Thermodynamical Stability of Complex Transition Metal Hydrides

Article pubs.acs.org/JPCC

Thermodynamical Stability of Complex Transition Metal Hydrides M2FeH6 Kazutoshi Miwa,*,† Shigeyuki Takagi,‡ Motoaki Matsuo,‡ and Shin-ichi Orimo‡ †

Toyota Central Research & Development Laboratories, Inc., Nagakute, Aichi 480-1192, Japan Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

‡

ABSTRACT: The thermodynamical stability of complex transition metal hydrides M2FeH6 is investigated by first-principles density-functional calculations. In addition to the reported alkaline-earth compounds (M = Mg, Ca, and Sr), hypothetical Mn2FeH6 and Zn2FeH6 are considered to examine chemical trends. Some double-cation systems, (MM′)FeH6, are also taken into consideration. A good correlation between the standard heats of formation of these compounds and the electronegativities of cation elements can be found as done in borohydrides [Nakamori et al., Phys. Rev. B 2006, 74, 045126]. A cation electronegativity is found to be a good indicator to estimate the stability of Febased complex transition metal hydrides.

■

INTRODUCTION Complex hydrides are one of the potential candidates for highcapacity hydrogen storage materials. A wide variety of complex hydrides can be found in the literature.1 However, most of them are thermodynamically too stable and release hydrogen only at elevated temperatures. Slow reaction kinetics is also a disadvantage for practical use, which makes a rehydriding reaction with gaseous hydrogen difficult. In this concern, we have recently shown that the complex transition metal hydride, YMn2H6, can be synthesized from the Laves-phase metal hydride YMn2H4.5 with gaseous hydrogen under moderate conditions.2 The substitution effects for this compound have been investigated theoretically.3 For many complex transition metal hydrides, complex anions obey the so-called 18-electron rule. In the case of YMn2H6,2 one of two Mn atoms in the unit cell forms an octahedral pentavalent [MnH6]5− anion whose internal bonds are essentially covalent. Deficient five electrons to form them are compensated by two cations, Y3+ and Mn2+. This charge compensation by cations is an important feature for the stability of complex hydrides. Since the ability of charge transfer can be measured by the electronegativity of cation elements, the cation electronegativity is expected to be a good indicator to estimate the stability of complex hydrides. In fact, a linear relationship between the standard heats of formation and the cation electronegativities has been proposed for borohydrides.4−7 If a similar relationship is also held for complex transition metal hydrides, it would be useful to tune their thermodynamical stabilities. In this study, the stability of complex transition metal hydrides M2FeH6 has been investigated by first-principles density-functional calculations. According to the 18-electron rule, the charge state of an FeH6 complex will be −4, and so M would be a divalent cation. We consider tetravalent [FeH6]4− rather than [MnH6]5− because the former can form a simple © 2013 American Chemical Society

compound containing a single type of cation. This simplicity will be convenient to analyze the charge transfer effect. Examples are Mg2FeH6,8 Ca2FeH6,9 and Sr2FeH6,10 with the K2PtCl6-type structure which is the same as that of YMn2H6. In addition to these alkaline-earth compounds, hypothetical Mn2FeH6 and Zn2FeH6 are taken into consideration to examine the chemical trends. We also conduct some doublecation systems, (MM′)FeH6.

■

METHDOLOGY

The present calculations have been performed using the ultrasoft pseudopotential method11,12 based on density functional theory.13,14 The generalized gradient approximation15 is adopted for the exchange-correlation energy. The cutoff energies used in this study are 15 and 120 hartree for the pseudowave functions and the charge density, respectively. The k-point grids for the Brillouin zone integration are generated to make the edge lengths of the grid elements as close to the target value of 0.08 bohr−1 as possible. These computational conditions give good convergence for the total energy within 1 meV/atom. The finite temperature effect as well as the zero-point energy contribution are taken into account within the harmonic approximation.16 The linear response method17−21 is used to obtain the phonon frequencies including the macroscopic polarization effect generated by lattice vibrations.

