour-folded 112-atom super-cell (1× 2× 2) with 7 Mg atoms at
16 (4b) sites and 9 Mg atoms at 32 (8c) sites resulting in the
occupancy of Mg to be 0.4375 and 0.28125 at (4b) and (8c),
respectively. Similarly, 9 Li atoms have been distributed over
16 (4b) sites and 23 Li atoms over 32 (8c) sites, thus giving
0.5625occupation numberat (4b) sites and0.71875 at (8c) sites.
Obviously, there are a large number of different crystal struc-
tures satisfying the site occupancy conditions described above.
For this reason we constructed five different configurations of
Li and Mg atoms differing between each other by a degree of
Table 1
Experimental and calculated structural parameters for -Li2Mg(NH)2
Exp. [19] Calc.
a (A) 9.7971 9.8937
b (A) 4.9927 4.9914
c (A) 5.2019 5.2238
V (A3) 254.19 257.97
Li/Mg (I) (4b)
x 0.0 −0.001
y 0.5 0.5074
z 0.25 0.2495
Occ. 0.589/0.411 0.5625/0.4375
Li/Mg (II) (8c) x 0.25 0.2563
y 0.0 0.0016
z 0.75 0.7547
Occ. 0.706/0.294 0.71875/0.28125
N (8c)
x 0.1357 0.1330
y 0.2785 0.2766
z 0.0 0.01
H (8c)
x 0.0644 0.0610
y 0.1427 0.1482
z −0.0440 −0.0657
Experimental values obtained from Ref. [19]
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O.I. Velikokhatnyi, P.N. Kumta / Materials Science and Engineering B 140 (2007) 114–122 117
homogeneity in the distribution of these different atoms. Two
of them represent two extreme cases of the atomic distributions.
One configuration represents a tendency of Li and Mg atoms
to aggregate in separate Li- and Mg-clusters within the super-
cell. Another configuration is characterized by as uniform as
possible distribution of both sorts of atoms over their appropri-
ate sites (4b and 8c) within fixed occupation numbers described
above. The additional three different lattice geometries of the
possible structures chosen for consideration in our study are the
intermediate degrees of the atomic distributions lying between
the first two cases described above. Calculations of the total
energy of all these structures allowed us to define the most sta-
bleatomic configurationand thus, to specify theparticular lattice
geometry, which most adequately corresponds to the real atomic
distribution.
According to the results of the calculation, the most stable
structure represents the second extreme type of metal order-
ing with quite uniformly distributed Li and Mg atoms over the
allowed sites of the lattice. The total energies of all the five
structures considered for the testing calculations were within∼1.7meV/atom, and the following tendency hasbeen observed:
an increase in the homogeneity of the metal atom distribution
leads to a lowering of the total energy for the structure thus
increasing its stability.
Another possible way to fit our constructed structure to the
one experimentally obtained is to compute an XRD powder pat-
tern of our suggested structure and compare it with the existing
pattern obtained by Rijssenbeek et al. [19]. All thefive structures
generated exhibit XRD patterns with the same peak positions as
the experimental pattern except with different intensities due to
the fractional occupancy of the metal atoms in the lattice, which
makes it impossible to construct a crystal lattice identical to thatobserved in experiment. Indeed, dealing with fixed positions
given for the certain sorts of atoms does not allow one to repro-
duce a lattice geometry characterized with fraction occupation
of the atoms in the lattice. Atomic disordering with random dis-
tribution of the different specific atoms may be better treated by
other theoretical techniques implementing the Coherent Poten-
tial Approximation (CPA), such as KKR-CPA [20] or the Exact
Maffin-Tin Orbitals EMTO-CPA approach [21]. However, we
believe thatourchoice of the four-folded super-cell nevertheless,
reasonably reflects the real atomic distribution in the lattice.
The other component of the reaction—magnesium amide
Mg(NH2)2 is characterized by a tetragonal unit cell belonging
to the space group No. 142 ( I 41 / acd ) with 224 atoms per unitcell [22,23]. Lithium hydride—a third reactant of the reaction
is known to adopt a cubic (fcc NaCl-type) crystal structure with
Fm3m spacegroupNo.225and8atomsperunitcell[24]. Table2
shows the experimental and calculated structural parameters for
the two different materials.
