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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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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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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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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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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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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.

7/24/2019 1-s2.0-S0921510707002164-main



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.

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