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J. Phys. Chem. C 2009, 113, 16834–16837
Rotational Diffusion in NaBH4 Arndt Remhof,†,* Zbigniev Łodziana,† Florian Buchter,† Pascal Martelli,† Flavio Pendolino,† Oliver Friedrichs,† Andreas Zu¨ttel,† and Jan Peter Embs‡ ¨ berlandstrasse 129, CH 8600 Empa, Swiss Federal Laboratories for Materials Testing and Research, U Du¨bendorf, Switzerland, Laboratory for Neutron Scattering, ETH Zu¨rich & Paul Scherrer Institut, CH-5232 Villigen, Switzerland, and Physical Chemistry, Saarland UniVersity, D-66123 Saarbru¨cken, Germany ReceiVed: July 1, 2009; ReVised Manuscript ReceiVed: July 31, 2009
Hydrogen dynamics in complex hydrides comprise long-range translational diffusion as well as localized motions like vibrations, librations, or rotations. All different motions are characterized by their specific length scale and time scales. Here we present a combined experimental and theoretical study on the rotational diffusion of the (BH4)- ions in crystalline NaBH4. The motion is thermally activated and characterized by an activation energy of 117 meV and a prefactor of 11 fs. Thereby the motion is dominated by 90° reorientations of the (BH4)- ion around the 4-fold symmetry axis of the cubic crystal. The experimental results are discussed on the basis of DFT calculations, revealing the potential energy landscape of a (BH4)- subunit in the crystalline matrix. Introduction Due to their outstanding volumetric and gravimetric hydrogen density, tetrahydroborates are currently discussed as possible future hydrogen storage materials.1 However, their utilization is hindered by their inappropriate thermodynamic stability and by slow sorption kinetics. While the dynamics of H in many metallic systems is well understood, only rudimentary knowledge exists for the dynamics of hydrogen in complex hydrides. The reason for this originates from the different structures of the hydrides. Hydrogen in most transition metals occupies interstitial sites and hydrogen can easily jump from interstice to interstice, especially in understoichiometric compounds. Accordingly, the diffusion of hydrogen in transition metals is fast with small activation energies. Hydrogen in complex hydrides, on the contrary, is covalently bound to the other element like Al or B, and arranged in subunits (“complexes”).2 The hydrogen dynamics in such systems comprises the internal H-vibrations within each complex, the rotation of the complex about specified axes, the motion of the (BH4) units with respect to the metal ions, and the diffusion of hydrogen. It is not known whether hydrogen can be removed from such a subunit without degradation of the whole compound, i.e., diffusion of hydrogen would then require the movement of the whole subunit and/or degradation of it.3 The decomposition/formation mechanisms are not known either. The current study focuses on the rotational diffusion of the BH4 units in sodium borohydride (NaBH4) by means of incoherent quasielastic neutron scattering (QENS). Sodium borohydride forms ionic crystals consisting of Na+ and BH4- ions. Within the BH4 unit the hydrogen atoms surround the boron in a tetrahedral configuration. NaBH4 undergoes a structural phase transition at 190 K.4 The ordered low temperature phase crystallizes in the tetragonal space group P4j21c (no. 114), with lattice parameters a ) 4.332 Å and c ) 5.869 Å.5 The disordered high temperature phase crystallizes * To whom correspondence should be addressed. E-mail:
[email protected] . † Empa. ‡ ETH, PSI & Uni Saarland.
Figure 1. Spatial arrangements of the two possible hydrogen tetrahedra, labeled H1 and H2 (red and blue), around the central B atom (gray). The positions of a 2-fold c2 axis and of a 3-fold c3 axis are indicated as dashed lines.
in a cubic lattice, with a lattice parameter of 6.13 Å.4-6 Previously, space groups Fm3jm (no. 225)4,7 or F4j3m (216) were assigned to the high temperature phase. The two structures differ by the absence of an inversion symmetry in F4j3m. Thereby the fully disordered F4j3m structure is identical to the Fm3jm structure. In this structures Na occupies the (4a) sites at the origin (0,0,0) and B the (4b) sites at (1/2,1/2,1/2). Hydrogen is statistically distributed over two (16c) sites, occupying the 8 corners of a cube around the B atom with 50% occupancy. This implies a random distribution of BH4 tetrahedra in two different 〈111〉 orientations along cube diagonal.4-6 Figure 1 displays the two possible spatial arrangements of the H atoms around the central B atom in red and blue, respectively. There are two sets of high symmetry axes connected with this structure. First, there are three 2-fold axes, called c2, which are normal to the cube’s face, and four 3-fold axes, called c3, which coincide with the body diagonals of the cube. The two possible arrangements may be transferred in one another by a 90° rotation about c2, while a rotation about c3 preserves the tetrahedron’s orientation.