3. Results and discussions
Table 1 lists the experimentally determined structural param-
eters and those calculated by us for the low-temperature phase,
-Li2Mg(NH)2. For a better comparison of the experimental
and calculated values the results obtained for the four-folded
Table 2
Experimental and calculated structural parameters for Mg(NH2)2, LiH, metal-
lic Libcc and Mghcp, as well as the inter-atomic distances for the H2 and N2
molecules
Exp. [22] Calc.
Mg(NH2)2
a (A) 10.37 10.445
b (A) 10.37 10.445
c (A) 20.15 20.312
V (A3) 2166.9 2216.0
Mg (32g)
x 0.373 0.3734
y 0.361 0.3603
z 0.063 0.0633
N1 (16e)
x 0.287 0.2886
y 0.0 0.0
z 0.25 0.25
N2 (16d)
x 0.0 0.0
y 0.25 0.25 z 0.257 0.2584
N3 (32g)
x 0.013 0.0151
y 0.023 0.0232
z 0.376 0.3753
H1 (32g)
x 0.236 0.2278
y 0.061 0.0558
z 0.271 0.2768
H2 (32g)
x 0.058 0.0568
y 0.201 0.1987
z 0.239 0.2273
H3 (32g)
x 0.229 0.2180
y 0.177 0.1754
z 0.104 0.0974
H1 (32g)
x 0.209 0.2067
y 0.285 0.2844
z 0.148 0.1518
Exp. Calc.
LiH
a (A) 4.085 [24] 4.015
Libcca (A) 3.510 [31] 3.452
Mghcp
a (A) 3.209 [32] 3.201
b (A) 3.209 [32] 3.201
c (A) 5.211 [32] 5.199
H2 molecule
d (H–H) (A) 0.746 [33] 0.749
N2 molecule
d (N–N) (A) 1.098 [33] 1.102
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118 O.I. Velikokhatnyi, P.N. Kumta / Materials Science and Engineering B 140 (2007) 114–122
Fig. 1. Total and partial electronic density of states calculated for LiH.
112-atomic super-cell were reduced to a conventional unit cell
containing 28 atoms. Similarly, Table 2 contains analogous data
for magnesium amide, lithium hydride, metallic Li and Mg, as
well as the inter-atomic distances for N2 and H2 molecules.
A comparison of the measured parameters and those obtainedusing ab initio calculations within the GGA approximation
shows very good agreement, which proves the accuracy of
the choice of the computational parameters, such as the cut-
off energy, numbers of k -points in the irreducible parts of the
Brillouin zones and the accuracy of the energy minimization
procedure. As for thecrystal structureof -Li2Mg(NH)2,ingen-
eral the structural parameters determined for a fully optimized
state of the structure obtained from our calculations matches
well with thestructural parameters presented in Ref. [19]. These
results thus confirm both the correctness of our calculations and
the experimental crystallographic parametersdeterminedfor the
recently identified lithium magnesium imide phase.For calculating the total and partial (component) densities
of states for LiH, Mg(NH2)2, and -Li2Mg(NH)2 the Wigner-
Seitz spheres with radii of 1.35, 1.45, 0.9, and 0.5 A have been
chosen for Li, Mg, N, and H, respectively. In Figs. 1–3 one can
see that all the three materials are dielectrics and exhibit direct
wide band gaps with values of 3.0, 3.05, and 2.35 eV for LiH,
Mg(NH2)2, and -Li2Mg(NH)2, respectively. The plot of the
density of states for LiH (Fig. 1) is very similar to that calcu-
lated by Smithson et al. [25]. To the best of our knowledge,
there are no existing ab initio calculations published in the lit-
erature for Mg(NH2)2 and -Li2Mg(NH)2. The calculations in
this work thus shows very good agreement between the experi-
mental and calculated structural parameters with a discrepancyof only 1.5–2% which validates the accuracy of our calculations
of the electronic structure for these twoamide and imide phases.
As mentioned earlier, the vibrational frequencies are neces-
sary to determine the zero-point corrections and the temperature
dependence of the thermodynamic properties, suchas enthalpies
of formation and the heat of the overall hydrogen storage
reaction.Forthephonon calculations,namely toobtain theforce-
constantsmatricesappropriate super-cellshave beenchosen.For
-Li2Mg(NH)2 and Mg(NH2)2 the original unit cells contain-
ing 112 and 224 atoms, respectively, have been utilized. Due
to very large sizes of the super-cells selected, it was impos-
sible to carry out an investigation on the convergence of the
Fig. 2. Total and partial electronic density of states calculated for Mg(NH2)2.
force matrix with respect to the super-cell sizes. However, webelieve that these unit cells sizes are quite large enough to elim-
inate interactions between equivalent atoms caused by periodic
boundary conditions. For lithium hydride, LiH as well as for the
gaseous molecules N2 and H2 (2× 2× 2) super-cellscontaining
64, 16, and 16 atoms, respectively, have been chosen to obtain
the force-constant matrices and vibrational frequencies of the
two materials.
