First-Principles Study of Structural Prototypes for NaAlH4: Elevated

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First-Principles Study of Structural Prototypes for NaAlH4: Elevated Pressure Polymorph in Symmetry Fmm2 Leads to a Single-Step Decomposition Pathway E. H. Majzoub* Center for Nanoscience and Department of Physics and Astronomy, University of Missouri − St. Louis, St. Louis, Missouri 63121, United States

E. Hazrati and G. A. de Wijs Radboud University Nijmegen, Institute for Molecules and Materials, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands S Supporting Information *

ABSTRACT: In situ high-temperature X-ray diffraction and hightemperature and pressure nuclear magnetic resonance studies of the complex metal hydride NaAlH4 have strongly suggested an intermediate phase or phases. In order to search for these phases, structural prototypes of NaAlH4 were generated using the method of prototype electrostatic ground states (PEGS). Structural motifs included tetrahedral [AlH4]− and [AlH6]3− octahedral anions. Structures were produced with Al−H coordination numbers from 4 to 6 and were examined for thermodynamic stability. We present a high-temperature phase in symmetry Fmm2 that is lower in total free energy than all currently known structures, including a structure presented in space group Cmcm, due to low rotational barriers for [AlH4]− anions. The Na−Al−H phase diagram, calculated in the harmonic approximation, indicates that at higher pressures, the I41/a NaAlH4 phase transforms to Fmm2 symmetry, which then decomposes directly into NaH and Al, eliminating the Na3AlH6 intermediate. The transition to Fmm2 is predicted to occur near 320 K at calculated pressures of about 1−2 bar. We also present calculations of NMR 27Al and 23Na chemical shifts for the structural prototypes. These results indicate a monotonic decrease of the 27Al chemical shift with increasing Al−H coordination number with an unambiguous identification of an Al/H ratio of 1:4 for the unknown high-temperature phase S105 identified by Conradi and coworkers (Conradi, M. S. et al. J. Phys. Chem. Lett. 2010, 1, (15), 2412−2416).

1. INTRODUCTION

These reactions occur at elevated temperatures with or without transition metal dopants that act to kinetically enhance the reactions.4,5 Studies on transition-metal-doped NaAlH4 complicate the analysis and identification of phases,6 and we focus our attention only on undoped sodium alanate. In-situ X-ray diffraction studies of the decomposition of pure NaAlH4 revealed an unknown phase below the melting temperature of 180 °C and was labeled X1 by Gross et al.7 This phase was reported to be transient and depended on the hydrogen backpressure in the experimental setup. The phase was thought to have cubic symmetry and may or may not be related to another phase labeled X2 in the same paper. Gross’ study was complicated by the decomposition reaction that begins near the melting temperature of NaAlH4 and produces the hexahydride phase, Na3AlH6, whose structure was determined

The accepted ground-state structure for sodium aluminum tetrahydride, NaAlH4, is body-centered tetragonal in space group I41/a, with lattice parameters of about a = 5.02 Å and c = 11.33 Å.2,3 NaAlH4, is thought to decompose in two steps, first into the hexahydride Na3AlH6, which further decomposes into NaH as follows (the enthalpy and critical temperature for each reaction are DFT-calculated values using the methods described in Section 2) NaAlH4 ⇌

1 2 Na3AlH6 + Al + H 2 3 3

(29.4kJ/mol H 2)

Tc = 27°C, P = 1bar

(1)

Na3AlH6 ⇌ 3NaH + Al +

3 H2 2

(46.7kJ/mol H 2)

Tc = 147°C, P = 1bar © 2013 American Chemical Society

Received: February 5, 2013 Revised: March 22, 2013 Published: March 26, 2013

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Figure 1. Bonding motifs of prototype crystal structures for NaAlH4 in space groups (left-to-right) Cm, Pmc21, and Amm2. All structures have an Al/ H ratio of 1:4. The chain structure in Cm contains bipyrimidal corner-sharing anions. The Pmc21 structure contains edge-sharing octahedra, while the structure in Amm2 contains corner sharing octahedra.

