Thermodynamic and ab initio investigation of the Al–H–Mg system

Computer Coupling of Phase Diagrams and Thermochemistry 31 (2007) 457–467 www.elsevier.com/locate/calphad

Thermodynamic and ab initio investigation of the Al–H–Mg system M. Palumbo a,∗ , F.J. Torres a , J.R. Ares b , C. Pisani a , J.F. Fernandez b , M. Baricco a a Dipartimento di Chimica I.F.M., Centro di Eccellenza NIS, Universit`a di Torino, via Giuria 7/9, 10125 Torino, Italy b Dpto. F´ısica de Materiales, Facultad de Ciencias, Universidad Aut´onoma de Madrid, Madrid 28049, Spain

Received 17 January 2007; received in revised form 16 April 2007; accepted 16 April 2007 Available online 22 May 2007

Abstract A coupled ab initio and thermodynamic study of the Al–H–Mg system has been carried out and a self-consistent thermodynamic database has been obtained. Magnesium alanate Mg(AlH4 )2 , a candidate material for hydrogen storage, has been included into the database. According to Density Functional first principles calculations, the alanate is an insulator and its thermodynamic properties have been obtained at room temperature. This compound has been found metastable at 298.15 K and 1 bar. The alanate has been found thermodynamically stable only at high pressure when the formation of the binary β-MgH2 phase is neglected. A reassessment of thermodynamic parameters of the liquid phase in the binary Mg–H system has also been carried out in order to be consistent with the Al–H system. The present results can reproduce reasonably well the available experimental data. c 2007 Elsevier Ltd. All rights reserved.

Keywords: Hydrogen storage materials; Magnesium alanate Mg(AlH4 )2 ; First principles calculations; Thermodynamic calculations; Phase diagrams

1. Introduction

β-MgH2 + 2Al → 1/2β-Al3 Mg2 + 1/2Al + H2

In the latest years, hydrogen storage in solid hydrides has been proposed as a promising way to fulfil the targets established in several countries for potential commercial automotive application, i.e. the Freedom Cars Program [1,2]. Up to now, the only group of materials which have properties meeting the targets are complex metal hydrides, having a mixed ionic–covalent bonding between metal and hydrogen complex [3]. Among them, magnesium alanate Mg(AlH4 )2 , an alkaline earth alanate, is a potential hydrogen storage candidate with a theoretical hydrogen content of 9.3 wt%. Moreover, it is based on two inexpensive light metals like Al and Mg. This compound decomposes in a two-step reaction [4–7]:

with a 2.3 wt% release of hydrogen. However, in order to be suitable for commercial applications in automotive, it is also important to evaluate the thermodynamic stability of candidate hydrides. The reversibility of the H2 uptake/release reaction is obviously necessary for applications. Moreover, a high heat release during these reactions can be a serious hindrance in building hydrogen storage devices. A number of experimental and theoretical investigations has been carried out on thermodynamic properties of the magnesium alanate Mg(AlH4 )2 and related reactions. The binary Al–H, Mg–H and Al–Mg systems have already been thermodynamically evaluated in the literature [8–11]. Nonetheless, a complete thermodynamic description of the ternary Al–H–Mg is still missing. The purpose of this paper is to provide a full thermodynamic description of this system by critically assessing all experimental information available by using the CALPHAD approach. Quantum mechanical ab initio DFT calculations have also been performed in order to evaluate the properties of the magnesium alanate.

Mg(AlH4 )2 → β-MgH2 + 2Al + 3H2

(1)

which occurs in the temperature range 383–473 K with a 7.0 wt% release hydrogen and a subsequent further decomposition: ∗ Corresponding author. Tel.: +39 0 116707567; fax: +39 0 116707855.

E-mail address: [email protected] (M. Palumbo). c 2007 Elsevier Ltd. All rights reserved. 0364-5916/$ - see front matter doi:10.1016/j.calphad.2007.04.005

(2)

