Thermodynamic analysis of hydrogen sorption reactions in Li–Mg–N–H systemsC. Moysés Araújo, Ralph H. Scheicher, and Rajeev Ahuja

Citation: Applied Physics Letters 92, 021907 (2008); doi: 10.1063/1.2830703 View online: http://dx.doi.org/10.1063/1.2830703 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/92/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in New ab initio potential energy surface and quantum dynamics of the reaction H(2S) + NH(X3) N(4S) + H2 J. Chem. Phys. 135, 104314 (2011); 10.1063/1.3636113 Alchemical derivatives of reaction energetics J. Chem. Phys. 133, 084104 (2010); 10.1063/1.3474502 Positron depth profiling of the structural and electronic structure transformations of hydrogenated Mg-based thinfilms J. Appl. Phys. 105, 043514 (2009); 10.1063/1.3075762 The importance of hydrogen’s potential-energy surface and the strength of the forming R – H bond in surfacehydrogenation reactions J. Chem. Phys. 124, 044705 (2006); 10.1063/1.2159482 Investigation of the hydrogenation properties of Zr films under unclean plasma conditions J. Vac. Sci. Technol. A 20, 1840 (2002); 10.1116/1.1506174

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Thermodynamic analysis of hydrogen sorption reactionsin Li–Mg–N–H systems

C. Moysés Araújoa� and Ralph H. ScheicherCondensed Matter Theory Group, Department of Physics, Uppsala University, P.O. Box 530,S-751 21 Uppsala, Sweden

Rajeev AhujaCondensed Matter Theory Group, Department of Physics, Uppsala University, Box 530, S-751 21 Uppsala,Sweden and Applied Materials Physics Group, Department of Materials and Engineering,Royal Institute of Technology (KTH), S-100 44 Stockholm, Sweden

�Received 9 November 2007; accepted 11 December 2007; published online 17 January 2008�

We report a comprehensive first-principles study of the thermodynamics of the hydrogen releasereaction from xLiH–yMg�NH2�2 mixtures involving the composition ratios �x=2, y=1�, �x=8, y=3�, and �x=12, y=3�, with special emphasis on the effect of the different intermediate steps. Forall three mixing ratios of LiH /Mg�NH2�2 we find that the hydrogen release is initiated by the samereaction with an enthalpy of 46.1 kJ /mol of H2 in excellent agreement with recent experimentalresults. Additionally, we also investigated the substitution of LiH by MgH2 as reaction partner ofMg�NH2�2 in the fully hydrogenated state. © 2008 American Institute of Physics.�DOI: 10.1063/1.2830703�

The actual grand challenge in the field of hydrogenstorage research lies in finding an on-board storage systemthat meets the requirements of high performance �highH-capacity, fast kinetics, and favorable thermodynamics�,safety, and cost effectiveness simultaneously.1–7 A great dealof attention has been paid to investigate the solid-statehydrogen storage in complex chemical hydrides �CCH�,following the pioneering work by Bogdanovic andSchwickardi,8 who showed that the addition of a smallamount of a certain catalyst, for instance TiCl3, cannot onlyfasten the kinetics of the hydrogen desorption from sodiumalanate, but, more importantly, can also make such a processreversible. Despite a great number of experimental and the-oretical works present in the current literature aimed at un-derstanding the role of different catalysts in CCH systems, aconclusive picture of the catalysis mechanisms has not yetemerged. A noteworthy progress in this field was achieved inan investigation by Chen et al.9 where the hydrogenation oflithium nitride, Li3N, was shown to be reversible without theneed for any catalyst. The process takes place in the follow-ing two-step reactions:

Li3N + H2 ↔ Li2NH + LiH �1�

Li2NH + H2 ↔ LiNH2 + LiH. �2�

Moreover, with 11.5 wt %, the hydrogen storage capacity ofthese reactions even exceeds current goals set by the U.S.Department of Energy. However, the involved thermody-namic and kinetic properties still require further improve-ment before this approach could be considered suitable foron-board applications. This is, on the one hand, due to strongpolar covalent bonds between hydrogen and nitrogen and, onthe other hand, due to the strong ionic bonds that hold theNH2

− and NH2− units, and H− �in the case of LiH�. Hence, agreat deal of effort has been made to devise ways to desta-bilize these systems, i.e., to weaken the chemical bonds be-

tween hydrogen and the host solid, while simultaneouslykeeping any detrimental impact on the hydrogen storage ca-pacity to a minimum.