by Rönnebro et al.8 It was not clear whether the new X1 and X2 phases were related to the structure of tetrahydride or hexahydride. More recently, in situ nuclear magnetic resonance studies by Conradi et al.1 were performed using a high-pressure cell that prevented the decomposition of NaAlH4 during heating of the sample up to and through the melt. This study identified a new phase containing 27Al with a shift of about 12 ppm higher than the 27Al in I41/a NaAlH4. This new species was labeled S105 due to its shift from the 27Al standard (see Table S1 in Supporting Information). We note that more recent experimental work in their group has placed the chemical shift of pure NaAlH4 and S105 at 97.5 ppm and 101.6 ppm, respectively.9 The limited loss of hydrogen from the samples in their experiments, and more recent experimental results,9 suggests that the resulting phase is 1:1:4 in Na/Al/H ratio, and we focused attention on prototypes of these structures. Both experimental observations of new phases from in situ Xray diffraction and NMR occur at high-temperature and are sensitive to varying or elevated pressure. We therefore calculated the phase diagram in the Na−Al−H system using structural prototypes for NaAlH4. It is important that these prototypes have chemical shifts in agreement with experimental values and we present first-principles calculated 27Al chemical shifts and electric field gradients for a range of Al−H coordinations from 4 to 6 for our NaAlH4 prototypes. Finally, and most importantly, we also present a candidate structure in symmetry Fmm2 with an Al−H coordination of four that contains nonlinked [AlH4]− anions, that obtains the lowest total free energy of all known NaAlH4 structural candidates, is predicted to be the observed structure at elevated temperature and H2 pressures above about 2 bar, and leads to a single-step decomposition pathway at elevated H2 overpressures.

energy as a function of temperature, was calculated in the harmonic approximation using the standard technique of summing over the zone-center phonon frequencies. Chemical shifts were calculated in linear response with the gauge-including projector augmented wave (GIPAW) method15 as implemented in VASP 5. Electric field gradients (EFGs) were also calculated with VASP 5, using the PAW method of ref 16. The Perdew, Burke, and Ernzerhof exchange correlation functional was used17,18 with standard PAW data sets as supplied with VASP. The frozen Na and Al cores were 1s22s2 and 1s22s22p6, respectively. The plane-wave kinetic energy cutoff Ecut = 900 eV. Brillouin zone integrals were performed on meshes with a k-point spacing of less than 0.025 Å−1. We checked that these meshes are more than sufficient for a few selected structures. Chemical shift calculations are shown in Table S2 (Supporting Information) for NaAlH4, Na3AlH6 and a few other compounds, and in Table S3 (Supporting Information) for small molecule test benchmark cases, comparing to shifts calculated with a quantum-chemical method.19 The relative shifts can be compared directly to experimental shifts from Table S1 (Supporting Information). For calculation of the rotational barriers of the [AlH4]− tetrahedra, the climbing image nudged elastic band (CI-NEB) method was used to determine the transition state (TS) by constructing a string of images between two adjacent potential energy minima.20,21 The string of images was relaxed until the forces perpendicular to the minimum energy path were less than 0.01 eV/Å. Sodium aluminum tetrahydride structure prototypes were generated using the prototype electrostatic ground state (PEGS) method, described in detail in ref 22. Briefly, the method utilizes the simplified Hamiltonian, H = Σi≠j(qiqj)/(rij) + (βij)/(r12 ij ), consisting of pairwise electrostatic interactions and soft-sphere repulsion to prevent ions from overlapping (βij = 0 when rij > (Ri + Rj), and 1 otherwise). A Metropolis Monte Carlo algorithm paired with simulated annealing was used to find the presumed ground state configuration for a collection of charge-balanced cations and anions. In a typical application, 1− 4 formula units (f.u.) for the compound structure are optimized. There were no a priori assumptions regarding symmetry. All defined objects were allowed to translate, swap positions, and rotate. The lattice vectors and cell shape were also optimized during the simulated anneal. A distance scaling method was used to smooth the potential energy surface; this dramatically improves the output structures. After the PEGS

