Polymorphism and Thermodynamics of Y(BH4)3 from First Principles

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J. Phys. Chem. C 2010, 114, 12833–12837

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Polymorphism and Thermodynamics of Y(BH4)3 from First Principles Young-Su Lee,* Jae-Hyeok Shim, and Young Whan Cho Materials/DeVices DiVision, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea ReceiVed: May 16, 2010; ReVised Manuscript ReceiVed: June 24, 2010

Structure and thermodynamics of the recently discovered two polymorphs of Y(BH4)3 are investigated by first-principles calculation. Simulated X-ray and neutron diffraction patterns combined with structure analysis from first principles enable us to assign a space group Fm3jc to the high-temperature polymorph among the several proposed space groups. An orientational disorder of [BH4]- groups is considered and compared with NaBH4, which has a disordered [BH4]- arrangement at room temperature. In the case of NaBH4, the structure stays in a local energy minimum irrespective of the [BH4]- orientation, but in Y(BH4)3, [BH4]- reorientation is suppressed by a strong repulsive force created by close H-H contacts and the structure becomes unstable, thus favoring an ordered [BH4]- arrangement. The calculated high energy barrier for the [BH4]- reorientation partly accounts for the slow phase transition observed in Y(BH4)3, again making a good contrast with the facile [BH4]- flipping in NaBH4. The thermodynamics of Y(BH4)3 appears quite attractive, exhibiting a lower dissociation temperature than Mg(BH4)2 under 1 bar of H2. 1. Introduction Metal borohydrides, M(BH4)n, have large hydrogen capacity and have been regarded as candidates for reversible hydrogen storage materials.1,2 One of the hurdles in utilizing M(BH4)n is their high thermal stability, and it has been a great challenge to determine a metal borohydride based system having an optimal stability. As a pure form of M(BH4)n, a handy criterion of estimating their stability is the electronegativity of the metal M;3,4 a less electronegative metal will fully donate its valence electron(s) to the [BH4] unit, thus forming a stronger ionic bonding. Partial donation would weaken the ionic bond strength and, at the same time, the B-H bond strength since [BH4]δ(δ < 1) is less stable than [BH4]-.5 In this regard, Y(BH4)3 is located in the right window in terms of electronegativity4 and hydrogen content (9.06 wt %). However, it is only recent that Y(BH4)3 has drawn attention6-10 and therefore further analysis on dehydrogenation reaction pathway, thermodynamics, reversibility, etc. needs to be carried out in order to fully assess its potential as a practical hydrogen storage material. We here present a first-principles study on the structure and thermodynamics of Y(BH4)3. Recently, a high-temperature polymorph of Y(BH4)3 was discovered and the crystal structure was resolved,8-10 but there still remains an ambiguity regarding [BH4]- orientational disorder. We try to elucidate this point by combining information from experiments, simulated diffraction patterns, and first-principles calculations. Comparison with the orientational disorder in NaBH4 is given in order to better understand the structure of Y(BH4)3. Finally, enthalpy and entropy of several possible dehydrogenation reaction pathways are estimated; the most energetically stable decomposition product is suggested and the thermal stability of Y(BH4)3 is compared with that of other metal borohydrides. 2. Computational Details Total energies were calculated in the framework of density functional theory (DFT). All the calculations were carried out * To whom correspondence should be addressed. E-mail: lee0su@ kist.re.kr.