■

RESULTS Crystal Structure. For alkaline-earth elements, the syntheses of K2PtCl6-type M2FeH6 (M = Mg, Ca, and Sr) Received: December 12, 2012 Revised: April 1, 2013 Published: April 1, 2013 8014

dx.doi.org/10.1021/jp3122159 | J. Phys. Chem. C 2013, 117, 8014−8019

The Journal of Physical Chemistry C

Article

Table 2. Structural Parameters of Mn2FeH6a

have been reported.8−10 The K2PtCl6-type structure is shown in Figure 1, where FeH6 anions form a face-centered-cubic

atom parameters lattice parameters (Å) a = 4.391 c = 6.182

Mn Fe H1 H2

position

x

y

z

4d 2a 4e 8h

0 0 0 0.2969

1/2 0 0 0.2021

1/4 0 0.2545 0

a

Crystallographic symmetry is I4/m (No. 87). The unit cell volume is 59.59 Å3.

which are shown in Table 3. Unlike Mn2FeH6, the deformation of the FeH6 complex is moderate, which is elongated along the (111) direction of the original cubic lattice. The symmetry becomes almost trigonal with the H−Fe−H bond angles of 77° and the Fe−H bond lengths of 1.59 Å. Electronic Structure. Figure 2 depicts electronic densities of states (DOS) for M2FeH6 (M = Mg, Ca, Sr, Mn, and Zn). All the electronic structures of these five compounds are nonmetallic. For Mg2FeH6, the valence states consist of nine bands. A partial DOS analysis suggests that the contribution of Mg orbitals to them is negligible. The lowest six bands, which lie from −9.5 to −1.7 eV, are mainly composed of H-1s orbitals. Fe-3d orbitals split into t2g and eg states due to the octahedral crystal field, and the former forms the remaining three valence bands. Figure 3 shows the valence charge contour plots, in which the contribution of H-1s and Fe-t2g bands is shown separately. The lower-lying H-1s bands hybridize with Fe orbitals (probably eg, 4s, and 4p) as seen in Figure 3(a), whereas the Fe-t2g states plotted in Figure 3(b) indicate no hybridization with H-1s orbitals since it is forbidden under the octahedral crystal field. As expected from the partial DOS analysis, the valence charge density around Mg is considerably low (not shown), which is invisible with the contour spacing in Figure 3. Magnesium atoms are thought to be ionized as +2. The electronic structures of Ca2FeH6 and Sr2FeH6 are quite similar to that of Mg2FeH6 except for narrowing the valence band widths. This narrowing is most likely due to their larger lattice constants which weaken the interaction between neighboring FeH6 complexes. The densities of states obtained for these alkaline-earth compounds agree well with those of the previous theoretical study with local density approximation,23 in which it has been suggested that the ionic bonding character is entirely dominant. For Mn2FeH6, Mn-3d orbitals are spin-polarized, and the majority (minority) spin states are fully occupied (unoccupied). This indicates that Mn atoms are in a high-spin +2 state with five unpaired electrons. The occupied Mn-3d bands, however, overlap with the Fe-t2g bands, and so some hybridization between Mn and Fe orbitals may exist. For Zn2FeH6, the Zn-3d bands appear in the energy range from −7.3 to −5.7 eV, which are often treated as core states. Because there is little contribution of Zn orbitals to the valence states except for the Zn-3d bands, the charge state of Zn atoms is also considered to be +2. To confirm the charge states of constituent atoms, we have calculated the Born effective charge tensors. In Table 4, the average values of three diagonal elements of the tensors are tabulated. The Born effective charges of the cations fall within the range of 1.75−2.26, which agree reasonably with the expected value of +2. According to the acoustic sum rule, the charge states of FeH6 complexes are evaluated to be −4.52 to

Figure 1. Crystal structure of K2PtCl6-type M2FeH6. Red, green, and blue spheres represent M, Fe, and H atoms, respectively.

sublattice and M cations occupy its tetrahedral sites. The optimized structural parameters for the alkaline-earth compounds are summarized in Table 1. The calculated parameters Table 1. Structural Parameters of M2FeH6 (M = Mg, Ca, and Sr)a a

M Mg Ca Sr

6.392 7.007 7.454

x (6.443) (7.036) (7.315)

0.2447 0.2292 0.2172

V (0.242) (0.230) (0.237)

65.30 86.02 103.52

a

Space group: Fm3̅m (No. 225). Lattice constant a (Å) and unit cell volume V (Å3). Atomic positions are 8c (1/4,1/4,1/4), 4a (0,0,0), and 24e (x,0,0) sites for M, Fe, and H, respectively. Experimental data are given in parentheses.