2. COMPUTATIONAL METHODS First-principles electronic-structure calculations were performed using the Vienna Ab-Initio Simulation Package (VASP).10−12 A plane wave basis set was used for the electronic wave functions with a cutoff energy of 600 eV. The generalized gradient approximation of Perdew and Wang13 (GGA-PW91) was used to represent electronic exchange-correlation effects. Brillouin zone integrals were performed over regular Monkhorst−Pack14 grids with a k-point spacing of less than 0.05 Å−1. Zone-center phonon frequencies were calculated using linear response in VASP 5. Crystal entropy, and therefore free 8865

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structures were generated, all structural parameters including lattice vectors, cell volume, and atomic positions, were optimized using the first-principles DFT techniques described above. Structure prototypes were subsequently searched for symmetry using the FINDSYM program in the ISOTROPY software package23 with an rms tolerance of 0.05 Å and their thermodynamic parameters calculated. The PEGS method has been successful in a wide variety of structural studies of the complex hydrides including materials discovery,24−26 confirmation of structures determined from diffraction data, 27 polymorphic transitions as function of temperature,28 and has even been extended to the study of nanoparticle complex hydrides.29

3. DISCUSSION 3.1. Structure Prototypes and Chemical Shifts. While the aluminum center in I41/a NaAlH4 has tetrahedral symmetry and is four-coordinated, this is not the only bonding motif for Al−H anions that maintains an Al/H ratio of 1:4. Sharing hydrogen atoms among the vertices of linked [AlH6]3− units will maintain the same ratio if four octahedral corners are shared between neighboring octahedra. We generated structures containing all possible combinations of corner and edge sharing among the octahedra that would result in an Al:H ratio of 1:4. The charges given to the nonlinked vertices were taken from 4-coordinated NaAlH4 Born effective charges to be −0.6675 e.22 Octahedra linked at vertices were free to rotate about the linked vertex and bend such that the Al−H−Al angle was optimized. Atomic positions and lattice parameters of structure prototypes, optimized via DFT, were allowed to break symmetry, in many cases resulting in structures with tetrahedral [AlH4]− or new bonding motifs not containing linked octahedra. Some bonding motifs with nontetrahedral Al−H are shown in Figure 1. The calculated 27Al shifts in these structures are consistent with the Al−H moieties with higher coordination than four. The structure in Figure 1a has an 27Al shift of about −47 ppm, while those in Figure 1b,c have shifts of about −66 ppm with respect to the 27Al in I41/a. It is immediately apparent from both the experimental values and the calculated shifts for 27Al in Na3AlH6 that 6-coordinated Al is not a candidate for the S105 phase (ref 30 and Tables S1 and S2 of the Supporting Information). Representative calculated shifts for structures with Al−H coordinations ranging from 4 to 6 are shown in Figure 2. The nonlinked [AlH6]3− and [AlH5]2− are both on the right-hand-side (most negative shift) of their spectrum. Sharing hydrogens between the units tends to increase the shifts. These results clearly indicate that only structures with 4-coordinated aluminum have shifts within the range of those measured for S105 (a comprehensive discussion on the relation between chemical shift and coordination as well as the quadrupole-induced shifts [see, for example, refs 31−33] can be found in the Supporting Information, Figure S1). We therefore focused our prototype prediction efforts around these types of structures. Additionally, only those 4-coordinated structures with tetrahedral [AlH4]− units had calculated shifts in correspondence with S105. Table 1 lists the calculated shifts for structures with tetrahedral [AlH4]− (see Supporting Information, Table S5 for a comprehensive listing). We note that the 23Na shifts of Fmm2 are close to that of I41/a.1 As indicated by Conradi and co-workers, the lack of distinct phase change seen in the XRD pattern of S105containing samples indicates that there is no new bulk phase formed. Evidently the structure is related to I41/a with defects

Figure 2. Calculated isotropic chemical shifts of 27Al versus the Al−H coordination number of PEGS-generated structure prototypes. The shifts are referenced to NaAlH4 (I41/a). Black circles, Al nuclei in structures with composition NanAlnH4n; red diamonds, structures with other compositions. The connected data points at δAl = −19 ppm pertain to a structure that is in-between 4 and 5-fold coordination.