Fig. 4 displays the phonon densities of states (DOS) derived
from our calculations of the phonon spectra of Li2Mg(NH)2,
Mg(NH2)2, and LiH. Again, the phonon DOS for LiH derived
from our calculations are in quite good agreement with the
results publishedby Roma etal. [26], calculatedwithin the linear
response formalism based on the density functionalperturbationtheory. Also, a qualitative agreement between our calculations
of the phonon DOS and the infra-red spectrum of Mg(NH2)2
obtained experimentally by Linde and Juza [27] can be seen
in Fig. 4b. The experimental spectrum is shown by the dashed
line.
The phonon DOS for Li2Mg(NH)2 (Fig. 4c) demon-
strates several sharp peaks in the 3200–3600cm−1 region.
Vibrational analysis of the structure shows that these peaks cor-
respond to N–H stretch modes. At the same time, Mg(NH2)2
(Fig. 4b) demonstrates two different groups of peaks within
1000–1500cm−1 wavenumberregion, andwithinthe frequency
range of 3200–3700 cm−1
corresponding to H–N–H deforma-
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O.I. Velikokhatnyi, P.N. Kumta / Materials Science and Engineering B 140 (2007) 114–122 119
Fig. 3. Total and partial electronic density of states calculated for -
Li2Mg(NH)2. The scale for the density of states corresponds to 28-atomic unit
cell.
tions (the first interval), and symmetric and asymmetric stretch
modes of the NH2 molecular units (the second interval of
frequencies). Boghler et al. [28] showed using infra-red and
Ramanspectroscopy, that thesemodes occur in thewavenumber
ranges of 1539–1561cm−1, 3258 cm−1, and 3310–3315 cm−1,
respectively. Thus, our results agree well with values observedexperimentally.
It should be mentioned that we also determined the vibra-
tional frequenciesω0 calculated forsinglemoleculesH2 and N2.
We obtained ω0(H2)=4501cm−1, and ω0(N2)=2603cm−1,
which is in quite good agreement with experimentally obtained
values (4405cm−1 and 2360cm−1, respectively [29]). Further-
more, it should be noted that these electronic and phonon DOS
have been determined by calculations for the first time for
Li2Mg(NH)2 and the good agreement of the DOS calculated
in this work for LiH with the published data serves to validate
the electronic and phonon structure information obtained using
the present approach.
Fig. 4. Phonon density of states calculated for (a) LiH, (b) Mg(NH2), and (c)
-Li2Mg(NH)2. Dashedline superimposed in (b)represents theIR spectrumfor
Mg(NH2) obtained from Ref. [27].
3.1. Enthalpies of formation
The enthalpies (or heats) of formation are the most important
thermodynamic parameters used to identify and classify hydro-
genstorage materials since they determinetheheat of theoverall
hydridingreaction,which,in turn, affects thetemperatures of the
reversible hydrogenation/dehydrogenation processes. The heat
of the reaction can be estimated from the difference between
the formation enthalpies before and after dehydrogenation. In
particular, the heat of the reaction (2) H R is determined as
follows:
H R = 12 (H Li2Mg(NH)2 −H Mg(NH2)2
− 2H LiH),
where H is the formation enthalpies of the different materials.
Since H =U + pV and considering that the term pV is on
the order of 10−1 J/mol for solids at atmospheric pressure, one
can assume U to be a reasonable measure of H , where U is
the internal energy of the system. The internal energy U can be
expressed as:
U = Eel.tot. + EZPE +Evib, (3)
where E el.tot. is the conventional total electronic energy cal-
culated by VASP at T = 0, and E ZPE is the zero-point energy
coming from zero-point oscillations and expressed as a sum of
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120 O.I. Velikokhatnyi, P.N. Kumta / Materials Science and Engineering B 140 (2007) 114–122
frequencies over the Brillouin zone for crystalline materials, or
(1/2) ω0 for H2 and N2 molecules (ω0—oscillation frequencies
at zero temperature). The last term is the temperature dependent
vibrational energy Evib =
qhωqg(ωq), where g(ωq, T ) is the
phonon density of states function that is given by 1/(e ω / kT − 1).