10.1021/jp906174e CCC: $40.75 2009 American Chemical Society Published on Web 09/01/2009
J. Phys. Chem. C, Vol. 113, No. 38, 2009 16835 In a combined experimental and theoretical study we examined the rotational motion of the BH4 tetrahedra in NaBH4 by means of QENS and DFT calculations. Thereby the experimentally obtained thermal activated reorientation is discussed on the basis of the calculated energy landscape for the rotation about the high symmetry axis. Experimental Results QENS measurements were carried out by using the time-offlight neutron spectrometer FOCUS for cold neutrons located at the continuous spallation source SINQ at the Paul Scherrer Institute in Villigen, Switzerland.8,9 The incident neutron wavelength was chosen to be 4 Å. At the setting used, the elastic scattering energy resolution, δ(E), was 0.2 meV, corresponding to an observable time scale of up to 3.5 ps. To avoid the strong neutron absorption by 10B that is present in natural boron, 11B enriched (99.5%) Na11BH4 (chemical purity >98%), purchased from Katchem, was used. The material was handled solely under inert gas conditions in Ar or in He. The samples were loaded in lead sealed flat 0.1 mm × 30.0 mm × 40.0 mm Al containers and oriented at an angle of 135° with respect to the incident beam. A packing density of 30% was chosen, leading to a neutron transmission (at the selected wavelength) of about 80%. Consequently, we expect to observe a reduction of the elastic line at low Q due to multiple scattering. The spectra were recorded in a range of scattering vectors of Q ) 0.7 to 2.5 Å-1. The data reduction was carried out by using the data analysis and visualization environment “DAVE”.10 The resulting QENS spectra were analyzed by using the general purpose curve fitting utility “PAN”, which is included in the DAVE distribution. Generally, the measured total incoherent scattering function Stot inc(Q,E) can be expressed as the convolution of the elastic line δ(E) and the Lorentzian shaped quasielastic broadening L(Q,E), with the resolution function of the instrument R(Q,E): tot Sinc (Q, E) ) R(Q, E) X (Ielδ(E) + IqeL(Q, E))
Figure 2. QENS of NaBH4, measured at T ) 300 K (top panel) and at Q ) 1.5 A-1 (bottom panel). The measured data are represented by black symbols. Solid black lines display fits to the data, each one consisting of a resolution broadened Delta function (red) and a Lorentzian profile (blue).
(1)
where Iel is the intensity of the elastic line and Iqe is the intensity of the quasielastic signal, i.e., the integrated intensity of the contribution of the Lorentzian contribution. Below 250 K no quasielastic broadening was found, showing that the hydrogen is frozen in on the time scale accessible by the instrument. At higher temperatures a quasielastic broadening is observed, whose width increases with temperature. The QENS spectra were modeled by using two components: first, a resolution limited elastic peak using a Gaussian line shape of width wel and an integrated area Iel, and second, a quasielasticbroadened component arising from the reorientational motion of the BH4 units using a Lorentzian line shape of width wqe and integrated area Iqe. In all fits, the peak centers were constrained to be the same for each component. The width of the elastic line was fixed to the width of the measured elastic line of a vanadium standard sample. Figure 2 shows typical examples of spectra together with the two-component fits. The quasielastic broadening was found to be independent of Q for the whole measured Q-range, indicative of localized hydrogen motion.11,12 The observed broadening displays a thermally activated Arrhenius behavior. The time τ corresponding to the broadening can be expressed as τ ) τ0 exp(Ea/ kBT), where kB is Boltzmann’s constant. The Arrhenius fit yields the prefactor τ0 and the activation energy as τ0 )
Figure 3. Thermally activated Arrhenius behavior of the rotational motion. The time τ corresponding width of the quasielastic broadening can be expressed as τ ) τ0 exp(Ea/kBT), with a prefactor of τ0 ) 11.1(0.6) fs, and an activation energy of Ea ) 117(1) meV.