that allow for line shape narrowing of the 27Al resonance. There are a variety of charged defects possible in NaAlH4 as discussed in the work of Michel and Ozolins.35 We have not attempted to calculate 27Al shifts for these structures because the defect densities were determined at pressures well below those where the S105 is experimentally prepared. The calculated shifts for the remaining [AlH4]− tetrahedra would be problematic to compute without more accurate densities and unit cell structures. We also note that 27Al calculated vacuum shifts for AlH3 and [AlH4]− molecules differ more than 200 ppm (see Supporting Information, Table S3). In contrast, all three phases of bulk AlH3, α, β, and γ, are composed of corner and edge sharing AlH6 octahedra (no free octahedra) and have isotropic chemical shifts between about 5 and 22 ppm referenced to aqueous Al(NO3)3.36 These shifts are at least 70 ppm upfield (down-frequency) from NaAlH4 and even further from the S105 shift. These shift values would be located around −70 ppm in our Figure 2, in units referenced to the 27Al in NaAlH4 (I41/a), and are in agreement with our calculated shifts for sixcoordinated Al. Evidently S105 is not bulk alane or a mobile AlH3 species. It is also clear from the work of Michel and Ozolins that prevalent defect densities are low enough that the dominant 27Al signal will be due to remaining [AlH4]− tetrahedra. This suggests that in an effort to form the thermdynamically favored high-temperature phases, defects are produced that provide a mechanism for 27Al line narrowing, such as increased rotational and translational motion. The barriers for rotational motion are discussed in detail below for I41/a and Fmm2. 3.2. Unreported Low-Energy Structure Symmetries. The PEGS search identified several structural prototypes that have not been reported previously, as well as others that have, such as the high-temperature candidate in symmetry Cmcm by Wood et al.37,34 The PEGS search finds several structures with lower T = 0K total energy (including ZPE) than Cmcm, in symmetries Cm, P4̅, P21 and P1̅. More importantly, when entropy was included, we identified two structures that have lower free energy than Cmcm at elevated temperatures up to the predicted transition temperature for the decomposition of NaAlH4. In fact, there is no temperature range in which the Cmcm structure obtains the lowest total free energy. The 8866

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Table 1. Low-Energy Structure Prototypes for NaAlH4 at T = 0 K Containing Tetrahedral AlH4 Unitsa prototype

space group

multiplicity Na,Al

δNa ppm

δAl ppm

Vzz[Al] V/Å2

Cq[Al] MHz

ΔE kJ/mol

ZPE meV/f.u.

NaAlH4 R2-n199 R2-n160 R3-n172

I41/a P21/m P21 P4̅

7.61 8.14 8.17

770 772 774

R2-n48

Pm

3.0 −2.5 1.7 3.3 −2.1 −4.0 2.0 −2.3 2.8 −2.5 −1.6 2.8 2.9

795

Cmcmb Pmn21 Fmm2

8.4 −7.2 4.7 9.2 −5.9 −11.4 5.5 −6.4 7.9 −7.1 −4.5 7.9 8.1

6.05

R2-n159 R2-n111 R3-n142

0.00 11.97 13.13 −5.32 3.17 8.48 1.36 12.47 12.80 12.67 11.03 19.14 5.59

796 766 772 790

I222

0.00 0.99 4.27 1.46 −0.44 −1.36 5.15 0.42 5.51 1.26 −0.50 1.41

0.00 3.42 4.93 5.04

R3-n139

4,4 2,2 2,2 1,1 2,2 4,2 2,4 4,4 2,2 8,4 4,8 2,1 0,1

8.32

776

a

The multiplicity of the sites in the conventional cell is provided to calculate weighted averages for comparison with experimental data. bIdentical to the Wood-Marzari Cmcm structure.34

Table 2. Energy Ordering (F = E − TS) of Structures at T = 360 Ka prototype

space group

ΔF kJ/mol

ρ g/cc

0.0000 1.1412 1.1702 1.2162 1.2915 1.3313 1.5772 2.2281 2.2866 3.1307

1.1211 1.1197 1.2995 1.1195 1.1048 1.1034 1.1326 0.9181 0.9185 1.1180

T = 360 K R3-n142 R3-n41 NaAlH4 R3-n175 NaAlH4-Cmcm R3-n91 R2-n199 R2-n172 R2-n186 R3-n164