with the Quantum-ESPRESSO package11,12 and the pseudopotential library therein.13 For the exchange-correlation functional, generalized gradient approximation by Perdew and Wang was adopted.14 The planewave cutoff of 50 Ry and charge density cutoff of 400 Ry were used. The enthalpy and entropy of several compounds were obtained within the harmonic approximation. The climbing image nudged elastic band (CI-NEB) method15 was used to estimate the activation energy for the [BH4]reorientation. 3. Results and Discussion 3.1. Structures and Energies of Y(BH4)3. We have compared the crystal structures and the total energies of the two polymorphs of Y(BH4)3. The calculated and experimental lattice parameters and atomic positions are summarized in Table. 1. The structural parameters of the low-temperature phase (henceforth referred to as R-Y(BH4)3) agree well with the previous reports6,9,10 which consistently found Pa3j space group. However, three different space groups, Fm3jc,9 Pm3jm,10 and F4j3c,8 have been discussed in the case of the high-temperature polymorph (henceforth referred to as β-Y(BH4)3). Figure 1 shows the crystal structures of R-Y(BH4)3 in Pa3j and β-Y(BH4)3 in Fm3jc space group. The Fm3jc structure by Frommen et al.9 has a fully ordered array of [BH4]- groups where alternating orientation is taken as shown in Figure 1b. On the other hand, the Pm3jm structure proposed by Ravnsbæk et al.10 has half the lattice parameter containing one formula unit, and the [BH4]- groups randomly take either of the two possible orientations. They also considered a short-range ordering in a way to reduce short H-H contacts, but their X-ray diffraction (XRD) data could not resolve this issue. Since XRD certainly has a limitation in locating the position of hydrogen atoms whereas neutron diffraction (ND) outperforms XRD in this respect, we simulate both XRD and ND patterns in order to see whether they can distinguish between Fm3jc and Pm3jm structure. The simulated patterns16 at a wavelength of 1.5 Å are presented in Figure 2. The two XRD patterns in Figure 2, panels a (Fm3jc) and b (Pm3jm), are almost identical as expected. On the contrary, the simulated ND patterns

10.1021/jp104447z  2010 American Chemical Society Published on Web 07/07/2010

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TABLE 1: Calculated Structural Parameters of r-Y(BH4)3 and β-Y(BH4)3 atomic positions compd

lattice parameter

atom

Wyckoff symbol

x

y

z

R-Y(BH4)3

space group Pa3j

a ) 10.858 10.852a 10.8522b 10.7445c

β-Y(BH4)3

Fm3jc

a ) 11.005 11.0086b 10.9094c

Y B H1 H2 H3 H4 Y B H

8c 24d 24d 24d 24d 24d 8b 24c 96i

0.2179 0.1930 0.2909 0.1043 0.1752 0.2014 0.0000 0.0000 0.0000

0.2179 0.2473 0.2534 0.2257 0.3475 0.1623 0.0000 0.0000 0.4069

0.2179 0.9682 0.0243 0.0351 0.9192 0.8942 0.0000 0.2500 0.3116

a

Reference 6. b Reference 9. c Reference 10. The lattice parameter of β-Y(BH4)3 is doubled to make a comparison easier.

Figure 1. Structure of (a) R-Y(BH4)3 in Pa3j space group and (b) β-Y(BH4)3 in Fm3jc space group. Y, B, and H atoms are shown in violet, green, and yellow, respectively.

Figure 2. Simulated XRD patterns of β-Y(BH4)3 in (a) Fm3jc and (b) Pm3jm. Simulated ND patterns of β-Y(BD4)3 in (c) Fm3jc and (d) Pm3jm. The wavelength is fixed at 1.5 Å.

of Y(BD4)3 provide an indisputable evidence in favor of the Fm3jc structure: the strongest (531) peak in Figure 2c (Fm3jc) is absent in Figure 2d (Pm3jm), and therefore the Fm3jc space group can be assigned to β-Y(BH4)3 based on the ND patterns.9 Another space group F4j3c mentioned by Jaro´n and Grochala8 is closely connected to the Fm3jc structure. The Wyckoff position of H atoms in Fm3jc has site symmetry of m, but even an infinitesimal degree of rotation of the [BH4]- groups around the axis connecting the two nearest Y3+ ions would allow H’s to escape from the mirror plane thereby reducing the symmetry to F4j3c. It would be practically impossible to distinguish between the two space groups if the angle of rotation is really small, but in our first-principles calculation we do not find any evidence of instability toward such rotation of [BH4]- and we conclude here that Fm3jc space group best describes the structure of β-Y(BH4)3. To find out a possible structural instability which is important in understanding thermodynamics of metal borohydrides,17-19