11.1(0.6) fs and Ea ) 117(1) meV, corresponding to 10.9(0.1) kJ/mol. The measured value of the activation energy fits nicely to the value of 11.2(0.5) kJ/mol obtained by NMR spectroscopy13 and the value of 12.1(0.5) kJ/mol measured by Raman spectroscopy.14 Figure 3 shows the experimentally obtained data together with the Arrhenius fit in the temperature range from 250 to 500 K. The error bars represent the scatter of the width (fwhm) of the Lorentzian contributions around their respective mean value. The elastic incoherent scattering factor (EISF) offers a model independent treatment of the measured data. The EISF
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Remhof et al.
1 EISF(Q) ) [1 + 3j0(Qa) + 3j0(Qa√2) + j0(Qa√3)] 8
(3) where j0(x) ) sin(x)/x is the zeroth order Bessel function and a ) 1.35 Å is the H-H distance, the length of the cube depicted in Figure 1. The rotational reorientations of the BH4- ion in NaBH4 are therefore analogous to the reorientations of the isostructural NH4+ ion in ammonium halides, which are classical examples of solid rotor phases.15 Equation 3 nicely reproduces the measured data for Q > 1 Å-1. The data deviate from the model for lower Q and do not extrapolate to unity for Q f 0. We attribute the deviation at low Q to multiple scattering, which enhances the inelastic part for small angles. Figure 4. Measured EISFs together with a model ESIF according to eq 3.
thereby is defined by the ratio of elastic to total scattering intensity:
EISF(Q) )
Iel(Q) Iel(Q) + Iqe(Q)
(2)
Generally, the exact shape of the measured quasielastic contribution to the spectra (S(Q,ω)) is the Fourier transform of the self-correlation function G(r,t) in space and time. Therefore the exact determination of the EISF involves the fitting of the measured data with the correct scattering functions obtained from a suitable model. Figure 4 displays the experimentally obtained EISFs, extracted from the QENS spectra according to eq 2, together with a model EISF describing 90° reorientations of the (BH4)- ion around the 4-fold symmetry axis of the cubic crystal. In this case, the EISF can be expressed as15
Discussion The experimentally obtained data may be explained on the basis of the potential energy landscape for a single BH4 tetrahedron within the NaBH4 structure. The rotational barriers were calculated for the structure of the high-T phase with space group F4j3m. We used the plane wave-density functional theory approach16 where atomic cores were represented by projected augmented waves.17 The lattice parameters and internal position of atoms were fully relaxed for the number of static orientations of BH4 until forces excerpted on atoms were smaller than 0.01 eV/Å. For calculation of the potential energy for the rotation of the molecular group a supercell with 96 atoms was constructed. All BH4 tetrahedra were initially in the same orientation. No atomic relaxation was performed during rotation of a single BH4 unit, such that the potential energy landscapes presented in Figure 5 render adiabatic barriers. Since the complete description of BH4 orientation in 3D space requires a three-parameter space based on Euler angles, we have decided to simplify the problem in
Figure 5. Potential energy landscape for BH4 rotation in NaBH4. The color scale is in eV, minima are depicted in blue, maxima are depicted in red. The top plot shows the energy profile for rotation along the c2 axis, and the right plot shows the lowest energy path for rotation around teh c3 axis, as marked by horizontal and vertical lines on the central plot.