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2. Critical assessment of experimental information and ab initio calculations Experimental investigations on the ternary Al–H–Mg system mostly concern the magnesium alanate Mg(AlH4 )2 and related chemical reactions. Magnesium alanate is mainly obtained by a metathesis reaction between MgCl2 and NaAlH4 , in diethyl ether (Et2 O) or tetrahydrofuran (THF) as a solvent, followed by a purification and a drying procedure [12,13]. An alternative synthesis method by a mechano-chemically activated reaction in ball milling equipment has also been reported recently, using different starting materials [5–7,14]. The crystal structure and lattice parameters of this compound have been determined by combined synchrotron Xray and neutron diffraction at 8, 111, 295 K [4]. Experimental and theoretical thermodynamic investigations on Mg(AlH4 )2 have been carried out by several authors [5–22]. The results are summarized in Table 1. With respect to experimental studies, they concern the thermal decomposition behaviour of the alanate, which occurs in the two-step reaction (1) and (2), and have been performed by DSC, TGA and complementary techniques. Dilts and Ashby [15] found that the first decomposition reaction step (1) is exothermic, but attributed it to the presence of THF residuals. Claudy et al. [12] reported an enthalpy value close to 0 kJ/mol for reaction (1). Kim et al. [6] claimed that Mg(AlH4 )2 samples prepared using Et2 O or THF as solvents are unsuitable for enthalpy measurements, since their residuals affect the DSC results. They prepared solvent-free alanate by ball milling and obtained a −18 kJ/mol value for the enthalpy of reaction (1). Dymova and co-workers [14] also obtained magnesium alanate by mechano-chemical activated synthesis but from different starting materials and investigated its decomposition behaviour by differential thermogas volumetry (DTA-DGV). According to their results, an intermediate metastable MgAlH5 compound occurs during Mg(AlH4 )2 decomposition, which has not been reported in previous studies. However, they do not report enthalpy values for reaction (1). Solvent-free mechano-chemical synthesized samples of the alanate have recently been reinvestigated by Mamatha et al. [5] and Varin et al. [7]. These latter studies have thoroughly analysed the decomposition reaction of the magnesium alanate using DSC at different heating rates. In both these latter studies, only impurities of NaCl, which is a by-product of milling synthesis reactions, are present in the investigated samples. These authors have chosen not to remove these impurities since NaCl does not affect DSC results, whereas removing salt using chemical methods might bring impurities which could change the thermal behaviour of Mg(AlH4 )2 . Mamatha et al. [5] reports three peaks in DSC measurements, corresponding to reactions (1) and (2) and melting respectively. For the first decomposition reaction (1) they have found an enthalpy value of 1.7 kJ/mol. Varin et al. [7] report DSC traces similar to those of Mamatha et al. [5] and also found decomposition signals very close to zero. In fact, these authors claim the endothermic or exothermic nature of this reaction cannot be unambiguously established owing

to the very small enthalpy of decomposition. Thus, except for the work by Kim et al. [6], the different investigations of the enthalpy of decomposition of magnesium alanate are in agreement with a value close to zero. Theoretical investigations on Mg(AlH4 )2 have been mainly focused in the computation of its enthalpy of formation by employing first principle calculations based on DFT methods. Beside of the work reported by Klaveness et al. [21] in which the reaction 3AlH3 + MgH2 → Mg(AlH4 )2 was used, most of these studies have considered the standard reaction from the elements, i.e. 2Al + 4H2 + Mg → Mg(AlH4 )2 . As summarized in Table 1, large discrepancies exist between the computed values. This is partly due to either including or neglecting rotational, vibrational and translational terms in the estimate of the reaction energy (which may amount up to ∼25 kJ/mol, see Ref. [18]), and partly to the difference in the computational techniques adopted (details in Refs [16,17]). Among theoretical studies related to the present problem, it is worth citing the calculations related to MgAlH5 , a compound suggested by Dymova et al. [21] as intermediate in reaction (1), it has also been investigated by first principles calculations; by considering 50 different potential atomic arrangements, its crystal structure has been predicted as monoclinic CaFeF5 type, P21 /c and an enthalpy of formation of −76 kJ/mol at 0 K. The direct experimental determination of the enthalpy of formation of Mg(AlH4 )2 is intrinsically difficult and no values have been reported in the literature. An indirect experimental estimate of the enthalpy of formation can be obtained by the enthalpy of reaction (1) and using the assessed value for the enthalpy of formation of the binary β-MgH2 hydride (−75.6 kJ/mol from Ref. [10]). All the binary systems (Al–H, Al–Mg, Mg–H) have already been assessed in the literature [8–11]. The enthalpy of formation of the binary hydrides AlH3 and MgH2 have been well investigate in the literature both from experiments and ab initio calculations. CALPHAD assessed values of these enthalpies (−11.6 and −75.6 kJ/mol for AlH3 and MgH2 , respectively), which will be used in present ab initio calculations (Section 4), can thus be considered reliable. 3. First principle calculations The crystal structure and the electronic and thermodynamic properties of magnesium alanate Mg(AlH4 )2 were theoretically studied with the periodic program CRYSTAL06 [23]. For the calculations, the B3LYP Hamiltonian and an all-electron double-zeta quality basis set were employed. In an initial stage, the system was fully relaxed using as starting point the crystal structure determined by means of neutron diffraction at 8 K by Fossdal and co-workers [4]. In that study, Mg(AlH4 )2 was reported to crystallize in the P3m1 space group and to be composed by distorted (AlH4 )− tetrahedra in which two types of hydrogen atoms can be distinguished, H1 and H2. The former is positioned at the extreme of the tetrahedron along the c-axis and is bonded only to aluminum, while the latter links the tetrahedra with the Mg2+ cations forming a layered structure along the c-axis (see Fig. 1). The main features of

ab initio, DFT, CRYSTAL code CALPHAD ab initio, DFT, VASP code ab initio, DFT, VASP code ab initio, DFT, VASP code Miedema model Cluster method, Turbomole package

−87.6a −79.0 −84.0 −38.6 −61.07 −43 (+20)b

−64.8

2Al + 4H2 + Mg → Mg(AlH4 )2

ab initio, DFT, PWSCF, PHONONS Cluster method, Turbomole package ab initio, DFT, VASP code Experimental