Figure 3. Calculated phonon density of states of β-Y(BH4)3 (+y axis) and R-Y(BH4)3 (-y axis). Gaussian broadening of 10 cm-1 is used. The orange and blue bars show calculated IR active mode frequencies and intensities of β-Y(BH4)3 and R-Y(BH4)3, respectively.

full phonon spectra are calculated and we find that both R- and β-Y(BH4)3 are stable without showing any imaginary frequencies. Phonon density of states (DOS) and IR active modes are shown in Figure 3. The phonon DOS of β-Y(BH4)3 (+y axis) is slightly up-shifted compared to that of R-Y(BH4)3 (-y axis), which would give higher zero point energy to β-Y(BH4)3, but no significant difference appears. The IR active modes are quite similar between the two polymorphs except for the mode splitting in R-Y(BH4)3 due to lower symmetry. The active mode frequencies and the associated intensities are in good agreement with the reported FT-IR spectrum.8 Against our expectation, the total energy of β-Y(BH4)3 turns out to be lower than that of R-Y(BH4)3 though the difference is not large, being 4.2 kJ/mol (2.7 meV/atom) as summarized in Table 2. Zero point energy of β-Y(BH4)3 is slightly larger by 0.7 kJ/mol, but this is not enough to overcome the total energy difference. While DFT calculation gives an excellent description of the structure including the lattice parameter change from Rto β-Y(BH4)3 by ca. 1.4%, it does not correctly predict a small difference in energy. We will elaborate on this point in the next section. 3.2. Structural Disorder. 3.2.1. Yttrium Borohydride. Here we examine the structure of Y(BH4)3 to understand why the ordered Fm3j c structure is more favored than the disordered Pm3jm structure. The key factor is the energy barrier for [BH4]reorientation since it would largely determine the degree of disorder at a given temperature.20 To estimate the energy barrier of rotation, the CI-NEB method is adopted. The calculation was done with one unit cell consisting of 8 formula units of Y(BH4)3. One [BH4]- is chosen since all the [BH4]- groups are symmetrically equivalent and it is rotated around the axis connecting the two nearest Y3+ ions as shown in Figure 4. The energy values of seven images along the minimum energy path are plotted in Figure 5. The rotating [BH4]- comes back to its

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TABLE 2: Total Energy, Enthalpy, and Entropy Change of the Polymorphic Phase Transformation and the Dehydrogenation Reactionsa reaction

∆E (kJ/mol H2), T)0K

∆H (kJ/mol H2), T ) 25 °C

∆S (J/K · mol H2), T ) 25 °C

T (°C), PH2 ) 1 bar

H2 capacity (wt %)

(a) R-Y(BH4)3 T β-Y(BH4)3 (b) β-Y(BH4)3 T 1/4YH3 + 3/4YB4 + 45/8H2 (c) β-Y(BH4)3 T 1/4YH2 + 3/4YB4 + 23/4H2 (d) β-Y(BH4)3 T 1/2YH3 + 1/2YB6 + 21/4H2 (e) β-Y(BH4)3 T 1/2YH2 + 1/2YB6 + 11/2H2 (f) β-Y(BH4)3 T YH3 + 3R-B + 9/2H2 (g) β-Y(BH4)3 T YH2 + 3R-B + 5H2 (h) β-Y(BH4)3 T Y + 3R-B + 6H2 (i) YH3 T YH2 + 1/2H2

-4.2 37.4 38.1 43.5 44.7 54.2 55.6 82.0 68.6

-3.9 22.5 23.6 28.0 29.8 36.2 39.5 68.3 69.1

-4.0 114.4 114.6 116.4 116.7 111.0 112.2 116.2 122.6

-78 -69 -33 -17 54 79 306 287

8.50 8.69 7.93 8.31 6.80 7.55 9.06 1.10

a

T is the temperature at which hydrogen partial pressure becomes 1 bar, and H2 capacity is the amount of hydrogen released through the given reaction.