Fmm2 Fmm2 I4-1/a Fmm2 Cmcmb C2 P21/m Fdd2 Fdd2 Cm

Figure 3. The free energy of competing structures at a hydrogen pressure of about 2.5 bar, ignoring possible decomposition reactions, that is, other competing phases such as Na3AlH6, and NaH. The transition to Fmm2 is predicted to occur at about 320 K and it remains the phase with lowest free energy among competing NaAlH4 phases.

a

Assuming there is no Fmm2 phase, 360 K is the predicted critical temperature of the first decomposition step to Na3AlH6 at an overpressure of about 5 bar H2. bIdentical to the Wood-Marzari Cmcm structure.34

4. CALCULATED Na−Al−H PHASE DIAGRAM The in situ X-ray diffraction data of Gross et al.7 is inconclusive with regard to a positive determination of the X1 phase. In all structures considered in this work, there was no one-to-one correspondence of calculated structure factors with the experimental data, precluding an unambiguous determination of the structure of X1, even accounting for an admixture of peaks from X1 and X2. We note that several structure factors from Fmm2 and related low energy phases such as Cmcm appear to have some correspondence with X1 and X2. For this reason, we calculated the phase diagram in the Na−Al−H system in an experimentally accessible pressure and temperature range. We used the Grand Canonical Linear Programming (GCLP) method, described in detail elsewhere,38 to minimize the Gibbs free energy at a given temperature T, and pressure P, determining the chemical potential μH2 of hydrogen gas. The addition of new structure prototypes in the Na−Al−H system requires that the reaction eqs 1 and 2 be reconsidered. Naturally, the energy ordering of the structures changes as the temperature is increased, and the ordering of structure candidates for NaAlH4 at the predicted temperature for the first step decomposition in eq 1 is shown in Table 2. Using this information, and minimizing the total Gibbs free energy for the

dramatic lowering of the free energy in the Fmm2 structure is due to a large increase in the entropy owing to smaller barriers for rotation of [AlH4]− units, as discussed in Section 3.3. The structure in symmetry Fmm2 is shown to have the lowest free energy of all structures considered in this work and is the predicted stable phase at temperatures above 120 °C and pressures above 1−2 bar H2 (see Figure 3). The conventional cell crystal structure for Fmm2 is shown in Figure 4, and full structural parameters of this phase are shown in Table 4. 3.3. Rotational Barriers for [AlH4]− Tetrahedra. The [AlH4]− tetrahedra have three (approximate) 2-fold rotational axes (C2 axis) and four 3-fold rotational axes (C3 axis). The calculated rotational barriers of [AlH4]− tetrahedra in the NaAlH4-I41/a and R3-n142-Fmm2 crystal structures are listed in Table 3. In the case of I41/a, all 3-fold rotations are equivalent. For R3-n142-Fmm2 there are two inequivalent Al sites and differences in barrier between various rotation axes. In both structures, rotations around the C2-axes are found to decompose into rotations around C3-axes. Most striking are the much lower (a factor 2) barriers for R3-n142-Fmm2. This gives rise to rapid reorientation, consistent with a narrowing of the 27 Al line in the NMR spectrum of S105. We note, however, that translations are needed in addition to rapid reorientation, to obtain the narrowing seen in S105.1 8867

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Figure 5. Calculated phase diagram in the Na−Al−H system. The intermediate Na3AlH6 phase is predicted to vanish at pressures above 190 bar H2, where the single-step decomposition of the Fmm2 NaAlH4 phase occurs.

candidates. At a pressure of 1 bar H2, we find the reaction pathway described in eqs 1 and 2. However, at a pressure of about 2 bar H2, we find the following reactions NaAlH4(I 41/a) ⇌ NaAlH4(Fmm2)

(8.9kJ/mol rxn)

Tc = 47°C, P = 2.5bar Figure 4. The crystal structure for high-temperature NaAlH4 in symmetry Fmm2.

