Thermodynamic Properties of Trialkali (Li, Na, K) Hexa-alanates: A

18598

J. Phys. Chem. C 2008, 112, 18598–18607

Thermodynamic Properties of Trialkali (Li, Na, K) Hexa-alanates: A Combined DFT and Experimental Study L. Jeloaica,† J. Zhang,‡ F. Cuevas,‡ M. Latroche,‡ and P. Raybaud*,† IFP, Direction Chimie et Physico-chimie Applique´es, et Direction Catalyse et Se´paration, Rond-point de l’e´changeur de Solaize, BP 3-69360 Solaize, France, and Chimie Me´tallurgique des Terres Rares, ICMPE-CNRS UMR 7182, 2-8 rue Henri Dunant, 94320 Thiais, France ReceiVed: May 27, 2008; ReVised Manuscript ReceiVed: August 29, 2008

The present work combines periodic density functional theory (DFT) calculations of thermodynamic properties and experimental synthesis to explore the ternary (Li, Na, K) phase diagram of LixNayK3-x-yAlH6 hexaalanates. About 70 virtual phases, of various possible structures and different alkali metal compositions are investigated by DFT simulations. The thermodynamic stability of each of the 10 phases found to exhibit relative low formation energies is tested versus the decomposition into mixtures of monoalkali hexa-alanates. Three potentially stable candidate phases are revealed. Among them, only LiNaKAlH6 may compete with the stability of the mixture of bialkali hexa-Alanate and monoalkali tetra-alanate phases according to DFT calculation. We attempt to synthesize different trialkali hexa-alanates by ball milling of NaH, LiH, KH, Al, and 2 mol % TiCl3 under hydrogen pressure of 10 MPa near room temperature. For the various tested compositions, the X-ray diffraction (XRD) analysis reveals only the formation of monoalkali hydrides and bialkali hexa-alanates mixed with the tetra-alanate KAlH4 phase. As a consequence of the experimental and theoretical investigations, the alternative furnished by trialkali hexa-alanates is seriously questioned. The LiNaKAlH6 phase, the best potential candidate according to DFT calculations, was not successfully formed by ball milling synthesis. Finally, we propose a general interpretation of the relative difference of Van’t Hoff plots of the first and the second dehydrogenation steps, which gives out the thermodynamic limit of alkali alanates as potential materials for on board reversible hydrogen storage. 1. Introduction The implementation of hydrogen-based propulsion systems is at present hampered by the absence of a viable on-board storage technology, which is capable to provide compact, light and affordable containment. Since the pioneer work of Bogdanovic´ and Schwickardi,1 who found that Ti-catalyzed NaAlH4 can release hydrogen under moderate conditions, the potential interest of alkali metal aluminum hydrides (AAlH4 and A3AlH6 with A ) Li, Na, K) for reversible hydrogen storage remains vivid. The theoretical values of intrinsic gravimetric density (close to 6 wt %) and volumetric density (close to 90 g/L) of alkali alanate phases make these compounds attractive for on board hydrogen storage. In particular, it is known that the alkali alanates release hydrogen following the three subsequent steps:

3AAlH4 f A3AlH6+2Al + 3H2

(1)

A3AlH6 f 3AH + Al + 3⁄2H2

(2)

3AH f 3A + 3⁄2H2

(3)

Due to the strong stability of the AH monohydrides, the third step occurs in (T, P) conditions not compatible with the on board storage of hydrogen, and is thus omitted in the actual context. In contrast, depending on the alkali metals, steps (1) and (2) occur for more reasonable (T, P) conditions, however still not compatible with on board hydrogen storage conditions and the * To whom correspondence should be addressed. Phone: +33.4.78.02. 56.20. Fax: +33.4.78.02.20.66. E-mail: [email protected]. † IFP. ‡ ICMPE-CNRS UMR 7182.

use of a fuel cell (20 °C < T < 80 °C and 1 < P < 10 bar). Hence, these materials are the subject of numerous experimental and theoretical investigations in order to attempt to improve the (T, P) conditions at which the highest gravimetric and volumetric H2 density may be reversibly stored.2,3 The position of the (T, P) Van’t Hoff plot depends directly on the dehydrogenation enthalpies of steps (1) and (2), annotated ∆H(i) dehyd in what follows. To fulfill the (T, P) on-board constraints, the values of ∆H(i) dehyd must be comprised between +25 and +50 kJ/mol H2 with an optimal value at 40 kJ/mol H2.3 Reactions with ∆H(i) dehyd higher than this range, will experience insufficient hydrogen pressure until the temperature becomes unacceptably high. On the other hand, if ∆H(i) dehyd is less than 25 kJ/mol of H2, the material will not be easily reversible. In order to optimize this thermodynamic value together with the storage capacity, one strategy, undertaken in the present work, is to change the chemical composition (i.e., partial substitution of elements) in alkaline metals of the tetra and/or hexa-alanates compounds and to explore whether new stable bi- or trialkali hexa-alanate phases can be involved during reactions (1) and (2) and improve the thermodynamic properties. A similar strategy was successfully applied for rare earth-nickel metal hydrides of LaNi5H6.5 type (used for stationary hydrogen storage) where the thermodynamic properties of the equilibrium plateau can be tuned by modifications of the alloy composition either in rare earth or transition metals.4,5 Extended prior theoretical works have demonstrated that DFT modeling is a reliable method to predict the thermodynamic properties of various hydrogen storage materials 6-10 and thus to explore the partial substitution of alkali elements in alanates. In particular, Løvvik et al.7,11,12 and Ceder et al.13 recently

10.1021/jp804652a CCC: $40.75  2008 American Chemical Society Published on Web 11/04/2008

Thermodynamic Properties of Hexa-alanates

J. Phys. Chem. C, Vol. 112, No. 47, 2008 18599

TABLE 1: Relevant Energy Values of the Mono- and Bi-alkali Hexa-alanates: Formation Energy (∆Eform), Mixing Energy (∆Emix), Decomposition Energy (∆Edecomp) in kJ/mol, (i) (i+1) ) for the Two Dehydrogenation Energy (∆Edehyd and ∆Edehyd (i+1) Dehydrogenation Reactions, and the Value ∆Edehyd (i) ∆Edehyd (Called δ∆Edehyd) in kJ/mol H2 phasesa

∆Eform

Li3AlH6 Na3AlH6 K3AlH6 LiK2AlH6 LiNa2AlH6 NaK2AlH6

-293.88 -191.33 -235.31 -293.53 -236.83 -265.94

(i) b ∆E(i+1) b δ∆E ∆Emix ∆Edecomp ∆Edehyd dehyd dehyd

-38.70 -11.32 -45.29

+25.78 +20.94 +13.99 +32.40 +21.64 +49.62

+1.56 +27.64 +53.92 +24.27 +15.92 +30.67

+27.34 +48.58 +67.91 +80.19 +49.05 +91.66

+25.78 +20.94 +13.99 +54.51 +31.66 +59.77

a The most stable experimental structures have been used for the calculations. b i ) 1 for monoalkali alanates, and i ) 11 for bialkali alanates.