are in fairly good agreement with the experimental data. The lattice constants increase in the order Mg2FeH6, Ca2FeH6, Sr2FeH6, reflecting the ionic radii of divalent cations, whereas the Fe−H bond lengths in FeH6 complexes are almost unchanged, which are 1.56, 1.61, and 1.62 Å for Mg2FeH6, Ca2FeH6, and Sr2FeH6, respectively. Hypothetical Mn2FeH6 and Zn2FeH6 are chosen as examples of compounds composed of more electronegative cations. For Mn2FeH6, the spin polarization is taken into account, and it is found that the antiferromagnetic (AFM) order for high-spin Mn2+ is energetically more stable than the ferromagnetic one. However, the AFM cubic phase shows softmode instabilities in the phonon analysis. There are three softmodes whose eigenvectors correspond to nearly rigid rotation of FeH6 complexes. Freezing them, the stable structure with crystallographic symmetry of I4/m is obtained: The full symmetry operations including the magnetic structure are schematically represented by I4 + 4 (I4/m − I4), where 4 is the spin inversion operator.22 The obtained structural parameters are given in Table 2. The FeH6 complex keeps nearly ideal octahedral symmetry with the Fe−H bond lengths of 1.57− 1.58 Å. Zn2FeH6 in the cubic phase also exhibits strong softmode instability. The relaxation of softmodes causes considerable reduction of symmetry. The finally obtained stable structure is triclinic with space group of P1̅, the structural parameters of 8015



Article

Table 3. Structural Parameters of Zn2FeH6a atom parameters lattice parameters (Å) α = 59.99° β = 62.28° γ = 64.92°

a = 5.308 b = 4.435 c = 4.430

a

Zn Fe H1 H2 H3

position

x

y

z

2i 1a 2i 2i 2i

0.0838 0 0.7639 0.2362 0.2374

0.3031 0 0.3415 0.9132 0.1731

0.3082 0 0.0728 0.1877 0.6716

Space group: P1̅ (No. 2). The unit cell volume is 79.38 Å3.

charge for Fe, suggesting that the internal bonding of FeH6 complexes is essentially covalent. This is consistent with the charge contour plot given in Figure 3(a). Phonon. The phonon densities of states for M2FeH6 (M = Mg, Ca, Sr, Mn, and Zn) are depicted in Figure 4, where the

Figure 2. Electronic densities of states for M2FeH6. Black solid lines indicate the total DOS. Red dotted lines denote the partial DOS due to cation M. The origins of energies are set to be the top of valence states.

Figure 4. Phonon density of states for M2FeH6.

macroscopic electric fields generated by lattice polar vibrations are taken into consideration. The Fe−H stretching modes have frequencies higher than 1480 cm−1. These frequencies are the highest in Mg2FeH6 and the lowest in Sr2FeH6: they tend to become lower with increasing unit cell volume.1 The H−Fe−H bending modes are located from 700 to 1000 cm−1, which form sharp peaks except for Mn2FeH6. A dispersive nature of the bending modes of Mn2FeH6 is presumable due to the effect of hybridization between Mn and Fe orbitals. No trends can be found between the bending-mode frequencies and the unit cell volumes. Thermodynamical Stability. The standard heats of formation of M2FeH6, ΔHform, are evaluated from the total energy calculations, and then the finite-temperature effect as well as the zero-point energy contribution are incorporated within the harmonic approximation.16 The results are listed in Table 5. The heat of formation of Mn2FeH6 is nearly zero, and that of Zn2FeH6 is positive, indicating that two hypothetical compounds are thermodynamically less stable. The definition of the electronegativity is not unique, and several methods to calculate it have been proposed,24−26 though all methods show the same periodic trends between elements. For borohydrides,4,6 the Pauling electronegativity scale24 has been used for cation elements. In this study, we use the Allred−Rochow scale.26 In Figure 5, the heats of formation are plotted as a function of the Allred−Rochow electronegativity of the cation elements, χAR. A good correlation between the heats of formation and the cation electro-

Figure 3. Valence charge contour plots for Mg2FeH6 in the (100) plane. Partial charge density summing up (a) the lowest six (H-1s) bands and (b) the highest three (Fe-t2g) bands. Contour spacing is 0.05 e/bohr3, and lines are omitted for the density higher than 1 e/ bohr3.