Table 3. The Calculated Rotational Barriers of [AlH4]− Tetrahedra around the C3 Axes in NaAlH4-I41/a and R3n142-Fmm2 rotation axis

1 2 Na3AlH6 + Al + H 2 3 3

(21.4kJ/mol H 2)

Tc = 57°C, P = 2.5bar 3 H2 2

(4)

(47.7kJ/mol H 2)

Tc = 177°C, P = 2.5bar

(5)

The polymorphic phase transition (3) from I41/a to Fmm2 is predicted to occur at about 47 °C at an overpressure of about 2 bar H2 with an enthalpy of 9 kJ/mol. The Fmm2 phase of NaAlH4 then decomposes following eq 4 to the hexahydride phase at a temperature of 57 °C with an enthalpy of about 22 kJ/mol H2. The decomposition of Na3AlH6 proceeds as usual. As the pressure is increased, there is a striking change of the decomposition pathway at a calculated pressure of about 190 bar. As the pressure is increased, the critical temperatures for the reactions in eqs 4 and 5 approach each other, eventually eliminating the intermediate Na3AlH6 phase

NaAlH4-I41/a 0.91 R3-n142-Fmm2 0.42 0.42 0.45 0.32 0.53

Table 4. Structural Parameters for NaAlH4 HighTemperature Candidate in Symmetry Fmm2 c = 6.43268

NaAlH4(Fmm2) ⇌

Na3AlH6 ⇌ 3NaH + Al +

barrier (eV)

Al[4a]-H[8c] Al[4a]-H[8d] Al[8c]-H[16e] Al[8c]-H[8c] Al[8c]-H[8c]

(3)

α = β = γ = 90°

NaAlH4(I 41/a) ⇌ NaAlH4(Fmm2)

a = 7.07137

b = 21.10304

atom

Wyckoff

x

y

z

H1 H2 H3 H4 H5 Na1 Na2 Al1 Al2

8d 8c 16e 8c 8c 8c 4a 4a 8c

0.18538 0.5 0.31344 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.43883 0.33586 0.39211 0.26818 0.66643 0.5 0.5 0.33317

0.57076 0.76626 0.06243 0.37478 0.34922 0.70719 0.42854 0.91941 0.21149

(8.9kJ/mol rxn)

Tc = 47°C, P = 190bar NaAlH4(Fmm2) ⇌ NaH + Al + (33.1kJ/mol H 2)

(6)

3 H2 2

Tc = 397°C, P = 190bar

(7)

This suggests that it may be possible to extract the hydrogen from this compound in a single step at elevated overpressure of H2. Because of the relatively low pressures investigated, we did not include pressure dependence on the stability of the solid phases for the transition from NaAlH4 I41/a → Fmm2, and hence it is flat in the phase diagram. At low temperature, and as the pressure becomes very low, there is an entropic driving force for hydrogen to be in the gas phase, and this drives the emergence of the hexahydride Na3AlH6 as shown in the phase

collection of all competing phases at varying temperature, one obtains the phase diagram. The full P−T phase diagram for Na−Al−H is shown in Figure 5, using all known Na−Al−H phases and PEGS-generated structure prototypes. In particular, NaH (Fm3m ̅ ), Na3AlH6 (P21), NaAlH4 (I41/a), and all NaAlH4 8868

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surroundings of the [AlH4]−, reflected in a mix of bi- and tridentite coordinations with Na+, apparently results in a more substantial deformation of the [AlH4]− units.