Figure 1. Calculated Van’t Hoff plots for (a) the mono alkali tetraand hexa-alanates, and (b) the bialkali hexa-alanates. The dashed lines correspond to the first dehydrogenation reactions (1) and (10), the full lines correspond to the second dehydrogenation reactions (2) and (11). The gray area corresponds to the thermodynamic target in (273 K < T < 373 K and 1 bar < P < 20 bar) conditions including those for on board hydrogen storage.

reported results on the stability of bialkali tetra-alanates at 0 K. No mixed alkali tetra-alanates were found to be stable by these studies, whereas three bialkali hexa-alanates (LiNa2AlH6, LiK2AlH6, and NaK2AlH6) were predicted to be stable. These results were supported by experimental works 14,15 which also encourages the exploration of new mixed alkali alanates. Indeed, despite the lack of evident improvements over the best system known, sodium alanate, these results have demonstrated that appropriate cation substitutions furnish an avenue to modify the unfavorable thermodynamics of the potentially interesting H-storage materials, thus leaving room for further investigations based on the synthesis of new complex alkali alanate phases. The challenge of the present work is to explore the trialkali hexa-alanate phases. For that purpose, we first use a DFT molecular modeling approach for screening a large number of LixNayK3-x-yAlH6 bulk phases spanning different lattice structures and various Li, Na, K composition ratio in the attempt to find the stable ones when compared to existing mono- and bialkali phases. The calculation of the Van’t Hoff plots for the dehydrogenation/rehydrogenation reactions is also undertaken in order to check whether the thermodynamic properties of the most important candidates are consistent with the bounds outlined above. In a second time, we attempt to synthesize by mechanical ball milling under hydrogen pressure the trialkali phases in the most promising domains of chemical compositions suggested by the DFT simulation.

2. Theoretical and Experimental Methods 2.1. Total Energy Calculations. Total energy calculations are performed within periodic density functional theory (DFT) and the generalized gradient approximation (GGA) of Perdew and Wang.16,17 To solve the Kohn-Sham equations, we use the Vienna ab initio Simulation Package (VASP).18,19 The electronic wave functions are described within the projector augmented waves (PAW) approach20 by explicitly treating one valence electron configurations for H (1s1) and Li (2s1), seven for Na (2p63s1), nine for K (3s23p64s1) and three for Al (3s23p1). The electronic convergence criterion in the self-consistent cycle is fixed at 0.1 meV per cell. Ground state geometries are determined by minimizing the stresses and Hellmann-Feynman forces with the conjugate-gradient algorithm until forces on all atomic sites have become less than 1 meV Å-1. In order to span the wide range of possible phases of the studied compounds, a very large number of simultaneous relaxations of cell volume and shape as well as atomic positions have been performed in two-step of increasing precision. Therefore, one large set of bulk geometric relaxations for systems of eight different composition rations in alkali metals and with different initial crystal structures is first performed. For this, various ordered structures for each of the composition are built from supercells containing 30-60 atomic sites including hydrogen. The energies are carried out by employing the real-space projection scheme with 1000 points in the sphere around each atom and a Gaussian broadening of 0.1 eV. After the selection of the lowest energy phases within each class of equivalent composition, a second set of optimizations at higher accuracy is performed on the ten phase structures prior to the analysis of the thermodynamic functions. From various tests, we found that integrating the Brillouin zone at 750 eV cutoff over k grids of around 7 × 7 × 7 points with tetrahedron plus Blo¨chl corrections method, ensures optimum accuracy in the total energies calculations of the studied systems. The variation in supercell’s size is related to the constraints imposed by the chemical composition. From the 0 K total energy calculations, we calculate energy descriptors such as the formation energy (∆Eform), the dehydrogenation reaction energy (∆E(i) dehyd), the mixing energy (∆Emix) and the decomposition energy (∆Edecomp). The formation energy (∆Eform) is clearly defined with respect to the energy of each element in its standard state. The dehydrogenation energies (∆E(i) dehyd), where i )1 or 2 indexes the step according to reactions (1) and (2) defined in introduction, or in their more general form defined by equations given in the following sections of the paper. We approximate the enthalpy of dehydrogenation by the energy of dehydrogenation at 0 K, thus neglecting the contribution of the lattice vibrations in solids and finite temperature. For the current work’s purpose, this approximation is sufficient as it leads to a reasonable energy values as detailed by previous theoretical studies.21 The finite temperature contributions to the vibrational enthalpy, in the approximation of harmonic lattice vibrations and the limit of high temperature, are determined by the equipartition theorem and thus independent of the phase considered. One may ascribe that it influences at little extent on the phase stability. By contrast, zero point vibrational contributions (of the bulk phase and H2 molecule) to the enthalpy of reactions of light hydrides, range typically within -20 to 0 kJ/mol H2,21 which can represent the accuracy reached on ∆E(i) dehyd. Nevertheless, they are partially offset by the H2 translational, rotational and PV contributions at finite temperature.

18600 J. Phys. Chem. C, Vol. 112, No. 47, 2008

Jeloaica et al.

TABLE 2: Cell Parameters (Å) and Angles (deg) of the Metastable Hexa-alanate Phasesa phase-formulab

space group

a

b

c

R

β

γ

H wt % (22)

H wt % (23)

H vol. dens

1-Li2Na1/2K1/2 2-Li3/2Na1/4K5/4 3-Li4/3Na1/3K4/3 4-Li7/4Na1/4K 5-Li5/3Na2/3K2/3 6-Li3/2Na1/2K 7-Li7/6NaK5/6 8-LiNaKb 9-Li2Na1/3K2/3 10-Li5/3Na1/3K

Pmmm Pmma P1 Pmma P3 Pmmm P1 P4/nmm P1 P1

10.222 10.756 5.364 10.663 10.53 10.737 9.045 5.358 10.363 10.605

7.415 7.719 9.445 7.664 10.53 7.584 9.075 5.358 10.344 10.592

10.536 9.445 13.159 10.619 13.025 10.736 10.349 7.650 13.212 13.055

90 90 90.75 90 90 90 88.80 90 89.37 90.02

90 90 89.84 90 90 90 92.34 90 91.32 89.93

90 90 90.09 90 120 90 119.07 90 120.57 120.11

6.58 5.74 5.60 6.05 6.21 5.89 5.79 5.60 6.45 5.99

3.88 3.08 2.96 3.36 3.52 3.22 3.13 2.96 3.75 3.31

49.9 44.6 44.8 45.9 47.8 45.6 40.3 45.4 49.1 47.1

a The gravimetric density (wt %) according to reactions (22) and (23) and hydrogen volumetric density (kg H/m3) are also given. b For the LiNaK phase, the crystallographic data of the four competing structures are reported in the Supporting Information.