Table 4. Average Born Effective Charges for M2FeH6 Mg2FeH6 Ca2FeH6 Sr2FeH6 Mn2FeH6 Zn2FeH6

M

Fe

H

2.08 2.23 2.26 1.75 1.88

−3.07 −2.21 −2.00 −4.51 −3.40

−0.18 −0.37 −0.42 0.17 −0.06

−3.50 which are in fairly good agreement with the value of −4 derived from the 18-electron count. In addition, if the internal bonding of an FeH6 complex is purely ionic, the Born effective charges should be +2 and −1 for Fe and H, respectively. None of the five compounds considered here show a positive effective 8016



Article

Table 5. Standard Heats of Formation of M2FeH6, ΔHform (kJ/mol)a ΔHform Mg2FeH6 Ca2FeH6 Sr2FeH6 Mn2FeH6 Zn2FeH6

−244.1 −461.2 −438.3 −4.8 50.5

a

Temperature T = 298.15 K and hydrogen partial pressure PH2 = 0.1 MPa.

Figure 6. Crystal structure of (MgMn)FeH6. The red, green, purple, and blue spheres represent Mg, Fe, Mn, and H atoms, respectively.

eV. The standard heat of formation is predicted to be −103.7 kJ/mol. The enthalpy change for the following mixing reaction 1 1 Mg 2FeH6 + Mn2FeH6 → (MgMn)FeH6 (3) 2 2 is a positive value of 20.8 kJ/mol, indicating that the synthesis of (MgMn)FeH6 may be difficult. Nevertheless, the obtained ΔHform for (MgMn)FeH6 is close to the average of those of single-cation compounds, Mg2FeH6 and Mn2FeH6. This result demonstrates that the mixing of cations is effective to control the stability of FeH6-based hydrides. The second example is (NaAl)FeH6, where two divalent cations are replaced by monovalent and trivalent ones. The softmode instabilities reduce the symmetry of the crystal to be trigonal. The optimized structure is depicted in Figure 7, the parameters of which are listed in Table 7. The electronic structure is nonmetallic with a band gap of 1.7 eV. The standard heat of formation is obtained as ΔHform = −134.7 kJ/ mol. Lastly, we consider (YLi)FeH6 which has been recently synthesized by hydrogenating a mixture of YFe2 and LiH.27 The structure has been determined to be cubic with the symmetry of F4̅3m. The optimized structural parameters are given in Table 8. The calculated lattice constant agrees well with the experimental value of 6.702 Å. The electronic structure is nonmetallic with a calculated band gap of 1.6 eV. The standard heat of formation is predicted to be ΔHform = −419.0 kJ/mol. In Figure 5, the calculated heats of formation of three double-cation compounds considered in this section are also plotted, where the average weight by valency of cations is taken for the Allred−Rochow electronegativities. They obey the linear relationship extracted from the single-cation results. The relation of eq 1 is expected to be held for the double-cation compounds. When the Pauling scale is adopted for the doublecation compounds, the linear relationship between ΔHform and χP is held well except for (YLi)FeH6. Equation 2 yields ΔHform = −313 kJ/mol for (YLi)FeH6, which is underestimated by about 100 kJ/mol. The Allred−Rochow scale is more appropriate than the Pauling scale, at least to estimate the stability of Fe-based complex hydrides. Hydrogen Desorption Reaction. Finally, we consider the hydrogen desorption reactions. Because the hydrogen desorption reaction of a complex hydride is usually accompanied with the formation of compounds such as a hydride, the thermodynamical stabilities of them have to be

Figure 5. Standard heat of formation of M2FeH6, ΔHform, as a function of the Allred−Rochow electronegativity of the cation element, χAR. Red circles are the results for single-cation compounds and blue triangles for double-cation compounds. The straight line is obtained by the least-squares fitting for the single-cation results.

negativities can be found as done in borohydrides. Assuming the linear relationship, the least-squares fitting yields ΔHform = 757.5χAR − 1207.4

(1)

with an absolute mean error of 20.4 kJ/mol. Since Mn2FeH6 obeys this relationship, an ionic interaction is thought to be dominant between Mn and FeH6, although weak hybridization between Mn and Fe orbitals may exist. A good correlation is also obtained with the Pauling scale χP: The calculated data can be fitted as ΔHform = 847.9χP − 1287.9