Experimental

Experimental

Experimental

Experimental

Experimental

CALPHAD

+139.5 +41 −20.4 Not reported

0

Not reported

−18

+1.7

∼0

+1

Mg(AlH4 )2 → βMgH2 + 2Al + 3H2

ab initio, DFT, VASP code

+12

αAlH3 + βMgH2 → MgAlH5

ab initio, DFT, CRYSTAL code ab initio, DFT, VASP code

+11.2 +29

2αAlH3 + βMgH2 → Mg(AlH4 )2

Method

Enthalpy change (kJ/mol)

Reaction

Table 1 Thermochemical data on Mg and Al hydrides from different sources

This work

[7]

[5]

[6]

[14]

[12]

[22] [20] [6] [15]

[21]

[20]

This work This work [17] [18] [16] [19]

This work [21]

References

(continued on next page)

at 0 K at 0 K at 0 K Mg(AlH4 )2 prepared by metathesis reaction of NaAlH4 /MgCl2 , reaction was found exothermic but attributed to the presence of THF residuals Mg(AlH4 )2 prepared by metathesis reaction of NaAlH4 /MgCl2 in THF, decomposition reaction at 435 K Mg(AlH4 )2 prepared by mechanochemical synthesis of MgH2 /AlCl3 , AlMgH5 claimed as possible intermediate compound during decomposition at 393–428 K Mg(AlH4 )2 prepared by mechanochemical synthesis of NaAlH4 /MgCl2 (milling time = 1 h), NaCl residual not removed, decomposition reaction at 388–413 K Mg(AlH4 )2 prepared by mechanochemical synthesis of NaAlH4 /MgCl2 (milling time = 3 h), NaCl residual removed (possible partial decomposition of Mg(AlH4 )2 in this process), decomposition reaction at 423 K Mg(AlH4 )2 prepared by mechanochemical synthesis of NaAlH4 /MgCl2 (milling time = 5, 10, 40 h), NaCl residual not removed, partial decomposition of Mg(AlH4 )2 for long milling time, decomposition reaction at 398–423 K at T = 435 K and P = 1 bar

at 0 K

T = 298.15 P = 1 bar T = 298.15 P = 1 bar at 0 K at 0 K at 0 K Xcalc (H) = 0.529, Xexp (H) = 0.727 Xcalc (H) calculated significantly differs from experimental value

T = 298.15 P = 1 bar at 0 K

Notes

M. Palumbo et al. / Computer Coupling of Phase Diagrams and Thermochemistry 31 (2007) 457–467 459

−63.36 −55.0 (−0.57 eV) −64 −65 (−54)b −75.6 −77.4 ± 4/−78.2 −79/−74.4 −70/−76.2 −70.7 − 76.84 −81.25

−11.6 −11.2 −9.9 ± 0.6 −12.6

H2 + Mg → βMgH2

Al + 3/2H2 → αAlH3 CALPHAD Experimental Experimental ab initio, DFT, VASP code

ab initio, DFT, VASP code ab initio, DFT, VASP code ab initio, DFT, VASP code Miedema model CALPHAD Experimental

Method

T = 298.15 P = 1 bar T = 298.15 P = 1 bar T = 298.15 P = 1 bar at 0 K

at 0 K at 0 K at 0 K Xcalc (H) = 0.634 Xexp (H) = 0.667 T = 298.15 P = 1 bar T = 298.15 P = 1 bar (values used in [99Zen] to obtain thermodynamic assessment)

Notes

Data refers to the reported reaction at 1 bar, except otherwise specified. SER refers to Standard Element Reference state, i.e. 298.15 K and 1 bar. a Value derived from result on reaction 2AlH + MgH → Mg(AlH ) using CALPHAD assessed values for AlH and MgH enthalpies of formations. 3 2 4 2 3 2 b Value given at calculated composition (in parenthesis value at experimental composition).

Enthalpy change (kJ/mol)

Reaction

Table 1 (continued)

[8] [34] [35] [36]

[16] [17] [36] [19] [10] References in [10]

References

460 M. Palumbo et al. / Computer Coupling of Phase Diagrams and Thermochemistry 31 (2007) 457–467

M. Palumbo et al. / Computer Coupling of Phase Diagrams and Thermochemistry 31 (2007) 457–467

461

Fig. 2. Total charge density plot of magnesium alanate in the (1 1 0) plane. The leftmost and rightmost Mg atoms are those at two opposite extremes of the trigonal cell (see Fig. 1). Isodensity lines are separated by 0.01 |e|/Bohr3 .