systems.15 It can be added that the DFT calculation of the entropy of the H2 isolated molecule leads to similar values used in the Van’t Hoff plots. The mixing energy (∆Emix) is defined for the bi- and trialkali hexa-alanates with respect to the mono alkali hexa-alanates:

x ⁄ 3 Li3AlH6+y ⁄ 3 Na3AlH6+ (3 -x-y) ⁄ 3 K3AlH6 f LixNayK3-x-yAlH6 (5) x ∆Emix ) E(LixNayK3-x-yAlH6) - E(Li3AlH6) 3 y 3-x-y E(Na3AlH6) E(K3AlH6) (6) 3 3

Figure 2. Trialkali hexa-alanate phase diagram. The stable bialkali hexa-alanates are shown by triangles. The 10 metastable trialkali phases explored in this work are represented by dots.

From the value of the dehydrogenation energy, ∆E(i) dehyd, it is possible to construct the Van’t Hoff plots and give an estimate of the equilibrium pressure and temperature at which the dehydrogenation may take place by using the following equation corresponding to reactions (1) and (2):

( )

i i ∆Hdehyd Peq ∆Sdehyd ln )+ P0 RT R ()

()

(4)

where Peq is the equilibrium H2 pressure at temperature T with P0 the standard pressure (1 atm), R is the universal gas constant, (i) and ∆H(i) dehyd and ∆Sdehyd are the dehydrogenation enthalpies and entropies of reactions (1) and (2). According to the aforemen(i) tioned approximation, ∆H(i) dehydwill be approximated by ∆Edehyd in eq 4. Bulk entropic contributions to ∆S(i) dehyd are rather small. Indeed, the contributions from the mixing of alkali metals into binary and ternary solid phases considered here do not exceed 2-3 J/K/mol H2, while the entropic contributions from lattice vibrations are even small, typically of the order of 0.2 kB. Finally, since the free energy of H2 molecule is quite sensitive to entropic effects at finite temperatures, it will be the main contribution to ∆S(i) dehyd and we make use of the experimental standard entropy of H2 (130.684 J/K/mol H2) in the expression of free energy for gas. For the current work’s purpose, the approximation ∆S(i) dehyd = ∆SH2 leads to reasonable energy values as shown by previous experimental and theoretical works.15,21 The dehydrogenation entropies ∆S(i) dehyd are generally close to 130 and 135 J/mol K at T around 500 K even for bialkali

A negative mixing energy indicates that the mixing process is favored. In contrast, if the mixing energy is positive, it is suspected that the bi- or trialkali hexa-alanate (LixNayK3-x-yAlH6) may segregate into monoalkali hexa-alanates. A last energy descriptor, called decomposition energy (∆Edecomp), will be considered to investigate the stability of trialkali hexa-alanates with respect to other bialkali hexa alanates, tetra-alanates and alkali hydrides. The specific expressions of ∆Edecomp will be given further in the manuscript. 2.2. Experimental Methods. Conventionally, alanates are prepared by a wet chemical route. NaH and Al are diluted in THF and hydrogen pressure up to 20 MPa at 150 °C is applied for few days. Subsequently, the NaAlH4 in solution is filtered and dried. Since the solubility of NaAlH4 is very low, high amount of solvent is necessary. Dymova et al.22 have shown that the synthesis of NaAlH4 can be obtained from Na, Al, and H2 at high temperature (280 °C), where Na is in liquid state, and high hydrogen pressure (17.5 MPa). Recently, alternative methods for the preparation of alanates have been investigated. Thus, it has been shown23 that NaAlH4 can be formed by milling NaH and Al under a hydrogen atmosphere of 8.3 MPa. TiCl3 (4 mol %) was added as a dopant. In the present work, we have attempted to prepare bialkali- and trialkali-alanates by the same ball milling method. Starting chemicals were NaH (95%), LiH (95%), Al (99%), and TiCl3 (99.99%) in powder form purchased from Sigma Aldrich, Germany. KH was received in mineral oil (30 wt %). It was washed and filtered several times with heptane in order to separate it from the oil, followed by evaporation of the solvent under primary vacuum. For the synthesis, a mixture of Al powder with the appropriate amount of different alkali hydrides and 2 mol% of TiCl3 were reactively milled under hydrogen at a pressure of about 10 MPa in a Fritsch Pulverisette 4 planetary mill. The attempted reaction is



xLiH + yNaH + (3 -x-y)KH + Al + 2 mol % TiCl3

⁄2H2 98 LixNayK3-x-yAlH6 (7)

3

The milling was performed at a rotation speed of 400 rpm with a ball-to-powder mass ratio of 90:1. Stainless steel balls of 15 mm in diameter were used. The milling vial, purchased from Evicomagnet (Germany), was equipped with gauges allowing to monitor pressure and temperature during the milling process. The milling was stopped after a sharp H2 pressure decrease was observed indicating that gas reaction with powders had occurred. All sample operations were done in argon filled and purified glovebox. The prepared samples were characterized by X-ray diffraction (XRD) using a diffractometer Bruker D8 Advance with Cu KR radiation. To prevent any reaction with air, a special airtight sample holder from Bruker was used for XRD measurements. Phase analysis and structural determination were done by using the full profile fitting program FULLPROF24 based on the Rietveld method. 3. Results and Discussion 3.1. Case of Bialkali Hexa-alanates. 3.1.1. Thermodynamic Stability. The theoretical investigations by Løvvik et al.7,12 and experimental works by Graetz et al.15 applied to bialkali hexaalanates show that three stable phases (LiNa2AlH6, NaK2AlH6, and K2LiAlH6) have been found to exist. The mixing energies reported for the three stable phases in Table 1 agree well with published DFT results.7,12 The calculated formation (∆Eform) and mixing (∆Emix) energies indicate that the three bialkali hexaalanates are stable with respect to the mono alkali hexa-alanates. Decomposition energies (∆Edecomp) of the hexa-alanates into tetra-alanates and simple alkali hydrides, AH, are calculated for the following processes:

A3AlH6 f AAlH4 + 2AH

(8)

AA′2AlH6 f A′AlH4 + A′ H + AH

(9)

AA2AlH6 f AAlH4 + 2A′ H

(10)