(2)

with an absolute mean error of 15.7 kJ/mol. The electronegativity of a cation element is a good indicator to estimate the thermodynamical stability of M2FeH6. Double-Cation Compounds. Since the number of divalent elements in the periodic table is limited, mixed-cation compounds are expected to be useful for exploring an FeH6based hydride with appropriate stability as a hydrogen storage material. In this section, we consider some hypothetical doublecation compounds. The first example of double-cation compounds is (MgMn)FeH6. The doubled K2PtCl2-type unit cell is chosen as the initial configuration, in which the rocksolt ordering is assumed for the arrangement of Mg and Mn atoms. The AFM order is found to be energetically favorable for high-spin Mn2+. The crystallographic symmetry of the optimized structure is reduced to P1 due to softmode instabilities, and the spin inversion operation {4 |(1/2),(1/2),(1/2)} is only retained. The optimized structure is shown in Figure 6, whose parameters are given in Table 6. The structure is pseudocubic, where FeH6 complexes are tilted keeping its octahedral shape. The electronic structure is nonmetallic with an energy gap of 1.2 8017



Article

Table 6. Structural Parameters of (MgMn)FeH6a atom parameters lattice parameters (Å) α = 90.01° β = 89.97° γ = 90.05°

a = 4.494 b = 4.490 c = 6.331

Mg Mn Fe H1 H2 H3 H4 H5 H6

position

x

y

z

1a 1a 1a 1a 1a 1a 1a 1a 1a

0.0001 0.0005 0 0.2371 0.7465 0.2467 0.7513 0.9736 0.0431

0.4999 0.4994 0 0.7459 0.2377 0.2489 0.7530 0.0358 0.9785

0.7499 0.2500 0 0.0318 0.9681 0.0035 0.9964 0.2461 0.7541

a Crystallographic symmetry is P1 (No. 1). Half of 18 atoms in the unit cell is only listed. A full list can be obtained by applying the spin inversion operation, {4|(1/2),(1/2),(1/2)}.

Table 9. Hydrogen Desorption Reaction and Thermodynamical Propertiesa reaction

ΔH

ΔS

Teq

Mg2FeH6 → 2Mg + Fe + 3H2 (MgMn)FeH6 → MgH2 + FeMn + 2H2 (NaAl)FeH6 → NaH + FeAl + (5/2)H2

81 22 10

128 123 126

632 180 79

Enthalpy change ΔH (kJ/mol H2), entropy change ΔS (J/mol H2·K), and equilibrium temperature at hydrogen partial pressure 0.1 MPa, Teq (K). The calculated standard heats of formation of products are −54.1, −6.8, −41.9, and −68.1 kJ/mol for MgH2, FeMn, NaH, and FeAl, respectively. a

accompanied with the formation of MgH2, which is consistent with the expermental observation.28 In fact, the enthalpy change of the reaction, Mg2FeH6 → 2MgH2 + Fe + H2, becomes 135 kJ/mol H2. So, hydrogen contained in Mg2FeH6 is fully released, where the theoretical mass fraction of released hydrogen is 5.8 mass %. The substitution of Mn for Mg destabilizes the compound since Mn is more electronegative than Mg. For (MgMn)FeH6, the enthalpy change becomes less endothermic, ΔH = 22 kJ/ mol H2, and the equilibrium temperature decreases to 180 K. In contrast to Mg2FeH6, the destabilized (MgMn)FeH6 forms MgH2 as a decomposed product because of its lower Teq, which causes a reduction of the effective hydrogen capacity. A heavier atomic mass of Mn is also a drawback. The mass fraction of released hydrogen is reduced to 2.9 mass %. The replacement of divalent Mg by monovalent Na and trivalent Al is also effective for destabilization because the averaged electronegativity of Na and Al is larger than that of Mg. For (NaAl)FeH6, we obtain ΔH = 10 kJ/mol H2 and Teq = 79 K. Though a hydrogen trap in the decomposed phase occurs as found in (MgMn)FeH6, it keeps the relatively high hydrogen capacity of 4.5 mass % since a hydrogen trapping phase is monohydride, NaH. In a practical viewpoint, since the equilibrium temperatures of (MgMn)FeH6 and (NaAl)FeH6 are too low, more precise adjustment of the thermodynamical properties is required. The gravimetric hydrogen capacity is another important issue. In this point, the replacement of divalent cations by monovalent and trivalent atoms is favorable to reduce an amount of trapped hydrogen in decomposed products.