Fig. 1. Relaxed crystal structure of magnesium alanate Mg(AlH4 )2 . Table 2 Calculated and experimental structural parameters of magnesium alanate Mg(AlH4 )2

a c H1z H2x H2z Al–H1 Al–H2 Mg–H

Experimental

Calculated

∆ (%)

5.2084 5.8392 0.4242 0.1671 0.8105 1.6052 1.6346 1.8700

5.2225 5.7635 0.4292 0.1692 0.8074 1.5786 1.6022 1.8902

0.3 −1.3 1.2 1.3 − 0.4 −1.7 −3.2 2.0

˚ atomic positions are in Lattice parameters and distances are expressed in A, fractionary units and ∆ (%) is the percentage error between calculated and experimental values.

the calculated relaxed structure are summarized in Table 2. The agreement with the experimental data is generally excellent, the largest errors occurring in the distances of the H atoms from the cations. Band structure and DOS were calculated for the relaxed structure. The obtained results are in good agreement with other studies previously reported [16–18], which confirms that magnesium alanate is an insulator. The calculated indirect band gap is 6.77 eV, considerably larger than that resulting from GGA calculations (≈4.5 eV), but close to that obtained by Løvvik and Molin [17] after inclusion of GW corrections (6.5 eV). The bonding in Mg(AlH4 )2 was further analyzed by plotting the total charge density in the [1 1 0] plane. As shown in Fig. 2, the sharing of charges between Mg and H2 is negligible in comparison with the electronic density present between hydrogen and aluminum atoms, which is a further indication of the purely ionic interaction between the Mg2+ and the (AlH4 )− subsystems. The formation of Mg(AlH4 )2 was studied according to the following solid state chemical reaction: MgH2 + 2AlH3 → Mg(AlH4 )2

(3)

the same used by Klaveness et al. in Ref. [21]. Due to the fact that the three species involved have a similar electronic structure (they are all ionic or semi-ionic crystalline compounds), they can be treated at the same level of accuracy with regards to both the theoretical approach and the setting of the computational parameters, which ensures a very effective cancellation of errors in the evaluation of energy differences. On the other hand, the possibility to obtain accurate simulations of the vibrational properties of the three compounds allows us to perform a thermodynamic description of reaction (3) and therefore to calculate a reliable estimate of the formation enthalpy of the alanate. As reported in Table 3, MgH2 and AlH3 crystallize in the P42 /mnm and R3c space groups. Taking again as a starting point their experimental geometries (References [24,25], respectively), the two structures were fully optimized. With the data summarized in Table 3, the electronic energy of reaction (3) was computed as the difference of the total energies in the relaxed geometries. The resulting value was 2.4 kJ/mol. In order to include the contribution from lattice vibrations, the vibrational modes of the three systems were computed within the harmonic approximation by diagonalizing the mass-weighted hessian matrix. By including the difference of the zero point energies (also included in Table 3), a reaction enthalpy of 5.7 kJ/mol at 0 K was obtained. Use of the vibrational partition function in the harmonic approximation resulted in an enthalpy of reaction of 11.2 kJ/mol and in a free energy of reaction of 0.6 kJ/mol at 300 K. These results are used in the following for thermodynamic calculations. 4. Thermodynamic modelling The pure solid elements in their stable phases at 298.15 K and 101 325 Pa were chosen as reference state (SER, Standard Element Reference) as recommended by SGTE (Scientific Group Thermodata Europe). The Gibbs free energy of the pure elements (lattice stabilities) is represented as a function of temperature in the form 0

G(T ) = a + bT + cT ln T + dT 2 + eT 3 + f /T X + gn T n

(4)

n

where a to f and gn are coefficients and n represents a set of integers. For condensed phases, the variation of the Gibbs free energy with pressure is negligible in the range of interest (<10 MPa) [26]. Thus, pressure dependence of the Gibbs energy was only taken into account for the gas phase. The corresponding coefficients for condensed phases in unary

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M. Palumbo et al. / Computer Coupling of Phase Diagrams and Thermochemistry 31 (2007) 457–467

Table 3 Space group, total electronic energy (E E ), zero point energy (E 0 ), thermal effects on the vibrational energy (E T ) and temperature times entropy term (T S) computed for MgH2 , AlH3 and Mg(AlH4 )2 compounds Compound

Space group

EE

E0

ET

MgH2 AlH3 Mg(AlH4 )2

P42 /mnm R3c P3m1

−201.280278 −244.199677 −689.678726

0.014474 0.024128 0.063984

0.001139 0.001352 0.005933

2.4

3.3

5.5

1E

TS 0.001759 0.001967 0.009724 10.6

The absolute energy values by unit formula are reported in Hartree, and the difference between energies (1E), obtained according with the stoichiometric coefficients of reaction MgH2 + 2AlH3 → Mg(AlH4 )2 , are expressed in kJ/mol.a E T and TS are computed at 300 K. a 1 Hartree = 2625.5 kJ/mol.

systems were taken from the compilation of Dinsdale [27]. The Gibbs energy functions for the gaseous state were obtained from JANAF tables [28]. The gas phase containing Al, H2 , H and Mg was considered as an ideal mixture. Moreover, an ideal gas behaviour has been assumed in the temperature and pressure range of interest. The molar Gibbs energy of the gas phase is then given by: i X h gas gas G Al,H2 ,H,Mg (T ) = xi 0 G i +RT ln (P/P0 ) i

+ RT

X

xi ln xi

(5)

i gas

where 0 G i is the standard Gibbs energy of the component i in the gas state, P0 is the standard pressure of 101 325 Pa, xi is the mole fraction of species i and R is the gas constant. The liquid phase has been described using the conventional equation developed by Muggianu et al. [29]. Accordingly, the Gibbs free energy is expressed as follows: G liq = ref G ref id