The values reported in Table 1 clearly confirm the trends observed in ref.13 revealing that the decomposition according to eq 8 is highly unfavored for the monoalkali systems. For the bialkali phases, two decomposition reactions (9) and (10) may be considered. The less endothermic values corresponding to reaction (9), reported in Table 1, shows that the bialkali systems are also stable (in agreement with earlier results). 3.1.2. Dehydrogenation/Hydrogenation Reactions. By analogy with reactions (1) and (2) for mono alkali systems, and taking into consideration that bialkali tetra-alanates do not exist 12,13 (i.e., the reacting phases for the first step is a mixture of two tetra-alanates), the two dehydrogenation steps for binary systems can be rewritten as follows

xAAlH4 + (3 -x)A′AlH4 f AxA3 -xAlH6 + 2Al + 3H2

(11) AxA3 -xAlH6 f xAH + (3 -x)A′H + Al + 3⁄2H2

(12) (12) In this case, ∆E(11) dehyd (i ) 11) and ∆Edehyd(i ) 12) stand for the energy variation of reaction (11), respectively (12). First, Table 1 shows that the calculated dehydrogenation energies of are pretty close to the experimental values of ∆Hdehyd found by Graetz et al.:15 +80.2 vs +82 kJ/mol H215 for LiK2AlH6, +49.1 vs +53.515 for LiNa2AlH6 and +91.7 vs +9715 for NaK2AlH6.

Then, it appears that the bialkali reactions exhibit similar ∆E(11) dehyd values as found for the combination of pure alkali reactions with equivalent stoichiometry. However, in the second step of dehydrogenation, ∆E(12) dehyd of bialkali compounds is shifted the by ∼+20 kJ/mol H2 toward higher endothermic values (as also (11) revealed by larger values of ∆E(12) dehyd - ∆Edehyd ) δ∆Edehyd). Figure 1, showing the calculated Van’t Hoff plots of monoalkali (Figure 1a) and bialkali (Figure 1b) alanates for the first and the second dehydrogenation reactions, is another way to illustrate these results. The position of the plots for bialkali systems are not improved with respect to the target (T, P) conditions (represented by the hatched area) when compared to the mono alkali systems. Furthermore, the unfavorable distance between the two Van’t Hoff plots (in line with the large value of δ∆Edehyd) makes hardly impossible the use of both reactions in practical hydrogen storage systems. For that reason, it is worth to investigate if new trialkali hexaalanates may exist with improved thermodynamic properties. 3.2. Exploration of New Trialkali Hexa-alanates 3.2.1. Structure and Composition of Trialkali Hexa-alanates. According to the high degree of freedom to explore trialkali hexaalanates, we have restricted the space of theoretical investigations to the region of high gravimetric H densities for hydrogen uptake of the trialkali phase diagram (see Figure 2). Therefore, our investigation focuses mainly on metastable phases with Li/ (Li + Na + K) atomic ratio greater than 33%, for which ten different compositions have been found to exhibit structures with low energy. The hydrogen storage capacities and main crystal structure properties of the simulated trialkali hexa-alanates are reported in Table 2 (the complete crystallographic data are given in the Supporting Information). The capacities depend on the two dehydrogenation steps involved in the process. The optimization of the hexa-alanate cell volumes enables the calculation of hydrogen volumetric density. Regarding the hydrogen gravimetric density, the trialkali hexa-alanate systems with high Li contents reach values close to 6 wt % when we consider the first two dehydrogenation steps (given by reactions (11) and (12)). The intrinsic hydrogen weight content of the ternary systems are close or above 3 wt % (reaction (12)). As for the intrinsic hydrogen volumetric density of the ternary systems, the values are between 40 and 50 kg/m3. We represent in Figure 3 five relevant hexa-alanate structures corresponding to the most stable systems found in this study. In the case of phase LiNaKAlH6 (phase 8), twelve different structures have been tested. Four of them are found very close in energy and for that reason, the complete crystallographic data of the four competing structures are reported in Supporting Information. In Figure 3, we have represented the three most stable structures, whereas in Tables 2 and 3, only the most stable one is reported. Several trends in the cationic positions appear from a more detailed analysis of the ternary crystal structures. If taken as reference the higher symmetric binary lattice structures, the tetrahedrons AlH6 rest perfectly aligned, while differently oriented from the cation standpoints. The small and strongly polarized Li cations prefer to be aligned along three H-Al-H axis connecting the six closest AlH6 octahedral complexes. As a result, short Li-H distances are found equal to 1.855, 2.013 and 2.277 Å in phase 8 with P4/nmm symmetry and the Li-H coordination number is exactly 6. In phase 3 with a lower symmetry, the Li positions verify a similar rule and Li-H distances are comprised between 1.786 and 2.243 Å

18602 J. Phys. Chem. C, Vol. 112, No. 47, 2008 with a coordination number close to 6. In contrast, the bigger Na and K cations tend to maximize the Na-H (K-H) coordination number: up to 12 in phase 8. The Na and K cations are precisely located on top of every 3-fold hollow H-sites constituted of Al-H lignads in AlH6 complexes. Hence, this leads to larger Na-H (K-H) distances: between 2.560 and 2.729 Å for Na-H, between 2.668 and 2.774 Å for K-H. Similar rules are observed in the LiNa2AlH6 and LiK2AlH6 structures. 3.2.2. Decomposition into Bialkali Hexa-alanates and Monoalkali Tetra-alanates. The mixing reactions (5) and (6) are not sufficient to evaluate the stability of our three candidate phases 2, 3, and 8. To further investigate their stabilities, we must check these phases do not decompose into other competitive phases such as bialkali hexa-alanates and tetra-alanates. We first consider the possible decompositions of trialkali into a mixture of bialkali phases and mono alkali hexa-alanates phases. Knowing that bialkali phases are stabilized versus mono alkali hexa-alanates (see Section 3.1 and earlier studies), the following decomposition reactions tend to maximize the number of binary phases present in the end products. For phase 2:

Li3⁄2Na1⁄4K5⁄4AlH6 f 3⁄8LiK2AlH6 + 1⁄4NaK2AlH6 + 3

⁄8Li3AlH6 (13)

with ∆Edecomp ) -26.48 kJ/mol,

Li3⁄2Na1⁄4K5⁄4AlH6 f 1⁄8LiNa2AlH6 + 5⁄8LiK2AlH6 + 1

⁄4Li3AlH6 (14)

with ∆Edecomp ) -26.24 kJ/mol.