Further, we will consider the influence of each of the three
terms in expression (3) on the enthalpies of formation of all thereactants in reaction (2) and on the net heat of the hydrogenation
process.
Thus, the enthalpy of formation as an example for
Li2Mg(NH)2 at T =0 and without ZPE correction can be
expressed as:
H el.tot[Li2Mg(NH)2]
= Eel.tot[Li2Mg(NH)2]− 2Eel.tot[Libcc]−Eel.tot[Mghcp]
−Eel.tot[N2]−Eel.tot[H2]. (4)
Similar expressions can be written for Mg(NH2)2 and LiH.
To obtain the ZPE corrections for the enthalpies of formation
of all the materials, the E ZPE energies must be calculated. The
ZPE correction to the enthalpy of formation for Li2Mg(NH)2
can be calculated in a manner similar to that above given as
follows:
H ZPE[Li2Mg(NH)2]
= EZPE[Li2Mg(NH)2]− 2EZPE[Libcc]−EZPE[Mghcp]
−EZPE[N2]−EZPE[H2]. (5)
Finally, the last vibrational term of the internal energy in Eq.
(3) allows us to estimate the temperature dependent correc-
tion for the internal energy and, as a result, the enthalpies of
formation and the heat of the overall reaction (2) at a finite tem-perature, in particular at T = 298 K. It should be noted that for
the individual molecules in addition to the vibrational energy
E vib = ω0g(ω0), the translational (3/2)kT , rotational (kT ), and
pV = kT energies (totally, (7/2)kT ) must be added. As a result,
the temperature correction H T for the formation enthalpy at
finite T for Li2Mg(NH)2 can be calculated as:
H T [Li2Mg(NH2)]
= Evib[Li2Mg(NH2)]− 2Evib[Libcc]− Evib[Mghcp]
− [Evib[N2]+ 72kT ]− [Evib[H2]+ 7
2kT ] (6)
The H T term for the other amide Mg(NH2)2 and hydride LiHcan also be obtained in a similar manner.
Table 3 shows the E el.tot. and E ZPE for all the complexes and
the elemental materials considered in the present study, as well
as the enthalpies of formation for Li2Mg(NH)2, Mg(NH2)2, and
LiH at T = 0 without and with the ZPE correction. These three
quantities yield the overall heat of reaction (2) to be 61.5kJ/mol
H2 without theZPEcorrection (i.e. based only on E el.tot. values),
and 42.6 kJ/mol H2 with ZPE correction at T = 0.
Theresulting enthalpies of formationandtheheat of theover-
all reaction (2) at T = 298 K are also shown in Table 3. As one
can see, the heat of the reaction at T = 298K is calculated to be
53.4kJ/mol H2. T
a b l e 3
T o t a l e l e c t r o n i c e n e r g i e s E e l . t o t ,
Z P E ,
a n d E v i b a
t T = 2 9 8 ◦ K f o r a l l t h e m a t e r i a l s a n d e l e m e n t a l c o m p o n e n t s p r e s e n t e d i n r e a c t i o n ( 2 )
E e l . t o t .