G

G

ex

liq

liq

+ id G

liq

+ ex G

liq

liq

liq

liq

= xAl G Al + xH G H + xMg G Mg

liq

= RT [xAl ln(xAl ) + xH ln(xH ) + xMg ln(xMg )]

liq

= xAl xH L Al,H + xAl xMg L Al,Mg + xH xMg L H,Mg

G

liq

liq

liq

liq

(6)

liq

liq

where ref G , id G , ex G are the reference Gibbs energy, the ideal mixing and the excess contributions to the free energy, liq liq liq respectively [30]. G Al , G H , G Mg are the Gibbs energy of liquid liq

liq

liq

Al, H and Mg, and L Al,H , L Al,Mg , L H,Mg are binary interaction parameters. It is noteworthy that the lattice stability of liquid H has not been clearly assessed yet and no standard agreement exists. Different authors [8,10] have determined different lattice stabilities for H based on binary experimental data they were considering. Thus the thermodynamic parameters in Eq. (4) for the liquid H phase are different in the binary Al–H [8] and Mg–H [10] systems. In order to maintain consistency in the ternary system, the lattice stability of liquid H in the Al–H system has been kept in the present database. A partial reassessment of the Mg–H system, limited to experimental data concerning the liquid phase, has been carried out in order to determine a new consistent set of parameters for this phase. Binary solid phases have been taken from the thermodynamic assessments carried out by Qiu et al. [8] (Al–H),

Zeng et al. [10] (Mg–H) and Zhong et al. [9] (Al–Mg). Since no experimental evidence exists of a solubility range in magnesium alanate, this compound has been considered as a stoichiometric phase. Accordingly, the Gibbs free energy of Mg(AlH4 )2 is expressed as follows: 0 0 G Mg(AlH4 )2 = xAl 0 G fcc Al +x H G H +x Mg G Mg gas

+ 1Hfor − T · 1Sfor

hcp

(7)

where the value of 1Hfor has been assessed on the basis of ab initio and experimental information. Unlike metallic alloys, the metal-hydrogen systems are characterized by relatively large negative entropy of mixing for solution of H in a metal and for formation of hydrides [31,32]. A first approximation consists on assuming that the entropy of formation of a metal hydride is mainly associated to the vanishing of the entropy of the H2 gas (S0 = 130 J/K mol). Thus a value 1S f = −130 J/K mol) is often adopted [33]. Experimental data on the entropy of formation of several metallic hydrides determined from p − x − T measurements on absortion/desortpion have been collected by Fukai [31]. These data confirm that the main contribution to the entropy of formation is due to hydrogen gas, but a lower −1 value is suggested (−100 J mol H−1 2 K ). From the present ab −1 has been initio calculations a value equal to −96 J mol H−1 2 K obtained, which has been taken as 1Sfor in our database (Eq. (7)). Consequences of adopting different values for the entropy of formation of the alanate are further discussed later. All thermodynamic calculations have been performed using the ThermoCalc software package and the thermodynamic model parameter for the magnesium alanate was determined, on the basis of the available experimental and ab initio information, using the PARROT optimization module. Assessed thermodynamic parameters are reported in the Appendix. 5. Results and discussion According to the calculated reaction enthalpy (+11.2 kJ/ mol) for Eq. (3) from present ab initio calculations and the CALPHAD assessed values of the enthalpy of formation for AlH3 (−11.6 kJ/mol, Ref. [8]) and for MgH2 (−75.6 kJ/mol, Ref. [10]), an enthalpy of formation of −87.6 kJ/mol is obtained for the magnesium alanate. This value, together with other calculated ab initio values for the enthalpy of formation and experimental enthalpies of the decomposition reaction listed in Table 1, has been used in order to obtain an assessed value of 1Hfor = −79 kJ/mol.

M. Palumbo et al. / Computer Coupling of Phase Diagrams and Thermochemistry 31 (2007) 457–467

Fig. 3. Calculated (lines) binary Mg–H temperature-composition phase diagram at different pressures (0.27, 0.53, 0.8, 1 bar) according to thermodynamic parameters of the liquid phase obtained in the present work. Experimental data (points) of H solubility in the liquid phase at different pressures are also reported.

An attempt to include the AlMgH5 phase in the present database using the ab initio calculated enthalpy of formation from Ref. [21] has been carried out unsuccessfully. The ab initio enthalpy of formation appears to overestimate the thermodynamic stability of this hypothetical compound, which would result more stable than the magnesium alanate. In fact, the same authors have calculated the enthalpy of reaction (3) obtaining a significantly higher value with respect to present work (Table 1). As mentioned in the previous section, a partial reassessment of the Mg–H system has been carried out here in order to obtain the lattice stability for liquid H. As reported in Fig. 3, a satisfactory agreement has been obtained between experimental data of H solubility in the liquid phase, at different temperatures and pressures, and the calculated lines of the phase diagram. The agreement is comparable with that obtained by Zeng et al. [10]. The calculated isothermal section of the ternary diagram at room temperature and 1 bar is shown in Fig. 4(a). Clearly, magnesium alanate is not thermodynamically stable under these conditions. The same result is obtained at higher pressures (10 and 100 bar). The binary β-MgH2 hydride is more stable than the magnesium alanate and would be observed when thermodynamic equilibrium is reached. The metastable isothermal section of the ternary diagram at 1 bar obtained by removing from the calculations the binary β-MgH2 is reported