Jeloaica et al. For phase 3:

Li4⁄3Na1⁄3K4⁄3AlH6 f 1⁄3LiK2AlH6 + 1⁄3NaK2AlH6 + 1

⁄3Li3AlH6 (15)


Li4⁄3Na1⁄3K4⁄3AlH6 f 2⁄3LiK2AlH6 + 1⁄6LiNa2AlH6 + 1

⁄6Li3AlH6 (16)

with ∆Edecomp ) -23.37 kJ/mol, For phase 8:

LiNaKAlH6 f 1⁄2LiK2AlH6 + 1⁄2LiNa2AlH6

(17)


LiNaKAlH6 f 1⁄2NaK2AlH6 + 1⁄4LiNa2AlH6 + 1

⁄4Li3AlH6 (18)

with ∆Edecomp ) -9.30 kJ/mol. According to the exothermic values of the above decomposition energies, it appears clearly that the stability of the trialkali hexa-alanates phases 2 and 3 is disfavored with respect to the bialkali phases. The case of phase 8 is slightly more favorable: due to the small exothermicity of the decomposition energy, and to the overall approximations made in our calculations (neglecting finite temperature effects), the existence of this phase cannot be fully excluded. Earlier studies 12,13 shown that the formation of bialkali tetraalanates from pure phases is not thermodynamically favored. Therefore, we must examine the decomposition processes that

Figure 3. Perspective and projected views of the optimized cells of the three most stable trialkali hexa-alanate phases found in this work: (a) Li3/2Na1/4K5/4AlH6 (phase 2 with the Pmma space group), (b) Li4/3Na1/3K4/3AlH6 (phase 3 with the P1 space group); (c) LiNaKAlH6 (phase 8 with the P4/nmm space group); (d) LiNaKAlH6 (phase 8 with the P3 space group); (e) LiNaKAlH6 (phase 8 with the F-43m space group). Large dark green balls, K; light green balls, Na; yellow balls, Li. The AlH6 complexes are shown in stick representation. The arrows indicate the Li · · · H-Al-H · · · Li axis used for the projected views.



induce the formation of KAlH4, the most stable among the three alkali tetra-alanates phases. In a similar approach as for the mono and bialkali phases, several decomposition processes into the different possible mono alkali tetra-alanates have been considered. It appears that the decomposition inducing the formation of KAlH4 is always the most exothermic one as described below. For phase 2,

Li3⁄2Na1⁄4K5⁄4AlH6 f KAlH4 + 1⁄4NaH + 1⁄4KH + 3⁄2LiH

(19) with ∆Edecomp ) -19.49 kJ/mol. For phase 3,

Li4⁄3Na1⁄3K4⁄3AlH6 f KAlH4 + 1⁄3NaH + 1⁄3KH + 4⁄3LiH

(20) with ∆Edecomp ) -11.65 kJ/mol. For phase 8,

LiNaKAlH6 f KAlH4 + NaH + LiH

(21)

with ∆Edecomp ) +1.24 kJ/mol. As a consequence, phases 2 and 3 are also unstable versus the KAlH4 phase, whereas the LiNaKAlH6 phase may compete with the decomposition into tetra-alanates. For the same reason as above-mentioned, it is difficult to conclude whether this phase may exist or not. At this stage, we can assert that this structure is the best candidate for a trialkali hexa-alanate phase and we will confront to experimental data to check its stability. 3.2.3. Dehydrogenation/Hydrogenation Reactions. We now consider the effect of the ternary systems on the (T, P) conditions of the first two steps of the dehydrogenation reaction. As for mono- and bialkali systems, the two following equations represent these two steps for ternary systems:

xLiAlH4+yNaAlH4+ (3 -x-y)KAlH4 f LixNayK3-x-yAlH6+2Al + 3H2 (22) LixNayK3-x-yAlH6 f xLiH + (3 -x)NaH + (3 -x-y)KH + Al + 3⁄2H2 (23) (23) In this case, ∆E(22) dehyd (i ) 22) and ∆Edehyd (i ) 23) stand for the energy variation of reaction (22), respectively (23). As previously, the instability of bialkali tetra-alanates implies that one must start from a mixture of mono alkali tetra-alanates, with the same composition as the ternary phase. Even if we have previously found that some ternary phases are unstable with respect to mono or bialkali hexa-alanates, we consider all of them and calculate their dehydrogenation energies as reported in Table 3 and the Van’t Hoff plots are drawn in Figure 4 for phases 2, 3, 4 and 8. These results show that for phases 1, 5, 6, and 7, the first step is more endothermic than the second (δ∆Edehyd < 0), which means that due to the high instability of the ternary phases, they will never appear on the dehydrogenation pathway. Similar trends have been reported for A3GaH6 and A3BH6 hydrides13 where the stability of tetra-alanates is also strongly favored. In the case of stable mono and bialkali hexa-alanates, this scenario never occurs (δ∆Edehyd > 0). For the less unstable trialkali phases 2, 3, 4 and 8, the positive value of δ∆Edehyd is in line with the usual thermochemistry of the alanate dehydrogenation. The Van’t Hoff plots reveal that the (T, P) conditions corresponding to the first dehydrogenation of phases 2, 3, 4, 8 and second dehydrogenation of phases 2, 3, 4 are close to the target region and far more favorable than the

binary phases (see Figure 1b). In particular, the case of the virtual phase 4 would be optimal because it crosses the target region with δ∆Edehyd close to 0, which means that the two dehydrogenation steps might occur simultaneously. If this phase exists, this would be an optimal situation for the (de)hydrogenation process. However, according to our previous calculation, this phase is not stable, putting forward the intrinsic paradoxical situation of these systems. Therefore, we find out that there is a direct correlation between the stability of the phase and the value of δ∆Edehyd. Figure 5 represents the evolution of δ∆Edehyd as a function of the mixing energies and it appears clearly that the relative position of the two Van’t Hoff lines corresponding to the two dehydrogenation steps depends linearly on the mixing energies. To minimize δ∆Edehyd, one must search for new phases which are close to the demixing region. As a relevant example, δ∆Edehyd of phase 4 or 10 are close to 0, however this phase falls already in the demixing region. The lower value of δ∆Edehyd with respect to this constraint is thus around +20 kJ/mol. This value was obtained for phases 2 and 3. However, these phases are unstable versus the bialkali phases as shown in the previous paragraph. Phase 8 is the only trialkali phase located far from the demixing region and its value of δ∆Edehyd remains higher than that of the LiNa2 phase. The linear trend can be deduced from eqs 5, 8, 22, and 23, leading to the following exact expression for δ∆Edehyd:

δ∆Edehyd ) -∆Emix + ∆Edecomp

(24)

where

∆Edecomp ) x∆Edecomp(Li3AlH6) + y∆Edecomp(Na3AlH6) + (3

-x-y)∆Edecomp(K3AlH6) (25)