( e V / f . u . )
Z P E
( e V / f . u . )
E v i b
T = 2 9 8 ( e V / f . u . )
H T = 0
e l . t o t
( k J / m o l )
H Z P E
( k J / m o l )
H T = 0 ( k J / m o l )
δ H T = 2 9 8 ( k J / m o l )
H T = 2 9 8 ( k J / m o l )
L i 2 M g ( N H ) 2
− 3 3 . 0
9 6
0 . 8 4
2 5
0 . 1
5 4
− 4 1 6 . 4
2 7 . 8
− 3 8
8 . 6
− 2 5 . 3
− 4 1
3 . 9
( − 4 1 8 . 8
o r − 4 4 8 . 8
)
M g ( N H 2
) 2
− 3 5 . 6
2 2
1 . 3 4
3
0 . 1
0 3
− 3 7 1 . 0
5 7 . 3
− 3 1
3 . 7
− 3 6 . 5
− 3 5
0 . 2
( − 3 2 5 o r − 3 5 1 ) [ 3 0 ]
L i H
− 6 . 1
7 3
0 . 2 2
4
0 . 0
6 6
− 8 4 . 2
4 . 1
− 8 0
. 1
− 5 . 2
− 8 5
. 3 ( 9 1 . 0
) [ 3 ]
L i b c c
− 1 . 9
0 2
0 . 0 4
2
0 . 0
4 4 1
0
0
0
0
0
M g h c p
− 1 . 4
8 3
0 . 0 2
9
0 . 0
5 2 8
0
0
0
0
0
N 2
− 1 6 . 6
9 4
0 . 1 6
2
0 . 0
3 3
0
0
0
0
0
H 2
− 6 . 7
9 8
0 . 2 7
9
0 . 0
6 2
0
0
0
0
0
O v e r a l l r e a c t i o n
6 1 . 5
k J / m o l H 2
− 1 8 . 8
5 k J / m o l H 2
4 2 . 6
5 k J / m o l H 2
1 0 . 8
k J / m o l H 2
5 3 . 4
5 ( 4 4 . 1
) [ 7 ] k J / m o l H 2
E n t h a l p i e s o f f o r m a t i o n w i t h o u t Z P E c o r r e c t i o n s a t T = 0 ; Z P E c o r r e c t i o n s t o t h e f o r m a t i o n e n t h a l p i e s ; e n t h a l p i e s o f f o r m a t i o n w i t h Z P E c o
r r e c t i o n s a t T = 0 ; v i b r a t i o n a l c o r r e c t i o n s t o t h e e n t h a l p i e s a t T = 2 9 8 K ,
H 2 9 8 ; a s w e l l a s t h e s t a n d a r d e n t h a l p i e s o f f o r m a t i o n a t T = 2 9 8 K f o r a l l t h e r e a c t a n t s o f t h e h y d r o g e n a t i o n r e a c t i o n .
T h e l a s t l i n e r e p r e s e n t s v a l u e s c o r r e s p o n d i n g t o t h e h e a t o f t h e o
v e r a l l r e a c t i o n .
A v a i l a b l e
e x p e r i m e n t a l v a l u e s f r o m t h e d i f f e r e n t r e f e r e n c
e s a r e g i v e n i n p a r e n t h e s e s .
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O.I. Velikokhatnyi, P.N. Kumta / Materials Science and Engineering B 140 (2007) 114–122 121
As mentioned earlier, the experimental heat of reaction (2)
is 44.1kJ/mol H2, which suggests that our calculated values
of 42.6kJ/mol H2 and 53.4kJ/mol H2 at zero temperature and
298 K, respectively, are in a reasonably good agreement with
the measured values. It should be mentioned that one of the
limitations with regards to the overall validity of the calcula-
tions is the lack of experimental values of the heat of formation
for Mg(NH2)2 and Li2Mg(NH)2. According to a recent exper-
imental study reported by Hu et al. [30] however, the standard
enthalpy of formation of Mg(NH2)2 was measured using two
different calorimetric methods. Differential scanning calorime-
try (DSC) measurements conducted by them gave a value of
−325 kJ/mol, while using the conventional calorimetry method
they estimated theenthalpy of formation to be−351± 2 kJ/mol.
Theenthalpy calculated within our approach (−350.2 kJ/mol) is
thus in excellent agreement with that obtained by the calorime-
try method reported by Hu et al. [30]. It should however be
noted that the experimental values seem to differ by ∼25 kJ/mol
for the two experimental techniques used, and neither method
can however be preferred with regards to the accuracy of themeasurements. These values combined with the experimental
data for LiH and the heat of reaction (2) allow one to evalu-
ate the standard enthalpy of formation for Li2Mg(NH)2. Simple
arithmetic thus gives H 298[Li2Mg(NH)2] to be in the range
between −418.8 and −448.8kJ/mol. In comparison, our cal-
culations give the temperature corrected value of the enthalpy
of formation to be −413.9 kJ/mol. This value differs from the
above mentioned indirectly obtained experimental values by 1.2
and 7.8%, respectively. Hence, it can be seen that there is in gen-
eral a good agreement between the calculated values of the heat
of the overall reaction (2) and the enthalpies of formation of
all the three reactants with those reported in the literature andshown in Table 3. It also can be seen, that taking into account the
zero-point energy correction drastically improves the accuracy
of the heat of the reaction from 61.5 kJ/mol H2 to 42.6kJ/mol
H2, although thecorrectionfor thenon-zerotemperature deterio-
rates the final result to some extent. However, as for the standard
enthalpies of formation of all the three reactants of reaction
(2) the finite temperature corrections H T =298 do improve the
results for T = 298 K rendering them to be more realistic (see the
last column of Table 3).