463

in Fig. 4(b). The β-Al3 Mg2 and γ -Al12 Mg17 , fcc Al, hcp Mg and gas phases appear in the diagram. Only at high pressure (100 bar) the magnesium alanate appears in the phase diagram (Fig. 4(c)). The temperature–pressure behaviour has been investigated for the ternary alloy at the composition of magnesium alanate (Fig. 5). According to these results, the high thermodynamic stability of β-MgH2 hinders the formation of the alanate even at high pressures (Fig. 5(a)). By removing the β-MgH2 compound from the calculation, the metastable P–T diagram in Fig. 5(b) is obtained where the Mg(AlH4 )2 is predicted to be stable at high pressures and low temperatures. On the contrary, at low pressures and high temperatures a mixture of β-Al3 Mg2 , fcc. Al and gas phases occurs. According to the present calculations, the formation of Mg(AlH4 )2 is predicted at pressures higher than 9.2 · 106 Pa at room temperature (T = 298.15 K), when the formation of the β-MgH2 hydride is avoided (Fig. 5(b)). Recent claims [31] of alanate formation at low pressure, 1 atm, and low temperature, 100 ◦ C, are not supported by our results. The synthesis procedures of the alanate, reported in the literature, seem thus to skip somewhat the formation of the more thermodynamically stable β-MgH2 hydride without requiring high pressures. However, the magnesium alanate is metastable at room temperature and 1 bar and it easily decomposes into the stable mixture β-MgH2 , fcc Al and gas phases upon heating as it has been well established experimentally (reaction 1). A long milling time also leads to decomposition of Mg(AlH4 )2 into the stable mixture [7]. Fig. 5(b) also shows the predicted stability of magnesium alanate when using our ab initio result for the enthalpy of formation (−87.6 kJ/mol). In this case, stability of Mg(AlH4 )2 is of course increased but it still remain unstable at room temperature and 1 bar. Moreover, it is by far metastable with respect to decomposition to MgH2 . Even if the enthalpy of formation of Mg(AlH4 )2 is changed up to ∼−94 kJ/mol, which would correspond to the lowest experimental value of decomposition enthalpy (of the order of ∼−18 kJ/mol as reported by Kim et al. [6]), it still results metastable with respect to MgH2 . A change on the entropy of formation value (i.e. using 130 J/K mol H2 instead of the ab initio value 96 J/K mol H2 ) will further destabilize the alanate, which would not appear at all in Fig. 5(b). Thus, adopting different values from assessed enthalpy and entropy of formation will not change our conclusion on thermodynamic instability of magnesium alanate. On further heating at 1 bar, reaction (2) is predicted to occur at 503 K, while a melting range of 724–744 K is calculated (Fig. 5(a)). This is also evidenced in Fig. 6, where the enthalpy of the equilibrium phase mixture, the metastable mixture obtained removing β-MgH2 from the calculation and the single magnesium alanate phase are reported as a function of temperature. According to experimental DSC results [5–7] the peak corresponding to reaction (2) has a broad shape and the onset temperature is thus difficult to establish. Nonetheless, the onset is in the temperature range 490–510 according to [5, 7], while a higher onset temperature has been obtained by Kim et al. [6]. The melting ranges reported by Mamatha

464

M. Palumbo et al. / Computer Coupling of Phase Diagrams and Thermochemistry 31 (2007) 457–467

Fig. 4. (a) Calculated isothermal section of the ternary phase diagram at 1 bar and 298.15 K including all phases. The same result is obtained at 10 and 100 bar. (b) Calculated isothermal section of the ternary phase diagram at 1 bar and 298.15 K obtained by neglecting the MgH2 hydride. (c) Calculated isothermal section of the ternary phase diagram at 100 bar and 298.15 K obtained by neglecting the MgH2 hydride.

Fig. 5. (a) Pressure–temperature equilibrium diagram for the magnesium alanate composition. (b) Pressure–temperature metastable diagram for the magnesium alanate composition obtained neglecting from the calculation the MgH2 hydride. Dotted line results when using the value from our ab initio calculations (−87.6 kJ/mol) for the enthalpy of formation of magnesium alanate.

et al. (715–729 K) and Varin et al. (717–735 K) are both in satisfactory agreement with the calculated range. In Fig. 6 the enthalpy of the equilibrium mixture, metastable mixture (obtained removing the β-MgH2 phase) and the magnesium alanate is reported as a function of temperature. Experimental data from the literature are also shown for comparison and the agreement is good except for the datum reported by Kim et al. [6], which appears significantly different. As already pointed out in Section 2, despite these authors

claimed their enthalpy value is different from oldest results by Dilts and Ashby [15] and Claudy et al. [12] since their samples are not affected by solvent effects, both latest achievements from Mamatha et al. [5] and Varin et al. [7] using also solvent free samples are not consistent with this value. 6. Conclusion Ab initio and thermodynamic calculations on the magnesium alanate Mg(AlH4 )2 and the Al–Mg–H system have been carried