∆Edecomp is the mean decomposition energy of the mono alkali hexalanates into tetra-alanates and simple hydrides (eq 7). For the systems explored in this work, this value remains almost constant (close to +20 kJ/mol H2), even if the slight dispersion of ∆Edecomp explains that the linear coefficient is not exactly equal to 1. This important result indicates that there is an intrinsic nonzero limit for δ∆Edehyd (δmin ) +20 kJ/mol H2). This δmin value, which is close to the maximal allowed energy span (25-50 kJ/mol H2) for on board storage (see Introduction), raises a serious obstacle for the use of mixed alkali hexaalanates. Indeed, if one of the dehydrogenation steps crosses the target (T, P) domain, the second one will not as illustrated for phase 2 in Figure 4. 3.3. Synthesis of Bialkali Hexa-alanates LiNa2AlH6 and NaK2AlH6. Before the tentative elaboration of new trialkali hexa-alanates, it was worth to demonstrate that the preparation of such phases was feasible according to our experimental setup. Thus, the compounds LiNa2AlH6 and NaK2AlH6 were prepared using the following reaction: 2 mol % TiCl3

LiH + 2NaH + Al + 3⁄2H2 98 LiNa2AlH6 (26) 2 mol % TiCl3

NaH + 2KH + Al + 3⁄2H2 98 NaK2AlH6 (27) NaH + TiCl3 f 3 NaCl + Ti

(28)

Figure 6 shows the temperature and hydrogen pressure evolutions as a function of the milling time for different syntheses. As an example, for LiNa2AlH6, the temperature


Jeloaica et al.

TABLE 3: Relevant Energy Values of the Trialkali Hexa-alanates: Formation Energy (∆Eform), Mixing Energy (i) (∆Emix) in kJ/mol, Dehydrogenation Energy (∆Edehyd ), and (23) - ∆E(22) (called δ∆E the value ∆Edehyd ) in kJ/mol H2 dehyd dehyd phase-formula

∆Eform

∆Emix

(22) ∆Edehyd

(23) ∆Edehyd

δ∆Edehyd

1-Li2Na1/2K1/2 2-Li3/2Na1/4K5/4 3-Li4/3Na1/3K4/3 4-Li7/4Na1/4K 5-Li5/3Na2/3K2/3 6-Li3/2Na1/2K 7-Li7/6NaK5/6 8-LiNaKa 9-Li2Na1/3K2/3 10-Li5/3Na1/3K

-228.13 -260.29 -261.08 -247.93 -230.18 -244.51 -214.15 -254.89 -242.31 -244.69

+38.89 +0.64 -4.63 +17.88 +27.90 +12.76 +29.28 -14.71 +27.16 +18.27

+27.60 +25.77 +26.19 +30.53 +28.29 +27.61 +34.56 +22.81 +25.15 +28.01

+11.71 +45.59 +50.82 +30.72 +22.48 +35.90 +26.17 +57.75 +20.61 +31.04

-15.89 +19.82 +24.63 +0.18 -5.81 +8.29 -8.39 +34.69 -4.53 +3.04

a

Structure with P4nmm symmetry.

Figure 6. Hydrogen pressure (top) and temperature (bottom) curve variations observed during the synthesis of LiNa2AlH6 (squares), NaK2AlH6 (circles), Li4/3Na1/3K4/3AlH6 (triangles), and LiNaKAlH6 (diamonds) by ball milling.

Figure 4. Calculated Van’t Hoff plots for the trialkali hexa-alanates. The dashed lines correspond to the first dehydrogenation reaction (22), the full lines correspond to the second dehydrogenation reaction (23). Note that the full black line corresponds to the Van’t Hoff plots of the second dehydrogenation reaction of phase 4 and also of the two successive dehydrogenation reactions of phase 8. The gray area corresponds to the target (T, P) conditions including those for on board hydrogen storage.

Figure 7. Rietveld analysis of sample LiNa2AlH6: observed (dots), calculated (solid line) and difference curves (bottom) are shown. Vertical bars (|) correspond to Bragg positions (Cu KR1,2) for LiNa2AlH6 (top) and NaCl (bottom) phases.

Figure 5. Correlation between δ∆Edehyd and the mixing energies as defined by eq 6 for the binary and ternary systems. The gray region represents the demixing domain where the mixed alkali phases are unstable versus the mono alkali hexa-alanates. The equation of the linear interpolation is δ ) -0.92∆Emix + 19.65 with r2 ) 0.997.

increases from room temperature up to a plateau around 36 °C. Such temperature rising is attributed to the friction between balls and vial wall. The hydrogen pressure first increases up to 10.7 MPa because of the increasing of temperature then decreases after 30 min of milling time to finally reach a plateau around 100 MPa after 3 h. The hydrogen uptake calculated from the observed pressure drop is in good agreement with the quantity of absorbed hydrogen according to reaction (26). XRD analysis confirms the formation of LiNa2AlH6 for the as-prepared sample (Figure 7), corresponding to the expected reaction (26). Rietveld analysis shows that the LiNa2AlH6 compound crystallizes in the Fm3m space group with a lattice

constant a ) 7.4179 Å, slightly larger than that reported for LiNa2AlH6 (7.4064 Å) prepared from NaAlH4 and LiH 15,25 without the use of Ti dopant. Our DFT calculation indicates that the cell parameter is slightly more contracted (7.349 Å) after full geometry optimization at 0 K. In addition, a small amount of NaCl (∼4 wt %) was detected. The NaCl formation is attributed to the decomposition of TiCl3 during milling and shows that titanium chloride may react with NaH according to reaction (28). Accordingly, other remaining reactants like Al or Ti should be observed but were not detected. The absence of reflections lines either from Al or Ti may suggest that Ti enters into the hexa-alanate phase. However, only Sun et al.26 have reported this possibility and many other works 27,28 show that Ti is associated with the Al on the surface. Since the Ti-Al alloy is in amorphous state, it is hardly observed by XRD. The same conditions were used to synthesize NaK2AlH6. X-ray diffraction after milling revealed the formation of NaK2AlH6 for the as-prepared sample (Figure 8), corresponding to the expected reaction (27) The structure characterization performed by Rietveld refinement assumes the Fm3m space group. The obtained lattice constant a ) 8.1342 Å is slightly larger but still fully compatible with the value reported by


Figure 8. Rietveld analysis of sample NaK2AlH6: observed (dots), calculated (solid line) and difference curves (bottom) are shown. Vertical bars (|) correspond to Bragg positions (Cu KR1,2) for NaK2AlH6 (top) and NaH (bottom) phases.