It should be mentioned that in the present study the very large
super cells chosen for the phonon calculations for Mg(NH2)2
and Li2Mg(NH)2 required the calculations to consume quite a
bit of the computational resources. Hence we did not evalu-ate the dependence of the zero-point energy corrections on the
cell volumes of the materials. Since the elements constituting
the materials are light, taking into account the ZPE dependence
on the cell volume might improve the calculated enthalpies of
formation and therefore, the heat of the hydrogenation reaction.
A few words however,shouldbe dedicated to thediscrepancy
between calculated and measured heats of the overall reaction
(2), which is∼20%. In termsofabsolutevalues of thepercentage
error, this could be considered unacceptable and one could per-
haps question the validity of the calculation. However, it should
be noted that the heat of the overall reaction is largely dependent
on calculation of the enthalpies of formation of the individual
reactants and products, namely Li2Mg(NH)2, Mg(NH2)2 and
LiH. By taking into account the accuracy of all the three indi-
vidual enthalpies of formation the cumulative error could be
even significantly larger. It is probably more prudent to see the
difference in the actual values of the heat of the overall reaction
rather than focusing on the percentage error.
Based on the difference between the experimental and calcu-
lated H 298 for LiH,whichis anerror of ∼7%,andassuming an
uncertainty in the measured enthalpies for Mg(NH2)2, obtained
from [30], which is of the order of ∼7%, combined with the
∼7% error in the heat of formation calculated for Li2Mg(NH)2,
the accuracy of the heat of the overall reaction (2) can be easily
estimated. Assuming that theaccuracies of thecalculated H 298
for the all three materials are within ±7% of the experimental
value, the maximum error for the heat of the reaction will be:
(0.07)12 (H 298[Li2Mg(NH)2]+∆H 298[Mg(NH2)2]
+2H 298[LiH]) ≈ ±30 kJ/molH2
It should be noted that during the calculation of H R there areseveralcancellationsof errorspresentedin E el.tot., E ZPE,and E vib
for metallic Libcc, Mghcp, and N2 molecule, resulting in a more
accurate final value of H R. Considering this it can be seen that
the calculated value of the heat of the overall reaction in our
case deviates from the experimental value by less than an abso-
lute value of 10 kJ/mol (53.4 kJ/mol versus 44.1kJ/mol). The
difference in 10 kJ/mol is still very much below the absolute
value of ±30 kJ/mol determined above considering the over-
all ∼7% error thus rendering the calculations presented in this
work quite acceptable. We believe that the major contribution to
this error for the heat of the reaction primarily arises from the
inability to treat the crystal structure of Li2Mg(NH)2 with frac-tionaloccupancy of metal atoms using theVASP technique. The
accuracy of our calculated values of the formation enthalpies for
Li2Mg(NH)2 and Mg(NH2)2 nevertheless, will however depend
on the availability of accurate experimental information.
4. Conclusions
In summary, the main outcome of the present study could be
described as follows:
1. For the first time the electronic structure and density of states
as well as the vibrational properties have been calculatedfor lithium magnesium imide Li2Mg(NH)2 and magnesium
amide Mg(NH2)2. It has been shown that GGA approxima-
tion to the exchange-correlation potential allows us to obtain
the calculated structural parameters of the materials with an
accuracy of ∼1.5–2%.
2. Thepresent approach provides a methodology to predict with
a rather reasonable accuracy different thermodynamic prop-
erties of hydrogen storage materials, such as enthalpies of
formation and heats of the overall reactions at finite temper-
ature, which is extremely useful in the design and evaluation
of current and next generation hydrogen storage materials
with improved hydrogen storage properties.
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122 O.I. Velikokhatnyi, P.N. Kumta / Materials Science and Engineering B 140 (2007) 114–122
3. Finally, the observed variation of ∼20% in the experimen-
tally determined heat of reaction (2) and the calculated value
might liein theinherentdifficulty to treat therandom distribu-
tion of Li and Mg atoms with fractional occupation numbers
using the VASP technique. In any case, the accuracy of the
approach can also be further validated with the availability
of an accurate experimental measurement of the enthalpies
of Li2Mg(NH)2 and Mg(NH2)2. Nevertheless, the experi-
mentally obtained heat of the overall reaction and enthalpies
of formation for LiH and Mg(NH2)2 clearly point in favor
of the rational implementation and viability of the present
approach.