One approach that has most widely been investigatedconsists of partially replacing Li by Mg leading to hydrogenstorage in the Mg�NH2�2–LiH mixture instead ofLiNH2–LiH mixture �see Eq. �2��. This has been achievedindependently by four research groups, using different start-ing materials. Both Luo10 and Xiong et al.11 investigated theH release from the 2LiNH2–MgH2 mixture. Leng et al.12

studied the H release from 3Mg�NH2�2–12LiH mixture. Fi-nally, Nakamori et al.13 followed a rather different approach,studying the hydrogenation of the Mg3N2–4Li3N mixture.The common outcome of all these experiments was a fullyhydrogenated state composed of a mixture of LiH andMg�NH2�2, however, with different composition ratios. Indetail, the following reversible hydrogen storage reactionshave been identified10–13

Li2Mg�NH�2 + 2H2 ↔ 2LiH + Mg�NH2�2, �3�

4Li2NH + Mg3N2 + 8H2 ↔ 8LiH + 3Mg�NH2�2, �4�

4Li3N + Mg3N2 + 12H2 ↔ 12LiH + 3Mg�NH2�2. �5�

These modified systems display much more favorablethermodynamics than those from Eqs. �1� and �2�. The hy-drogen desorption pressure is above 1 MPa at 180 °C. More-over, their theoretical hydrogen capacity is quite high,namely 5.6 wt % for Eq. �3�, 6.9 wt % for Eq. �4�, and9.1 wt % for Eq. �5�. It is due to these results that the Li–Mg–N–H system has received significant attention over thepast years and has been regarded as a rather promising lightmetal hydride for applications in hydrogen storage. However,a fundamental understanding of the mechanism and thermo-dynamics involved in those reactions is missing.

The aim of this letter is to provide a complete first-principles analysis of the varied thermodynamics of hydro-gen sorption reactions in Li–Mg–N–H systems. We willa�Electronic mail: moyses.araujo@fysik.uu.se.

APPLIED PHYSICS LETTERS 92, 021907 �2008�

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show that the complete dehydrogenation process forLiH /Mg�NH2�2 ratios of 2 /1, 8 /3, and 12 /3 proceed in one,two, and three reaction steps, respectively. In particular, for acomposition ratio of 12 /3, we confirm by theoretical meansthat Li3N and Mg3N2 mix up to form LiMgN for which wehave found a mixing enthalpy of 56.1 kJ /mol of Mg3N2.Finally, we have also computationally studied the thermody-namics of hydrogen absorption/desorption cycles when LiHis replaced by MgH2 as reaction partner of Mg�NH2�2 in thefully hydrogenated state.

All calculations were performed at 0 K. Thus, the en-thalpy �H reduces to the sum of electronic total energy �ET�,zero-point vibration energy �EZP�, and the pV term: �H0

=ET+EZP+ pV. It is characteristic for the solid-state phasethat the pV term can usually be neglected,14 and we followthis strategy in the present study as well. The vibrational freeenergies that appear at finite temperatures are expected toconstitute only a small contribution to the reaction enthalpy,which will not change our conclusions concerning the trendsin the thermodynamics of Eqs. �3�–�5�. To calculate the en-thalpy of an H2 gas molecule, we have taken into accountonly the electronic total energy and the zero-point vibrationenergy. Again, we note that the vibrational entropy at finitetemperatures will not change the trends that are the focus ofthis investigation. Such a procedure has been shown to besuitable for hydrogen storage reactions involving complexchemical hydrides.14 The calculations of total energies andzero-point vibration energies were carried out within theframework of the generalized gradient approximation15 todensity functional theory16 by using the projector augmentedwave method,17 as implemented in the Vienna Ab initioSimulation Package18 �VASP�. We tested all results reportedhere for convergence with respect to both cutoff energy andnumber of k points in a mesh generated by the Monkhorst-Pack method.19 Ionic positions and cell parameters were re-laxed with respect to minimum forces and stress using eitherconjugate-gradient or quasi-Newton algorithms. Zero-pointvibration energies were obtained from the diagonalization ofthe Hessian matrix at the gamma point. To calculate the en-ergetics of the H2 molecule, we have used a cubic supercellwith large lattice parameters �chosen to be 21 Å�, which en-sures a negligibly small intermolecular interaction. Thephases, cohesive energies per formula unit, and zero-pointvibration energies of all reactants and products appearing inthe present study are summarized in Table I.