Figure 10. Rietveld analysis for the ball milled sample with Li4/3 Na1/3K4/3AlH6 composition: observed (dots), calculated (solid line) and difference curves (bottom) are shown. Vertical bars (|) correspond to Bragg positions (Cu KR1,2) for NaK2AlH6, KAlH4 and LiH phases from top to bottom.

sample is shown in Figure 10. From this refinement, it is obtained that the sample contains NaK2AlH6 (47 wt %), KAlH4 (34 wt %) and LiH (19 wt %). It is worth noting that the determined quantity of LiH is poorly reliable due to the weak X-ray diffraction scattering of light atoms Li and H. NaCl and possibly LiCl may be also present but were not included in the refinement. Actually, it has been shown by our DFT calculations (see Section 3.2.2) that the nominal Li4/3Na1/3K4/3AlH6 phase is not stable with respect to the mixture of LiH, the tetra-alanate KAlH4 and bialkali hexa-Alanate NaK2AlH6 (eqs 15, 16, and 20). This instability can also be compared with the energy balance of the two following competitive reactions: 4

Figure 9. Comparison between XRD experimental data for the ball milled sample with Li4/3Na1/3K4/3AlH6 composition (circles) and simulated one (black line) for the DFT optimized Li4/3Na1/3K4/3AlH6 structure.

⁄3LiH + 1⁄3NaH + 4⁄3KH + Al + 3⁄2H2 f Li4⁄3Na1⁄3K4⁄3AlH6

(29) 4

⁄3LiH + 1⁄3NaH + 4⁄3KH + Al + 3⁄2H2 f 1⁄3NaK2AlH6 + ⁄3KAlH4 + 4⁄3LiH (30)

2

Sorby29 (8.118 Å) and Graetz (8.121 Å)15 and with the DFT calculations carried in present work which gives a value of 8.114 Å after optimization at 0 K. 3.4. Attempt to Synthesize Trialkali Hexa-alanates Li4/3Na1/3K4/3AlH6 (Phase 3) and LiNaKAlH6 (Phase 8). The sample with nominal composition of Li4/3Na1/3K4/3AlH6 (phase 3) was prepared by ball milling of a mixture of LiH, NaH, KH, Al and 2 mol % TiCl3 for 2 h. As shown in Figure 6, the temperature in the vial follows the same trend as for LiNa2AlH6. The hydrogen absorption occurs after 15 min of milling and is completed after 45 min. The reaction is kinetically faster than for LiNa2AlH6. The XRD pattern of the obtained ball milled sample does not exhibit the structure predicted by DFT calculation for Li4/3Na1/3K4/3AlH6 (phase 3). In Figure 9, the measured XRD pattern and the DFT calculated one are compared and it clearly shows important differences. The experimental pattern can be fitted with three phases: NaK2AlH6 (space group Fm3m), KAlH4 (space group Pnma30) and LiH. The obtained unit cell parameters for the hydride KAlH4 phase, a ) 8.8826 Å, b ) 5.8248 Å and c ) 7.3615 Å, are slightly larger than those found for the deuteride KAlD430 (a ) 8.8514 Å, b ) 5.8119 Å, c ) 7.3457 Å). The refinement of the experimental diffraction pattern for the ball milled Li4/3Na1/3K4/3AlH6

A linear combination of eqs 15, 16, and 20 shows that the reaction energy of eq 30 is more exothermic than that of eq 29 by -27.58 kJ/mol, which confirms the instability of the virtual trialkali phase. The product mass balance for equation 29 is 44 wt % of NaK2AlH6, 46 wt % of KAlH4 and 10 wt % of LiH in good agreement with the above results from XRD analysis. The formation of the tetra-alanate KAlH4 and bialkali hexa-alanate NaK2AlH6 occurs through a significant hydrogen uptake in agreement with the pressure drop in the ball-milling system as shown in Figure 6. We have also attempted to synthesize the less unstable phase as predicted by DFT calculations, i.e., LiNaKAlH6 (phase 8). It was prepared by ball milling of a mixture of LiH, NaH, KH, Al, and 2 mol % TiCl3 for 2 h. The hydrogen absorption occurs after 15 min of milling and is completed after 1 h. The XRD pattern can be indexed with six phases: NaK2AlH6, KAlH4, NaH, LiH, LiNa2AlH6, and NaCl. The. Rietveld analysis is shown in Figure 11. The phase mass fraction is NaK2AlH6 (39 wt %), KAlH4 (38 wt %), LiNa2AlH6 (6 wt %), NaH (12 wt %), LiH (≈2 wt %) and NaCl (3 wt %). Therefore, the LiNaKAlH6 phase is not stable with respect to the abovereported mixture under our experimental conditions. This


Jeloaica et al.

Figure 11. Rietveld analysis of the sample with LiNaKAlH6 composition: observed (dots), calculated (solid line) and difference curves (bottom) are shown. Vertical bars (|) correspond to Bragg positions (Cu KR1,2) for NaK2AlH6, KAlH4, LiNa2AlH6, NaH, LiH, and NaCl phases from top to bottom.

instability can be compared with the energy balance of the following competitive reactions:

LiH + NaH + KH + Al + 3⁄2H2 f LiNaKAlH6

(31)

LiH + NaH + KH + Al + ⁄2H2 f ⁄3NaK2AlH6+ 3

1

⁄3KAlH4+ 1⁄3LiNa2AlH6 + 2⁄3LiH (32)

1

As for the Li4/3Na1/3K4/3AlH6 composition, the reaction energy of eq 32 is more exothermic than that of eq 31 by -11.67 kJ/ mol (as a result of the combination of decomposition energies 17, 18, and 21). The product mass balance for this equation is 44 wt % of NaK2AlH6, 23 wt % of KAlH4, 28 wt % of LiNa2AlH6, and 5 wt % of LiH, rather close to the above results from XRD analysis. Some NaH did not react due, probably, to the slow kinetics for LiNa2AlH6 formation (see Section 3.3). This can also explain the low formation of LiNa2AlH6. To summarize, trialkali Li4/3Na1/3K4/3AlH6 (phase 3) and LiNaKAlH6 (phase 8) hexa-alanates could not be obtained by near room temperature ball-milling under ∼10 MPa of hydrogen pressure. These hexa-alanates are unstable as compared to alkali hydrides, and mono (KAlH4), and bialkali (NaK2AlH6 and LiNa2AlH6) alanate mixtures under the present experimental conditions. 4. Conclusions Our study has addressed the issue of improving the thermodynamic properties of alkali alanates as H-storage materials for on-board applications, by changes in the chemical compositions of the systems. Based on DFT simulation, we have investigated various possible structures of LixNayK3-x-yAlH6 compositions within a range of Li atomic ratio Li/(Li + Na + K) g 33%. After systematically screening a large number of crystal structures and compositions of trialkali compounds by full structure optimizations, ten structures with different Li/Na/K composition ratios that exhibited low formation energies have been chosen for further testing of the thermodynamic stability. The calculated thermodynamic properties have revealed that seven out of the 10 low-energy phases are not stable versus an equivalent mixture of mono alkali hexa-alanates. For the other three phases (Li3/2Na1/4K5/4, LiNaKAlH6, and Li4/3Na1/3 K4/3AlH6) which exhibit exothermic mixing energy with respect to the mono alkali hexa-alanates, the calculation has