Figure 4. Atomic configuration of β-Y(BH4)3 at image number 3. Y, B, and H atoms are shown in violet, green, and yellow, respectively. Atoms in gray show the initial configuration at image number 0 or at θ ) 0°. Initially, the closest H-H distance is 2.54 Å, but it becomes 1.48 Å at θ ) 90° without relaxation. When relaxation is allowed, the rotating [BH4]- pushes away the four neighboring [BH4]- groups thereby increasing H-H up to 1.72 Å.

Figure 5. CI-NEB results of [BH4]- reorientation energy in Y(BH4)3. Black circles and gray squares are for β-Y(BH4)3 and R-Y(BH4)3, respectively. Open circles show energy change when [BH4]- is rigidly rotated by θ without relaxation.

original position when θ ) 180°, so the images 0 and 6 are identical. The ∆E at the saddle point is calculated to be 0.68 eV for β-Y(BH4)3 (black circles) and 0.44 eV for R-Y(BH4)3 (gray squares). When the [BH4]- group is rigidly rotated by θ without structure relaxation (open circles) the barrier becomes as high as 1.17 eV in β-Y(BH4)3. This large energy barrier can be attributed to the special arrangement of the four nearby [BH4]- groups which approach very closely to the rotating [BH4]- as shown in Figure 4. In the Fm3jc structure, when θ )

0°, the alternating [BH4]- orientation optimally avoids close H-H contacts and the shortest H-H distance is as long as 2.54 Å (excluding the H-H distances between the H’s belonging to the same boron). Rigid rotation of [BH4]- creates four very short H-H contacts and the repulsive force becomes maximum at θ ) 90°. When structure relaxation is allowed, the energy is lowered by pushing away the four nearby [BH4]- groups increasing the shortest H-H distance from 1.48 to 1.72 Å. The structural difference between R- and β-Y(BH4)3 can be interpreted in terms of the [BH4]- orientation. In Figure 1, one can easily notice that half the [BH4]- groups in R-Y(BH4)3 take different orientations compared to β-Y(BH4)3. If the R-Y(BH4)3 structure is made by simply flipping the orientation of 12 [BH4]groups in β-Y(BH4)3 without structure relaxation, 24 H-H pairs will have the distance of 1.48 Å resulting in a very unstable structure. The less regular atomic arrangement in R-Y(BH4)3 is the result of a reorganization to avoid such close H-H contacts and the shortest distance in the optimized R-Y(BH4)3 is stretched up to 2.14 Å. Considering this large repulsive force and the structural distortion created by the close H-H contacts, it is not likely that completely regular Y, B positions are maintained while only [BH4]- groups take random orientations as suggested in the Pm3jm structure. We would like to emphasize that the flipped state is not only energetically unfavorable but also unstable being the maximum energy point along the θ coordinate in Figure 5. Indeed, the large barrier we find in CI-NEB calculation may partly account for rather slow phase transformation and coexisting R- and β-Y(BH4)3 at room temperature.8,9 If the phase transformation is initiated and proceeds by the rotation of [BH4]- groups then the high barrier would certainly slow down the process. Finally, our DFT calculation results predict that R-Y(BH4)3 would be a high temperature polymorph since R-Y(BH4)3 has higher enthalpy and entropy (see Table 2). If the experimentally observed phase transition at ∼180 °C10 does reflect the real equilibrium condition, then it might be the case that DFT calculation overestimates H-H repulsion, which would stabilize β-Y(BH4)3 with respect to R-Y(BH4)3 and would increase vibration frequencies of β-Y(BH4)3 by forming a steeper than true energy well for atomic vibrations, causing smaller entropy. It would be worthwhile to see whether this reasoning can be extended to explain why the DFT-predicted phase is more stable than the experimentally found low-temperature phase of Mg(BH4)2.21-25 We note that this is only one of several possibilities that are responsible for such a mismatch between experiments and DFT predictions since the way we treat the finite-temperature effect is not at all comprehensive. On the experimental side, a precise measurement on the temperature

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Figure 6. Structure of NaBH4. Na, B, and H atoms are shown in blue, green (or red), and yellow, respectively. Two possible orientations are indicated by red and green boron atom. At room temperature, [BH4]groups are randomly oriented. The numbers indicate H-H distance in Å.