diagram. However the kinetics would be very slow at these temperatures and unlikely to occur, suggesting that the Fmm2 phase could appear at low pressures, rather than the decomposition reaction. The fact that this does not occur suggests that the structural transformation from I41/a → Fmm2 has kinetic barriers for atomic rearrangement at least as high as the decomposition reaction in eq 1, or that anharmonic terms in the crystal Hamiltonian make this energetically unfavorable. 4.1. Comparison of Fmm2, Cmcm, and I41/a Structures. Both Fmm2 and Cmcm share common structural features. The Fmm2 structure is distinguished from I41/a by the coordination of the Na atoms with [AlH4]− units. In Fmm2, there are two symmetry-distinct Na Wyckoff positions. Each 4a and 8c Na atom is six-coordinated with [AlH4]− units, two oriented in a bidentate configuration and opposing one another, with the remaining four units canted toward a tridentate configuration. In contrast, the I41/a structure has only one Na symmetry, and none of the coordinating [AlH4]− are in a bidentate orientation. The Na- [AlH4]− configuration in the low-energy Cm structures is identical to that of Fmm2, and a small rms distortion (0.05 Å) of the Cm structure yields Fmm2 symmetry. In the Cmcm structure, the single Na position is also six-coordinated with [AlH4]− groups with two opposing bidentate [AlH4]− and the remaining anions canted toward a tridentate orientation. The Fmm2 and I41/a structures have distinctly different cell volumes of 80 and 69 Å3/f.u., respectively. The cell volume for the Cmcm structure is 81.2 Å3, similar to Fmm2. The increased volume presumably allows for the lower rotational barriers for [AlH4]− in the Fmm2 structure as discussed in Section 3.3. We provide calculated Xray diffraction spectra in Figure S2 (Supporting Information) for comparison to experimental data. Equations 8 and 9 define scale-invariant distortions of the tetrahedra, in which dav is the average edge length of the edges forming the tetrahedra, and ri⃗ are vertex positions of the edge lengths, that is, the H−H distances, so that a perfect tetrahedron has σ = 0. dav =

σ=

1 6

5. CONCLUSIONS We have presented a comprehensive structure search for hightemperature candidates of NaAlH4 using the PEGS method and find many low-energy candidates. One candidate in symmetry Fmm2 is predicted to have the lowest total free energy at slightly elevated temperatures and pressures. We have also calculated the phase diagram for the ternary Na−Al−H system at experimentally accessible temperatures and pressures. The Fmm2 polymorph of NaAlH4 is predicted to be the observed phase at pressures above about 2 bar H2 and temperatures above 320 K. The elimination of the intermediate Na3AlH6 phase field at about 190 bar and the single-step decomposition of Fmm-2 NaAlH4 is a remarkable result. Given the physical accuracy of DFT, typically ±10 kJ/mol H2 for a hydride reaction, it may be that the pressure range in which this transition occurs is lower than 190 bar. This may provide insight into methods of extracting the hydrogen content of NaAlH4 and other complex hydrides through fewer steps than was previously thought necessary. The calculated chemical shifts for the PEGS structure prototypes indicate a monotonically decreasing shift for 27Al with increasing Al−H coordination number. The tetrahedral [AlH4]− anion is unambiguously identified with the chemical shift seen in S105. There is no new bulk phase visible in the XRD pattern of S105-containing NaAlH4 despite the additional phase visible in NMR.1 This suggests that there could be an amorphous phase that gives rise to the S105 shift seen in the 27 Al resonance. Alternatively the S105 might indeed be a highly defective NaAlH4 (I41/a) with a similar lattice as I41/a but with (possibly oxygen containing) defects. Such defects could provide the “internal space” that enables fast rotational and translational jumps of the [AlH4]− ions. The thermodynamic calculations clearly suggest that a structure with larger volume per [AlH4]− unit is favored at elevated temperature. It could be that, in an attempt to form the Fmm2 phase, for example, that the larger cell volume makes more favorable the formation of the particular lattice defects that provide additional 27Al line narrowing, if the S105 phase were a defected NaAlH4 structure. We note that the Fmm2 structure may ultimately not form due to anharmonic effects, not included in our calculations, that could instead stabilize a defected I41/a structure, for example. Finally, we have identified many competitive structures for polymorphs in the NaAlH4 system that may be related to S105, X1, or X2. None of the predicted polymorphs of NaAlH4 provide X-ray structure factors in agreement with observations of in situ XRD at elevated temperatures and low H 2 overpressure. To our knowledge, there are no such in situ measurements at pressures above 1 bar H2, where the Fmm2 phase is predicted to be observed. High-pressure measurements on pure NaAlH4 are therefore suggested. Another, perhaps very important possibility is that impurities such as oxygen, play a significant role in the phase diagram at temperatures above ambient.

∑ | ri⃗ −→⎯rj| (8)

i