shown that Li3/2Na1/4K5/4, and Li4/3Na1/3K4/3AlH6 phases can decompose into a mixture of bialkali (LiK2AlH6 and NaK2AlH6) hexa-alanates and the tetra-alanate KAlH4 phase. The situation is energetically slightly more favorable for the LiNaKAlH6 phase, though the decomposition in a mixture of bialkali hexa-alanates (Li2NaAlH6 and LiK2AlH6) and KAlH4 tetra-alanate has a comparable stability. According to the accuracy of our calculations, it was thus difficult to rule out the possible formation of such a phase and the experimental approach has helped us to bring a definitive answer. Therefore, we attempted to synthesize different trialkali hexa-alanates by ball milling of NaH, LiH, KH, Al, and TiCl3 under hydrogen pressure of 10 MPa and a temperature close to room temperature. XRD analysis of the various compositions tested only revealed the formation of monoalkali hydrides, bialkali hexa-alanates and KAlH4 tetra-alanate mixture. These experimental results corroborate the theoretical prediction of the high instability of trialkali phases. Even in the region of composition close to the most stable phase LiNaKAlH6 found by simulation, our attempt has remained unsuccessful. Finally, we have calculated the equilibrium pressure and temperature given by the Van’t Hoff plots for the two dehydrogenation steps in all simulated trialkali alanates. It is interesting to notice, that among the eight calculated phases, no significant improvement on dehydrogenation energies was obtained. Furthermore, we put forward the existence of an intrinsic thermodynamic limit in the relative position of the Van’t Hoff plots corresponding to the two dehydrogenation steps of alanates. The difference between the two dehydrogenation energies reaches a limit of +20 kJ/ mol H2 (correlated to the intrinsic demixing region of the mixed alkali phases) which implies that both Van’t Hoff plots cannot simultaneously cross the targeted (P, T) region for on board hydrogen storage. Even if one can suggest to explore the synthesis of ternary alanates at lower temperature and higher pressure in future investigations, our results strongly indicate that it will be difficult to improve the intrinsic thermodynamic properties of hexaalanates by only varying their alkali metal compositions. Acknowledgment. This work has been performed within the ALHAMO project (ANR-06-PANH-019) sponsored by the Agence Nationale de la Recherche (ANR). ALHAMO is a joint project of the Centre National de la Recherche Scientifique (CNRS), IFP, PSA Peugeot Citroe¨n and Alphea Hydroge`ne. Supporting Information Available: Crystallographic data. This material is available free of charge via the Internet at http:// pubs.acs.org. Note Added after ASAP Publication. This article was published on the web on November 4, 2008. Changes have been made to eq 25. The correct version was published on November 7, 2008. References and Notes (1) Bogdanovic, B.; Schwickardi, M. J. Alloys Comp. 1997, 253, 1. (2) Schlappach, L.; Zu¨ttel, A. Nature 2001, 414, 353. (3) Zu¨ttel, A. Mater. Today 2003, 6, 24. (4) Latroche, M.; Percheron-Guegan, A.; Chabre, Y. J. Alloys Comp. 1999, 295, 637. (5) Cuevas, F.; Joubert, J. M.; Latroche, M.; Percheron-Guegan, A. Appl. Phys. A 2001, 72, 225–238.

Thermodynamic Properties of Hexa-alanates (6) Smithson, H.; Marianetti, C. A.; Morgan, D.; Ven, A. V. d.; Predith, A.; Ceder, G. Phys. ReV. B 2002, 66, 144107. (7) Løvvik, O. M.; Swang, O. Europhys. Lett. 2004, 67, 607. (8) Hector, L. G.; Herbst, J. F. J. Phys.: Condens. Matter 2008, 20, 064229. (9) Wolverton, C.; Siegel, D. J.; Akbarzadeh, A. R.; Ozolinsˇ, V. J. Phys.: Condens. Matter 2008, 20, 064228. (10) Alapati, S. V.; Johnson, J. K.; Sholl, D. S. Phys. Chem. Chem. Phys. 2007, 9, 1438. (11) Løvvik, O. M.; Opalka, S. M.; Brinks, H. W.; Hauback, B. C. Phys. ReV. B 2004, 69, 134117. (12) Løvvik, O. M.; Swang, O.; Opalka, S. M. J. Mater. Res. 2005, 20, 3199. (13) Dompablo, M. E. A. y. d.; Ceder, G. J. Alloys Comp. 2004, 364, 6. (14) Bastide, J. P.; Claudy, P.; Letoffe, J. M.; Hajri, J. E. ReV. Chim. Min. 1987, 24, 248. (15) Graetz, J.; Lee, Y.; Reilly, J. J.; Park, S.; Vogt, T. Phys. ReV. B 2005, 71, 184115. (16) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (17) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (18) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169.

J. Phys. Chem. C, Vol. 112, No. 47, 2008 18607 (19) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (20) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (21) Alapati, S. V.; Johnson, J. K.; Sholl, D. S. J. Phys. Chem. C 2007, 111, 1584. (22) Dymova, T. N.; Eliseeva, N. G.; Bakum, S. I.; Dergache, Ym. Dokl. Akad. Nauk SSSR 1974, 215, 1369–1372. (23) Bellosta von Colbe, J. M.; Felderhoff, M.; Bogdanovic, B.; Schuth, F.; Weidenthaler, C. Chem. Commun. 2005, 4732–4734. (24) Rodriguez Carvajal, J. Physica B 1993, 192, 55–69. (25) Brinks, H. W.; Hauback, B. C.; Jensen, C. M.; Zidan, R. J. Alloys Comp. 2005, 392, 27–30. (26) Sun, D. L.; Kiyobayashi, T.; Takeshita, H. T.; Kuriyama, N.; Jensen, C. M. J. Alloys Comp. 2002, 337, L8. (27) Balogh, M. P.; Tibbetts, G. G.; Pinkerton, F. E.; Meisner, G. P.; Olk, C. H. J. Alloys Comp. 2003, 350, 136. (28) Brinks, H. W.; Jensen, C. M.; Srinivasan, S. S.; Hauback, B. C.; Blanchard, D.; Murphy, K. J. Alloys Comp. 2004, 376, 215. (29) Sorby, M. H.; Brinks, H. W.; Fossdal, A.; Thorshaug, K.; Hauback, B. C. J. Alloys Comp. 2006, 415, 284–287. (30) Hauback, B. C.; Brinks, H. W.; Heyn, R. H.; Blom, R.; Fjellvåg, H. J. Alloys Comp. 2005, 394, 35–38.

JP804652A

Thermodynamic Properties of Trialkali (Li, Na, K) Hexa-alanates: A

Recommend Documents