J. Phys. Chem. C, Vol. 113, No. 38, 2009 16837 order to represent it in two dimensions. Therefore, only rotational motion about the c2 and c3 axes was considered. The origin of the coordinate system was chosen to be an energy minimum. As expected from its 3-fold symmetry, further minima occur at c3 ) 120° and at c3) 240°. Due to the parallel alignment of all surrounding tetrahedra, a rotation about the c2 axis exhibits a 2-fold symmetry, where the local energy minima are spaced by 180°. The energetic minimum is reached when the tetrahedron is aligned antiparallel to the others. The 90° jump along c2 leads to a reorientation of the tetrahedron into a parallel alignment. The energy minima related to this position are located at c2 ) 90° and 270° and are less pronounced. The calculation yields the barrier height of ∼220 meV for the antiparallel to parallel reorientation, while the barrier between the parallel to antiparallel orientation is ∼110 meV. In the real crystal, there is an uniform distribution of BH4 orientations in the crystal, such that all orientations are equivalent. Energetically, both positions will be degenerated and from an energetic point of view, the c2 axis will have 4-fold c4 symmetry with 50% occupation of each site. The height of the barrier will be in between the two extreme cases. Relaxation processes of the surrounding tetrahedra will in principle lower the barrier; however, the time scale of the hoping process is faster than thermal lattice vibrations which justifies our adiabatic apporach. The barrier height for a rotation about a c3 axis is ∼0.32 eV and it is larger than that for a c2 axis. Therefore, rotations about the c2 axes are favored energetically. The reorientational motion of the BH4 tetrahedra will therefore be dominated by rotation about the c2 axes. Due to symmetry, each tetrahedron possesses three equivalent, orthogonal c2 axes. Each individual hydrogen atom may reach any of the eight possible positions by subsequent rotation about one of the c2 axes. There is no preferred orientation. In other words, if one could label a single H atom and monitor its position as a function of time, the probability to find it in any of the 8 corners of the cube depicted in Figure 1 would be 1/8. Conclusion We examined the hydrogen dynamics in the picosecond range in NaBH4 by means of combined QENS and DFT calculation. Within the experimentally accessible time range (∼0.1-3.5 ps)
we observed a single thermally activated localized diffusional motion. The Arrhenius fit yields a prefactor of τ0 ) 11.1(0.6) fs, and an activation energy of Ea ) 117(1) meV, which is in good agreement with NMR and Raman measurements. The measured EISF suggests 90° reorientation jumps of the (BH4)ion. The energy barriers for the rotational reorientation were calculated by DFT methods. The calculations clearly show that the rotation about the c2 axis is energetically more favorable than the rotation of the c3 axis. By subsequent rotations about the c2 axes, each orientation may be reached. Acknowledgment. We thank Prof. R. Hempelmann for stimulating discussions. CPU time allocation at the CSCS supercomputer centre (Manno) is kindly acknowledged. Financial support by the Swiss National Science Foundation (SNF), Project No. 200021-119972/1, and by the European Commission DG Research (Contract No. MRTN-CT-2006-032474/HYDROGEN) is gratefully acknowledged. References and Notes (1) Schlapbach, L.; Zu¨ttel, A. Nature (London) 2001, 414, 353. (2) Zu¨ttel, A.; Borgschulte, A.; Orimo, S. I. Scr. Mater. 2007, 56, 823. (3) Du, A. J.; Smith, S. C.; Lu, G. Q. Phys. ReV. B 2006, 74, 193405. (4) Abrahams, S. C.; Kalnajs, J. J. Chem. Phys. 1954, 22, 434. (5) Fischer, P.; Zu¨ttel, A. Mater. Sci. Forum (EPDIC 8) 2004, 443444, 287. (6) Davis, R. L.; Kennard, C. H. L. J. Solid State Chem. 1985, 59, 393. (7) Filinchuk, Y.; Hagemann, H. Eur. J. Inorg. Chem. 2008, 20, 3127. (8) Mesot, J.; Janssen, S.; Holitzner, L.; Hempelmann, R. J. Neutron Res. 1996, 3, 293. (9) Janssen, S.; Mesot, J.; Holitzner, L.; Furrer, A.; Hempelmann, R. Phys. B 1997, 234-236, 1174. (10) http://www.ncnr.nist.gov/dave. (11) Be´e M. Quasielastic Neutron Scattering; Adam Hilger: Philadelphia, PA, 1988. (12) Hempelmann R. Quasielastic Neutron Scattering and Solid State Diffusion; McGraw Hill Book Co.: Oxford, UK, 2000. (13) Tsang, T.; Farrar, T. C. J. Chem. Phys. 1969, 50, 3498. (14) Hagemann, H.; Gomes, S.; Renaudin, G.; Yvon, K. J. Alloys Compd. 2004, 363, 129. (15) Lechner, R. E.; Badurek, G.; Dianoux, A. J.; Hervet, H.; Volino, F. J. Chem. Phys. 1980, 73, 934. (16) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (17) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953.
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