465

M. Palumbo et al. / Computer Coupling of Phase Diagrams and Thermochemistry 31 (2007) 457–467 Table A.1 Gas phase G(GAS,H2;0) G(GAS,AL;0) G(GAS,H;0) G(GAS,MG;0)

GH2GAST + R*T*LN(1E−05*P); GALGAST + R*T*LN(1E−05*P) GHGAST + R*T*LN(1E−05*P) GMGGAST + R*T*LN(1E−05*P)

Liquid phase G(LIQUID,AL;0) G(LIQUID,H;0) G(LIQUID,MG;0)

L(LIQUID,AL,MG;0) L(LIQUID,AL,MG;1) L(LIQUID,AL,H;0) L(LIQUID,H,MG;0)

11 005.553−11.8408737*T + 7.9401E−20*T**7 + GHSERAL# (298.15 < T < 923 K) 10 481.974 − 11.252014*T + 1.234264E + 28*T**( − 9) + GHSERAL (923 < T < 3000 K) +8035 + 25*T + 2*T*LN(T) + 0.5*GH2GAST#; −165.097 + 134.838617*T − 26.1849782*T*LN(T) + 4.858E − 04*T**2 − 1.393669E −06*T**3 + 78 950*T**( − 1) − 8.0176E − 20*T**7 (298.15 < T < 923 K) − 5439.869 + 195.324057*T − 34.3088*T*LN(T) (923 < T < 3000 K) −9.0315816E + 03 + 4.8547124E + 00*T −8.9111184E + 02 + 1.1368285E + 00*T 51228 − 11.4752*T 1.30404878E + 04 − 3.9621749*T

Bcc phase G(BCC A2,AL:VA;0) G(BCC A2,MG:VA;0)

+10 083 − 4.813*T + GHSERAL +3100 − 2.1*T + GHSERMG

Fcc phase G(FCC G(FCC G(FCC G(FCC G(FCC G(FCC G(FCC

A1,AL:VA;0) A1,AL:H;0) A1,MG:VA;0) A1,AL,MG:VA;0) A1,AL,MG:VA;1) A1,AL,MG:VA;2) A1,AL:H,VA;0)

+GHSERAL 100 000 + GHSERAL + 0.5*GH2GAST +2600 − .9*T + GHSERMG; 1.5876100E + 03 + 2.1413324E + 00*T 1.1795327E + 03 − 6.9523422E − 01*T −8.6682189E + 02 −45 805 + 56.4302*T

Hcp phase G(HCP G(HCP G(HCP G(HCP G(HCP G(HCP

A3,AL:VA;0) A3,MG:VA;0) A3,AL,MG:VA;0) A3,AL,MG:VA;1) A3,AL,MG:VA;2) A3,MG:H;0)

+5481 − 1.8*T + GHSERAL +GHSERMG 4.2719648E + 03 − 2.1898692E + 00*T −1.0768640E + 00 + 1.0148480E + 00*T −9.6593125E + 02 +87394.9 − 122.339*T + GMGH2 − 0.75*GH2GAST

β-Al3 Mg2 phase (exact stoichiometry isAl140 Mg89 ) G(ALMG BETA,MG:AL;0)

−8.0913627E + 05 + 1.1501663E + 02*T + 89*GHSERMG + 140*GHSERAL

ε-Al30 Mg23 phase G(ALMG EPS,MG:AL;0)

−1.7208069E + 05 − 5.8490582E + 00*T + 23*GHSERMG + 30*GHSERAL

γ -Al12 Mg17 phase G(ALMG G(ALMG G(ALMG G(ALMG G(ALMG G(ALMG

GAMMA,MG:AL:AL;0) GAMMA,MG:MG:AL;0) GAMMA,MG:AL:MG;0) GAMMA,MG:MG:MG;0) GAMMA,MG:AL:AL,MG;0) GAMMA,MG:MG:AL,MG;0)

8.3600000E + 03 + 2.0338857E + 01*T + 5*GHSERMG + 24*GHSERAL −1.0430883E + 05 + 2.3495281E + 01*T + 17*GHSERMG + 12*GHSERAL 1.8055600E + 05 − 1.3806900E + 02*T + 17*GHSERMG + 12*GHSERAL 1.3937100E + 05 − 8.7319000E + 01*T + 29*GHSERMG 1.1310000E + 05 − 1.4500000E + 01*T 1.1310000E + 05 − 1.4500000E + 01*T

β-MgH2 phase G(MGH2 ALFA,H2MG1;0)

GMGH2

AlH3 phase G(ALH3 ALFA,AL1H3;0)

−28 415 + 213.712933*T − 41.75632*T*LN(T) − 0.014548469*T**2 + 446 400*T**( − 1)

Mg(AlH4 )2 phase G(AL2H8MG,AL2H8MG1;0)