Figure 7. Crystal structure of (NaAl)FeH6. The red, purple, green, and blue spheres represent Na, Al, Fe, and H atoms, respectively.

Table 7. Structural Parameters of (NaAl)FeH6a atom parameters lattice parameters (Å) a = 4.284 c = 15.634

a

position

x

y

z

1a 1a 1a 2b 2b

0 0 0 0.9512 0.3853

0 0 0 0.2726 0.4178

0.1861 0.6730 0 0.0598 0.2671

Na Al Fe H1 H2

Space group: R3 (No. 146).

Table 8. Structural Parameters of (YLi)FeH6a atom parameters lattice parameters (Å) a = 6.646

a

Y Li Fe H

position

x

y

z

4c 4d 4a 24f

1/4 3/4 0 0.2384

1/4 3/4 0 0

1/4 3/4 0 0

Space group: F4̅3m (No. 216).

taken into account. In Table 9, the expected hydrogen desorption reactions and the corresponding thermodynamical properties are shown for some selected FeH6-based compounds. It is known that Mg2FeH6 is a stable compound. The hydrogen desorption reaction is predicted to be largely endothermic with the enthalpy change ΔH = 81 kJ/mol H2. The equilibrium temperature at hydrogen partial pressure 0.1 MPa is obtained as Teq = 632 K. The desorption reaction is not

■

SUMMARY The thermodynamical stability of complex transition metal hydrides M2FeH6 has been investigated by first-principles 8018



Article

(13) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136, B864−B871. (14) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133− A1138. (15) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (16) Siegel, D. J.; Wolverton, C.; Ozoliņs,̌ V. Reaction Energetics and Crystal Structure of Li4BN3H10 from First Principles. Phys. Rev. B 2007, 75, 014101-1−014101-11. (17) Gonze, X. First-Principles Responses of Solids to Atomic Displacements and Homogeneous Electric Fields: Implementation of a Conjugate-Gradient Algorithm. Phys. Rev. B 1997, 55, 10337−10354. (18) Gonze, X.; Lee, C. Dynamical Matrices, Born Effective Charges, Dielectric Permittivity tensors, and Interatomic Force Constants from Density-Functional Perturbation Theory. Phys. Rev. B 1997, 55, 10355−10368. (19) Dal Corso, A. Density-Functional Perturbation Theory with Ultrasoft Pseudopotentials. Phys. Rev. B 2001, 64, 235118−1− 235118−17. (20) Baroni, S.; de Gironcoli, S.; Dal Corso, A.; Giannozzi, P. Phonons and Related Crystal Properties from Density-Functional Perturbation Theory. Rev. Mod. Phys. 2001, 73, 515−562. (21) Miwa, K. Prediction of Raman Spectra with Ultrasoft Pseudopotentials. Phys. Rev. B 2011, 84, 094304−1−094304−13. (22) Since the present calculations do not include the spin−orbit interaction, this operator solely exchanges the up-spin and down-spin components, by which the time reversal symmetry is not broken. (23) Halilov, S. V.; Singh, D. J.; Gupta, M.; Gupta, R. Stability and Electronic Structure of the Complex K2PtCl6-Structure Hydrides DMH6 (D = Mg,Ca,Sr; M = Fe,Ru,Os). Phys. Rev. B 2004, 70, 195117−1−195117−11. (24) Pauling, L. The Nature of the Chemical Bond. IV. The Energy of Single Bonds and the Relative Electronegativity of Atoms. J. Am. Chem. Soc. 1932, 54, 3570−3582. (25) Mulliken, R. S. A New Electroaffinity Scale; Together with Data on Valence States and on Valence Ionization Potentials and Electron Affinities. J. Chem. Phys. 1934, 2, 782−793. (26) Allred, A. L.; Rochow, E. G. A Scale of Electronegativity Based on Electrostatic Force. J. Inorg. Nucl. Chem. 1958, 5, 264−268. (27) Matsuo, M.; Saitoh, H.; Machida, A.; Sato, R.; Takagi, S.; Miwa, K.; Watanuki, T.; Katayama, Y.; Aoki, K.; Orimo, S. Formation of an Fe−H Complex Anion in YFe2: Adjustment of Imbalanced Charge by Using Additional Li as an Electron Donor. RSC Adv. 2013, 3, 1013− 1016. (28) Bogdanovic, B.; Reiser, A.; Schlichte, K.; Spliethoff, B.; Tesche, B. Thermodynamics and Dynamics of the Mg-Fe-H System and its Potential for Thermochemical Thermal Energy Storage. J. Alloys Compd. 2002, 345, 77−89.