Let us emphasize at this point that one of the noteworthyapproaches, when trying to improve the thermodynamics ofhydrogen release from lithium amide, lies in replacing LiH

by MgH2. This approach leads to the stabilization of theMg�NH2�2 phase during the rehydrogenation process, inpreference over a return to the initial reactants, MgH2 andLiNH2. Therefore, we concentrate first on investigating theenergetics of the following reaction:

2LiNH2 + MgH2 → Mg�NH2�2 + 2LiH. �6�

We find this reaction to be exothermic with an enthalpyof 68.8 kJ /mol of Mg�NH2�2 at 0 K. Thus, the formation ofMg�NH2�2 /2LiH mixture is indeed a lower energy statewhen compared to the formation of 2LiNH2 /MgH2 mixture.This result is also in good agreement with a recent experi-mental observation in which such a reaction was found totake place at 220 °C at 100 bar without hydrogen release.20

The thermodynamic conditions in the experiment were cho-sen to assure that no hydrogen would be released.

We now discuss the thermodynamics of the reaction inEq. �3�, which was originally obtained from the replacementof LiH by MgH2 as reaction partner of LiNH2 in the fullyhydrogenated state. The corresponding enthalpy diagram isdisplayed in Fig. 1�a�. We find the reaction Ia→ IIa to beendothermic with an enthalpy of 46.1 kJ /mol of H2. Thisfirst-principles result is in excellent agreement with a recentexperimental report21 which determined an overall reactionenthalpy of 46 kJ /mol of H2 for the formation of the firstplateau pressure �formation of Li2Mg�NH�2� during the hy-drogen release from 12 LiH+3 Mg�NH2�2 mixture. In thisstudy, many LiH /Mg�NH2�2 ratios were investigated but forall hydrogen started to desorb at around the same tempera-ture. In fact, as we will demonstrate in the following discus-sion, the initial hydrogen release reaction turns out to bealways the same for these systems, no matter what the actualmixing ratio of LiH and Mg�NH2�2 is.

The enthalpy diagram for the hydrogen sorption reac-tions for the mixture with a LiH /Mg�NH2�2 ratio of 8 /3 isdisplayed in Fig. 1�b�. Our results indicate that the hydrogenrelease in this system will take place in a two-step reaction.For the first step �Ib→ IIb�, we find the same reaction en-thalpy of 46.1 kJ /mol of H2 since the reaction is, in fact, thesame as for the mixing ratio of 2 /1. For the second step�IIb→ IIIb�, the reaction enthalpy calculated by us is found tobe nearly twice as large, namely 84.1 kJ /mol of H2. It isimportant to emphasize that only due to the stabilization ofLi2Mg�NH�2 the reaction 8LiH+3Mg�NH2�2→4Li2NH+Mg3N2+8H2 cannot take place as the initial hydrogen re-lease reaction and, thus, the stabilization of Li2Mg�NH�2 iscausing the higher required temperature for the second step

TABLE I. Space group, cohesive energy, and zero-point energy for everyreactant and product involved in this study.

Compound Space group Cohesive energy �eV� EZP �eV�

H2 �gas phase� 4.57 0.27LiH Fm-3m 4.79 0.22Li3N P6 /mmm 11.75 0.30Li2NH Pnma 12.89 0.48LiNH2 I-4 13.53 0.72MgH2 P42 /mmm 6.70 0.38Mg3N2 Ia-3 18.84 0.37Mg�NH2�2 I41 /acd 24.80 1.29LiMgN Pnma 10.38 0.21Li2Mg�NH�2

a Iba2 23.80 0.91

aRef. 24. FIG. 1. �Color online� Enthalpy diagrams for the corresponding reactions in�a� Eq. �3�, �b� Eq. �4�, and �c� Eq. �5�.

021907-2 Moysés Araújo, Scheicher, and Ahuja Appl. Phys. Lett. 92, 021907 �2008�

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�IIb→ IIIb�. If Li2Mg�NH�2 would not be stabilized,6.9 wt % could be released with a reaction enthalpy of55.6 kJ /mol of H2.