and the heat of R- to β-Y(BH4)3 transformation would be helpful in clarifying this issue. 3.2.2. Sodium Borohydride. Inspection of the structure of NaBH4 which has randomly oriented [BH4]- groups26-31 would provide a better understanding as to why orientational disorder is unlikely in Y(BH4)3. In Figure 6, two possible orientations of [BH4]- in NaBH4 are drawn in green and red boron atoms. The structure has F4j3m space group when all the [BH4]- groups take the same orientation, but it is energetically unfavorable since this arrangement creates 24 H-H pairs in relatively close contact (∼2.3 Å) in one unit cell. Random orientation would reduce this number to 12 pairs and layer-by-layer ordering as in the P42/nmc structure26,29 would reduce it to 8 pairs.32 Starting from a hypothetical P4j3m structure in Figure 6 where only the center [BH4]- takes a different orientation, we calculate the energy of reorientation when [BH4]- is rotated by θ around the axis drawn in the figure. We apply this operation on the [BH4]- groups sitting on the z ) 1/2 plane. The CI-NEB results are summarized in Figure 7. To begin with, rotating the center [BH4]- would generate F4j3m-like structure and rotating the corner one would generate P42/nmc-like structure. The two energies indicated by the dashed blue lines are calculated from these two structures with optimized lattice parameters while the lattice parameter during the CI-NEB calculation is fixed to that of the P4j3m structure. The calculated lattice parameter of the P4j3m structure is 6.081 Å and that of F4j3m is 6.120 Å, being close to an experimental value of 6.148 Å.26 The lattice parameters of the P42/nmc structure are a ) 4.339 Å and c ) 5.879 Å, again in close agreement with experimental values of a ) 4.332 Å and c ) 5.869 Å.26 To check the effect of cell size on the energy of rotation, the same calculations were carried out with the 2 × 2 × 2 supercell (192 atoms) of the P4j3m structure and the energies along the minimum energy path are shown in the right panel of Figure 7 in solid symbols. Again, one [BH4]- is flipped as schematically drawn in the figure. The different cell size does not cause a large difference; the two sets of simulation show the same trend and are also quantitatively similar. Three main differences can be immediately found when compared with Y(BH4)3. First of all, the NaBH4 structure stays in a local minimum irrespective of the [BH4]- orientation and this we deem to be the most important difference. Second, reorientation costs much less, especially when the starting point

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Figure 7. CI-NEB results of reorientation energy in NaBH4. Red and green circles indicate two different [BH4]- orientations following the same color scheme in Figure 6. The data in the left panel are for a single [BH4]- group rotation in unit cell and the data in the right panel are for the same operation in the 2 × 2 × 2 supercell. Open symbols show energy change when a [BH4]- group is rigidly rotated by θ without relaxation.

is energetically unfavorable: the energy barrier for switching from the F4j3m to the P4j3m strucure is as small as 0.020 eV in a one unit cell calculation. The calculated energy barrier of ∼0.1 eV agrees well with an experimental one of 0.117 eV.33 Third, the relaxation effect is much smaller. The open symbols in the right panel of Figure 7 show the energy change upon rigid rotation by θ, and the energy maxima increase by less than 0.1 eV compared to those of the CI-NEB calculations. Different from the case of β-Y(BH4)3, neighboring [BH4]- groups do not approach very closely, having the minimum distance of 2.19 Å at θ ) 50°. 3.3. Thermodynamics of Dehydrogenation. The calculated enthalpy and entropy of several dehydrogenation reactions are listed in Table 2. More stable β-Y(BH4)3 is used as a standard state of Y(BH4)3. Among the three borides considered (R-B, YB4, and YB6), dissociation into YB4 turns out to be the most favorable, which is consistent with a recent experimental observation.10 Since YH3 is more stable than YH2 at the predicted equilibrium dehydrogenation temperature, reaction b (Table 2) would represent overall thermodynamics of dehydrogenation of Y(BH4)3, with a caveat that intermediate steps are not taken into account.9,10 The associated enthalpy (22.5 kJ/ mol of H2) and the equilibrium temperature (-78 °C) seem largely underestimated when compared with experiments which observed a major hydrogen release event at 200-300 °C. This discrepancy may come from inaccuracy in the DFT total energy calculations, or the way the finite temperature effect is treated, or slow kinetics of dehydrogenation. However, the experimental stability trend among selected high-capacity borohydrides, LiBH4 > Ca(BH4)2 > Mg(BH4)2 > Y(BH4)3 (in descending order of stability), is well reproduced by DFT calculations when the overall dehydrogenation reactions are compared,4,34 and therefore we can conclude that Y(BH4)3 can certainly offer even lower dehydrogenation temperature than Mg(BH4)2 that has been actively investigated due to its favorable thermodynamics.22,35-38 The stability of Y(BH4)3 is on par with the recently synthesized Ce(BH4)339 but Y(BH4)3 is superior in terms of hydrogen capacity. Although thermodynamics of Y(BH4)3 is more suitable than Mg(BH4)2, hydrogen capacity of 8.50 wt % sounds less attractive than 14.94 wt % of Mg(BH4)2. One way to increase the capacity