Acknowledgments
The authors are grateful and sincerely appreciate the assis-
tance of Dr. Ping Chen for initially providing the structural
data of the lithium magnesium imide. Also, the authors wish to
thank Prof. D. Alf e for his help in use of the phonon calculation
program “PHON”, as well as Dr. G.E. Blomgren for fruitful dis-cussions of the current work. The authors also acknowledge the
support of the Pittsburgh Super-computing Center for generous
allocation of computation units.
References
[1] Z.W. Xiong, G. Wu, J. Hu, P. Chen, Adv. Mater. 16 (2004) 1523.
[2] T. Ichikawa, N. Hanada, S. Isobe, H. Leng, H. Fujii, J. Phys. Chem. B 108
(2004) 7887.
[3] P. Chen, Z. Xiong, J. Luo, J. Lin, K.L. Tan, Nature 420 (2002) 302.
[4] L. Schlapbach, A. Zuttel, Nature 414 (2001) 353.
[5] F. Pinkerton, B.G. Wicke, Ind. Phys. 10 (1) (2004) 20.
[6] W. Luo, J. Alloys Compd. 381 (2004) 284.
[7] Z. Xiong, J. Hu, G. Wu, P. Chen, W. Luo, K. Gross, J. Wang, J. Alloys
Compd. 398 (2005) 235.
[8] W. Luo, E. Ronnebro, J. Alloys Compd. 404–406 (2005) 392.
[9] J.F. Herbst, L.G. Hector Jr., Phys. Rev. B 72 (2005) 125120.
[10] K. Miwa, N. Ohba, S. Towata, Phys. Rev. B 71 (2005) 195109.
[11] Y. Song, Z.X. Guo, Phys. Rev. B 74 (2006) 195120.
[12] G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251.
[13] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15.[14] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244.
[15] D. Alf e (1998). Program available at http://chianti.geol.ucl.ac.uk/ ∼dario.
[16] G. Kresse, J. Furthmuller, J. Hafner, Europhys. Lett. 32 (1995) 729.
[17] K. Parlinski, Z.Q. Li, Y. Kawazoe, Phys. Rev. Lett. 78 (1997) 4063.
[18] Y. Gao, J. Rijssenbeek, J.-C. Zhao, Symposium on Advanced Materials for
Energy Conversion III TMS Annual Meeting & Exhibition, 2006.
[19] J. Rijssenbeek,Y.Gao, J.C.Hanson,Q. Huang, C. Jones, B.H.Toby, Crystal
structure determination and reaction pathway of amide-hydride mixture, J.
Alloys Compd. (2007), in press, doi:10.1016/j.jallcom.2006.12.008.
[20] J. Korringa, Physica 13 (1947) 392;
W. Kohn, N. Rostoker, Phys. Rev. 94 (1954) 1111.
[21] L. Vitos, Phys. Rev. B 64 (2001) 014107.
[22] H. Jacobs, Z. Anorg. Allg. Chem. 382 (2) (1971) 97.
[23] H. Jacobs, R. Juza, Z. Anorg. Allg. Chem. 370 (5/6) (1969) 254.
[24] E. Zintl, A. Harder, Z. Phys. Chem. B28 (1935) 478.[25] H. Smithson, C.A. Marianetti, D. Morgan, A. Van der Ven, A. Predith, G.
Ceder, Phys. Rev. B 66 (2002) 144107.
[26] G. Roma, C.M. Bertoni, S. Baroni, Solid State Commun. 98 (1996) 203.
[27] G. Linde, R. Juza, Z. Anorg. Allg. Chem. 409 (1974) 199.
[28] J.-P. Boghler, R.R. Essman, H. Jacobs, J. Mol. Struct. 348 (1995) 325.
[29] G. Herzberg, Molecular Spectra and Molecular Structure. 1. Diatomic
Molecules, Prentice-Hall, New-York, 1939.
[30] J. Hu, G. Wu, Y. Liu, Z. Xiong, P. Chen, K. Murata, K. Sakata, G. Wolf, J.
Phys. Chem. B 110 (2006) 14688.
[31] M.R. Nadler, C.P. Kempfer, Anal. Chem. 31 (1959) 2109.
[32] C.B. Walker, M. Marezio, Acta Met. 7 (1959) 769.
[33] CRC Handbook of Chemistry and Physics, 67th ed., CRC Press, Boca
Raton, FL, 1986, p. F-159.