−79 000 + 386*T + GHSERMG + 2*GHSERAL + 4*GH2GAST

Symbols: GH2GAST

−9522.97393 + 78.5273873*T − 31.35707*T*LN(T) + .0027589925*T**2 − 7.46390667E − 07*T**3 + 56582.3*T**( − 1) 298.15 < T < 1000 K (continued on next page)

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Table A.1 (continued) + 180.10884 − 15.6128262*T − 17.84857*T*LN(T) − .00584168*T**2 + 3.14618667E − 07*T**3 −1 280 036*T**( − 1); 1000 < T < 2100 K −18 840.1661 + 92.3120249*T − 32.05082*T*LN(T) − .0010728235*T**2 + 1.14281783E − 08*T**3 + 3 561 002.5*T**( − 1); 2100 < T < 3000 K GHSERMG

− 8367.34 + 143.675547*T − 26.1849782*T*LN(T) + 4.858E − 04*T**2 − 1.393669E − 06*T**3 + 78950*T**( − 1) 298.15 < T < 923 K −14130.185 + 204.716215*T − 34.3088*T*LN(T) + 1.038192E + 28*T**( − 9) 923 K < T < 3000 K

GHSERAL

− 7976.15 + 137.093038*T − 24.3671976*T*LN(T) − .001884662*T**2 − 8.77664E − 07*T**3 + 74 092*T**( − 1) 298.15 < T < 700 K −11276.24 + 223.048446*T − 38.5844296*T*LN(T) + .018531982*T**2 − 5.764227E − 06*T**3 + 74 092*T**( − 1) 700 < T < 933.47 K −11 278.378 + 188.684153*T − 31.748192*T*LN(T) − 1.230524E + 28*T**( − 9) 933.47 < T < 3000 K

GALGAST

323947.58 − 25.14809*T − 20.859*T*LN(T) + 4.5664E − 5*T**2 − 3.942E − 9*T**3 − 24275.5*T**( − 1)

GHGAST

211 801.621 + 24.498982*T − 20.78611*T*LN(T)

GMGGAST

+140 825.883 − 8.26178024*T − 20.96302*T*LN(T) + 1.331861E − 04*T**2 − 1.51554617E − 08*T**3 + 5221.91*T**( − 1) 298.15 < T < 2900 K +141 959.02 + 20.1923537*T − 25.1271*T*LN(T) + .002179723*T**2 − 1.502275E − 07*T**3 − 3 744 678*T**( − 1) 2900 < T < 3000 K

GMGH2

−84 674.5998 + 145.79017*T − 24.84122*T*LN(T) − 0.017626985*T**2 − 3.380145E − 09*T**3 + 162.2085*T**( − 1) 298.15 < T < 600 K −108 422.153 + 495.654655*T − 75*T*LN(T) − 3.6920685E − 16*T**(2) + 5.93903667E − 20*T**(3) − 1.7334725E − 08*T**( − 1) 600 < T < 3000 K

metastable compounds. A reassessment of the parameters for the liquid Mg–H phase has been carried out in order to achieve consistency with the parameters of the liquid Al–H phase. Mg(AlH4 )2 has been found metastable with respect to β-MgH2 . Ab initio results reported in the literature for AlMgH5 have been found to overestimate the thermodynamic stability of this compound. Mg(AlH4 )2 phase becomes stable only at high pressure (>100 bar) and neglecting the formation of the β-MgH2 phase. Due to its thermodynamic instability with respect to β-MgH2 , magnesium alanate appears unsuitable as a hydrogen storage material. Acknowledgements

Fig. 6. Enthalpy of the stable equilibrium, metastable (MgH2 removed) and magnesium alanate phases as a function of temperature at 1 bar. Experimental points from refs. [5–7,12] are also reported for comparison. These data of the enthalpy of reaction have been normalized in order to be directly comparable with the enthalpy line of the equilibrium mixture (continuous line).

out. The fully relaxed crystal structure of Mg(AlH4 )2 has been predicted and it is in agreement with the experimental results from X-ray and neutron diffraction. According to the calculated Density of State (DOS) and band structure the alanate is an insulator. The enthalpy and Gibbs energy of formation have been obtained and used in subsequent thermodynamic calculations. A full thermodynamic database for the Al–H–Mg system has been obtained, including the magnesium alanate and other

The present study was performed in the frame of the CMA European Network of Excellence. We acknowledge financial support by the European Commission under contract n◦ NMP3 CT 2005 500145, the Project of Regione Piemonte, Codice C72 “Innovative materials for hydrogen storage” and the “Complex Solid State Reactions for Energy Efficient Hydrogen Storage” (contract n◦ MRTN-CT-2006-035366). Two of us (J.R.A. and J.F.F.) thank the Spanish MEC (MAT2005-06738-C02-01) for support. Appendix Summary of thermodynamic parameters describing the Al–H–Mg system is given in Table A.1. Except where otherwise specified, temperature range is 298.15 < T < 3000 K.

M. Palumbo et al. / Computer Coupling of Phase Diagrams and Thermochemistry 31 (2007) 457–467

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