For a LiH /Mg�NH2�2 mixing ratio of 12 /3, the enthalpydiagram calculated by us is shown in Fig. 1�c�. Here, we findthat in order to achieve complete hydrogen release, threesteps are required. We notice that, once again, the initialhydrogen release step �Ic→ IIc� possesses a reaction enthalpyof 46.1 kJ /mol of H2 for the reason already discussed in theprevious paragraph. Similarly, the second step �IIc→ IIIc�possesses the same reaction enthalpy of 84.1 kJ /mol of H2as found for the mixing ratio of 8 /3. The third step �IIIc

→ IVc� finally involves a reaction enthalpy of 103.9 kJ /molof H2, even larger than the previous two. Generally, one findsthat increasing the LiH /Mg�NH2�2 mixing ratio by addingLiH does not lead to an increased amount of hydrogen des-orbed in the first step. Instead, a portion of LiH will not takepart in the initial reaction and store hydrogen until furtherrelease can be achieved at higher desorption temperatures.

We would like to add that based on our calculations, forEq. �5�, the final product appears not to be 4 Li3N+Mg3N2�plus the desorbed hydrogen gas�, but instead Li3N willrather react with Mg3N2 to form the mixed compoundLiMgN. The most stable fully dehydrogenated state is, thus,3 Li3N+3 LiMgN which is lower in energy than the combi-nation of 4 Li3N+Mg3N2 by 56.1 kJ /mol of Mg3N2.

As discussed above, the partial substitution of Li by Mgalways leads to the replacement of LiNH2 by Mg�NH2�2 inthe fully hydrogenated state. On this basis, and followingrecent experiments22,23 we decided to investigate the effectsof replacing LiH by MgH2 as a reaction partner ofMg�NH2�2. The complete dehydrogenation is achieved for aMgH2 /Mg�NH2�2 ratio of 2 /1 where Mg3N2 may be stabi-lized following the hydrogen release. 4 H2 molecules arereleased in an endothermic reaction for which we have foundan enthalpy of 11.5 kJ /mol of H2. By raising the pressure, itmight be possible to stabilize this state. The hydrogen con-tent for this system is rather high, namely 7.4 wt %.

In summary, we have provided a systematic theoreticalinvestigation of the thermodynamics of hydrogen storage re-actions in the Li–Mg–N–H systems. By employing first-principles calculations, we have shown that the mixture ofMg�NH2�2 and LiH is energetically more stable than that ofLiNH2 and MgH2, illustrating that the stabilization of thehydrogenated state in Eq. �3� is driven by equilibrium ther-modynamic conditions rather than reaction barriers.

We find for all three mixing ratios of LiH /Mg�NH2�2

that the hydrogen release is initiated by the same reactionwith an enthalpy of 46.1 kJ /mol of H2 in excellent agree-ment with experiment.21 This initial release is followed by asecond desorption step for mixing ratios 8 /3 and 12 /3 with alarger reaction enthalpy �84.1 kJ /mol of H2�, and for themixing ratio 12 /3 by a third step with an even larger reactionenthalpy of 103.9 kJ /mol of H2. Thus, while the weight per-centage of hydrogen stored in the respective reactions withvarious mixing ratios differs, the actual amount of hydrogengas released at the lowest �and presumably only practical�

temperature remains the same. Higher temperatures are re-quired to desorb all the hydrogen stored in the system, whichrenders it virtually inaccessible at conditions suitable for ve-hicular hydrogen storage applications.

Furthermore, we have found that the most stable dehy-drogenated state for the mixing ratio 12 /3 is not the oneshown in Eq. �5�, but rather Li3N mixed with Mg3N2 form-ing LiMgN. The corresponding mixing enthalpy is56.1 kJ /mol of Mg3N2.

Finally, we have investigated the replacement of LiH byMgH2 as reaction partner of Mg�NH2�2 in the fully hydro-genated state. Here, we conclude that the fully dehydroge-nated state is achieved for a MgH2 /Mg�NH2�2 ratio of 2 /1where Mg3N2 is stabilized following the H2 release. Thissystem shows great potential as a feasible hydrogen storagemedium with a high weight percentage of absorbed hydrogenof 7.4 wt %. Although the reaction enthalpy was found to bemerely 11.5 kJ /mol of H2, implying that the hydrogenatedstate is not stable at ambient conditions, it might neverthelessstill be possible to control the hydrogen sorption mechanismby applying higher pressure to the system.

We are grateful to the Swedish National Infrastructure�SNIC� for computing time. Financial support from Swedishfunding agencies STINT, VR, FUTURA, SSF, and GG isalso acknowledged.

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021907-3 Moysés Araújo, Scheicher, and Ahuja Appl. Phys. Lett. 92, 021907 �2008�

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