density-functional calculations. It is found that the electronegativity of cation elements is a good indicator to estimate the thermodynamical stability of M2FeH6: The standard heats of formation can be approximately represented by a linear function of the cation electronegativity. For single-cation compounds, both the Allred−Rochow scale and the Pauling scale give a good correlation. When the double-cation compounds are taken into consideration, the former scale becomes more appropriate. A similar relation is also expected to be held for other complex transition metal hydrides such as a Mn-based one, which will be useful for exploring a compound with suitable stability as a hydrogen storage material.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS We thank M. Aoki, T. Noritake, S. Towata, R. Sato, and K. Aoki for valuable discussions. REFERENCES

(1) Yvon, K. Complex Transition-Metal Hydrides. Chimia 1998, 52, 613−619. (2) Matsuo, M.; Miwa, K.; Semboshi, S.; Li, H.-W.; Kano, M.; Orimo, S. First-Principles Studies of Complex Hydride YMn2H6 and its Synthesis from Metal Hydride YMn2H4.5. Appl. Phys. Lett. 2011, 98, 221908-1−221908-3. (3) Takagi, S.; Miwa, K.; Ikeshoji, T.; Matsuo, M.; Kano, M.; Orimo, S. Theoretical Investigation of Fe Substitution for Mn in Complex Hydride YMn2H6. Appl. Phys. Lett. 2012, 100, 021908-1−021908-3. (4) Nakamori, Y.; Miwa, K.; Ninomiya, A.; Li, H.-W.; Ohba, N.; Towata, S.; Züttel, A.; Orimo, S. Correlation between Thermodynamical Stabilities of Metal Borohydrides and Cation Electronegativites: First-Principles Calculations and Experiments. Phys. Rev. B 2006, 74, 045126-1−045126-9. (5) Miwa, K.; Aoki, M.; Noritake, T.; Ohba, N.; Nakamori, Y.; Towata, S.; Züttel, A.; Orimo, S. Thermodynamical Stability of Calcium Borohydride Ca(BH4)2. Phys. Rev. B 2006, 74, 155122-1− 155122-5. (6) Miwa, K.; Ohba, N.; Towata, S.; Nakamori, Y.; Züttel, A.; Orimo, S. First-Principles Study of Thermodynamical Stability of Metal Borohydrides: Aluminum Borohydride Al(BH4)3. J. Alloys Compd. 2007, 446−447, 310−314. (7) Sato, T.; Miwa, K.; Nakamori, Y.; Ohoyama, K.; Li, H.-W.; Noritake, T.; Aoki, M.; Towata, S.; Orimo, S. Experimental and Computational Studies on Solvent-Free Rare-Earth Metal Borohydrides R(BH4)3 (R = Y, Dy, and Gd). Phys. Rev. B 2008, 77, 1041141−104114-1-8. (8) Didisheim, J.-J.; Zolliker, P.; Yvon, K.; Fischer, P.; Schefer, J.; Gubeimann, M.; Williams, A. F. Dimagnesium Iron(II) Hydride, Mg2FeH6, Containing Octahedral FeH64− anions. Inorg. Chem. 1984, 23, 1953−1957. (9) Hagemann, H.; D’Anna, V.; Daku, L. M. L.; Gomes, S.; Renaudin, G.; Yvon, K. Structural and Vibrational Properties of Ca2FeH6 and Sr2RuH6. J. Phys. Chem. Solid 2011, 72, 286−289. (10) Huang, B.; Bonhomme, F.; Selvam, P.; Yvon, K.; Fischer, P. New Ternary and Quaternary Metal Hydrides with K2PtCl6-type Structure. J. Less-Common Met. 1991, 171, 301−311. (11) Vanderbilt, D. Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism. Phys. Rev. B 1990, 41, 7892−7895. (12) Laasonen, K.; Pasquarello, A.; Car, R.; Lee, C.; Vanderbilt, D. Car-Parrinello Molecular Dynamics with Vanderbilt Ultrasoft Pseudopotentials. Phys. Rev. B 1993, 47, 10142−10153. 8019


Thermodynamical Stability of Complex Transition Metal Hydrides

Recommend Documents