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is to mix with the same molar quantity of LiBH4. If the dehydrogenation reaction proceeds as follows

LiBH4 + Y(BH4)3 T LiH + YB4 + (15/2)H2

(1) the released hydrogen will increase up to 9.74 wt %. The question is whether Y(BH4)3 can effectively destabilize LiBH4 so that the above reaction is finished at relatively low temperature. Another interesting point of discussion is reversibility of such a composite system. A recent study by the present authors has shown that when 4LiBH4 + YH3 composite is dehydrogenated following the reaction below

4LiBH4 + YH3 T 4LiH + YB4 + (15/2)H2

(2)

about 70% of hydrogen is reversibly absorbed at the first cycle even without a catalytic additive.40 The final products of reactions 1 and 2 are identical except for the molar ratio LiH/ YB4 and reaction 1 may exhibit better reversibilty than pure Y(BH4)3, where only 1.1-1.3 wt % of rehydrogenation has been achieved so far.7 4. Conclusions The structure and thermodynamics of Y(BH4)3 has been investigated by first-principles calculations. The calculated structural parameters show excellent agreement with experimental values. The simulated ND patterns and the high energy cost of the [BH4]- reorientation predicted by the present study exclude the possibility for β-Y(BH4)3 to have the disordered Pm3jm space group. The calculated energy barrier of the [BH4]reorientation in Y(BH4)3 is much higher than that of NaBH4, which has randomly oriented [BH4]- groups at room temperature. The thermal stability of Y(BH4)3 appears quite promising with a smaller enthalpy of dehydrogenation than that of Mg(BH4)2. Acknowledgment. This work has been sponsored by the Hydrogen Energy R&D Center, one of the 21st Century Frontier R&D Programs funded by the Ministry of Education, Science and Technology of Korea. References and Notes (1) Zu¨ttel, A.; Wenger, P.; Rentsch, S.; Sudan, P.; Mauron, P.; Emmenegger, C. J. Power Sources 2003, 118, 1. (2) Orimo, S.; Nakamori, Y.; Eliseo, J. R.; Zu¨ttel, A.; Jensen, C. M. Chem. ReV. 2007, 107, 4111. (3) Nakamori, Y.; Miwa, K.; Ninomiya, A.; Li, H.-W.; Ohba, N.; Towata, S.; Zu¨ttel, A.; Orimo, S. Phys. ReV. B 2006, 74, 045126. (4) Nakamori, Y.; Li, H.-W.; Matsuo, M.; Miwa, K.; Towata, S.; Orimo, S. J. Phys. Chem. Solids 2008, 69, 2292. (5) Du, A. J.; Smith, S. C.; Lu, G. Q. Phys. ReV. B 2006, 74, 193405. (6) Sato, T.; Miwa, K.; Nakamori, Y.; Ohoyama, K.; Li, H.-W.; Noritake, T.; Aoki, M.; Towata, S.; Orimo, S. Phys. ReV. B 2008, 77, 104114.

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